Daily Papers

Recent advances in Large Audio Language Models (LALMs) have extended Text-to-Speech (TTS) to interactive role-play scenarios, which demand high expressiveness and strict adherence to role-play instructions. However, existing models struggle to maintain stylistic consistency with character profiles and scene descriptions across multi-turn dialogues. A critical bottleneck is the lack of objective metrics for quantifying speaking style. To bridge this gap, we propose Mean Continuation Log-Probability (MCLP) as both an evaluation metric and a reward signal, validated on LALM-based Role-Play TTS (RP-TTS) tasks. Critically, we leverage the In-Context Learning capability of pre-trained LALMs to formulate MCLP via a continuation log-probability prediction. This metric quantifies stylistic consistency by measuring the likelihood of the ground-truth speech conditioned on the generated speech. Furthermore, we employ MCLP as a reinforcement learning reward to enhance the style alignment between generated speech and Role-Play instructions. To facilitate evaluation, we construct an RP-TTS dataset with rich scene and character annotations. Experimental results demonstrate that our method significantly outperforms strong LALM baselines on both objective and subjective metrics.

Predictive business process monitoring methods exploit logs of completed cases of a process in order to make predictions about running cases thereof. Existing methods in this space are tailor-made for specific prediction tasks. Moreover, their relative accuracy is highly sensitive to the dataset at hand, thus requiring users to engage in trial-and-error and tuning when applying them in a specific setting. This paper investigates Long Short-Term Memory (LSTM) neural networks as an approach to build consistently accurate models for a wide range of predictive process monitoring tasks. First, we show that LSTMs outperform existing techniques to predict the next event of a running case and its timestamp. Next, we show how to use models for predicting the next task in order to predict the full continuation of a running case. Finally, we apply the same approach to predict the remaining time, and show that this approach outperforms existing tailor-made methods.

In this paper, we tackle the important yet under-investigated problem of making long-horizon prediction of event sequences. Existing state-of-the-art models do not perform well at this task due to their autoregressive structure. We propose HYPRO, a hybridly normalized probabilistic model that naturally fits this task: its first part is an autoregressive base model that learns to propose predictions; its second part is an energy function that learns to reweight the proposals such that more realistic predictions end up with higher probabilities. We also propose efficient training and inference algorithms for this model. Experiments on multiple real-world datasets demonstrate that our proposed HYPRO model can significantly outperform previous models at making long-horizon predictions of future events. We also conduct a range of ablation studies to investigate the effectiveness of each component of our proposed methods.

Information systems generate a large volume of event log data during business operations, much of which consists of low-value and redundant information. When performance predictions are made directly from these logs, the accuracy of the predictions can be compromised. Researchers have explored methods to simplify and compress these data while preserving their valuable components. Most existing approaches focus on reducing the dimensionality of the data by eliminating redundant and irrelevant features. However, there has been limited investigation into the efficiency of execution both before and after event log simplification. In this paper, we present a prediction point selection algorithm designed to avoid the simplification of all points that function similarly. We select sequences or self-loop structures to form a simplifiable segment, and we optimize the deviation between the actual simplifiable value and the original data prediction value to prevent over-simplification. Experiments indicate that the simplified event log retains its predictive performance and, in some cases, enhances its predictive accuracy compared to the original event log.

Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second, we identify the culprit to be the log-likelihood loss, along with certain conditions that exacerbate the issue. Third, we present an alternative formulation, termed β-NLL, in which each data point's contribution to the loss is weighted by the β-exponentiated variance estimate. We show that using an appropriate β largely mitigates the issue in our illustrative example. Fourth, we evaluate this approach on a range of domains and tasks and show that it achieves considerable improvements and performs more robustly concerning hyperparameters, both in predictive RMSE and log-likelihood criteria.

Fine-tuning large language models (LLMs) on reasoning benchmarks via reinforcement learning requires a specific reward function, often binary, for each benchmark. This comes with two potential limitations: the need to design the reward, and the potentially sparse nature of binary rewards. Here, we systematically investigate rewards derived from the probability or log-probability of emitting the reference answer (or any other prompt continuation present in the data), which have the advantage of not relying on specific verifiers and being available at scale. Several recent works have advocated for the use of similar rewards (e.g., VeriFree, JEPO, RLPR, NOVER). We systematically compare variants of likelihood-based rewards with standard baselines, testing performance both on standard mathematical reasoning benchmarks, and on long-form answers where no external verifier is available. We find that using the log-probability of the reference answer as the reward for chain-of-thought (CoT) learning is the only option that performs well in all setups. This reward is also consistent with the next-token log-likelihood loss used during pretraining. In verifiable settings, log-probability rewards bring comparable or better success rates than reinforcing with standard binary rewards, and yield much better perplexity. In non-verifiable settings, they perform on par with SFT. On the other hand, methods based on probability, such as VeriFree, flatline on non-verifiable settings due to vanishing probabilities of getting the correct answer. Overall, this establishes log-probability rewards as a viable method for CoT fine-tuning, bridging the short, verifiable and long, non-verifiable answer settings.

Deploying LLMs raises two coupled challenges: (1) monitoring - estimating where a model underperforms as traffic and domains drift - and (2) improvement - prioritizing data acquisition to close the largest performance gaps. We test whether an inference-time signal can estimate slice-level accuracy under domain shift. For each response, we compute an output-entropy profile from final-layer next-token probabilities (from top-k logprobs) and summarize it with eleven statistics. A lightweight classifier predicts instance correctness, and averaging predicted probabilities yields a domain-level accuracy estimate. We evaluate on ten STEM reasoning benchmarks with exhaustive train/test compositions (k in {1,2,3,4}; all "10 choose k" combinations), across nine LLMs from six families (3B-20B). Estimates often track held-out benchmark accuracy, and several models show near-monotonic ordering of domains. Output-entropy profiles are thus an accessible signal for scalable monitoring and for targeting data acquisition.

Counterfactual Risk Minimization (CRM) is a framework for dealing with the logged bandit feedback problem, where the goal is to improve a logging policy using offline data. In this paper, we explore the case where it is possible to deploy learned policies multiple times and acquire new data. We extend the CRM principle and its theory to this scenario, which we call "Sequential Counterfactual Risk Minimization (SCRM)." We introduce a novel counterfactual estimator and identify conditions that can improve the performance of CRM in terms of excess risk and regret rates, by using an analysis similar to restart strategies in accelerated optimization methods. We also provide an empirical evaluation of our method in both discrete and continuous action settings, and demonstrate the benefits of multiple deployments of CRM.

In reasoning about sequential events it is natural to pose probabilistic queries such as "when will event A occur next" or "what is the probability of A occurring before B", with applications in areas such as user modeling, medicine, and finance. However, with machine learning shifting towards neural autoregressive models such as RNNs and transformers, probabilistic querying has been largely restricted to simple cases such as next-event prediction. This is in part due to the fact that future querying involves marginalization over large path spaces, which is not straightforward to do efficiently in such models. In this paper we introduce a general typology for predictive queries in neural autoregressive sequence models and show that such queries can be systematically represented by sets of elementary building blocks. We leverage this typology to develop new query estimation methods based on beam search, importance sampling, and hybrids. Across four large-scale sequence datasets from different application domains, as well as for the GPT-2 language model, we demonstrate the ability to make query answering tractable for arbitrary queries in exponentially-large predictive path-spaces, and find clear differences in cost-accuracy tradeoffs between search and sampling methods.

Reinforcement learning with verifiable rewards (RLVR) has become a central component of large language model (LLM) post-training. Unlike supervised fine-tuning (SFT), RLVR lets an LLM generate multiple candidate solutions and reinforces those that lead to a verifiably correct final answer. However, in practice, RLVR often requires thousands of training steps to reach strong performance, incurring substantial computation largely attributed to prolonged exploration. In this work, we make a surprising observation: during RLVR, LLMs evolve in a strongly linear manner. Specifically, both model weights and model output log-probabilities exhibit strong linear correlations with RL training steps. This suggests that RLVR predominantly amplifies trends that emerge early in training, rather than continuously discovering new behaviors throughout the entire optimization trajectory. Motivated by this linearity, we investigate whether future model states can be predicted from intermediate checkpoints via extrapolation, avoiding continued expensive training. We show that Weight Extrapolation produces models with performance comparable to standard RL training while requiring significantly less computation. Moreover, Logits Extrapolation consistently outperforms continued RL training on all four benchmarks by extrapolating beyond the step range where RL training remains stable.

Forecasting multiple future events within a given time horizon is essential for applications in finance, retail, social networks, and healthcare. Marked Temporal Point Processes (MTPP) provide a principled framework to model both the timing and labels of events. However, most existing research focuses on predicting only the next event, leaving long-horizon forecasting largely underexplored. To address this gap, we introduce HoTPP, the first benchmark specifically designed to rigorously evaluate long-horizon predictions. We identify shortcomings in widely used evaluation metrics, propose a theoretically grounded T-mAP metric, present strong statistical baselines, and offer efficient implementations of popular models. Our empirical results demonstrate that modern MTPP approaches often underperform simple statistical baselines. Furthermore, we analyze the diversity of predicted sequences and find that most methods exhibit mode collapse. Finally, we analyze the impact of autoregression and intensity-based losses on prediction quality, and outline promising directions for future research. The HoTPP source code, hyperparameters, and full evaluation results are available at GitHub.

Variational inference (VI) seeks to approximate a target distribution pi by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates pi by minimizing the Kullback-Leibler (KL) divergence to pi over the space of Gaussians. In this work, we develop the (Stochastic) Forward-Backward Gaussian Variational Inference (FB-GVI) algorithm to solve Gaussian VI. Our approach exploits the composite structure of the KL divergence, which can be written as the sum of a smooth term (the potential) and a non-smooth term (the entropy) over the Bures-Wasserstein (BW) space of Gaussians endowed with the Wasserstein distance. For our proposed algorithm, we obtain state-of-the-art convergence guarantees when pi is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when pi is only log-smooth.

Exploration is essential in modern learning, from reinforcement learning environments with small neural policies to large language models (LLMs). Existing work, such as DPO, leverages full sequence log-likelihoods to capture an entire trajectory of the model's decisions, while methods like GRPO aggregate per-token ratios into a trajectory-level update. However, both often limit exploration on long-horizon tasks. We introduce History-Aggregated Exploratory Policy Optimization (HAEPO), a history-aware exploratory loss to combat these shortcomings. HAEPO compresses each trajectory into the sum of its logarithmic probabilities (a cumulative logarithmic likelihood), and applies a Plackett-Luce softmax across trajectories to obtain normalized weights proportional to their returns, thus encouraging broader exploration. We add entropy regularization to stabilize the aggressive updates to prevent premature collapse and a soft KL penalty relative to a frozen copy of the previous (reference) policy. Empirically, HAEPO converges fast, explores thoroughly, aligns closely with true rewards, and demonstrates robust learning behavior better or at par with PPO, GRPO, and DPO across diverse tasks. Thus, HAEPO provides a stable and interpretable framework by explicitly leveraging full-trajectory history while balancing exploration and stability.

The 100 MW cryogenic liquid oxygen/hydrogen multi-injector combustor BKD operated by the DLR Institute of Space Propulsion is a research platform that allows the study of thermoacoustic instabilities under realistic conditions, representative of small upper stage rocket engines. We use data from BKD experimental campaigns in which the static chamber pressure and fuel-oxidizer ratio are varied such that the first tangential mode of the combustor is excited under some conditions. We train an autoregressive Bayesian neural network model to forecast the amplitude of the dynamic pressure time series, inputting multiple sensor measurements (injector pressure/ temperature measurements, static chamber pressure, high-frequency dynamic pressure measurements, high-frequency OH* chemiluminescence measurements) and future flow rate control signals. The Bayesian nature of our algorithms allows us to work with a dataset whose size is restricted by the expense of each experimental run, without making overconfident extrapolations. We find that the networks are able to accurately forecast the evolution of the pressure amplitude and anticipate instability events on unseen experimental runs 500 milliseconds in advance. We compare the predictive accuracy of multiple models using different combinations of sensor inputs. We find that the high-frequency dynamic pressure signal is particularly informative. We also use the technique of integrated gradients to interpret the influence of different sensor inputs on the model prediction. The negative log-likelihood of data points in the test dataset indicates that predictive uncertainties are well-characterized by our Bayesian model and simulating a sensor failure event results as expected in a dramatic increase in the epistemic component of the uncertainty.

Modern data acquisition routinely produce massive amounts of event sequence data in various domains, such as social media, healthcare, and financial markets. These data often exhibit complicated short-term and long-term temporal dependencies. However, most of the existing recurrent neural network based point process models fail to capture such dependencies, and yield unreliable prediction performance. To address this issue, we propose a Transformer Hawkes Process (THP) model, which leverages the self-attention mechanism to capture long-term dependencies and meanwhile enjoys computational efficiency. Numerical experiments on various datasets show that THP outperforms existing models in terms of both likelihood and event prediction accuracy by a notable margin. Moreover, THP is quite general and can incorporate additional structural knowledge. We provide a concrete example, where THP achieves improved prediction performance for learning multiple point processes when incorporating their relational information.

Supervised fine-tuning (SFT) is the standard approach for post-training large language models (LLMs), yet it often shows limited generalization. We trace this limitation to its default training objective: negative log likelihood (NLL). While NLL is classically optimal when training from scratch, post-training operates in a different paradigm and could violate its optimality assumptions, where models already encode task-relevant priors and supervision can be long and noisy. To this end, we study a general family of probability-based objectives and characterize their effectiveness under different conditions. Through comprehensive experiments and extensive ablation studies across 7 model backbones, 14 benchmarks, and 3 domains, we uncover a critical dimension that governs objective behavior: the model-capability continuum. Near the model-strong end, prior-leaning objectives that downweight low-probability tokens (e.g., -p, -p^{10}, thresholded variants) consistently outperform NLL; toward the model-weak end, NLL dominates; in between, no single objective prevails. Our theoretical analysis further elucidates how objectives trade places across the continuum, providing a principled foundation for adapting objectives to model capability. Our code is available at https://github.com/GaotangLi/Beyond-Log-Likelihood.

Logs, being run-time information automatically generated by software, record system events and activities with their timestamps. Before obtaining more insights into the run-time status of the software, a fundamental step of log analysis, called log parsing, is employed to extract structured templates and parameters from the semi-structured raw log messages. However, current log parsers are all syntax-based and regard each message as a character string, ignoring the semantic information included in parameters and templates. Thus, we propose the semantic-based parser SemParser to unlock the critical bottleneck of mining semantics from log messages. It contains two steps, an end-to-end semantic miner and a joint parser. Specifically, the first step aims to identify explicit semantics inside a single log, and the second step is responsible for jointly inferring implicit semantics and computing structural outputs based on the contextual knowledge base. To analyze the effectiveness of our semantic parser, we first demonstrate that it can derive rich semantics from log messages collected from six widely-applied systems with an average F1 score of 0.985. Then, we conduct two representative downstream tasks, showing that current downstream models improve their performance with appropriately extracted semantics by 1.2%-11.7% and 8.65% on two anomaly detection datasets and a failure identification dataset, respectively. We believe these findings provide insights into semantically understanding log messages for the log analysis community.

We propose an approach to estimate the number of samples required for a model to reach a target performance. We find that the power law, the de facto principle to estimate model performance, leads to large error when using a small dataset (e.g., 5 samples per class) for extrapolation. This is because the log-performance error against the log-dataset size follows a nonlinear progression in the few-shot regime followed by a linear progression in the high-shot regime. We introduce a novel piecewise power law (PPL) that handles the two data regimes differently. To estimate the parameters of the PPL, we introduce a random forest regressor trained via meta learning that generalizes across classification/detection tasks, ResNet/ViT based architectures, and random/pre-trained initializations. The PPL improves the performance estimation on average by 37% across 16 classification and 33% across 10 detection datasets, compared to the power law. We further extend the PPL to provide a confidence bound and use it to limit the prediction horizon that reduces over-estimation of data by 76% on classification and 91% on detection datasets.

Predictable behavior from scaling advanced AI systems is an extremely desirable property. Although a well-established literature exists on how pretraining performance scales, the literature on how particular downstream capabilities scale is significantly muddier. In this work, we take a step back and ask: why has predicting specific downstream capabilities with scale remained elusive? While many factors are certainly responsible, we identify a new factor that makes modeling scaling behavior on widely used multiple-choice question-answering benchmarks challenging. Using five model families and twelve well-established multiple-choice benchmarks, we show that downstream performance is computed from negative log likelihoods via a sequence of transformations that progressively degrade the statistical relationship between performance and scale. We then reveal the mechanism causing this degradation: downstream metrics require comparing the correct choice against a small number of specific incorrect choices, meaning accurately predicting downstream capabilities requires predicting not just how probability mass concentrates on the correct choice with scale, but also how probability mass fluctuates on specific incorrect choices with scale. We empirically study how probability mass on the correct choice co-varies with probability mass on incorrect choices with increasing compute, suggesting that scaling laws for incorrect choices might be achievable. Our work also explains why pretraining scaling laws are commonly regarded as more predictable than downstream capabilities and contributes towards establishing scaling-predictable evaluations of frontier AI models.

As large language models (LMs) advance, there is an increasing need to control their outputs to align with human values (e.g., detoxification) or desired attributes (e.g., personalization, topic). However, autoregressive models focus on next-token predictions and struggle with global properties that require looking ahead. Existing solutions either tune or post-train LMs for each new attribute - expensive and inflexible - or approximate the Expected Attribute Probability (EAP) of future sequences by sampling or training, which is slow and unreliable for rare attributes. We introduce TRACE (Tractable Probabilistic Reasoning for Adaptable Controllable gEneration), a novel framework that efficiently computes EAP and adapts to new attributes through tractable probabilistic reasoning and lightweight control. TRACE distills a Hidden Markov Model (HMM) from an LM and pairs it with a small classifier to estimate attribute probabilities, enabling exact EAP computation over the HMM's predicted futures. This EAP is then used to reweigh the LM's next-token probabilities for globally compliant continuations. Empirically, TRACE achieves state-of-the-art results in detoxification with only 10% decoding overhead, adapts to 76 low-resource personalized LLMs within seconds, and seamlessly extends to composite attributes.

Reliable forecasting of the future behavior of road agents is a critical component to safe planning in autonomous vehicles. Here, we represent continuous trajectories as sequences of discrete motion tokens and cast multi-agent motion prediction as a language modeling task over this domain. Our model, MotionLM, provides several advantages: First, it does not require anchors or explicit latent variable optimization to learn multimodal distributions. Instead, we leverage a single standard language modeling objective, maximizing the average log probability over sequence tokens. Second, our approach bypasses post-hoc interaction heuristics where individual agent trajectory generation is conducted prior to interactive scoring. Instead, MotionLM produces joint distributions over interactive agent futures in a single autoregressive decoding process. In addition, the model's sequential factorization enables temporally causal conditional rollouts. The proposed approach establishes new state-of-the-art performance for multi-agent motion prediction on the Waymo Open Motion Dataset, ranking 1st on the interactive challenge leaderboard.

The widespread adoption of large language models (LLMs) makes it important to recognize their strengths and limitations. We argue that in order to develop a holistic understanding of these systems we need to consider the problem that they were trained to solve: next-word prediction over Internet text. By recognizing the pressures that this task exerts we can make predictions about the strategies that LLMs will adopt, allowing us to reason about when they will succeed or fail. This approach - which we call the teleological approach - leads us to identify three factors that we hypothesize will influence LLM accuracy: the probability of the task to be performed, the probability of the target output, and the probability of the provided input. We predict that LLMs will achieve higher accuracy when these probabilities are high than when they are low - even in deterministic settings where probability should not matter. To test our predictions, we evaluate two LLMs (GPT-3.5 and GPT-4) on eleven tasks, and we find robust evidence that LLMs are influenced by probability in the ways that we have hypothesized. In many cases, the experiments reveal surprising failure modes. For instance, GPT-4's accuracy at decoding a simple cipher is 51% when the output is a high-probability word sequence but only 13% when it is low-probability. These results show that AI practitioners should be careful about using LLMs in low-probability situations. More broadly, we conclude that we should not evaluate LLMs as if they are humans but should instead treat them as a distinct type of system - one that has been shaped by its own particular set of pressures.

Users of music streaming, video streaming, news recommendation, and e-commerce services often engage with content in a sequential manner. Providing and evaluating good sequences of recommendations is therefore a central problem for these services. Prior reweighting-based counterfactual evaluation methods either suffer from high variance or make strong independence assumptions about rewards. We propose a new counterfactual estimator that allows for sequential interactions in the rewards with lower variance in an asymptotically unbiased manner. Our method uses graphical assumptions about the causal relationships of the slate to reweight the rewards in the logging policy in a way that approximates the expected sum of rewards under the target policy. Extensive experiments in simulation and on a live recommender system show that our approach outperforms existing methods in terms of bias and data efficiency for the sequential track recommendations problem.

Modern reasoning models continue generating long after the answer is already determined. Across five model configurations, two families, and three benchmarks, we find that 52--88\% of chain-of-thought tokens are produced after the answer is recoverable from a partial prefix. This post-commitment generation reveals a structural phenomenon: the detection--extraction gap. Free continuations from early prefixes recover the correct answer even at 10\% of the trace, while forced extraction fails on 42\% of these cases. The answer is recoverable from the model state, yet prompt-conditioned decoding fails to extract it. We formalize this mismatch via a total-variation bound between free and forced continuation distributions, yielding quantitative estimates of suffix-induced shift. Exploiting this asymmetry, we propose Black-box Adaptive Early Exit (), which uses free continuations for both detection and extraction, truncating 70--78\% of serial generation while improving accuracy by 1--5\,pp across all models. For thinking-mode models, early exit prevents post-commitment overwriting, yielding gains of up to 5.8\,pp; a cost-optimized variant achieves 68--73\% reduction at a median of 9 API calls. Code is available at https://github.com/EdWangLoDaSc/know2say.

Conformal prediction offers a powerful framework for building distribution-free prediction intervals for exchangeable data. Existing methods that extend conformal prediction to sequential data rely on fitting a relatively complex model to capture temporal dependencies. However, these methods can fail if the sample size is small and often require expensive retraining when the underlying data distribution changes. To overcome these limitations, we propose Reservoir Conformal Prediction (ResCP), a novel training-free conformal prediction method for time series. Our approach leverages the efficiency and representation learning capabilities of reservoir computing to dynamically reweight conformity scores. In particular, we compute similarity scores among reservoir states and use them to adaptively reweight the observed residuals at each step. With this approach, ResCP enables us to account for local temporal dynamics when modeling the error distribution without compromising computational scalability. We prove that, under reasonable assumptions, ResCP achieves asymptotic conditional coverage, and we empirically demonstrate its effectiveness across diverse forecasting tasks.

The ability of deep learning models to learn continuously is essential for adapting to new data categories and evolving data distributions. In recent years, approaches leveraging frozen feature extractors after an initial learning phase have been extensively studied. Many of these methods estimate per-class covariance matrices and prototypes based on backbone-derived feature representations. Within this paradigm, we introduce FeNeC (Feature Neighborhood Classifier) and FeNeC-Log, its variant based on the log-likelihood function. Our approach generalizes the existing concept by incorporating data clustering to capture greater intra-class variability. Utilizing the Mahalanobis distance, our models classify samples either through a nearest neighbor approach or trainable logit values assigned to consecutive classes. Our proposition may be reduced to the existing approaches in a special case while extending them with the ability of more flexible adaptation to data. We demonstrate that two FeNeC variants achieve competitive performance in scenarios where task identities are unknown and establish state-of-the-art results on several benchmarks.

Large Language Models (LLMs) are increasingly employed in real-world applications, driving the need to evaluate the trustworthiness of their generated text. To this end, reliable uncertainty estimation is essential. Since current LLMs generate text autoregressively through a stochastic process, the same prompt can lead to varying outputs. Consequently, leading uncertainty estimation methods generate and analyze multiple output sequences to determine the LLM's uncertainty. However, generating output sequences is computationally expensive, making these methods impractical at scale. In this work, we inspect the theoretical foundations of the leading methods and explore new directions to enhance their computational efficiency. Building on the framework of proper scoring rules, we find that the negative log-likelihood of the most likely output sequence constitutes a theoretically grounded uncertainty measure. To approximate this alternative measure, we propose G-NLL, which has the advantage of being obtained using only a single output sequence generated by greedy decoding. This makes uncertainty estimation more efficient and straightforward, while preserving theoretical rigor. Empirical results demonstrate that G-NLL achieves state-of-the-art performance across various LLMs and tasks. Our work lays the foundation for efficient and reliable uncertainty estimation in natural language generation, challenging the necessity of more computationally involved methods currently leading the field.

The attention mechanism in Transformers is an important primitive for accurate and scalable sequence modeling. Its quadratic-compute and linear-memory complexity however remain significant bottlenecks. Linear attention and state-space models enable linear-time, constant-memory sequence modeling and can moreover be trained efficiently through matmul-rich parallelization across sequence length. However, at their core these models are still RNNs, and thus their use of a fixed-size hidden state to model the context is a fundamental limitation. This paper develops log-linear attention, an attention mechanism that balances linear attention's efficiency and the expressiveness of softmax attention. Log-linear attention replaces the fixed-size hidden state with a logarithmically growing set of hidden states. We show that with a particular growth function, log-linear attention admits a similarly matmul-rich parallel form whose compute cost is log-linear in sequence length. Log-linear attention is a general framework and can be applied on top of existing linear attention variants. As case studies, we instantiate log-linear variants of two recent architectures -- Mamba-2 and Gated DeltaNet -- and find they perform well compared to their linear-time variants.

The increasing complexity of computer systems necessitates innovative approaches to fault and error management, going beyond traditional manual log analysis. While existing solutions using large language models (LLMs) show promise, they are limited by a gap between natural and domain-specific languages, which restricts their effectiveness in real-world applications. Our approach addresses these limitations by integrating interpretable domain knowledge into open-source LLMs through continual pre-training (CPT), enhancing performance on log tasks while retaining natural language processing capabilities. We created a comprehensive dataset, NLPLog, with over 250,000 question-answer pairs to facilitate this integration. Our model, SuperLog, trained with this dataset, achieves the best performance across four log analysis tasks, surpassing the second-best model by an average of 12.01%. Our contributions include a novel CPT paradigm that significantly improves model performance, the development of SuperLog with state-of-the-art results, and the release of a large-scale dataset to support further research in this domain.

Electronic Health Records (EHRs) contain rich temporal dynamics that conventional encoding approaches fail to adequately capture. While Large Language Models (LLMs) show promise for EHR modeling, they struggle to reason about sequential clinical events and temporal dependencies. We propose Next Event Prediction (NEP), a framework that enhances LLMs' temporal reasoning through autoregressive fine-tuning on clinical event sequences. By reformulating EHRs as timestamped event chains and predicting future medical events, NEP explicitly models disease progression patterns and causal relationships. Extensive evaluations across oncology survival prediction and clinical diagnosis tasks demonstrate NEP's superiority, outperforming specialized EHR models by 4.6% AUROC and general-purpose LLMs by 7.2% C-index in temporal reasoning tasks. Our analyses reveal dual benefits: state-of-the-art prediction accuracy combined with clinically interpretable attention patterns that align with known disease pathways.

Next-token prediction (NTP) has driven the success of large language models (LLMs), but it struggles with long-horizon reasoning, planning, and creative writing, with these limitations largely attributed to teacher-forced training. Multi-token prediction (MTP) partially mitigates these issues by predicting several future tokens at once, but it mostly captures short-range dependencies and offers limited improvement. We propose future summary prediction (FSP), which trains an auxiliary head to predict a compact representation of the long-term future, preserving information relevant for long-form generations. We explore two variants of FSP: handcrafted summaries, for example, a bag of words summary of the future sequence, and learned summaries, which use embeddings produced by a reverse language model trained from right-to-left order. Large-scale pretraining experiments (3B and 8B-parameter models) demonstrate that FSP provides improvements over both NTP and MTP across math, reasoning, and coding benchmarks.

Forecasting future events based on evidence of current conditions is an innate skill of human beings, and key for predicting the outcome of any decision making. In artificial vision for example, we would like to predict the next human action before it happens, without observing the future video frames associated to it. Computer vision models for action anticipation are expected to collect the subtle evidence in the preamble of the target actions. In prior studies recurrence modeling often leads to better performance, the strong temporal inference is assumed to be a key element for reasonable prediction. To this end, we propose a unified recurrence modeling for video action anticipation via message passing framework. The information flow in space-time can be described by the interaction between vertices and edges, and the changes of vertices for each incoming frame reflects the underlying dynamics. Our model leverages self-attention as the building blocks for each of the message passing functions. In addition, we introduce different edge learning strategies that can be end-to-end optimized to gain better flexibility for the connectivity between vertices. Our experimental results demonstrate that our proposed method outperforms previous works on the large-scale EPIC-Kitchen dataset.

Most existing forecasting systems are memory-based methods, which attempt to mimic human forecasting ability by employing various memory mechanisms and have progressed in temporal modeling for memory dependency. Nevertheless, an obvious weakness of this paradigm is that it can only model limited historical dependence and can not transcend the past. In this paper, we rethink the temporal dependence of event evolution and propose a novel memory-anticipation-based paradigm to model an entire temporal structure, including the past, present, and future. Based on this idea, we present Memory-and-Anticipation Transformer (MAT), a memory-anticipation-based approach, to address the online action detection and anticipation tasks. In addition, owing to the inherent superiority of MAT, it can process online action detection and anticipation tasks in a unified manner. The proposed MAT model is tested on four challenging benchmarks TVSeries, THUMOS'14, HDD, and EPIC-Kitchens-100, for online action detection and anticipation tasks, and it significantly outperforms all existing methods. Code is available at https://github.com/Echo0125/Memory-and-Anticipation-Transformer.

Most work on sequential learning assumes a fixed set of actions that are available all the time. However, in practice, actions can consist of picking subsets of readings from sensors that may break from time to time, road segments that can be blocked or goods that are out of stock. In this paper we study learning algorithms that are able to deal with stochastic availability of such unreliable composite actions. We propose and analyze algorithms based on the Follow-The-Perturbed-Leader prediction method for several learning settings differing in the feedback provided to the learner. Our algorithms rely on a novel loss estimation technique that we call Counting Asleep Times. We deliver regret bounds for our algorithms for the previously studied full information and (semi-)bandit settings, as well as a natural middle point between the two that we call the restricted information setting. A special consequence of our results is a significant improvement of the best known performance guarantees achieved by an efficient algorithm for the sleeping bandit problem with stochastic availability. Finally, we evaluate our algorithms empirically and show their improvement over the known approaches.

Large Language Models (LLMs) have recently been successfully applied to regression tasks -- such as time series forecasting and tabular prediction -- by leveraging their in-context learning abilities. However, their autoregressive decoding process may be ill-suited to continuous-valued outputs, where obtaining predictive distributions over numerical targets requires repeated sampling, leading to high computational cost and inference time. In this work, we investigate whether distributional properties of LLM predictions can be recovered without explicit autoregressive generation. To this end, we study a set of regression probes trained to predict statistical functionals (e.g., mean, median, quantiles) of the LLM's numerical output distribution directly from its internal representations. Our results suggest that LLM embeddings carry informative signals about summary statistics of their predictive distributions, including the numerical uncertainty. This investigation opens up new questions about how LLMs internally encode uncertainty in numerical tasks, and about the feasibility of lightweight alternatives to sampling-based approaches for uncertainty-aware numerical predictions.

Learning a good history representation is one of the core challenges of reinforcement learning (RL) in partially observable environments. Recent works have shown the advantages of various auxiliary tasks for facilitating representation learning. However, the effectiveness of such auxiliary tasks has not been fully convincing, especially in partially observable environments that require long-term memorization and inference. In this empirical study, we investigate the effectiveness of future prediction for learning the representations of histories, possibly of extensive length, in partially observable environments. We first introduce an approach that decouples the task of learning history representations from policy optimization via future prediction. Then, our main contributions are two-fold: (a) we demonstrate that the performance of reinforcement learning is strongly correlated with the prediction accuracy of future observations in partially observable environments, and (b) our approach can significantly improve the overall end-to-end approach by preventing high-variance noisy signals from reinforcement learning objectives to influence the representation learning. We illustrate our claims on three types of benchmarks that necessitate the ability to process long histories for high returns.

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models. While existing analyses identify that RLVR-induced changes are sparse, they primarily focus on the magnitude of these updates, largely overlooking their direction. In this work, we argue that the direction of updates is a more critical lens for understanding RLVR's effects, which can be captured by the signed, token-level log probability difference Δlog p between the base and final RLVR models. Through statistical analysis and token-replacement interventions, we demonstrate that Δlog p more effectively identifies sparse, yet reasoning-critical updates than magnitude-based metrics (\eg divergence or entropy). Building on this insight, we propose two practical applications: (1) a test-time extrapolation method that amplifies the policy along the learned Δlog p direction to improve reasoning accuracy without further training; (2) a training-time reweighting method that focuses learning on low-probability (corresponding to higher Δlog p) tokens, which improves reasoning performance across models and benchmarks. Our work establishes the direction of change as a key principle for analyzing and improving RLVR.

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the sequential predictive conformal inference (SPCI). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of SPCI compared to other existing methods under the desired empirical coverage.

Many real-world prediction problems lack labels observable at prediction time, creating a temporal gap between prediction and outcome that yields supervision only after events resolve. To address this setting, we extend reinforcement learning with verifiable rewards to temporally resolved real-world prediction, and use it to train language models to make probabilistic forecasts under causally masked information with retrospective evaluation using proper scoring rules. Supervision is derived solely from post-resolution outcomes, preserving delayed-reward semantics. On real-world forecasting benchmarks, Qwen3-32B trained using Foresight Learning improves Brier score by 27% and halves calibration error relative to its pretrained baseline, and outperforms Qwen3-235B on both constructed future-event prediction tasks and the Metaculus benchmark despite a 7x parameter disadvantage.

Software systems often record important runtime information in logs to help with troubleshooting. Log-based anomaly detection has become a key research area that aims to identify system issues through log data, ultimately enhancing the reliability of software systems. Traditional deep learning methods often struggle to capture the semantic information embedded in log data, which is typically organized in natural language. In this paper, we propose LogLLM, a log-based anomaly detection framework that leverages large language models (LLMs). LogLLM employs BERT for extracting semantic vectors from log messages, while utilizing Llama, a transformer decoder-based model, for classifying log sequences. Additionally, we introduce a projector to align the vector representation spaces of BERT and Llama, ensuring a cohesive understanding of log semantics. Unlike conventional methods that require log parsers to extract templates, LogLLM preprocesses log messages with regular expressions, streamlining the entire process. Our framework is trained through a novel three-stage procedure designed to enhance performance and adaptability. Experimental results across four public datasets demonstrate that LogLLM outperforms state-of-the-art methods. Even when handling unstable logs, it effectively captures the semantic meaning of log messages and detects anomalies accurately.

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforcing invertibility. However, prior work trained invertible residual networks for density estimation by relying on biased log-density estimates whose bias increased with the network's expressiveness. We give a tractable unbiased estimate of the log density using a "Russian roulette" estimator, and reduce the memory required during training by using an alternative infinite series for the gradient. Furthermore, we improve invertible residual blocks by proposing the use of activation functions that avoid derivative saturation and generalizing the Lipschitz condition to induced mixed norms. The resulting approach, called Residual Flows, achieves state-of-the-art performance on density estimation amongst flow-based models, and outperforms networks that use coupling blocks at joint generative and discriminative modeling.

This study evaluates deep neural networks for forecasting probability distributions of financial returns. 1D convolutional neural networks (CNN) and Long Short-Term Memory (LSTM) architectures are used to forecast parameters of three probability distributions: Normal, Student's t, and skewed Student's t. Using custom negative log-likelihood loss functions, distribution parameters are optimized directly. The models are tested on six major equity indices (S\&P 500, BOVESPA, DAX, WIG, Nikkei 225, and KOSPI) using probabilistic evaluation metrics including Log Predictive Score (LPS), Continuous Ranked Probability Score (CRPS), and Probability Integral Transform (PIT). Results show that deep learning models provide accurate distributional forecasts and perform competitively with classical GARCH models for Value-at-Risk estimation. The LSTM with skewed Student's t distribution performs best across multiple evaluation criteria, capturing both heavy tails and asymmetry in financial returns. This work shows that deep neural networks are viable alternatives to traditional econometric models for financial risk assessment and portfolio management.

Automated log analysis is crucial to ensure high availability and reliability of complex systems. The advent of LLMs in NLP has ushered in a new era of language model-driven automated log analysis, garnering significant interest. Within this field, two primary paradigms based on language models for log analysis have become prominent. Small Language Models (SLMs) follow the pre-train and fine-tune paradigm, focusing on the specific log analysis task through fine-tuning on supervised datasets. On the other hand, LLMs following the in-context learning paradigm, analyze logs by providing a few examples in prompt contexts without updating parameters. Despite their respective strengths, we notice that SLMs are more cost-effective but less powerful, whereas LLMs with large parameters are highly powerful but expensive and inefficient. To trade-off between the performance and inference costs of both models in automated log analysis, this paper introduces an adaptive log analysis framework known as AdaptiveLog, which effectively reduces the costs associated with LLM while ensuring superior results. This framework collaborates an LLM and a small language model, strategically allocating the LLM to tackle complex logs while delegating simpler logs to the SLM. Specifically, to efficiently query the LLM, we propose an adaptive selection strategy based on the uncertainty estimation of the SLM, where the LLM is invoked only when the SLM is uncertain. In addition, to enhance the reasoning ability of the LLM in log analysis tasks, we propose a novel prompt strategy by retrieving similar error-prone cases as the reference, enabling the model to leverage past error experiences and learn solutions from these cases. Extensive experiments demonstrate that AdaptiveLog achieves state-of-the-art results across different tasks, elevating the overall accuracy of log analysis while maintaining cost efficiency.

Large language models demonstrate remarkable in-context learning capabilities, adapting to new tasks without parameter updates. While this phenomenon has been successfully modeled as implicit Bayesian inference, recent empirical findings reveal a fundamental contradiction: transformers systematically violate the martingale property, a cornerstone requirement of Bayesian updating on exchangeable data. This violation challenges the theoretical foundations underlying uncertainty quantification in critical applications. Our theoretical analysis establishes four key results: (1) positional encodings induce martingale violations of order Theta(log n / n); (2) transformers achieve information-theoretic optimality with excess risk O(n^{-1/2}) in expectation over orderings; (3) the implicit posterior representation converges to the true Bayesian posterior in the space of sufficient statistics; and (4) we derive the optimal chain-of-thought length as k^* = Theta(nlog(1/varepsilon)) with explicit constants, providing a principled approach to reduce inference costs while maintaining performance. Empirical validation on GPT-3 confirms predictions (1)-(3), with transformers reaching 99\% of theoretical entropy limits within 20 examples. Our framework provides practical methods for extracting calibrated uncertainty estimates from position-aware architectures and optimizing computational efficiency in deployment.

A fundamental open challenge in modern LLM scaling is the lack of understanding around emergent capabilities. In particular, language model pretraining loss is known to be highly predictable as a function of compute. However, downstream capabilities are far less predictable -- sometimes even exhibiting emergent jumps -- which makes it challenging to anticipate the capabilities of future models. In this work, we first pose the task of emergence prediction: given access to current LLMs that have random few-shot accuracy on a task, can we predict whether future models (GPT-N+1) will have non-trivial accuracy on that task? We then discover a simple insight for this problem: finetuning LLMs on a given task can shift the point in scaling at which emergence occurs towards less capable models. To operationalize this insight, we can finetune LLMs with varying amounts of data and fit a parametric function that predicts when emergence will occur (i.e., "emergence laws"). We validate this approach using four standard NLP benchmarks where large-scale open-source LLMs already demonstrate emergence (MMLU, GSM8K, CommonsenseQA, and CoLA). Using only small-scale LLMs, we find that, in some cases, we can accurately predict whether models trained with up to 4x more compute have emerged. Finally, we present a case study of two realistic uses for emergence prediction.

We formulate the predicted-updates dynamic model, one of the first beyond-worst-case models for dynamic algorithms, which generalizes a large set of well-studied dynamic models including the offline dynamic, incremental, and decremental models to the fully dynamic setting when given predictions about the update times of the elements. In the most basic form of our model, we receive a set of predicted update times for all of the updates that occur over the event horizon. We give a novel framework that "lifts" offline divide-and-conquer algorithms into the fully dynamic setting with little overhead. Using this, we are able to interpolate between the offline and fully dynamic settings; when the ell_1 error of the prediction is linear in the number of updates, we achieve the offline runtime of the algorithm (up to poly log n factors). Provided a fully dynamic backstop algorithm, our algorithm will never do worse than the backstop algorithm regardless of the prediction error. Furthermore, our framework achieves a smooth linear trade-off between ell_1 error in the predictions and runtime. These correspond to the desiderata of consistency, robustness, and graceful degradation of the algorithms-with-predictions literature. We further extend our techniques to incremental and decremental settings, transforming algorithms in these settings when given predictions of only the deletion and insertion times, respectively. Our framework is general, and we apply it to obtain improved efficiency bounds over the state-of-the-art dynamic algorithms for a variety of problems including triconnectivity, planar digraph all pairs shortest paths, k-edge connectivity, and others, for prediction error of reasonable magnitude.

Adaptive behavior often requires predicting future events. The theory of reinforcement learning prescribes what kinds of predictive representations are useful and how to compute them. This paper integrates these theoretical ideas with work on cognition and neuroscience. We pay special attention to the successor representation (SR) and its generalizations, which have been widely applied both as engineering tools and models of brain function. This convergence suggests that particular kinds of predictive representations may function as versatile building blocks of intelligence.

Learning continuously during all model lifetime is fundamental to deploy machine learning solutions robust to drifts in the data distribution. Advances in Continual Learning (CL) with recurrent neural networks could pave the way to a large number of applications where incoming data is non stationary, like natural language processing and robotics. However, the existing body of work on the topic is still fragmented, with approaches which are application-specific and whose assessment is based on heterogeneous learning protocols and datasets. In this paper, we organize the literature on CL for sequential data processing by providing a categorization of the contributions and a review of the benchmarks. We propose two new benchmarks for CL with sequential data based on existing datasets, whose characteristics resemble real-world applications. We also provide a broad empirical evaluation of CL and Recurrent Neural Networks in class-incremental scenario, by testing their ability to mitigate forgetting with a number of different strategies which are not specific to sequential data processing. Our results highlight the key role played by the sequence length and the importance of a clear specification of the CL scenario.

Reasoning failures in large language models (LLMs) are typically measured only at the end of a generation, yet many failures manifest as a process-level breakdown: the model "loses the thread" mid-reasoning. We study whether such breakdowns are detectable from inference-time observables available in standard APIs (token log probabilities), without any training or fine-tuning. We define a simple instability signal that combines consecutive-step distributional shift (JSD) and uncertainty (entropy), summarize each trace by its peak instability strength, and show that this signal reliably predicts failure. Across GSM8K and HotpotQA, instability strength predicts wrong answers with above-chance AUC and yields monotonic bucket-level accuracy decline at scale across model sizes. Crucially, we show that instability is not uniformly harmful: early instability can reflect subsequent stabilization and a correct final answer (corrective instability), whereas late instability is more often followed by failure (destructive instability), even at comparable peak magnitudes, indicating that recoverability depends not only on how strongly the distribution changes but also on when such changes occur relative to the remaining decoding horizon. The method is model-agnostic, training-free, and reproducible, and is presented as a diagnostic lens rather than a corrective or control mechanism.

Can a mere next-token predictor faithfully model human intelligence? We crystallize this intuitive concern, which is fragmented in the literature. As a starting point, we argue that the two often-conflated phases of next-token prediction -- autoregressive inference and teacher-forced training -- must be treated distinctly. The popular criticism that errors can compound during autoregressive inference, crucially assumes that teacher-forcing has learned an accurate next-token predictor. This assumption sidesteps a more deep-rooted problem we expose: in certain classes of tasks, teacher-forcing can simply fail to learn an accurate next-token predictor in the first place. We describe a general mechanism of how teacher-forcing can fail, and design a minimal planning task where both the Transformer and the Mamba architecture empirically fail in that manner -- remarkably, despite the task being straightforward to learn. We provide preliminary evidence that this failure can be resolved when training to predict multiple tokens in advance. We hope this finding can ground future debates and inspire explorations beyond the next-token prediction paradigm. We make our code available under https://github.com/gregorbachmann/Next-Token-Failures

Gradient descent has proven to be a powerful and effective technique for optimization in numerous machine learning applications. Recent advances in computational neuroscience have shown that learning in standard gradient descent optimization formulation is not consistent with learning in biological systems. This has opened up interesting avenues for building biologically inspired learning techniques. One such approach is inspired by Dale's law, which states that inhibitory and excitatory synapses do not swap roles during the course of learning. The resulting exponential gradient descent optimization scheme leads to log-normally distributed synaptic weights. Interestingly, the density that satisfies the Fokker-Planck equation corresponding to the stochastic differential equation (SDE) with geometric Brownian motion (GBM) is the log-normal density. Leveraging this connection, we start with the SDE governing geometric Brownian motion, and show that discretizing the corresponding reverse-time SDE yields a multiplicative update rule, which surprisingly, coincides with the sampling equivalent of the exponential gradient descent update founded on Dale's law. Furthermore, we propose a new formalism for multiplicative denoising score-matching, subsuming the loss function proposed by Hyvaerinen for non-negative data. Indeed, log-normally distributed data is positive and the proposed score-matching formalism turns out to be a natural fit. This allows for training of score-based models for image data and results in a novel multiplicative update scheme for sample generation starting from a log-normal density. Experimental results on MNIST, Fashion MNIST, and Kuzushiji datasets demonstrate generative capability of the new scheme. To the best of our knowledge, this is the first instance of a biologically inspired generative model employing multiplicative updates, founded on geometric Brownian motion.

The stable periodic patterns present in time series data serve as the foundation for conducting long-horizon forecasts. In this paper, we pioneer the exploration of explicitly modeling this periodicity to enhance the performance of models in long-term time series forecasting (LTSF) tasks. Specifically, we introduce the Residual Cycle Forecasting (RCF) technique, which utilizes learnable recurrent cycles to model the inherent periodic patterns within sequences, and then performs predictions on the residual components of the modeled cycles. Combining RCF with a Linear layer or a shallow MLP forms the simple yet powerful method proposed in this paper, called CycleNet. CycleNet achieves state-of-the-art prediction accuracy in multiple domains including electricity, weather, and energy, while offering significant efficiency advantages by reducing over 90% of the required parameter quantity. Furthermore, as a novel plug-and-play technique, the RCF can also significantly improve the prediction accuracy of existing models, including PatchTST and iTransformer. The source code is available at: https://github.com/ACAT-SCUT/CycleNet.

Memory-based meta-learning is a technique for approximating Bayes-optimal predictors. Under fairly general conditions, minimizing sequential prediction error, measured by the log loss, leads to implicit meta-learning. The goal of this work is to investigate how far this interpretation can be realized by current sequence prediction models and training regimes. The focus is on piecewise stationary sources with unobserved switching-points, which arguably capture an important characteristic of natural language and action-observation sequences in partially observable environments. We show that various types of memory-based neural models, including Transformers, LSTMs, and RNNs can learn to accurately approximate known Bayes-optimal algorithms and behave as if performing Bayesian inference over the latent switching-points and the latent parameters governing the data distribution within each segment.

Recent large-scale neural autoregressive sequence models have shown impressive performances on a variety of natural language generation tasks. However, their generated sequences often exhibit degenerate properties such as non-termination, undesirable repetition, and premature termination, when generated with decoding algorithms such as greedy search, beam search, top-k sampling, and nucleus sampling. In this paper, we focus on the problem of non-terminating sequences resulting from an incomplete decoding algorithm. We first define an incomplete probable decoding algorithm which includes greedy search, top-k sampling, and nucleus sampling, beyond the incomplete decoding algorithm originally put forward by Welleck et al. (2020). We then propose a non-monotonic self-terminating language model, which significantly relaxes the constraint of monotonically increasing termination probability in the originally proposed self-terminating language model by Welleck et al. (2020), to address the issue of non-terminating sequences when using incomplete probable decoding algorithms. We prove that our proposed model prevents non-terminating sequences when using not only incomplete probable decoding algorithms but also beam search. We empirically validate our model on sequence completion tasks with various architectures.

The output structure of database-like tables, consisting of values structured in horizontal rows and vertical columns identifiable by name, can cover a wide range of NLP tasks. Following this constatation, we propose a framework for text-to-table neural models applicable to problems such as extraction of line items, joint entity and relation extraction, or knowledge base population. The permutation-based decoder of our proposal is a generalized sequential method that comprehends information from all cells in the table. The training maximizes the expected log-likelihood for a table's content across all random permutations of the factorization order. During the content inference, we exploit the model's ability to generate cells in any order by searching over possible orderings to maximize the model's confidence and avoid substantial error accumulation, which other sequential models are prone to. Experiments demonstrate a high practical value of the framework, which establishes state-of-the-art results on several challenging datasets, outperforming previous solutions by up to 15%.

Recommender systems are among the most impactful applications of artificial intelligence, serving as critical infrastructure connecting users, merchants, and platforms. However, most current industrial systems remain heavily reliant on historical co-occurrence patterns and log-fitting objectives, i.e., optimizing for past user interactions without explicitly modeling user intent. This log-fitting approach often leads to overfitting to narrow historical preferences, failing to capture users' evolving and latent interests. As a result, it reinforces filter bubbles and long-tail phenomena, ultimately harming user experience and threatening the sustainability of the whole recommendation ecosystem. To address these challenges, we rethink the overall design paradigm of recommender systems and propose RecGPT, a next-generation framework that places user intent at the center of the recommendation pipeline. By integrating large language models (LLMs) into key stages of user interest mining, item retrieval, and explanation generation, RecGPT transforms log-fitting recommendation into an intent-centric process. To effectively align general-purpose LLMs to the above domain-specific recommendation tasks at scale, RecGPT incorporates a multi-stage training paradigm, which integrates reasoning-enhanced pre-alignment and self-training evolution, guided by a Human-LLM cooperative judge system. Currently, RecGPT has been fully deployed on the Taobao App. Online experiments demonstrate that RecGPT achieves consistent performance gains across stakeholders: users benefit from increased content diversity and satisfaction, merchants and the platform gain greater exposure and conversions. These comprehensive improvement results across all stakeholders validates that LLM-driven, intent-centric design can foster a more sustainable and mutually beneficial recommendation ecosystem.

Logs generated by large-scale software systems provide crucial information for engineers to understand the system status and diagnose problems of the systems. Log parsing, which converts raw log messages into structured data, is the first step to enabling automated log analytics. Existing log parsers extract the common part as log templates using statistical features. However, these log parsers often fail to identify the correct templates and parameters because: 1) they often overlook the semantic meaning of log messages, and 2) they require domain-specific knowledge for different log datasets. To address the limitations of existing methods, in this paper, we propose LogPPT to capture the patterns of templates using prompt-based few-shot learning. LogPPT utilises a novel prompt tuning method to recognise keywords and parameters based on a few labelled log data. In addition, an adaptive random sampling algorithm is designed to select a small yet diverse training set. We have conducted extensive experiments on 16 public log datasets. The experimental results show that LogPPT is effective and efficient for log parsing.

Continual Learning is an important and challenging problem in machine learning, where models must adapt to a continuous stream of new data without forgetting previously acquired knowledge. While existing frameworks are built on PyTorch, the rising popularity of JAX might lead to divergent codebases, ultimately hindering reproducibility and progress. To address this problem, we introduce SequeL, a flexible and extensible library for Continual Learning that supports both PyTorch and JAX frameworks. SequeL provides a unified interface for a wide range of Continual Learning algorithms, including regularization-based approaches, replay-based approaches, and hybrid approaches. The library is designed towards modularity and simplicity, making the API suitable for both researchers and practitioners. We release SequeL\url{https://github.com/nik-dim/sequel} as an open-source library, enabling researchers and developers to easily experiment and extend the library for their own purposes.

We prove an inverse approximation theorem for the approximation of nonlinear sequence-to-sequence relationships using recurrent neural networks (RNNs). This is a so-called Bernstein-type result in approximation theory, which deduces properties of a target function under the assumption that it can be effectively approximated by a hypothesis space. In particular, we show that nonlinear sequence relationships that can be stably approximated by nonlinear RNNs must have an exponential decaying memory structure - a notion that can be made precise. This extends the previously identified curse of memory in linear RNNs into the general nonlinear setting, and quantifies the essential limitations of the RNN architecture for learning sequential relationships with long-term memory. Based on the analysis, we propose a principled reparameterization method to overcome the limitations. Our theoretical results are confirmed by numerical experiments. The code has been released in https://github.com/radarFudan/Curse-of-memory

Long-horizon LLM agents depend on intermediate information-gathering turns, yet training feedback is usually observed only at the final answer, because process-level rewards require high-quality human annotation. Existing turn-level shaping methods reward turns that increase the likelihood of a gold answer, but they require answer supervision or stable task-specific verifiers. Conversely, label-free RL methods extract self-signals from output distributions, but mainly at the answer or trajectory level and therefore cannot assign credit to intermediate turns. We propose Self-Induced Outcome Potential (SIOP), which treats semantic clusters of final answers as latent future outcome states for potential-based turn-level credit assignment. For each query, SIOP samples multiple rollouts, clusters final answers into semantic outcome modes, and builds a reliability-aware target distribution over these states. It then rewards turns for increasing posterior support for reliable future states using a tractable cluster-level approximation. The objective generalizes information-potential shaping from gold-answer supervision to settings without task-specific gold verifiers while avoiding the broadcasted rollout-level advantages used by standard GRPO. We formalize the framework, characterize its supervised gold-answer limit, and show that SIOP improves average performance over verifier-free outcome-level baselines on seven search-augmented agentic reasoning benchmarks while approaching a gold-supervised outcome baseline. Code is available at https://github.com/dl-m9/SIOP.git.

We study the problem of predicting numeric labels that are constrained to the integers or to a subrange of the integers. For example, the number of up-votes on social media posts, or the number of bicycles available at a public rental station. While it is possible to model these as continuous values, and to apply traditional regression, this approach changes the underlying distribution on the labels from discrete to continuous. Discrete distributions have certain benefits, which leads us to the question whether such integer labels can be modeled directly by a discrete distribution, whose parameters are predicted from the features of a given instance. Moreover, we focus on the use case of output distributions of neural networks, which adds the requirement that the parameters of the distribution be continuous so that backpropagation and gradient descent may be used to learn the weights of the network. We investigate several options for such distributions, some existing and some novel, and test them on a range of tasks, including tabular learning, sequential prediction and image generation. We find that overall the best performance comes from two distributions: Bitwise, which represents the target integer in bits and places a Bernoulli distribution on each, and a discrete analogue of the Laplace distribution, which uses a distribution with exponentially decaying tails around a continuous mean.

Black-box machine learning models are now routinely used in high-risk settings, like medical diagnostics, which demand uncertainty quantification to avoid consequential model failures. Conformal prediction is a user-friendly paradigm for creating statistically rigorous uncertainty sets/intervals for the predictions of such models. Critically, the sets are valid in a distribution-free sense: they possess explicit, non-asymptotic guarantees even without distributional assumptions or model assumptions. One can use conformal prediction with any pre-trained model, such as a neural network, to produce sets that are guaranteed to contain the ground truth with a user-specified probability, such as 90%. It is easy-to-understand, easy-to-use, and general, applying naturally to problems arising in the fields of computer vision, natural language processing, deep reinforcement learning, and so on. This hands-on introduction is aimed to provide the reader a working understanding of conformal prediction and related distribution-free uncertainty quantification techniques with one self-contained document. We lead the reader through practical theory for and examples of conformal prediction and describe its extensions to complex machine learning tasks involving structured outputs, distribution shift, time-series, outliers, models that abstain, and more. Throughout, there are many explanatory illustrations, examples, and code samples in Python. With each code sample comes a Jupyter notebook implementing the method on a real-data example; the notebooks can be accessed and easily run using our codebase.

Large Language Models (LLMs) leverage step-by-step reasoning to solve complex problems. Standard evaluation practice involves generating a complete reasoning trace and assessing the correctness of the final answer presented at its conclusion. In this paper, we challenge the reliance on the final answer by posing the following two questions: Does the final answer reliably represent the model's optimal conclusion? Can alternative reasoning paths yield different results? To answer these questions, we analyze intermediate reasoning steps, termed subthoughts, and propose a method based on our findings. Our approach involves segmenting a reasoning trace into sequential subthoughts based on linguistic cues. We start by prompting the model to generate continuations from the end-point of each intermediate subthought. We extract a potential answer from every completed continuation originating from different subthoughts. We find that aggregating these answers by selecting the most frequent one (the mode) often yields significantly higher accuracy compared to relying solely on the answer derived from the original complete trace. Analyzing the consistency among the answers derived from different subthoughts reveals characteristics that correlate with the model's confidence and correctness, suggesting potential for identifying less reliable answers. Our experiments across various LLMs and challenging mathematical reasoning datasets (AIME2024 and AIME2025) show consistent accuracy improvements, with gains reaching up to 13\% and 10\% respectively. Implementation is available at: https://github.com/hammoudhasan/SubthoughtReasoner.

The Information Bottleneck (IB) method frequently suffers from unstable optimization, characterized by abrupt representation shifts near critical points of the IB trade-off parameter, beta. In this paper, I introduce a novel approach to achieve stable and convex IB optimization through symbolic continuation and entropy-regularized trajectories. I analytically prove convexity and uniqueness of the IB solution path when an entropy regularization term is included, and demonstrate how this stabilizes representation learning across a wide range of eta values. Additionally, I provide extensive sensitivity analyses around critical points (beta) with statistically robust uncertainty quantification (95% confidence intervals). The open-source implementation, experimental results, and reproducibility framework included in this work offer a clear path for practical deployment and future extension of my proposed method.

We consider learning in an adversarial Markov Decision Process (MDP) where the loss functions can change arbitrarily over K episodes and the state space can be arbitrarily large. We assume that the Q-function of any policy is linear in some known features, that is, a linear function approximation exists. The best existing regret upper bound for this setting (Luo et al., 2021) is of order mathcal O(K^{2/3}) (omitting all other dependencies), given access to a simulator. This paper provides two algorithms that improve the regret to mathcal O(sqrt K) in the same setting. Our first algorithm makes use of a refined analysis of the Follow-the-Regularized-Leader (FTRL) algorithm with the log-barrier regularizer. This analysis allows the loss estimators to be arbitrarily negative and might be of independent interest. Our second algorithm develops a magnitude-reduced loss estimator, further removing the polynomial dependency on the number of actions in the first algorithm and leading to the optimal regret bound (up to logarithmic terms and dependency on the horizon). Moreover, we also extend the first algorithm to simulator-free linear MDPs, which achieves mathcal O(K^{8/9}) regret and greatly improves over the best existing bound mathcal O(K^{14/15}). This algorithm relies on a better alternative to the Matrix Geometric Resampling procedure by Neu & Olkhovskaya (2020), which could again be of independent interest.

The GPT-4 technical report suggests that downstream performance can be predicted from pre-training signals, but offers little methodological detail on how to quantify this. This work address this gap by modeling knowledge retention, the capacity of a pre-trained language model to memorize factual information from its corpus, and introduce a principled method to estimate it prior to training. We propose Size-dependent Mutual Information (SMI), an information-theoretic predictor that integrates knowledge frequency, knowledge specificity, and model size to forecast closed-book question answering (QA) accuracy. SMI is validated through large-scale document retrieval over the disclosed pre-training corpora of 21 public and 3 custom models, combined with a robust multi-template QA evaluation. Experiments show that SMI significantly outperforms repetition-based baselines and achieves R^2 > 0.7 in predicting QA accuracy for models above 1B parameters, without additional training. The analysis further reveals diminishing returns from scaling data and model size and provides evidence for an intrinsic upper bound on knowledge retention achievable by pre-training alone, motivating retrieval and other augmentation strategies.

Diffusion language models (DLMs) have strong theoretical efficiency but are limited by fixed-length decoding and incompatibility with key-value (KV) caches. Block diffusion mitigates these issues, yet still enforces a fixed block size and requires expensive training. We introduce Next Sequence Prediction (NSP), which unifies next-token and next-block prediction, enabling the model to adaptively determine the generation length at each step. When the length is fixed to 1, NSP reduces to standard next-token prediction. Building on NSP, we propose Sequential Diffusion Language Model (SDLM), which can retrofit pre-trained autoregressive language models (ALMs) at minimal cost. Specifically, SDLM performs diffusion inference within fixed-size mask blocks, but dynamically decodes consecutive subsequences based on model confidence, thereby preserving KV-cache compatibility and improving robustness to varying uncertainty and semantics across the sequence. Experiments show that SDLM matches or surpasses strong autoregressive baselines using only 3.5M training samples, while achieving 2.1 higher throughput than Qwen-2.5. Notably, the SDLM-32B model delivers even more pronounced efficiency gains, demonstrating the strong scalability potential of our modeling paradigm. Project page and codes: https://github.com/OpenGVLab/SDLM

This paper studies learning logic rules for reasoning on knowledge graphs. Logic rules provide interpretable explanations when used for prediction as well as being able to generalize to other tasks, and hence are critical to learn. Existing methods either suffer from the problem of searching in a large search space (e.g., neural logic programming) or ineffective optimization due to sparse rewards (e.g., techniques based on reinforcement learning). To address these limitations, this paper proposes a probabilistic model called RNNLogic. RNNLogic treats logic rules as a latent variable, and simultaneously trains a rule generator as well as a reasoning predictor with logic rules. We develop an EM-based algorithm for optimization. In each iteration, the reasoning predictor is first updated to explore some generated logic rules for reasoning. Then in the E-step, we select a set of high-quality rules from all generated rules with both the rule generator and reasoning predictor via posterior inference; and in the M-step, the rule generator is updated with the rules selected in the E-step. Experiments on four datasets prove the effectiveness of RNNLogic.

Autoregressive models (ARMs) have become the workhorse for sequence generation tasks, since many problems can be modeled as next-token prediction. While there appears to be a natural ordering for text (i.e., left-to-right), for many data types, such as graphs, the canonical ordering is less obvious. To address this problem, we introduce a variant of ARM that generates high-dimensional data using a probabilistic ordering that is sequentially inferred from data. This model incorporates a trainable probability distribution, referred to as an order-policy, that dynamically decides the autoregressive order in a state-dependent manner. To train the model, we introduce a variational lower bound on the exact log-likelihood, which we optimize with stochastic gradient estimation. We demonstrate experimentally that our method can learn meaningful autoregressive orderings in image and graph generation. On the challenging domain of molecular graph generation, we achieve state-of-the-art results on the QM9 and ZINC250k benchmarks, evaluated using the Fr\'{e}chet ChemNet Distance (FCD).

Many existing evaluation benchmarks for Large Language Models (LLMs) quickly become outdated due to the emergence of new models and training data. These benchmarks also fall short in assessing how LLM performance changes over time, as they consist of static questions without a temporal dimension. To address these limitations, we propose using future event prediction as a continuous evaluation method to assess LLMs' temporal generalization and forecasting abilities. Our benchmark, Daily Oracle, automatically generates question-answer (QA) pairs from daily news, challenging LLMs to predict "future" event outcomes. Our findings reveal that as pre-training data becomes outdated, LLM performance degrades over time. While Retrieval Augmented Generation (RAG) has the potential to enhance prediction accuracy, the performance degradation pattern persists, highlighting the need for continuous model updates.

Log analysis is crucial for ensuring the orderly and stable operation of information systems, particularly in the field of Artificial Intelligence for IT Operations (AIOps). Large Language Models (LLMs) have demonstrated significant potential in natural language processing tasks. In the AIOps domain, they excel in tasks such as anomaly detection, root cause analysis of faults, operations and maintenance script generation, and alert information summarization. However, the performance of current LLMs in log analysis tasks remains inadequately validated. To address this gap, we introduce LogEval, a comprehensive benchmark suite designed to evaluate the capabilities of LLMs in various log analysis tasks for the first time. This benchmark covers tasks such as log parsing, log anomaly detection, log fault diagnosis, and log summarization. LogEval evaluates each task using 4,000 publicly available log data entries and employs 15 different prompts for each task to ensure a thorough and fair assessment. By rigorously evaluating leading LLMs, we demonstrate the impact of various LLM technologies on log analysis performance, focusing on aspects such as self-consistency and few-shot contextual learning. We also discuss findings related to model quantification, Chinese-English question-answering evaluation, and prompt engineering. These findings provide insights into the strengths and weaknesses of LLMs in multilingual environments and the effectiveness of different prompt strategies. Various evaluation methods are employed for different tasks to accurately measure the performance of LLMs in log analysis, ensuring a comprehensive assessment. The insights gained from LogEvals evaluation reveal the strengths and limitations of LLMs in log analysis tasks, providing valuable guidance for researchers and practitioners.

Recent paradigms in Random Projection Layer (RPL)-based continual representation learning have demonstrated superior performance when building upon a pre-trained model (PTM). These methods insert a randomly initialized RPL after a PTM to enhance feature representation in the initial stage. Subsequently, a linear classification head is used for analytic updates in the continual learning stage. However, under severe domain gaps between pre-trained representations and target domains, a randomly initialized RPL exhibits limited expressivity under large domain shifts. While largely scaling up the RPL dimension can improve expressivity, it also induces an ill-conditioned feature matrix, thereby destabilizing the recursive analytic updates of the linear head. To this end, we propose the Stochastic Continual Learner with MemoryGuard Supervisory Mechanism (SCL-MGSM). Unlike random initialization, MGSM constructs the projection layer via a principled, data-guided mechanism that progressively selects target-aligned random bases to adapt the PTM representation to downstream tasks. This facilitates the construction of a compact yet expressive RPL while improving the numerical stability of analytic updates. Extensive experiments on multiple exemplar-free Class Incremental Learning (CIL) benchmarks demonstrate that SCL-MGSM achieves superior performance compared to state-of-the-art methods.

In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary structure of the data, and with quantification of predictive uncertainty. Motivated by these challenges we introduce a probabilistic Bayesian online learning model by using a (possibly pretrained) neural representation and a state space model over the linear predictor weights. Non-stationarity over the linear predictor weights is modelled using a parameter drift transition density, parametrized by a coefficient that quantifies forgetting. Inference in the model is implemented with efficient Kalman filter recursions which track the posterior distribution over the linear weights, while online SGD updates over the transition dynamics coefficient allows to adapt to the non-stationarity seen in data. While the framework is developed assuming a linear Gaussian model, we also extend it to deal with classification problems and for fine-tuning the deep learning representation. In a set of experiments in multi-class classification using data sets such as CIFAR-100 and CLOC we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.

Bayesian inference provides principled uncertainty quantification but is often limited by challenges of prior elicitation, likelihood misspecification, and computational burden. The martingale posterior (MGP, Fong et al., 2023) offers an alternative, replacing prior-likelihood elicitation with a predictive rule - namely, a sequence of one-step-ahead predictive distributions - for forward data generation. The utility of MGPs depends on the choice of predictive rule, yet the literature has offered few compelling examples. Foundation transformers are well-suited here, as their autoregressive generation mirrors this forward simulation and their general-purpose design enables rich predictive modeling. We introduce TabMGP, an MGP built on TabPFN, a transformer foundation model that is currently state-of-the-art for tabular data. TabMGP produces credible sets with near-nominal coverage and often outperforms both existing MGP constructions and standard Bayes.

The rapid advancements in computing dramatically increase the scale and cost of training Large Language Models (LLMs). Accurately predicting downstream task performance prior to model training is crucial for efficient resource allocation, yet remains challenging due to two primary constraints: (1) the "emergence phenomenon", wherein downstream performance metrics become meaningful only after extensive training, which limits the ability to use smaller models for prediction; (2) Uneven task difficulty distributions and the absence of consistent scaling laws, resulting in substantial metric variability. Existing performance prediction methods suffer from limited accuracy and reliability, thereby impeding the assessment of potential LLM capabilities. To address these challenges, we propose a Clustering-On-Difficulty (COD) downstream performance prediction framework. COD first constructs a predictable support subset by clustering tasks based on difficulty features, strategically excluding non-emergent and non-scalable clusters. The scores on the selected subset serve as effective intermediate predictors of downstream performance on the full evaluation set. With theoretical support, we derive a mapping function that transforms performance metrics from the predictable subset to the full evaluation set, thereby ensuring accurate extrapolation of LLM downstream performance. The proposed method has been applied to predict performance scaling for a 70B LLM, providing actionable insights for training resource allocation and assisting in monitoring the training process. Notably, COD achieves remarkable predictive accuracy on the 70B LLM by leveraging an ensemble of small models, demonstrating an absolute mean deviation of 1.36% across eight important LLM evaluation benchmarks.

Recent advancements in large language models (LLMs) often rely on generating intermediate reasoning steps to enhance accuracy. However, little work has examined how reasoning utility contributes to the final answer's correctness. Due to the stochastic nature of autoregressive generation, generating more context does not guarantee increased confidence in the answer. If we could predict, during generation, whether a reasoning step will be useful, we could stop early or prune ineffective steps, avoiding distractions in the final decision. We present an oracle study on MATH dataset, using Qwen2.5-32B and GPT-4o to generate reasoning chains, and then employing a separate model (Qwen3-8B) to quantify the utility of these chains for final accuracy. Specifically, we measure the model's uncertainty on the answer span Y at each reasoning step using conditional entropy (expected negative log-likelihood over the vocabulary) with context expanding step by step. Our results show a clear pattern: conditional entropy that decreases over steps is strongly associated with correct answers, whereas flat or increasing entropy often results in wrong answers. We also corroborate that incorrect reasoning paths tend to be longer than correct ones, suggesting that longer reasoning does not necessarily yield better outcomes. These findings serve as a foundation to inspire future work on designing efficient reasoning pipelines that detect and avoid unproductive reasoning early.

Modern language models can contain billions of parameters, raising the question of whether they can generalize beyond the training data or simply regurgitate their training corpora. We provide the first non-vacuous generalization bounds for pretrained large language models (LLMs), indicating that language models are capable of discovering regularities that generalize to unseen data. In particular, we derive a compression bound that is valid for the unbounded log-likelihood loss using prediction smoothing, and we extend the bound to handle subsampling, accelerating bound computation on massive datasets. To achieve the extreme level of compression required for non-vacuous generalization bounds, we devise SubLoRA, a low-dimensional non-linear parameterization. Using this approach, we find that larger models have better generalization bounds and are more compressible than smaller models.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the log-likelihood of the model. Central to our approach is an upper bound on the log-partition function parametrized by a function q that we express as a flexible neural network. Our bound makes it possible to track the partition function during learning, to speed-up sampling, and to train a broad class of hybrid directed/undirected models via a unified variational inference framework. We empirically demonstrate the effectiveness of our method on several popular generative modeling datasets.

In location estimation, we are given n samples from a known distribution f shifted by an unknown translation lambda, and want to estimate lambda as precisely as possible. Asymptotically, the maximum likelihood estimate achieves the Cram\'er-Rao bound of error mathcal N(0, 1{nmathcal I}), where mathcal I is the Fisher information of f. However, the n required for convergence depends on f, and may be arbitrarily large. We build on the theory using smoothed estimators to bound the error for finite n in terms of mathcal I_r, the Fisher information of the r-smoothed distribution. As n to infty, r to 0 at an explicit rate and this converges to the Cram\'er-Rao bound. We (1) improve the prior work for 1-dimensional f to converge for constant failure probability in addition to high probability, and (2) extend the theory to high-dimensional distributions. In the process, we prove a new bound on the norm of a high-dimensional random variable whose 1-dimensional projections are subgamma, which may be of independent interest.

Understanding the gradient variance of black-box variational inference (BBVI) is a crucial step for establishing its convergence and developing algorithmic improvements. However, existing studies have yet to show that the gradient variance of BBVI satisfies the conditions used to study the convergence of stochastic gradient descent (SGD), the workhorse of BBVI. In this work, we show that BBVI satisfies a matching bound corresponding to the ABC condition used in the SGD literature when applied to smooth and quadratically-growing log-likelihoods. Our results generalize to nonlinear covariance parameterizations widely used in the practice of BBVI. Furthermore, we show that the variance of the mean-field parameterization has provably superior dimensional dependence.

We study the probabilistic modeling performed by Autoregressive Large Language Models (LLMs) through the angle of time directionality, addressing a question first raised in (Shannon, 1951). For large enough models, we empirically find a time asymmetry in their ability to learn natural language: a difference in the average log-perplexity when trying to predict the next token versus when trying to predict the previous one. This difference is at the same time subtle and very consistent across various modalities (language, model size, training time, ...). Theoretically, this is surprising: from an information-theoretic point of view, there should be no such difference. We provide a theoretical framework to explain how such an asymmetry can appear from sparsity and computational complexity considerations, and outline a number of perspectives opened by our results.

Time series forecasting is not just numerical extrapolation, but often requires reasoning with unstructured contextual data such as news or events. While specialized Time Series Foundation Models (TSFMs) excel at forecasting based on numerical patterns, they remain unaware to real-world textual signals. Conversely, while LLMs are emerging as zero-shot forecasters, their performance remains uneven across domains and contextual grounding. To bridge this gap, we introduce Nexus, a multi-agent forecasting framework that decomposes prediction into specialized stages: isolating macro-level and micro-level temporal fluctuations, and integrating contextual information when available before synthesizing a final forecast. This decomposition enables Nexus to adapt from seasonal signals to volatile, event-driven information without relying on external statistical anchors or monolithic prompting. We show that current-generation LLMs possess substantially stronger intrinsic forecasting ability than previously recognized, depending critically on how numerical and contextual reasoning are organized. Evaluated on data strictly succeeding LLM knowledge cutoffs spanning Zillow real estate metrics and volatile stock market equities, Nexus consistently matches or outperforms state-of-the-art TSFMs and strong LLM baselines. Beyond numerical accuracy, Nexus produces high-quality reasoning traces that explicitly show the fundamental drivers behind each forecast. Our results establish that real-world forecasting is an agentic reasoning problem extending well beyond only sequence modeling.

Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help us predict which type of event will happen next and when. We model streams of discrete events in continuous time, by constructing a neurally self-modulating multivariate point process in which the intensities of multiple event types evolve according to a novel continuous-time LSTM. This generative model allows past events to influence the future in complex and realistic ways, by conditioning future event intensities on the hidden state of a recurrent neural network that has consumed the stream of past events. Our model has desirable qualitative properties. It achieves competitive likelihood and predictive accuracy on real and synthetic datasets, including under missing-data conditions.

Predictive models often need to work with incomplete information in real-world tasks. Consequently, they must provide reliable probability or confidence estimation, especially in large-scale decision-making and planning tasks. Current large language models (LLMs) are insufficient for accurate estimations, but they can generate relevant factors that may affect the probabilities, produce coarse-grained probabilities when the information is more complete, and help determine which factors are relevant to specific downstream contexts. In this paper, we make use of these capabilities of LLMs to provide a significantly more accurate probabilistic estimation. We propose BIRD, a novel probabilistic inference framework that aligns a Bayesian network with LLM abductions and then estimates more accurate probabilities in a deduction step. We show BIRD provides reliable probability estimations that are 30% better than those provided directly by LLM baselines. These estimates further contribute to better and more trustworthy decision making.

Next-token prediction serves as the foundational learning task enabling reasoning in LLMs. But what should the learning task be when aiming to equip MLLMs with temporal reasoning capabilities over video inputs? Existing tasks such as video question answering often rely on annotations from humans or much stronger MLLMs, while video captioning tends to entangle temporal reasoning with spatial information. To address this gap, we propose next-event prediction (NEP), a learning task that harnesses future video segments as a rich, self-supervised signal to foster temporal reasoning. We segment each video into past and future frames: the MLLM takes the past frames as input and predicts a summary of events derived from the future frames, thereby encouraging the model to reason temporally in order to complete the task. To support this task, we curate V1-33K, a dataset comprising 33,000 automatically extracted video segments spanning diverse real-world scenarios. We further explore a range of video instruction-tuning strategies to study their effects on temporal reasoning. To evaluate progress, we introduce FutureBench to assess coherence in predicting unseen future events. Experiments validate that NEP offers a scalable and effective training paradigm for fostering temporal reasoning in MLLMs.

Detecting the anomalies of web applications, important infrastructures for running modern companies and governments, is crucial for providing reliable web services. Many modern web applications operate on web APIs (e.g., RESTful, SOAP, and WebSockets), their exposure invites intended attacks or unintended illegal visits, causing abnormal system behaviors. However, such anomalies can share very similar logs with normal logs, missing crucial information (which could be in database) for log discrimination. Further, log instances can be also noisy, which can further mislead the state-of-the-art log learning solutions to learn spurious correlation, resulting superficial models and rules for anomaly detection. In this work, we propose MINES which infers explainable API invariants for anomaly detection from the schema level instead of detailed raw log instances, which can (1) significantly discriminate noise in logs to identify precise normalities and (2) detect abnormal behaviors beyond the instrumented logs. Technically, MINES (1) converts API signatures into table schema to enhance the original database shema; and (2) infers the potential database constraints on the enhanced database schema to capture the potential relationships between APIs and database tables. MINES uses LLM for extracting potential relationship based on two given table structures; and use normal log instances to reject and accept LLM-generated invariants. Finally, MINES translates the inferred constraints into invariants to generate Python code for verifying the runtime logs. We extensively evaluate MINES on web-tamper attacks on the benchmarks of TrainTicket, NiceFish, Gitea, Mastodon, and NextCloud against baselines such as LogRobust, LogFormer, and WebNorm. The results show that MINES achieves high recall for the anomalies while introducing almost zero false positives, indicating a new state-of-the-art.

Anticipating supply chain disruptions before they materialize is a core challenge for firms and policymakers alike. A key difficulty is learning to reason reliably about infrequent, high-impact events from noisy and unstructured inputs - a setting where general-purpose models struggle without task-specific adaptation. We introduce an end-to-end framework that trains LLMs to produce calibrated probabilistic forecasts using realized disruption outcomes as supervision. The resulting model substantially outperforms strong baselines - including GPT-5 - on accuracy, calibration, and precision. We also show that training induces more structured and reliable probabilistic reasoning without explicit prompting. These results suggest a general pathway for training domain-specific forecasting models that produce decision-ready signals. To support transparency we open-source the evaluation dataset used in this study. Dataset: https://huggingface.co/datasets/LightningRodLabs/supply-chain-predictions

To schedule LLM inference, the shortest job first (SJF) principle is favorable by prioritizing requests with short output lengths to avoid head-of-line (HOL) blocking. Existing methods usually predict a single output length for each request to facilitate scheduling. We argue that such a point estimate does not match the stochastic decoding process of LLM inference, where output length is uncertain by nature and determined by when the end-of-sequence (EOS) token is sampled. Hence, the output length of each request should be fitted with a distribution rather than a single value. With an in-depth analysis of empirical data and the stochastic decoding process, we observe that output length follows a heavy-tailed distribution and can be fitted with the log-t distribution. On this basis, we propose a simple metric called Tail Inflated Expectation (TIE) to replace the output length in SJF scheduling, which adjusts the expectation of a log-t distribution with its tail probabilities to account for the risk that a request generates long outputs. To evaluate our TIE scheduler, we compare it with three strong baselines, and the results show that TIE reduces the per-token latency by 2.31times for online inference and improves throughput by 1.42times for offline data generation.

Reinforcement Learning with Verifiable Rewards (RLVR) has been an effective approach for improving Large Language Models' reasoning in domains such as coding and mathematics. Here, we apply RLVR methods towards forecasting future real-world events - a challenging task for RL due to the very noisy (and delayed) outcomes involved. Using a novel dataset of recent questions from a prediction market, and accompanying relevant news headlines, we show that a compact (14B) reasoning model can be trained to match or surpass the predictive accuracy of frontier models like o1, while greatly improving probabilistic calibration. The model's performance is also practically meaningful: in a Polymarket trading simulation, we estimate that its bets would have yielded a return on investment of over 10% across all questions in the test set. We detail and compare approaches used in training our model, including augmenting our training-data with synthetic prediction questions, guardrails for learning stability, and median prediction sampling at inference-time.

Foundation models of time series have not been fully developed due to the limited availability of time series corpora and the underexploration of scalable pre-training. Based on the similar sequential formulation of time series and natural language, increasing research demonstrates the feasibility of leveraging large language models (LLM) for time series. Nevertheless, the inherent autoregressive property and decoder-only architecture of LLMs have not been fully considered, resulting in insufficient utilization of LLM abilities. To fully revitalize the general-purpose token transition and multi-step generation capability of large language models, we propose AutoTimes to repurpose LLMs as autoregressive time series forecasters, which projects time series into the embedding space of language tokens and autoregressively generates future predictions with arbitrary lengths. Compatible with any decoder-only LLMs, the consequent forecaster exhibits the flexibility of the lookback length and scalability with larger LLMs. Further, we formulate time series as prompts, extending the context for prediction beyond the lookback window, termed in-context forecasting. By introducing LLM-embedded textual timestamps, AutoTimes can utilize chronological information to align multivariate time series. Empirically, AutoTimes achieves state-of-the-art with 0.1% trainable parameters and over 5times training/inference speedup compared to advanced LLM-based forecasters. Code is available at this repository: https://github.com/thuml/AutoTimes.

Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. However, as found in previous works, NCE may perform poorly in many tasks due to its flat loss landscape and slow convergence. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models from the perspective of compositional optimization. To tackle the partition function, a noise distribution is introduced such that the log partition function can be written as a compositional function whose inner function can be estimated with stochastic samples. Hence, the objective can be optimized by stochastic compositional optimization algorithms. Despite being a simple method, we demonstrate that it is more favorable than NCE by (1) establishing a fast convergence rate and quantifying its dependence on the noise distribution through the variance of stochastic estimators; (2) developing better results for one-dimensional Gaussian mean estimation by showing our objective has a much favorable loss landscape and hence our method enjoys faster convergence; (3) demonstrating better performance on multiple applications, including density estimation, out-of-distribution detection, and real image generation.

Understanding and anticipating vulnerability-related activity is a major challenge in cyber threat intelligence. This work investigates whether vulnerability sightings, such as proof-of-concept releases, detection templates, or online discussions, can be forecast over time. Building on our earlier work on VLAI, a transformer-based model that predicts vulnerability severity from textual descriptions, we examine whether severity scores can improve time-series forecasting as exogenous variables. We evaluate several approaches for short-term forecasting of sightings per vulnerability. First, we test SARIMAX models with and without log(x+1) transformations and VLAI-derived severity inputs. Although these adjustments provide limited improvements, SARIMAX remains poorly suited to sparse, short, and bursty vulnerability data. In practice, forecasts often produce overly wide confidence intervals and sometimes unrealistic negative values. To better capture the discrete and event-driven nature of sightings, we then explore count-based methods such as Poisson regression. Early results show that these models produce more stable and interpretable forecasts, especially when sightings are aggregated weekly. We also discuss simpler operational alternatives, including exponential decay functions for short forecasting horizons, to estimate future activity without requiring long historical series. Overall, this study highlights both the potential and the limitations of forecasting rare and bursty cyber events, and provides practical guidance for integrating predictive analytics into vulnerability intelligence workflows.

Class incremental learning (CIL) is a challenging setting of continual learning, which learns a series of tasks sequentially. Each task consists of a set of unique classes. The key feature of CIL is that no task identifier (or task-id) is provided at test time. Predicting the task-id for each test sample is a challenging problem. An emerging theory-guided approach (called TIL+OOD) is to train a task-specific model for each task in a shared network for all tasks based on a task-incremental learning (TIL) method to deal with catastrophic forgetting. The model for each task is an out-of-distribution (OOD) detector rather than a conventional classifier. The OOD detector can perform both within-task (in-distribution (IND)) class prediction and OOD detection. The OOD detection capability is the key to task-id prediction during inference. However, this paper argues that using a traditional OOD detector for task-id prediction is sub-optimal because additional information (e.g., the replay data and the learned tasks) available in CIL can be exploited to design a better and principled method for task-id prediction. We call the new method TPL (Task-id Prediction based on Likelihood Ratio). TPL markedly outperforms strong CIL baselines and has negligible catastrophic forgetting. The code of TPL is publicly available at https://github.com/linhaowei1/TPL.

The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence measures. Surprisingly, an equally important problem, estimating an unknown Markov chain from its samples, is still far from understood. We consider two problems related to the min-max risk (expected loss) of estimating an unknown k-state Markov chain from its n sequential samples: predicting the conditional distribution of the next sample with respect to the KL-divergence, and estimating the transition matrix with respect to a natural loss induced by KL or a more general f-divergence measure. For the first measure, we determine the min-max prediction risk to within a linear factor in the alphabet size, showing it is Omega(kloglog n / n) and O(k^2loglog n / n). For the second, if the transition probabilities can be arbitrarily small, then only trivial uniform risk upper bounds can be derived. We therefore consider transition probabilities that are bounded away from zero, and resolve the problem for essentially all sufficiently smooth f-divergences, including KL-, L_2-, Chi-squared, Hellinger, and Alpha-divergences.

Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the assumption of exchangeability is not valid. The key idea of the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti's Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework in both exchangeable and Markovian settings. In particular, while the lack of exchangeability introduced by Markovian samples constitutes a violation of a crucial assumption for classical conformal prediction, the proposed method views it as an advantage that can be exploited to improve the performance further. Detailed numerical and empirical results that complement the theoretical conclusions are provided to illustrate the practical feasibility of the proposed method.

Speculative decoding accelerates LLM inference by drafting a tree of candidate continuations and verifying it in one target forward. Existing drafters fall into two camps with opposite weaknesses. Autoregressive drafters such as EAGLE-3 preserve dependence along each draft path but call the drafter once per tree depth, making drafting a non-trivial share of per-iteration latency. Parallel drafters cut drafter calls by predicting multiple future positions in one forward, but each position is predicted without seeing the others, producing paths the verifier rejects. In this paper, we propose SpecBlock, a block-iterative drafter that combines path dependence with cheap drafting. Each drafter forward produces K dependent positions and we call this a block. The draft tree grows through repeated block expansions. Two mechanisms explicitly carry path dependence to keep later draft positions accurate. Within each block, a layer-wise shift carries the previous position's hidden state into every decoder layer. Across blocks, each new block can start from any position of the previous block, inheriting its hidden state to extend the path. To spend verifier budget where acceptance is likely, a co-trained rank head replaces the fixed top-k tree by allocating per-position branching during drafting. To avoid training the drafter on prefixes it never produces at inference, a valid-prefix mask drops the loss at later positions once an earlier one is wrong. Beyond static drafting, a cost-aware bandit at deployment uses free verifier feedback to update the drafter selectively, only when the expected throughput gain exceeds the update cost. Experiments show that SpecBlock improves mean speedup by 8-13% over EAGLE-3 at 44-52% of its drafting cost, and cost-aware adaptation extends this lead to 11-19%.

Many empirical studies of labor market questions rely on estimating relatively simple predictive models using small, carefully constructed longitudinal survey datasets based on hand-engineered features. Large Language Models (LLMs), trained on massive datasets, encode vast quantities of world knowledge and can be used for the next job prediction problem. However, while an off-the-shelf LLM produces plausible career trajectories when prompted, the probability with which an LLM predicts a particular job transition conditional on career history will not, in general, align with the true conditional probability in a given population. Recently, Vafa et al. (2024) introduced a transformer-based "foundation model", CAREER, trained using a large, unrepresentative resume dataset, that predicts transitions between jobs; it further demonstrated how transfer learning techniques can be used to leverage the foundation model to build better predictive models of both transitions and wages that reflect conditional transition probabilities found in nationally representative survey datasets. This paper considers an alternative where the fine-tuning of the CAREER foundation model is replaced by fine-tuning LLMs. For the task of next job prediction, we demonstrate that models trained with our approach outperform several alternatives in terms of predictive performance on the survey data, including traditional econometric models, CAREER, and LLMs with in-context learning, even though the LLM can in principle predict job titles that are not allowed in the survey data. Further, we show that our fine-tuned LLM-based models' predictions are more representative of the career trajectories of various workforce subpopulations than off-the-shelf LLM models and CAREER. We conduct experiments and analyses that highlight the sources of the gains in the performance of our models for representative predictions.

By encoding time series as a string of numerical digits, we can frame time series forecasting as next-token prediction in text. Developing this approach, we find that large language models (LLMs) such as GPT-3 and LLaMA-2 can surprisingly zero-shot extrapolate time series at a level comparable to or exceeding the performance of purpose-built time series models trained on the downstream tasks. To facilitate this performance, we propose procedures for effectively tokenizing time series data and converting discrete distributions over tokens into highly flexible densities over continuous values. We argue the success of LLMs for time series stems from their ability to naturally represent multimodal distributions, in conjunction with biases for simplicity, and repetition, which align with the salient features in many time series, such as repeated seasonal trends. We also show how LLMs can naturally handle missing data without imputation through non-numerical text, accommodate textual side information, and answer questions to help explain predictions. While we find that increasing model size generally improves performance on time series, we show GPT-4 can perform worse than GPT-3 because of how it tokenizes numbers, and poor uncertainty calibration, which is likely the result of alignment interventions such as RLHF.

Rate control algorithms are at the heart of video conferencing platforms, determining target bitrates that match dynamic network characteristics for high quality. Recent data-driven strategies have shown promise for this challenging task, but the performance degradation they introduce during training has been a nonstarter for many production services, precluding adoption. This paper aims to bolster the practicality of data-driven rate control by presenting an alternative avenue for experiential learning: leveraging purely existing telemetry logs produced by the incumbent algorithm in production. We observe that these logs contain effective decisions, although often at the wrong times or in the wrong order. To realize this approach despite the inherent uncertainty that log-based learning brings (i.e., lack of feedback for new decisions), our system, Mowgli, combines a variety of robust learning techniques (i.e., conservatively reasoning about alternate behavior to minimize risk and using a richer model formulation to account for environmental noise). Across diverse networks (emulated and real-world), Mowgli outperforms the widely deployed GCC algorithm, increasing average video bitrates by 15-39% while reducing freeze rates by 60-100%.

Contemporary predictive models are hard to interpret as their deep nets exploit numerous complex relations between input elements. This work suggests a theoretical framework for model interpretability by measuring the contribution of relevant features to the functional entropy of the network with respect to the input. We rely on the log-Sobolev inequality that bounds the functional entropy by the functional Fisher information with respect to the covariance of the data. This provides a principled way to measure the amount of information contribution of a subset of features to the decision function. Through extensive experiments, we show that our method surpasses existing interpretability sampling-based methods on various data signals such as image, text, and audio.

Adapting reasoning models to new tasks during post-training with only output-level supervision stalls under reinforcement learning from verifiable rewards (RLVR) when the initial success probability p_0 is small. Using the Tsallis q-logarithm, we define a loss family J_Q that interpolates between RLVR (at q{=}0, the exploitation pole) and the log-marginal-likelihood over latent trajectories (at q{=}1, the density-estimation pole). All members share the same per-example gradient direction, differing only by a scalar amplification P_{θ^{-q}} that reweights each instance independently of the learning rate. This amplification is the mechanism that addresses cold-start stalling: under gradient flow, the exploitation pole requires Ω(1{p_0}) time to escape cold start, while the density-estimation pole escapes in Θbig(log(1{p_0})big); intermediate q trades escape speed against noise memorization. Because P_θ is intractable, we derive two Monte Carlo estimators from the two factorizations of the gradient: Gradient-Amplified RL (GARL) samples from the prior and amplifies the RL gradient, and Posterior-Attenuated Fine-Tuning (PAFT) importance-resamples from the posterior and runs standard SFT. Both have bias Obig(q{M P_θ^{q+1}}big); GARL has lower variance, PAFT has semantically coherent gradients. On FinQA, HotPotQA, and MuSiQue, GARL at q{=}0.75 substantially mitigates cold-start stalling, escaping cold start where GRPO fails entirely. In warm start, GARL at low q dominates FinQA where training is stable; on HotPotQA and MuSiQue, GARL destabilizes during training, and PAFT at q{=}0.75 provides stable gradients (best overall on HotPotQA at 47.9 maj@16, +14.4 over GRPO).

Continuous-valued Autoregressive (AR) image generation models have demonstrated notable superiority over their discrete-token counterparts, showcasing considerable reconstruction quality and higher generation fidelity. However, the computational demands of the autoregressive framework result in significant inference overhead. While speculative decoding has proven effective in accelerating Large Language Models (LLMs), their adaptation to continuous-valued visual autoregressive models remains unexplored. This work generalizes the speculative decoding algorithm from discrete tokens to continuous space. By analyzing the intrinsic properties of output distribution, we establish a tailored acceptance criterion for the diffusion distributions prevalent in such models. To overcome the inconsistency that occurred in speculative decoding output distributions, we introduce denoising trajectory alignment and token pre-filling methods. Additionally, we identify the hard-to-sample distribution in the rejection phase. To mitigate this issue, we propose a meticulous acceptance-rejection sampling method with a proper upper bound, thereby circumventing complex integration. Experimental results show that our continuous speculative decoding achieves a remarkable 2.33times speed-up on off-the-shelf models while maintaining the output distribution. Codes will be available at https://github.com/MarkXCloud/CSpD

Large Reasoning Models (LRMs) introduce new opportunities for safety monitoring through their Chain of Thought (CoT) reasoning. However, CoT is not always faithful to the model's final output, undermining its reliability as a monitoring tool. To address this, we investigate the hidden representations of LRMs to determine whether future behavior can be predicted from prompt and CoT representations. By evaluating a probe at each generated token, we construct a probe trajectory, the continuous evolution of a concept's probability across the reasoning process. We find that future model behavior is more distinguishable when examined over the full trajectory than from a single static prediction. To characterize these temporal dynamics, we extract signal-processing features that capture volatility, trend, and steady-state behavior, significantly improving the separation of future model states. We also present two methodological insights. First, template-based training data achieves near-parity with dynamically generated model responses, eliminating the need for a costly initial inference and labeling. Second, the choice of pooling operation is critical: average-pooling and last-token methods collapse to near-random performance, while max-pooling achieves up to 95% AUROC and yields stable probe trajectories. Using four datasets and four reasoning models across the domains of safety and mathematics, we demonstrate that trajectory features encode task-specific dynamics that improve outcome separability. These findings establish probe trajectories as a complementary framework for monitoring LRM behavior. Warning: This article contains potentially harmful content.

Time series forecasting (TSF) remains a challenging and largely unsolved problem in machine learning, despite significant recent efforts leveraging Large Language Models (LLMs), which predominantly rely on Transformer architectures. Empirical evidence consistently shows that even powerful Transformers often fail to outperform much simpler models, e.g., linear models, on TSF tasks; however, a rigorous theoretical understanding of this phenomenon remains limited. In this paper, we provide a theoretical analysis of Transformers' limitations for TSF through the lens of In-Context Learning (ICL) theory. Specifically, under AR(p) data, we establish that: (1) Linear Self-Attention (LSA) models cannot achieve lower expected MSE than classical linear models for in-context forecasting; (2) as the context length approaches to infinity, LSA asymptotically recovers the optimal linear predictor; and (3) under Chain-of-Thought (CoT) style inference, predictions collapse to the mean exponentially. We empirically validate these findings through carefully designed experiments. Our theory not only sheds light on several previously underexplored phenomena but also offers practical insights for designing more effective forecasting architectures. We hope our work encourages the broader research community to revisit the fundamental theoretical limitations of TSF and to critically evaluate the direct application of increasingly sophisticated architectures without deeper scrutiny.

Truly proactive AI systems must anticipate what we will do next. This foresight demands far richer information than the sparse signals we type into our prompts -- it demands reasoning over the entire context of what we see and do. We formalize this as next action prediction (NAP): given a sequence of a user's multimodal interactions with a computer (screenshots, clicks, sensor data), predict that user's next action. Progress on this task requires both new data and modeling approaches. To scale data, we annotate longitudinal, naturalistic computer use with vision-language models. We release an open-source pipeline for performing this labeling on private infrastructure, and label over 360K actions across one month of continuous phone usage from 20 users, amounting to 1,800 hours of screen time. We then introduce LongNAP, a user model that combines parametric and in-context learning to reason over long interaction histories. LongNAP is trained via policy gradient methods to generate user-specific reasoning traces given some context; retrieve relevant traces from a library of past traces; and then apply retrieved traces in-context to predict future actions. Using an LLM-as-judge evaluation metric (0-1 similarity to ground truth), LongNAP significantly outperforms supervised finetuning and prompted baselines on held-out data (by 79% and 39% respectively). Additionally, LongNAP generalizes to held out users when trained across individuals. The space of next actions a user might take at any moment is unbounded, spanning thousands of possible outcomes. Despite this, 17.1% of LongNAP's predicted trajectories are well-aligned with what a user does next (LLM-judge score geq 0.5). This rises to 26% when we filter to highly confident predictions. In sum, we argue that learning from the full context of user behavior to anticipate user needs is now a viable task with substantial opportunity.

Extending the forecasting time is a critical demand for real applications, such as extreme weather early warning and long-term energy consumption planning. This paper studies the long-term forecasting problem of time series. Prior Transformer-based models adopt various self-attention mechanisms to discover the long-range dependencies. However, intricate temporal patterns of the long-term future prohibit the model from finding reliable dependencies. Also, Transformers have to adopt the sparse versions of point-wise self-attentions for long series efficiency, resulting in the information utilization bottleneck. Going beyond Transformers, we design Autoformer as a novel decomposition architecture with an Auto-Correlation mechanism. We break with the pre-processing convention of series decomposition and renovate it as a basic inner block of deep models. This design empowers Autoformer with progressive decomposition capacities for complex time series. Further, inspired by the stochastic process theory, we design the Auto-Correlation mechanism based on the series periodicity, which conducts the dependencies discovery and representation aggregation at the sub-series level. Auto-Correlation outperforms self-attention in both efficiency and accuracy. In long-term forecasting, Autoformer yields state-of-the-art accuracy, with a 38% relative improvement on six benchmarks, covering five practical applications: energy, traffic, economics, weather and disease. Code is available at this repository: https://github.com/thuml/Autoformer.

Given a prefix (context), open-ended generation aims to decode texts that are coherent, which do not abruptly drift from previous topics, and informative, which do not suffer from undesired repetitions. In this paper, we propose Look-back, an improved decoding algorithm that leverages the Kullback-Leibler divergence to track the distribution distance between current and historical decoding steps. Thus Look-back can automatically predict potential repetitive phrase and topic drift, and remove tokens that may cause the failure modes, restricting the next token probability distribution within a plausible distance to the history. We perform decoding experiments on document continuation and story generation, and demonstrate that Look-back is able to generate more fluent and coherent text, outperforming other strong decoding methods significantly in both automatic and human evaluations.

Detecting anomalous events in online computer systems is crucial to protect the systems from malicious attacks or malfunctions. System logs, which record detailed information of computational events, are widely used for system status analysis. In this paper, we propose LogBERT, a self-supervised framework for log anomaly detection based on Bidirectional Encoder Representations from Transformers (BERT). LogBERT learns the patterns of normal log sequences by two novel self-supervised training tasks and is able to detect anomalies where the underlying patterns deviate from normal log sequences. The experimental results on three log datasets show that LogBERT outperforms state-of-the-art approaches for anomaly detection.

Due to the sheer size of software logs, developers rely on automated techniques for log analysis. One of the first and most important steps of automated log analysis is log abstraction, which parses the raw logs into a structured format. Prior log abstraction techniques aim to identify and abstract all the dynamic variables in logs and output a static log template for automated log analysis. However, these abstracted dynamic variables may also contain important information that is useful to different tasks in log analysis. In this paper, we investigate the characteristics of dynamic variables and their importance in practice, and explore the potential of a variable-aware log abstraction technique. Through manual investigations and surveys with practitioners, we find that different categories of dynamic variables record various information that can be important depending on the given tasks, the distinction of dynamic variables in log abstraction can further assist in log analysis. We then propose a deep learning based log abstraction approach, named VALB, which can identify different categories of dynamic variables and preserve the value of specified categories of dynamic variables along with the log templates (i.e., variable-aware log abstraction). Through the evaluation on a widely used log abstraction benchmark, we find that VALB outperforms other state-of-the-art log abstraction techniques on general log abstraction (i.e., when abstracting all the dynamic variables) and also achieves a high variable-aware log abstraction accuracy that further identifies the category of the dynamic variables. Our study highlights the potential of leveraging the important information recorded in the dynamic variables to further improve the process of log analysis.

Autonomous Vehicles (AVs) collect and pseudo-label terabytes of multi-modal data localized to HD maps during normal fleet testing. However, identifying interesting and safety-critical scenarios from uncurated driving logs remains a significant challenge. Traditional scenario mining techniques are error-prone and prohibitively time-consuming, often relying on hand-crafted structured queries. In this work, we revisit spatio-temporal scenario mining through the lens of recent vision-language models (VLMs) to detect whether a described scenario occurs in a driving log and, if so, precisely localize it in both time and space. To address this problem, we introduce RefAV, a large-scale dataset of 10,000 diverse natural language queries that describe complex multi-agent interactions relevant to motion planning derived from 1000 driving logs in the Argoverse 2 Sensor dataset. We evaluate several referential multi-object trackers and present an empirical analysis of our baselines. Notably, we find that naively repurposing off-the-shelf VLMs yields poor performance, suggesting that scenario mining presents unique challenges. Our code and dataset are available at https://github.com/CainanD/RefAV/ and https://argoverse.github.io/user-guide/tasks/scenario_mining.html

Progress in large language models is constrained by an evaluation bottleneck: build a benchmark, evaluate models and settings, then iterate. We therefore ask a simple question: can we forecast outcomes before running any experiments? We study text-only performance forecasting: estimating a model's score from a redacted task description and intended configuration, with no access to dataset instances. To support systematic study, we curate PRECOG, a corpus of redacted description-performance pairs spanning diverse tasks, domains, and metrics. Experiments show the task is challenging but feasible: models equipped with a retrieval module that excludes source papers achieve moderate prediction performance with well-calibrated uncertainty, reaching mean absolute error as low as 8.7 on the Accuracy subset at high-confidence thresholds. Our analysis indicates that stronger reasoning models engage in diverse, iterative querying, whereas current open-source models lag and often skip retrieval or gather evidence with limited diversity. We further test a zero-leakage setting, forecasting on newly released datasets or experiments before their papers are indexed, where GPT-5 with built-in web search still attains nontrivial prediction accuracy. Overall, our corpus and analyses offer an initial step toward open-ended anticipatory evaluation, supporting difficulty estimation and smarter experiment prioritization.

Since large language models have approached human-level performance on many tasks, it has become increasingly harder for researchers to find tasks that are still challenging to the models. Failure cases usually come from the long-tail distribution - data that an oracle language model could assign a probability on the lower end of its distribution. Current methodology such as prompt engineering or crowdsourcing are insufficient for creating long-tail examples because humans are constrained by cognitive bias. We propose a Logic-Induced-Knowledge-Search (LINK) framework for systematically generating long-tail knowledge statements. Grounded by a symbolic rule, we search for long-tail values for each variable of the rule by first prompting a LLM, then verifying the correctness of the values with a critic, and lastly pushing for the long-tail distribution with a reranker. With this framework we construct a dataset, Logic-Induced-Long-Tail (LINT), consisting of 200 symbolic rules and 50K knowledge statements spanning across four domains. Human annotations find that 84% of the statements in LINT are factually correct. In contrast, ChatGPT and GPT4 struggle with directly generating long-tail statements under the guidance of logic rules, each only getting 56% and 78% of their statements correct. Moreover, their "long-tail" generations in fact fall into the higher likelihood range, and thus are not really long-tail. Our findings suggest that LINK is effective for generating data in the long-tail distribution while enforcing quality. LINT can be useful for systematically evaluating LLMs' capabilities in the long-tail distribution. We challenge the models with a simple entailment classification task using samples from LINT. We find that ChatGPT and GPT4's capability in identifying incorrect knowledge drop by ~3% in the long-tail distribution compared to head distribution.

To combat the memory bandwidth-bound nature of autoregressive LLM inference, previous research has proposed the speculative decoding framework. To perform speculative decoding, a small draft model proposes candidate continuations of the input sequence, that are then verified in parallel by the base model. One way to specify the draft model, as used in the recent Medusa decoding framework, is as a collection of light-weight heads, called draft heads, that operate on the base model's hidden states. To date, all existing draft heads have been sequentially independent, meaning that they speculate tokens in the candidate continuation independently of any preceding tokens in the candidate continuation. In this work, we propose Hydra heads, a sequentially dependent, drop-in replacement for standard draft heads that significantly improves speculation accuracy. Decoding with Hydra heads improves throughput compared to Medusa decoding with standard draft heads. We further explore the design space of Hydra head training objectives and architectures, and propose a carefully-tuned Hydra head recipe, which we call Hydra++, that improves decoding throughput by 1.31x and 2.71x compared to Medusa decoding and autoregressive decoding, respectively. Overall, Hydra heads are a simple intervention on standard draft heads that significantly improve the end-to-end speed of draft head based speculative decoding.

Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and test whether having access to the true posterior is guaranteed to prevent catastrophic forgetting in Bayesian neural networks. To do this we perform sequential Bayesian inference using Hamiltonian Monte Carlo. We propagate the posterior as a prior for new tasks by fitting a density estimator on Hamiltonian Monte Carlo samples. We find that this approach fails to prevent catastrophic forgetting demonstrating the difficulty in performing sequential Bayesian inference in neural networks. From there we study simple analytical examples of sequential Bayesian inference and CL and highlight the issue of model misspecification which can lead to sub-optimal continual learning performance despite exact inference. Furthermore, we discuss how task data imbalances can cause forgetting. From these limitations, we argue that we need probabilistic models of the continual learning generative process rather than relying on sequential Bayesian inference over Bayesian neural network weights. In this vein, we also propose a simple baseline called Prototypical Bayesian Continual Learning, which is competitive with state-of-the-art Bayesian continual learning methods on class incremental continual learning vision benchmarks.

Uncovering early-stage metrics that reflect final model performance is one core principle for large-scale pretraining. The existing scaling law demonstrates the power-law correlation between pretraining loss and training flops, which serves as an important indicator of the current training state for large language models. However, this principle only focuses on the model's compression properties on the training data, resulting in an inconsistency with the ability improvements on the downstream tasks. Some follow-up works attempted to extend the scaling-law to more complex metrics (such as hyperparameters), but still lacked a comprehensive analysis of the dynamic differences among various capabilities during pretraining. To address the aforementioned limitations, this paper undertakes a comprehensive comparison of model capabilities at various pretraining intermediate checkpoints. Through this analysis, we confirm that specific downstream metrics exhibit similar training dynamics across models of different sizes, up to 67 billion parameters. In addition to our core findings, we've reproduced Amber and OpenLLaMA, releasing their intermediate checkpoints. This initiative offers valuable resources to the research community and facilitates the verification and exploration of LLM pretraining by open-source researchers. Besides, we provide empirical summaries, including performance comparisons of different models and capabilities, and tuition of key metrics for different training phases. Based on these findings, we provide a more user-friendly strategy for evaluating the optimization state, offering guidance for establishing a stable pretraining process.

Clinical case reports encode temporal patient trajectories that are often underexploited by traditional machine learning methods relying on structured data. In this work, we introduce the forecasting problem from textual time series, where timestamped clinical findings -- extracted via an LLM-assisted annotation pipeline -- serve as the primary input for prediction. We systematically evaluate a diverse suite of models, including fine-tuned decoder-based large language models and encoder-based transformers, on tasks of event occurrence prediction, temporal ordering, and survival analysis. Our experiments reveal that encoder-based models consistently achieve higher F1 scores and superior temporal concordance for short- and long-horizon event forecasting, while fine-tuned masking approaches enhance ranking performance. In contrast, instruction-tuned decoder models demonstrate a relative advantage in survival analysis, especially in early prognosis settings. Our sensitivity analyses further demonstrate the importance of time ordering, which requires clinical time series construction, as compared to text ordering, the format of the text inputs that LLMs are classically trained on. This highlights the additional benefit that can be ascertained from time-ordered corpora, with implications for temporal tasks in the era of widespread LLM use.

System logs are a critical resource for monitoring and managing distributed systems, providing insights into failures and anomalous behavior. Traditional log analysis techniques, including template-based and sequence-driven approaches, often lose important semantic information or struggle with ambiguous log patterns. To address this, we present EnrichLog, a training-free, entry-based anomaly detection framework that enriches raw log entries with both corpus-specific and sample-specific knowledge. EnrichLog incorporates contextual information, including historical examples and reasoning derived from the corpus, to enable more accurate and interpretable anomaly detection. The framework leverages retrieval-augmented generation to integrate relevant contextual knowledge without requiring retraining. We evaluate EnrichLog on four large-scale system log benchmark datasets and compare it against five baseline methods. Our results show that EnrichLog consistently improves anomaly detection performance, effectively handles ambiguous log entries, and maintains efficient inference. Furthermore, incorporating both corpus- and sample-specific knowledge enhances model confidence and detection accuracy, making EnrichLog well-suited for practical deployments.

Recent sequence modeling approaches using selective state space sequence models, referred to as Mamba models, have seen a surge of interest. These models allow efficient processing of long sequences in linear time and are rapidly being adopted in a wide range of applications such as language modeling, demonstrating promising performance. To foster their reliable use in real-world scenarios, it is crucial to augment their transparency. Our work bridges this critical gap by bringing explainability, particularly Layer-wise Relevance Propagation (LRP), to the Mamba architecture. Guided by the axiom of relevance conservation, we identify specific components in the Mamba architecture, which cause unfaithful explanations. To remedy this issue, we propose MambaLRP, a novel algorithm within the LRP framework, which ensures a more stable and reliable relevance propagation through these components. Our proposed method is theoretically sound and excels in achieving state-of-the-art explanation performance across a diverse range of models and datasets. Moreover, MambaLRP facilitates a deeper inspection of Mamba architectures, uncovering various biases and evaluating their significance. It also enables the analysis of previous speculations regarding the long-range capabilities of Mamba models.

A natural strategy for continual learning is to weigh a Bayesian ensemble of fixed functions. This suggests that if a (single) neural network could be interpreted as an ensemble, one could design effective algorithms that learn without forgetting. To realize this possibility, we observe that a neural network classifier with N parameters can be interpreted as a weighted ensemble of N classifiers, and that in the lazy regime limit these classifiers are fixed throughout learning. We call these classifiers the neural tangent experts and show they output valid probability distributions over the labels. We then derive the likelihood and posterior probability of each expert given past data. Surprisingly, the posterior updates for these experts are equivalent to a scaled and projected form of stochastic gradient descent (SGD) over the network weights. Away from the lazy regime, networks can be seen as ensembles of adaptive experts which improve over time. These results offer a new interpretation of neural networks as Bayesian ensembles of experts, providing a principled framework for understanding and mitigating catastrophic forgetting in continual learning settings.