Daily Papers

AI-agent guardrails are memoryless: each message is judged in isolation, so an adversary who spreads a single attack across dozens of sessions slips past every session-bound detector because only the aggregate carries the payload. We make three contributions to cross-session threat detection. (1) Dataset. CSTM-Bench is 26 executable attack taxonomies classified by kill-chain stage and cross-session operation (accumulate, compose, launder, inject_on_reader), each bound to one of seven identity anchors that ground-truth "violation" as a policy predicate, plus matched Benign-pristine and Benign-hard confounders. Released on Hugging Face as intrinsec-ai/cstm-bench with two 54-scenario splits: dilution (compositional) and cross_session (12 isolation-invisible scenarios produced by a closed-loop rewriter that softens surface phrasing while preserving cross-session artefacts). (2) Measurement. Framing cross-session detection as an information bottleneck to a downstream correlator LLM, we find that a session-bound judge and a Full-Log Correlator concatenating every prompt into one long-context call both lose roughly half their attack recall moving from dilution to cross_session, well inside any frontier context window. Scope: 54 scenarios per shard, one correlator family (Anthropic Claude), no prompt optimisation; we release it to motivate larger, multi-provider datasets. (3) Algorithm and metric. A bounded-memory Coreset Memory Reader retaining highest-signal fragments at K=50 is the only reader whose recall survives both shards. Because ranker reshuffles break KV-cache prefix reuse, we promote CSR_prefix (ordered prefix stability, LLM-free) to a first-class metric and fuse it with detection into CSTM = 0.7 F_1(CSDA@action, precision) + 0.3 CSR_prefix, benchmarking rankers on a single Pareto of recall versus serving stability.

Being able to provide explanations for a model's decision has become a central requirement for the development, deployment, and adoption of machine learning models. However, we are yet to understand what explanation methods can and cannot do. How do upstream factors such as data, model prediction, hyperparameters, and random initialization influence downstream explanations? While previous work raised concerns that explanations (E) may have little relationship with the prediction (Y), there is a lack of conclusive study to quantify this relationship. Our work borrows tools from causal inference to systematically assay this relationship. More specifically, we study the relationship between E and Y by measuring the treatment effect when intervening on their causal ancestors, i.e., on hyperparameters and inputs used to generate saliency-based Es or Ys. Our results suggest that the relationships between E and Y is far from ideal. In fact, the gap between 'ideal' case only increase in higher-performing models -- models that are likely to be deployed. Our work is a promising first step towards providing a quantitative measure of the relationship between E and Y, which could also inform the future development of methods for E with a quantitative metric.

Energy-energy correlators are constructed by averaging the number of charged particle pairs within jets, weighted by the product of their transverse momenta, as a function of the angular separation of the particles within a pair. They are sensitive to a multitude of perturbative and nonperturbative quantum chromodynamics phenomena in high-energy particle collisions. Using lead-lead data recorded with the CMS detector, energy-energy correlators inside high transverse momentum jets are measured in heavy ion collisions for the first time. The data are obtained at a nucleon-nucleon center-of-mass energy of 5.02 TeV and correspond to an integrated luminosity of 1.70 nb^{-1}. A similar analysis is done for proton-proton collisions at the same center-of-mass energy to establish a reference. The ratio of lead-lead to proton-proton energy-energy correlators reveals significant jet substructure modifications in the quark-gluon plasma. The results are compared to different models that incorporate either color coherence or medium response effects, where the two effects predict similar substructure modifications.

Recent developments in large-scale machine learning suggest that by scaling up data, model size and training time properly, one might observe that improvements in pre-training would transfer favorably to most downstream tasks. In this work, we systematically study this phenomena and establish that, as we increase the upstream accuracy, the performance of downstream tasks saturates. In particular, we investigate more than 4800 experiments on Vision Transformers, MLP-Mixers and ResNets with number of parameters ranging from ten million to ten billion, trained on the largest scale of available image data (JFT, ImageNet21K) and evaluated on more than 20 downstream image recognition tasks. We propose a model for downstream performance that reflects the saturation phenomena and captures the nonlinear relationship in performance of upstream and downstream tasks. Delving deeper to understand the reasons that give rise to these phenomena, we show that the saturation behavior we observe is closely related to the way that representations evolve through the layers of the models. We showcase an even more extreme scenario where performance on upstream and downstream are at odds with each other. That is, to have a better downstream performance, we need to hurt upstream accuracy.

An industrial process includes many devices, variables, and sub-processes that are physically or electronically interconnected. These interconnections imply some level of correlation between different process variables. Since most of the alarms in a process plant are defined on process variables, alarms are also correlated. However, this can be a nuisance to operators, for one fault might trigger a, sometimes large, number of alarms. So, it is essential to find and correct correlated alarms. In this paper, we study different methods and techniques proposed to measure correlation or similarity between alarms. The similarity indices are first analytically calculated and then studied and compared. The results are also validated using Monte-Carlo simulation.

Counterfactual data augmentation has recently emerged as a method to mitigate confounding biases in the training data for a machine learning model. These biases, such as spurious correlations, arise due to various observed and unobserved confounding variables in the data generation process. In this paper, we formally analyze how confounding biases impact downstream classifiers and present a causal viewpoint to the solutions based on counterfactual data augmentation. We explore how removing confounding biases serves as a means to learn invariant features, ultimately aiding in generalization beyond the observed data distribution. Additionally, we present a straightforward yet powerful algorithm for generating counterfactual images, which effectively mitigates the influence of confounding effects on downstream classifiers. Through experiments on MNIST variants and the CelebA datasets, we demonstrate the effectiveness and practicality of our approach.

Transfer learning is a popular method for tuning pretrained (upstream) models for different downstream tasks using limited data and computational resources. We study how an adversary with control over an upstream model used in transfer learning can conduct property inference attacks on a victim's tuned downstream model. For example, to infer the presence of images of a specific individual in the downstream training set. We demonstrate attacks in which an adversary can manipulate the upstream model to conduct highly effective and specific property inference attacks (AUC score > 0.9), without incurring significant performance loss on the main task. The main idea of the manipulation is to make the upstream model generate activations (intermediate features) with different distributions for samples with and without a target property, thus enabling the adversary to distinguish easily between downstream models trained with and without training examples that have the target property. Our code is available at https://github.com/yulongt23/Transfer-Inference.

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.

Transfer learning is a classic paradigm by which models pretrained on large "upstream" datasets are adapted to yield good results on "downstream" specialized datasets. Generally, more accurate models on the "upstream" dataset tend to provide better transfer accuracy "downstream". In this work, we perform an in-depth investigation of this phenomenon in the context of convolutional neural networks (CNNs) trained on the ImageNet dataset, which have been pruned - that is, compressed by sparsifying their connections. We consider transfer using unstructured pruned models obtained by applying several state-of-the-art pruning methods, including magnitude-based, second-order, re-growth, lottery-ticket, and regularization approaches, in the context of twelve standard transfer tasks. In a nutshell, our study shows that sparse models can match or even outperform the transfer performance of dense models, even at high sparsities, and, while doing so, can lead to significant inference and even training speedups. At the same time, we observe and analyze significant differences in the behaviour of different pruning methods.

Pretext-based self-supervised learning learns the semantic representation via a handcrafted pretext task over unlabeled data and then uses the learned representation for downstream tasks, which effectively reduces the sample complexity of downstream tasks under Conditional Independence (CI) condition. However, the downstream sample complexity gets much worse if the CI condition does not hold. One interesting question is whether we can make the CI condition hold by using downstream data to refine the unlabeled data to boost self-supervised learning. At first glance, one might think that seeing downstream data in advance would always boost the downstream performance. However, we show that it is not intuitively true and point out that in some cases, it hurts the final performance instead. In particular, we prove both model-free and model-dependent lower bounds of the number of downstream samples used for data refinement. Moreover, we conduct various experiments on both synthetic and real-world datasets to verify our theoretical results.

In this paper, we propose a dimensionless anomaly detection method for multivariate streams. Our method is independent of the unit of measurement for the different stream channels, therefore dimensionless. We first propose the variance norm, a generalisation of Mahalanobis distance to handle infinite-dimensional feature space and singular empirical covariance matrix rigorously. We then combine the variance norm with the path signature, an infinite collection of iterated integrals that provide global features of streams, to propose SigMahaKNN, a method for anomaly detection on (multivariate) streams. We show that SigMahaKNN is invariant to stream reparametrisation, stream concatenation and has a graded discrimination power depending on the truncation level of the path signature. We implement SigMahaKNN as an open-source software, and perform extensive numerical experiments, showing significantly improved anomaly detection on streams compared to isolation forest and local outlier factors in applications ranging from language analysis, hand-writing analysis, ship movement paths analysis and univariate time-series analysis.

Communication is defined as "Who says what to whom with what effect." A message from a communicator generates downstream receiver effects, also known as behavior. Receiver behavior, being a downstream effect of the message, carries rich signals about it. Even after carrying signals about the message, the behavior data is often ignored while training large language models. We show that training LLMs on receiver behavior can actually help improve their content-understanding abilities. Specifically, we show that training LLMs to predict the receiver behavior of likes and comments improves the LLM's performance on a wide variety of downstream content understanding tasks. We show this performance increase over 40 video and image understanding tasks over 23 benchmark datasets across both 0-shot and fine-tuning settings, outperforming many supervised baselines. Moreover, since receiver behavior, such as likes and comments, is collected by default on the internet and does not need any human annotations to be useful, the performance improvement we get after training on this data is essentially free-lunch. We release the receiver behavior cleaned comments and likes of 750k images and videos collected from multiple platforms along with our instruction-tuning data.

Most contemporary neural learning systems rely on epoch-based optimization and repeated access to historical data, implicitly assuming reversible computation. In contrast, real-world environments often present information as irreversible streams, where inputs cannot be replayed or revisited. Under such conditions, conventional architectures degrade into reactive filters lacking long-horizon coherence. This paper introduces Stream Neural Networks (StNN), an execution paradigm designed for irreversible input streams. StNN operates through a stream-native execution algorithm, the Stream Network Algorithm (SNA), whose fundamental unit is the stream neuron. Each stream neuron maintains a persistent temporal state that evolves continuously across inputs. We formally establish three structural guarantees: (1) stateless mappings collapse under irreversibility and cannot encode temporal dependencies; (2) persistent state dynamics remain bounded under mild activation constraints; and (3) the state transition operator is contractive for λ < 1, ensuring stable long-horizon execution. Empirical phase-space analysis and continuous tracking experiments validate these theoretical results. The execution principles introduced in this work define a minimal substrate for neural computation under irreversible streaming constraints.

Electroencephalography (EEG) offers a non-invasive lens into human brain activity, but building large-scale models is hampered by topological heterogeneity: each public EEG data defines its own electrode layout, limiting generalization. We introduce LUNA (Latent Unified Network Architecture), a self-supervised foundation model that reconciles disparate electrode geometries while scaling linearly -- not quadratically -- with channel count. LUNA compresses multi-channel EEG into a fixed-size, topology-agnostic latent space via learned queries and cross-attention. Downstream transformer blocks then operate exclusively on this latent representation using patch-wise temporal self-attention, decoupling computation from electrode count. Pre-trained on TUEG and Siena (over 21,000 hours of raw EEG across diverse montages) using a masked-patch reconstruction objective, LUNA transfers effectively to four downstream tasks: abnormality detection, artifact rejection, slowing classification, and emotion recognition. It demonstrates highly competitive performance across several benchmarks, achieving state-of-the-art results on TUAR and TUSL, e.g., 0.921 AUROC on TUAR, while reducing FLOPs by 300x and trimming GPU memory use by up to 10x. Critically, these gains are consistent across all evaluated electrode configurations. Code is available at https://github.com/pulp-bio/BioFoundation

Linear transformation of the inputs alters the training performance of feed-forward networks that are otherwise equivalent. However, most linear transforms are viewed as a pre-processing operation separate from the actual training. Starting from equivalent networks, it is shown that pre-processing inputs using linear transformation are equivalent to multiplying the negative gradient matrix with an autocorrelation matrix per training iteration. Second order method is proposed to find the autocorrelation matrix that maximizes learning in a given iteration. When the autocorrelation matrix is diagonal, the method optimizes input gains. This optimal input gain (OIG) approach is used to improve two first-order two-stage training algorithms, namely back-propagation (BP) and hidden weight optimization (HWO), which alternately update the input weights and solve linear equations for output weights. Results show that the proposed OIG approach greatly enhances the performance of the first-order algorithms, often allowing them to rival the popular Levenberg-Marquardt approach with far less computation. It is shown that HWO is equivalent to BP with Whitening transformation applied to the inputs. HWO effectively combines Whitening transformation with learning. Thus, OIG improved HWO could be a significant building block to more complex deep learning architectures.

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

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.

Large language models can generate fluent answers that are unfaithful to the provided context, while many safeguards rely on external verification or a separate judge after generation. We introduce internal flow signatures that audit decision formation from depthwise dynamics at a fixed inter-block monitoring boundary. The method stabilizes token-wise motion via bias-centered monitoring, then summarizes trajectories in compact moving readout-aligned subspaces constructed from the top token and its close competitors within each depth window. Neighboring window frames are aligned by an orthogonal transport, yielding depth-comparable transported step lengths, turning angles, and subspace drift summaries that are invariant to within-window basis choices. A lightweight GRU validator trained on these signatures performs self-checking without modifying the base model. Beyond detection, the validator localizes a culprit depth event and enables a targeted refinement: the model rolls back to the culprit token and clamps an abnormal transported step at the identified block while preserving the orthogonal residual. The resulting pipeline provides actionable localization and low-overhead self-checking from internal decision dynamics. Code is available at github.com/EavnJeong/Internal-Flow-Signatures-for-Self-Checking-and-Refinement-in-LLMs.

Self-predictive unsupervised learning methods such as BYOL or SimSiam have shown impressive results, and counter-intuitively, do not collapse to trivial representations. In this work, we aim at exploring the simplest possible mathematical arguments towards explaining the underlying mechanisms behind self-predictive unsupervised learning. We start with the observation that those methods crucially rely on the presence of a predictor network (and stop-gradient). With simple linear algebra, we show that when using a linear predictor, the optimal predictor is close to an orthogonal projection, and propose a general framework based on orthonormalization that enables to interpret and give intuition on why BYOL works. In addition, this framework demonstrates the crucial role of the exponential moving average and stop-gradient operator in BYOL as an efficient orthonormalization mechanism. We use these insights to propose four new closed-form predictor variants of BYOL to support our analysis. Our closed-form predictors outperform standard linear trainable predictor BYOL at 100 and 300 epochs (top-1 linear accuracy on ImageNet).

We present a technique for translating a black-box machine-learned classifier operating on a high-dimensional input space into a small set of human-interpretable observables that can be combined to make the same classification decisions. We iteratively select these observables from a large space of high-level discriminants by finding those with the highest decision similarity relative to the black box, quantified via a metric we introduce that evaluates the relative ordering of pairs of inputs. Successive iterations focus only on the subset of input pairs that are misordered by the current set of observables. This method enables simplification of the machine-learning strategy, interpretation of the results in terms of well-understood physical concepts, validation of the physical model, and the potential for new insights into the nature of the problem itself. As a demonstration, we apply our approach to the benchmark task of jet classification in collider physics, where a convolutional neural network acting on calorimeter jet images outperforms a set of six well-known jet substructure observables. Our method maps the convolutional neural network into a set of observables called energy flow polynomials, and it closes the performance gap by identifying a class of observables with an interesting physical interpretation that has been previously overlooked in the jet substructure literature.

Recent work has made clear that the residual pathway is not mere optimization plumbing; it is part of the model's representational machinery. We agree, but argue that the cleanest way to organize this design space is through a two-axis view of the Transformer. A decoder evolves information along two ordered dimensions: sequence position and layer depth. Self-attention already provides adaptive mixing along the sequence axis, whereas the residual stream usually performs fixed addition along the depth axis. If we fix a token position and treat layer index as the ordered variable, then a causal depth-wise residual attention read is exactly the same local operator as causal short sliding-window attention (ShortSWA), except written over depth rather than over sequence. This is the core residual stream duality behind Transformer^2. This perspective also clarifies the recent literature. ELC-BERT and DenseFormer already show that learned aggregation over depth can outperform uniform residual accumulation, while Vertical Attention, DeepCrossAttention (DCA), MUDDFormer, and Attention Residuals move further toward explicit attention-based routing over earlier layers. The key point, however, is that operator-level duality does not imply systems-level symmetry. For large-scale autoregressive models, sequence-axis ShortSWA is usually the more hardware-friendly placement because it reuses token-side sliding-window kernels, KV-cache layouts, and chunked execution. If the goal is instead to change the shortcut itself, Deep Delta Learning (DDL) is the cleaner intervention because it modifies the residual operator directly rather than adding a separate cross-layer retrieval path. Our recommendation is therefore simple: use DDL when the shortcut is the object of interest, and use sequence-axis ShortSWA when the goal is local adaptive mixing.

Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical difficulties of estimating time-varying and high-dimensional covariance matrices often limits existing methods to handling at most a few hundred dimensions or requires making strong assumptions on the dependence between series. We propose to combine an RNN-based time series model with a Gaussian copula process output model with a low-rank covariance structure to reduce the computational complexity and handle non-Gaussian marginal distributions. This permits to drastically reduce the number of parameters and consequently allows the modeling of time-varying correlations of thousands of time series. We show on several real-world datasets that our method provides significant accuracy improvements over state-of-the-art baselines and perform an ablation study analyzing the contributions of the different components of our model.

We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow on an implicit Riemannian manifold, we analyze the layerwise covariance spectrum of activations, where C^{(ell)}=E[h^{(ell)}h^{(ell)top}], and track deviations from a random-matrix bulk. Across model scales (1.5B--30B), we observe a sharp reduction in effective dimensionality consistent with a phase transition: an order parameter based on sparsity/localization, Ω(h)=1-|h|_1/(d|h|_2), exhibits a discontinuity near a critical normalized depth γ_capprox 0.42 in sufficiently large models. We formalize the forward pass as a discrete coarse-graining map and relate the appearance of stable "concept basins" to fixed points of this renormalization-like dynamics. The resulting low-entropy regime is characterized by a spectral tail collapse and by the formation of transient, reusable object-like structures in representation space, which we call Transient Class Objects (TCOs). We provide theoretical conditions connecting logical separability to spectral decay and validate the predicted signatures with layerwise probes on multiple open-weight model families.

Stream networks, a unique class of spatiotemporal graphs, exhibit complex directional flow constraints and evolving dependencies, making uncertainty quantification a critical yet challenging task. Traditional conformal prediction methods struggle in this setting due to the need for joint predictions across multiple interdependent locations and the intricate spatio-temporal dependencies inherent in stream networks. Existing approaches either neglect dependencies, leading to overly conservative predictions, or rely solely on data-driven estimations, failing to capture the rich topological structure of the network. To address these challenges, we propose Spatio-Temporal Adaptive Conformal Inference (STACI), a novel framework that integrates network topology and temporal dynamics into the conformal prediction framework. STACI introduces a topology-aware nonconformity score that respects directional flow constraints and dynamically adjusts prediction sets to account for temporal distributional shifts. We provide theoretical guarantees on the validity of our approach and demonstrate its superior performance on both synthetic and real-world datasets. Our results show that STACI effectively balances prediction efficiency and coverage, outperforming existing conformal prediction methods for stream networks.

Multivariate time series forecasting plays a crucial role in various fields such as finance, traffic management, energy, and healthcare. Recent studies have highlighted the advantages of channel independence to resist distribution drift but neglect channel correlations, limiting further enhancements. Several methods utilize mechanisms like attention or mixer to address this by capturing channel correlations, but they either introduce excessive complexity or rely too heavily on the correlation to achieve satisfactory results under distribution drifts, particularly with a large number of channels. Addressing this gap, this paper presents an efficient MLP-based model, the Series-cOre Fused Time Series forecaster (SOFTS), which incorporates a novel STar Aggregate-Redistribute (STAR) module. Unlike traditional approaches that manage channel interactions through distributed structures, e.g., attention, STAR employs a centralized strategy to improve efficiency and reduce reliance on the quality of each channel. It aggregates all series to form a global core representation, which is then dispatched and fused with individual series representations to facilitate channel interactions effectively.SOFTS achieves superior performance over existing state-of-the-art methods with only linear complexity. The broad applicability of the STAR module across different forecasting models is also demonstrated empirically. For further research and development, we have made our code publicly available at https://github.com/Secilia-Cxy/SOFTS.

The pretrain-finetune paradigm has shown outstanding performance on many applications of deep learning, where a model is pre-trained on a upstream large dataset (e.g. ImageNet), and is then fine-tuned to different downstream tasks. Though for most cases, the pre-training stage is conducted based on supervised methods, recent works on self-supervised pre-training have shown powerful transferability and even outperform supervised pre-training on multiple downstream tasks. It thus remains an open question how to better generalize supervised pre-training model to downstream tasks. In this paper, we argue that the worse transferability of existing supervised pre-training methods arise from the negligence of valuable intra-class semantic difference. This is because these methods tend to push images from the same class close to each other despite of the large diversity in their visual contents, a problem to which referred as "overfit of upstream tasks". To alleviate this problem, we propose a new supervised pre-training method based on Leave-One-Out K-Nearest-Neighbor, or LOOK for short. It relieves the problem of overfitting upstream tasks by only requiring each image to share its class label with most of its k nearest neighbors, thus allowing each class to exhibit a multi-mode distribution and consequentially preserving part of intra-class difference for better transferring to downstream tasks. We developed efficient implementation of the proposed method that scales well to large datasets. Experimental studies on multiple downstream tasks show that LOOK outperforms other state-of-the-art methods for supervised and self-supervised pre-training.

Multimodal large language models (MLLMs) have shown strong performance on offline video understanding, but most are limited to offline inference or have weak online reasoning, making multi-turn interaction over continuously arriving video streams difficult. Existing streaming methods typically use an interleaved perception-generation paradigm, which prevents concurrent perception and generation and leads to early memory decay as streams grow, hurting long-range dependency modeling. We propose Think While Watching, a memory-anchored streaming video reasoning framework that preserves continuous segment-level memory during multi-turn interaction. We build a three-stage, multi-round chain-of-thought dataset and adopt a stage-matched training strategy, while enforcing strict causality through a segment-level streaming causal mask and streaming positional encoding. During inference, we introduce an efficient pipeline that overlaps watching and thinking and adaptively selects the best attention backend. Under both single-round and multi-round streaming input protocols, our method achieves strong results. Built on Qwen3-VL, it improves single-round accuracy by 2.6% on StreamingBench and by 3.79% on OVO-Bench. In the multi-round setting, it maintains performance while reducing output tokens by 56%. Code is available at: https://github.com/wl666hhh/Think_While_Watching/

Multi-stream transformer architectures have recently been proposed as a promising direction for managing representation collapse and the vanishing gradient problem for residual connections, yet their internal mechanisms remain unexplored. In particular, the recently introduced Manifold-Constrained Hyper-Connections (mHC) architecture posits multiple residual streams with constrained interaction, but lacks in-depth mechanistic analysis. We present the first open-source mHC language model (https://huggingface.co/wgpeng/mhc-780m) and analyze the multiple-stream architecture with a suite of representation-level metrics and causal interventions to probe how parallel streams encode and utilize information. Specifically, we introduce a systematic stream ablation-and-rescue framework that enables direct causal comparison of residual streams during inference. Through targeted pairwise interventions and controlled recovery experiments, we distinguish functional redundancy from asymmetric utilization and reveal how information is distributed across streams beyond what is observable from representational similarity alone.

We used a dataset of daily Bloomberg Financial Market Summaries from 2010 to 2023, reposted on large financial media, to determine how global news headlines may affect stock market movements using ChatGPT and a two-stage prompt approach. We document a statistically significant positive correlation between the sentiment score and future equity market returns over short to medium term, which reverts to a negative correlation over longer horizons. Validation of this correlation pattern across multiple equity markets indicates its robustness across equity regions and resilience to non-linearity, evidenced by comparison of Pearson and Spearman correlations. Finally, we provide an estimate of the optimal horizon that strikes a balance between reactivity to new information and correlation.

In the artificial neuron, I replace the dot product with the weighted Lehmer mean, which may emulate different cases of a generalized mean. The single neuron instance is replaced by a multiplet of neurons which have the same averaging weights. A group of outputs feed forward, in lieu of the single scalar. The generalization parameter is typically set to a different value for each neuron in the multiplet. I further extend the concept to a multiplet taken from the Gini mean. Derivatives with respect to the weight parameters and with respect to the two generalization parameters are given. Some properties of the network are investigated, showing the capacity to emulate the classical exclusive-or problem organically in two layers and perform some multiplication and division. The network can instantiate truncated power series and variants, which can be used to approximate different functions, provided that parameters are constrained. Moreover, a mean case slope score is derived that can facilitate a learning-rate novelty based on homogeneity of the selected elements. The multiplet neuron equation provides a way to segment regularization timeframes and approaches.

The residual stream mediates communication between transformer decoder layers via linear reads and writes of non-linear computations. While sparse-dictionary learning-based methods locate features in the residual stream, and activation patching methods discover circuits within the model, the mechanism by which features flow through the residual stream remains understudied. Understanding this dynamic can better inform jailbreaking protections, enable early detection of model mistakes, and their correction. In this work, we propose Activation Transport Operators (ATO), linear maps from upstream to downstream residuals k layers later, evaluated in feature space using downstream SAE decoder projections. We empirically demonstrate that these operators can determine whether a feature has been linearly transported from a previous layer or synthesised from non-linear layer computation. We develop the notion of transport efficiency, for which we provide an upper bound, and use it to estimate the size of the residual stream subspace that corresponds to linear transport. We empirically demonstrate the linear transport, report transport efficiency and the size of the residual stream's subspace involved in linear transport. This compute-light (no finetuning, <50 GPU-h) method offers practical tools for safety, debugging, and a clearer picture of where computation in LLMs behaves linearly.

Causal discovery with latent confounders is an important but challenging task in many scientific areas. Despite the success of some overcomplete independent component analysis (OICA) based methods in certain domains, they are computationally expensive and can easily get stuck into local optima. We notice that interestingly, by making use of higher-order cumulants, there exists a closed-form solution to OICA in specific cases, e.g., when the mixing procedure follows the One-Latent-Component structure. In light of the power of the closed-form solution to OICA corresponding to the One-Latent-Component structure, we formulate a way to estimate the mixing matrix using the higher-order cumulants, and further propose the testable One-Latent-Component condition to identify the latent variables and determine causal orders. By iteratively removing the share identified latent components, we successfully extend the results on the One-Latent-Component structure to the Multi-Latent-Component structure and finally provide a practical and asymptotically correct algorithm to learn the causal structure with latent variables. Experimental results illustrate the asymptotic correctness and effectiveness of the proposed method.

As we show in this paper, the prediction for output token n+1 of Transformer architectures without one of the mechanisms of positional encodings and causal attention is invariant to permutations of input tokens 1, 2, ..., n-1. Usually, both mechanisms are employed and the symmetry with respect to the input tokens is broken. Recently, it has been shown that one can train Transformers without positional encodings. This must be enabled by the causal attention mechanism. In this paper, we elaborate on the argument that the causal connection mechanism must be responsible for the fact that Transformers are able to model input sequences where the order is important. Vertical "slices" of Transformers are all encouraged to represent the same location k in the input sequence. We hypothesize that residual connections contribute to this phenomenon, and demonstrate evidence for this.

Visual autoregressive models typically adhere to a raster-order ``next-token prediction" paradigm, which overlooks the spatial and temporal locality inherent in visual content. Specifically, visual tokens exhibit significantly stronger correlations with their spatially or temporally adjacent tokens compared to those that are distant. In this paper, we propose Neighboring Autoregressive Modeling (NAR), a novel paradigm that formulates autoregressive visual generation as a progressive outpainting procedure, following a near-to-far ``next-neighbor prediction" mechanism. Starting from an initial token, the remaining tokens are decoded in ascending order of their Manhattan distance from the initial token in the spatial-temporal space, progressively expanding the boundary of the decoded region. To enable parallel prediction of multiple adjacent tokens in the spatial-temporal space, we introduce a set of dimension-oriented decoding heads, each predicting the next token along a mutually orthogonal dimension. During inference, all tokens adjacent to the decoded tokens are processed in parallel, substantially reducing the model forward steps for generation. Experiments on ImageNet256times 256 and UCF101 demonstrate that NAR achieves 2.4times and 8.6times higher throughput respectively, while obtaining superior FID/FVD scores for both image and video generation tasks compared to the PAR-4X approach. When evaluating on text-to-image generation benchmark GenEval, NAR with 0.8B parameters outperforms Chameleon-7B while using merely 0.4 of the training data. Code is available at https://github.com/ThisisBillhe/NAR.

Flow models are effective at progressively generating realistic images, but they generally struggle to capture long-range dependencies during the generation process as they compress all the information from previous time steps into a single corrupted image. To address this limitation, we propose integrating autoregressive modeling -- known for its excellence in modeling complex, high-dimensional joint probability distributions -- into flow models. During training, at each step, we construct causally-ordered sequences by sampling multiple images from the same semantic category and applying different levels of noise, where images with higher noise levels serve as causal predecessors to those with lower noise levels. This design enables the model to learn broader category-level variations while maintaining proper causal relationships in the flow process. During generation, the model autoregressively conditions the previously generated images from earlier denoising steps, forming a contextual and coherent generation trajectory. Additionally, we design a customized hybrid linear attention mechanism tailored to our modeling approach to enhance computational efficiency. Our approach, termed ARFlow, under 400k training steps, achieves 14.08 FID scores on ImageNet at 128 * 128 without classifier-free guidance, reaching 4.34 FID with classifier-free guidance 1.5, significantly outperforming the previous flow-based model SiT's 9.17 FID. Extensive ablation studies demonstrate the effectiveness of our modeling strategy and chunk-wise attention design.

Recently, channel-independent methods have achieved state-of-the-art performance in multivariate time series (MTS) forecasting. Despite reducing overfitting risks, these methods miss potential opportunities in utilizing channel dependence for accurate predictions. We argue that there exist locally stationary lead-lag relationships between variates, i.e., some lagged variates may follow the leading indicators within a short time period. Exploiting such channel dependence is beneficial since leading indicators offer advance information that can be used to reduce the forecasting difficulty of the lagged variates. In this paper, we propose a new method named LIFT that first efficiently estimates leading indicators and their leading steps at each time step and then judiciously allows the lagged variates to utilize the advance information from leading indicators. LIFT plays as a plugin that can be seamlessly collaborated with arbitrary time series forecasting methods. Extensive experiments on six real-world datasets demonstrate that LIFT improves the state-of-the-art methods by 5.5% in average forecasting performance. Our code is available at https://github.com/SJTU-Quant/LIFT.

Neural networks often exhibit emergent behavior, where qualitatively new capabilities arise from scaling up the amount of parameters, training data, or training steps. One approach to understanding emergence is to find continuous progress measures that underlie the seemingly discontinuous qualitative changes. We argue that progress measures can be found via mechanistic interpretability: reverse-engineering learned behaviors into their individual components. As a case study, we investigate the recently-discovered phenomenon of ``grokking'' exhibited by small transformers trained on modular addition tasks. We fully reverse engineer the algorithm learned by these networks, which uses discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle. We confirm the algorithm by analyzing the activations and weights and by performing ablations in Fourier space. Based on this understanding, we define progress measures that allow us to study the dynamics of training and split training into three continuous phases: memorization, circuit formation, and cleanup. Our results show that grokking, rather than being a sudden shift, arises from the gradual amplification of structured mechanisms encoded in the weights, followed by the later removal of memorizing components.

Vision-language models (VLMs) achieve strong multimodal performance, yet how computation is organized across populations of neurons remains poorly understood. In this work, we study VLMs through the lens of neural topology, representing each layer as a within-layer correlation graph derived from neuron-neuron co-activations. This view allows us to ask whether population-level structure is behaviorally meaningful, how it changes across modalities and depth, and whether it identifies causally influential internal components under intervention. We show that correlation topology carries recoverable behavioral signal; moreover, cross-modal structure progressively consolidates with depth around a compact set of recurrent hub neurons, whose targeted perturbation substantially alters model output. Neural topology thus emerges as a meaningful intermediate scale for VLM interpretability: richer than local attribution, more tractable than full circuit recovery, and empirically tied to multimodal behavior. Code is publicly available at https://github.com/he-h/vlm-graph-probing.

Evaluating retrieval-augmented generation (RAG) pipelines requires corpora where ground truth is knowable, temporally structured, and cross-artifact properties that real-world datasets rarely provide cleanly. Existing resources such as the Enron corpus carry legal ambiguity, demographic skew, and no structured ground truth. Purely LLM-generated synthetic data solves the legal problem but introduces a subtler one: the generating model cannot be prevented from hallucinating facts that contradict themselves across documents.We present OrgForge, an open-source multi-agent simulation framework that enforces a strict physics-cognition boundary: a deterministic Python engine maintains a SimEvent ground truth bus; large language models generate only surface prose, constrained by validated proposals. An actor-local clock enforces causal timestamp correctness across all artifact types, eliminating the class of timeline inconsistencies that arise when timestamps are sampled independently per document. We formalize three graph-dynamic subsystems stress propagation via betweenness centrality, temporal edge-weight decay, and Dijkstra escalation routing that govern organizational behavior independently of any LLM. Running a configurable N-day simulation, OrgForge produces interleaved Slack threads, JIRA tickets, Confluence pages, Git pull requests, and emails, all traceable to a shared, immutable event log. We additionally describe a causal chain tracking subsystem that accumulates cross-artifact evidence graphs per incident, a hybrid reciprocal-rank-fusion recurrence detector for identifying repeated failure classes, and an inbound/outbound email engine that routes vendor alerts, customer complaints, and HR correspondence through gated causal chains with probabilistic drop simulation. OrgForge is available under the MIT license.

The current popular two-stream, two-stage tracking framework extracts the template and the search region features separately and then performs relation modeling, thus the extracted features lack the awareness of the target and have limited target-background discriminability. To tackle the above issue, we propose a novel one-stream tracking (OSTrack) framework that unifies feature learning and relation modeling by bridging the template-search image pairs with bidirectional information flows. In this way, discriminative target-oriented features can be dynamically extracted by mutual guidance. Since no extra heavy relation modeling module is needed and the implementation is highly parallelized, the proposed tracker runs at a fast speed. To further improve the inference efficiency, an in-network candidate early elimination module is proposed based on the strong similarity prior calculated in the one-stream framework. As a unified framework, OSTrack achieves state-of-the-art performance on multiple benchmarks, in particular, it shows impressive results on the one-shot tracking benchmark GOT-10k, i.e., achieving 73.7% AO, improving the existing best result (SwinTrack) by 4.3\%. Besides, our method maintains a good performance-speed trade-off and shows faster convergence. The code and models are available at https://github.com/botaoye/OSTrack.

Causality testing, the act of determining cause and effect from measurements, is widely used in physics, climatology, neuroscience, econometrics and other disciplines. As a result, a large number of causality testing methods based on various principles have been developed. Causal relationships in complex systems are typically accompanied by entropic exchanges which are encoded in patterns of dynamical measurements. A data compression algorithm which can extract these encoded patterns could be used for inferring these relations. This motivates us to propose, for the first time, a generic causality testing framework based on data compression. The framework unifies existing causality testing methods and enables us to innovate a novel Compression-Complexity Causality measure. This measure is rigorously tested on simulated and real-world time series and is found to overcome the limitations of Granger Causality and Transfer Entropy, especially for noisy and non-synchronous measurements. Additionally, it gives insight on the `kind' of causal influence between input time series by the notions of positive and negative causality.

Current paradigms for code verification rely heavily on external mechanisms-such as execution-based unit tests or auxiliary LLM judges-which are often labor-intensive or limited by the judging model's own capabilities. This raises a fundamental, yet unexplored question: Can an LLM's functional correctness be assessed purely from its internal computational structure? Our primary objective is to investigate whether the model's neural dynamics encode internally decodable signals that are predictive of logical validity during code generation. Inspired by mechanistic interpretability, we propose to treat code verification as a mechanistic diagnostic task, mapping the model's explicit algorithmic trajectory into line-level attribution graphs. By decomposing complex residual flows, we aim to identify the structural signatures that distinguish sound reasoning from logical failure within the model's internal circuits. Analysis across Python, C++, and Java confirms that intrinsic correctness signals are robust across diverse syntaxes. Topological features from these internal graphs predict correctness more reliably than surface heuristics and enable targeted causal interventions to fix erroneous logic. These findings establish internal introspection as a decodable property for verifying generated code. Our code is at https:// github.com/bruno686/CodeCircuit.

Interpretability research now offers a variety of techniques for identifying abstract internal mechanisms in neural networks. Can such techniques be used to predict how models will behave on out-of-distribution examples? In this work, we provide a positive answer to this question. Through a diverse set of language modeling tasks--including symbol manipulation, knowledge retrieval, and instruction following--we show that the most robust features for correctness prediction are those that play a distinctive causal role in the model's behavior. Specifically, we propose two methods that leverage causal mechanisms to predict the correctness of model outputs: counterfactual simulation (checking whether key causal variables are realized) and value probing (using the values of those variables to make predictions). Both achieve high AUC-ROC in distribution and outperform methods that rely on causal-agnostic features in out-of-distribution settings, where predicting model behaviors is more crucial. Our work thus highlights a novel and significant application for internal causal analysis of language models.

Stock price forecasting has remained an extremely challenging problem for many decades due to the high volatility of the stock market. Recent efforts have been devoted to modeling complex stock correlations toward joint stock price forecasting. Existing works share a common neural architecture that learns temporal patterns from individual stock series and then mixes up temporal representations to establish stock correlations. However, they only consider time-aligned stock correlations stemming from all the input stock features, which suffer from two limitations. First, stock correlations often occur momentarily and in a cross-time manner. Second, the feature effectiveness is dynamic with market variation, which affects both the stock sequential patterns and their correlations. To address the limitations, this paper introduces MASTER, a MArkert-Guided Stock TransformER, which models the momentary and cross-time stock correlation and leverages market information for automatic feature selection. MASTER elegantly tackles the complex stock correlation by alternatively engaging in intra-stock and inter-stock information aggregation. Experiments show the superiority of MASTER compared with previous works and visualize the captured realistic stock correlation to provide valuable insights.

We implement and benchmark on IBM Quantum hardware the circuit family proposed by Violaris for estimating operational inter-branch communication witnesses, defined as correlations in classical measurement records produced by compiled Wigner's-friend-style circuits. We realize a five-qubit instance of the protocol as an inter-register message-transfer pattern within a single circuit, rather than physical signaling, and evaluate its behavior under realistic device noise and compilation constraints. The circuit encodes branch-conditioned evolution of an observer subsystem whose dynamics depend on a control qubit, followed by a controlled transfer operation that probes correlations between conditional measurement contexts. Executing on the ibm_fez backend with 20000 shots, we observe population-based visibility of 0.877, coherence witnesses of 0.840 and -0.811 along orthogonal axes, and a phase-sensitive magnitude of approximately 1.17. While the visibility metric is insensitive to some classes of dephasing, the coherence witnesses provide complementary sensitivity to off-diagonal noise. This work does not test or discriminate among interpretations of quantum mechanics. Instead, it provides a reproducible operational constraint pipeline for evaluating detectability of non-ideal channels relative to calibrated device noise.

Convergent Cross Mapping (CCM) is a powerful method for detecting causality in coupled nonlinear dynamical systems, providing a model-free approach to capture dynamic causal interactions. Partial Cross Mapping (PCM) was introduced as an extension of CCM to address indirect causality in three-variable systems by comparing cross-mapping quality between direct cause-effect mapping and indirect mapping through an intermediate conditioning variable. However, PCM remains limited to univariate delay embeddings in its cross-mapping processes. In this work, we extend PCM to the multivariate setting, introducing multiPCM, which leverages multivariate embeddings to more effectively distinguish indirect causal relationships. We further propose a multivariate cross-mapping framework (MXMap) for causal discovery in dynamical systems. This two-phase framework combines (1) pairwise CCM tests to establish an initial causal graph and (2) multiPCM to refine the graph by pruning indirect causal connections. Through experiments on simulated data and the ERA5 Reanalysis weather dataset, we demonstrate the effectiveness of MXMap. Additionally, MXMap is compared against several baseline methods, showing advantages in accuracy and causal graph refinement.

Doubly-stochastic matrices (DSM) are increasingly utilized in structure-preserving deep architectures -- such as Optimal Transport layers and Sinkhorn-based attention -- to enforce numerical stability and probabilistic interpretability. In this work, we identify a critical spectral degradation phenomenon inherent to these constraints, termed the Homogeneity Trap. We demonstrate that the maximum-entropy bias, typical of Sinkhorn-based projections, drives the mixing operator towards the uniform barycenter, thereby suppressing the subdominant singular value σ_2 and filtering out high-frequency feature components. We derive a spectral bound linking σ_2 to the network's effective depth, showing that high-entropy constraints restrict feature transformation to a shallow effective receptive field. Furthermore, we formally demonstrate that Layer Normalization fails to mitigate this collapse in noise-dominated regimes; specifically, when spectral filtering degrades the Signal-to-Noise Ratio (SNR) below a critical threshold, geometric structure is irreversibly lost to noise-induced orthogonal collapse. Our findings highlight a fundamental trade-off between entropic stability and spectral expressivity in DSM-constrained networks.

In this paper, we study the flow of signals through linear paths with the nonlinear condition that a node emits a signal when it receives external stimuli or when two incoming signals from other nodes arrive coincidentally with a combined amplitude above a fixed threshold. Sets of such nodes form a polychrony group and can sometimes lead to cascades. In the context of this work, cascades are polychrony groups in which the number of nodes activated as a consequence of other nodes is greater than the number of externally activated nodes. The difference between these two numbers is the so-called profit. Given the initial conditions, we predict the conditions for a vertex to activate at a prescribed time and provide an algorithm to efficiently reconstruct a cascade. We develop a dictionary between polychrony groups and graph theory. We call the graph corresponding to a cascade a chinampa. This link leads to a topological classification of chinampas. We enumerate the chinampas of profits zero and one and the description of a family of chinampas isomorphic to a family of partially ordered sets, which implies that the enumeration problem of this family is equivalent to computing the Stanley-order polynomials of those partially ordered sets.

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.

Multivariate time series is prevalent in many scientific and industrial domains. Modeling multivariate signals is challenging due to their long-range temporal dependencies and intricate interactions--both direct and indirect. To confront these complexities, we introduce a method of representing multivariate signals as nodes in a graph with edges indicating interdependency between them. Specifically, we leverage graph neural networks (GNN) and attention mechanisms to efficiently learn the underlying relationships within the time series data. Moreover, we suggest employing hierarchical signal decompositions running over the graphs to capture multiple spatial dependencies. The effectiveness of our proposed model is evaluated across various real-world benchmark datasets designed for long-term forecasting tasks. The results consistently showcase the superiority of our model, achieving an average 23\% reduction in mean squared error (MSE) compared to existing models.

Branch prediction is arguably one of the most important speculative mechanisms within a high-performance processor architecture. A common approach to improve branch prediction accuracy is to employ lengthy history records of previously seen branch directions to capture distant correlations between branches. The larger the history, the richer the information that the predictor can exploit for discovering predictive patterns. However, without appropriate filtering, such an approach may also heavily disorganize the predictor's internal mechanisms, leading to diminishing returns. This paper studies a fundamental control-flow property: the sparsity in the correlation between branches and recent history. First, we show that sparse branch correlations exist in standard applications and, more importantly, such correlations can be computed efficiently using sparse modeling methods. Second, we introduce a sparsity-aware branch prediction mechanism that can compactly encode and store sparse models to unlock essential performance opportunities. We evaluated our approach for various design parameters demonstrating MPKI improvements of up to 42% (2.3% on average) with 2KB of additional storage overhead. Our circuit-level evaluation of the design showed that it can operate within accepted branch prediction latencies, and under reasonable power and area limitations.

I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented by a one-parameter family of operators, evolving on its own time scale. I formalize stratified state spaces capturing multiple levels of synchronized behavior, define an asynchronous evolution metric that quantifies phase-offset distances between subsystems, and characterize emergent coherent topologies arising when subsystems synchronize. Within this framework, I develop formal operators for the evolution of each subsystem and give precise conditions under which phase-aligned synchronization occurs across the lattice. The main results include: (1) the existence and uniqueness of coherent (synchronized) states under a contractive coupling condition, (2) stability of these coherent states and criteria for their emergence as a collective phase transition in a continuous operator topology, and (3) the influence of symmetries, with group-invariant coupling leading to flow-invariant synchrony subspaces and structured cluster dynamics. Proofs are given for each theorem, demonstrating full mathematical rigor. In a final section, I discuss hypothetical applications of this framework to symbolic lattice systems (e.g. subshifts), to invariant group actions on dynamical lattices, and to operator fields over stratified manifolds in the spirit of noncommutative geometry. Throughout, I write in the first person to emphasize the exploratory nature of this work. The paper avoids any reference to cosmology or observers, focusing instead on clean, formal mathematics suitable for a broad array of dynamical systems.

We show that PLDR-LLMs pretrained at self-organized criticality exhibit reasoning at inference time. The characteristics of PLDR-LLM deductive outputs at criticality is similar to second-order phase transitions. At criticality, the correlation length diverges, and the deductive outputs attain a metastable steady state. The steady state behaviour suggests that deductive outputs learn representations equivalent to scaling functions, universality classes and renormalization groups from the training dataset, leading to generalization and reasoning capabilities in the process. We can then define an order parameter from the global statistics of the model's deductive output parameters at inference. The reasoning capabilities of a PLDR-LLM is better when its order parameter is close to zero at criticality. This observation is supported by the benchmark scores of the models trained at near-criticality and sub-criticality. Our results provide a self-contained explanation on how reasoning manifests in large language models, and the ability to reason can be quantified solely from global model parameter values of the deductive outputs at steady state, without any need for evaluation of curated benchmark datasets through inductive output for reasoning and comprehension.

Inspired by the Many-Worlds Interpretation (MWI), this work introduces a novel neural network architecture that splits the same input signal into parallel branches at each layer, utilizing a Hyper Rectified Activation, referred to as ANDHRA. The branched layers do not merge and form separate network paths, leading to multiple network heads for output prediction. For a network with a branching factor of 2 at three levels, the total number of heads is 2^3 = 8 . The individual heads are jointly trained by combining their respective loss values. However, the proposed architecture requires additional parameters and memory during training due to the additional branches. During inference, the experimental results on CIFAR-10/100 demonstrate that there exists one individual head that outperforms the baseline accuracy, achieving statistically significant improvement with equal parameters and computational cost.

We present Three-Phase Transformer (3PT), a residual-stream structural prior for decoder-only Transformers on a standard SwiGLU + RMSNorm + RoPE + GQA backbone. The hidden vector is partitioned into N equally-sized cyclic channels, each maintained by phase-respecting ops: a per-channel RMSNorm, a 2D Givens rotation between attention and FFN that rotates each channel by theta + i*(2*pi/N), and a head-count constraint aligning GQA heads with the partition. The architecture is a self-stabilizing equilibrium between scrambling and re-imposition, not a bolted-on module. The partition carves out a one-dimensional DC subspace orthogonal to the channels, into which we inject a fixed Gabriel's horn profile r(p) = 1/(p+1) as an absolute-position side-channel composing orthogonally with RoPE's relative-position rotation. The canonical N=3 borrows its metaphor from balanced three-phase AC, where three sinusoids 120 degrees apart sum to zero with no anti-correlated pair. At 123M parameters on WikiText-103, 3PT achieves -7.20% perplexity (-2.62% bits-per-byte) over a matched RoPE-Only baseline at +1,536 parameters (0.00124% of total), with 1.93x step-count convergence speedup (1.64x wall-clock). N behaves as a parameter-sharing knob rather than a unique optimum: at 5.5M an N-sweep over {1,2,3,4,6,8,12} is near-monotone with N=1 winning; at 123M a three-seed sweep finds N=3 and N=1 statistically indistinguishable. The load-bearing mechanism is the channel-partitioned residual stream, per-block rotation, per-phase normalization, and horn DC injection. We characterize (a) self-stabilization of the geometry without explicit enforcement, a novel instance of the conservation-law framework for neural networks; (b) a U-shaped depth profile of rotation-angle drift at 12 layers; (c) orthogonal composition with RoPE, attention, and FFN.

Despite its widespread use in neural networks, error backpropagation has faced criticism for its lack of biological plausibility, suffering from issues such as the backward locking problem and the weight transport problem. These limitations have motivated researchers to explore more biologically plausible learning algorithms that could potentially shed light on how biological neural systems adapt and learn. Inspired by the counter-current exchange mechanisms observed in biological systems, we propose counter-current learning (CCL), a biologically plausible framework for credit assignment in neural networks. This framework employs a feedforward network to process input data and a feedback network to process targets, with each network enhancing the other through anti-parallel signal propagation. By leveraging the more informative signals from the bottom layer of the feedback network to guide the updates of the top layer of the feedforward network and vice versa, CCL enables the simultaneous transformation of source inputs to target outputs and the dynamic mutual influence of these transformations. Experimental results on MNIST, FashionMNIST, CIFAR10, and CIFAR100 datasets using multi-layer perceptrons and convolutional neural networks demonstrate that CCL achieves comparable performance to other biologically plausible algorithms while offering a more biologically realistic learning mechanism. Furthermore, we showcase the applicability of our approach to an autoencoder task, underscoring its potential for unsupervised representation learning. Our work presents a direction for biologically inspired and plausible learning algorithms, offering an alternative mechanism of learning and adaptation in neural networks.

As artificial intelligence models have exploded in scale and capability, understanding of their internal mechanisms remains a critical challenge. Inspired by the success of dynamical systems approaches in neuroscience, here we propose a novel framework for studying computations in deep learning systems. We focus on the residual stream (RS) in transformer models, conceptualizing it as a dynamical system evolving across layers. We find that activations of individual RS units exhibit strong continuity across layers, despite the RS being a non-privileged basis. Activations in the RS accelerate and grow denser over layers, while individual units trace unstable periodic orbits. In reduced-dimensional spaces, the RS follows a curved trajectory with attractor-like dynamics in the lower layers. These insights bridge dynamical systems theory and mechanistic interpretability, establishing a foundation for a "neuroscience of AI" that combines theoretical rigor with large-scale data analysis to advance our understanding of modern neural networks.

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are only selective for a small number of linear projections of a potentially high-dimensional input. Here we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g. naturalistic) stimulus distribution, we review several inference methods, focussing in particular on two information-theory-based approaches (maximization of stimulus energy or of noise entropy) and a likelihood-based approach (Bayesian spike-triggered covariance, extensions of generalized linear models). We analyze the formal connection between the likelihood-based and information-based approaches to show how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.

The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of time series, with each token formed by multiple variates of the same timestamp. However, Transformers are challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Besides, the embedding for each temporal token fuses multiple variates that represent potential delayed events and distinct physical measurements, which may fail in learning variate-centric representations and result in meaningless attention maps. In this work, we reflect on the competent duties of Transformer components and repurpose the Transformer architecture without any modification to the basic components. We propose iTransformer that simply applies the attention and feed-forward network on the inverted dimensions. Specifically, the time points of individual series are embedded into variate tokens which are utilized by the attention mechanism to capture multivariate correlations; meanwhile, the feed-forward network is applied for each variate token to learn nonlinear representations. The iTransformer model achieves state-of-the-art on challenging real-world datasets, which further empowers the Transformer family with promoted performance, generalization ability across different variates, and better utilization of arbitrary lookback windows, making it a nice alternative as the fundamental backbone of time series forecasting. Code is available at this repository: https://github.com/thuml/iTransformer.

Hypergraphs are a powerful abstraction for representing higher-order interactions between entities of interest. To exploit these relationships in making downstream predictions, a variety of hypergraph neural network architectures have recently been proposed, in large part building upon precursors from the more traditional graph neural network (GNN) literature. Somewhat differently, in this paper we begin by presenting an expressive family of parameterized, hypergraph-regularized energy functions. We then demonstrate how minimizers of these energies effectively serve as node embeddings that, when paired with a parameterized classifier, can be trained end-to-end via a supervised bilevel optimization process. Later, we draw parallels between the implicit architecture of the predictive models emerging from the proposed bilevel hypergraph optimization, and existing GNN architectures in common use. Empirically, we demonstrate state-of-the-art results on various hypergraph node classification benchmarks. Code is available at https://github.com/yxzwang/PhenomNN.

The "pre-training rightarrow downstream adaptation" presents both new opportunities and challenges for Continual Learning (CL). Although the recent state-of-the-art in CL is achieved through Parameter-Efficient-Tuning (PET) adaptation paradigm, only prompt has been explored, limiting its application to Transformers only. In this paper, we position prompting as one instantiation of PET, and propose a unified CL framework with general PET, dubbed as Learning-Accumulation-Ensemble (LAE). PET, e.g., using Adapter, LoRA, or Prefix, can adapt a pre-trained model to downstream tasks with fewer parameters and resources. Given a PET method, our LAE framework incorporates it for CL with three novel designs. 1) Learning: the pre-trained model adapts to the new task by tuning an online PET module, along with our adaptation speed calibration to align different PET modules, 2) Accumulation: the task-specific knowledge learned by the online PET module is accumulated into an offline PET module through momentum update, 3) Ensemble: During inference, we respectively construct two experts with online/offline PET modules (which are favored by the novel/historical tasks) for prediction ensemble. We show that LAE is compatible with a battery of PET methods and gains strong CL capability. For example, LAE with Adaptor PET surpasses the prior state-of-the-art by 1.3% and 3.6% in last-incremental accuracy on CIFAR100 and ImageNet-R datasets, respectively. Code is available at https://github.com/gqk/LAE.

Modelling the complex spatiotemporal patterns of large-scale brain dynamics is crucial for neuroscience, but traditional methods fail to capture the rich structure in modalities such as magnetoencephalography (MEG). Recent advances in deep learning have enabled significant progress in other domains, such as language and vision, by using foundation models at scale. Here, we introduce MEG-GPT, a transformer based foundation model that uses time-attention and next time-point prediction. To facilitate this, we also introduce a novel data-driven tokeniser for continuous MEG data, which preserves the high temporal resolution of continuous MEG signals without lossy transformations. We trained MEG-GPT on tokenised brain region time-courses extracted from a large-scale MEG dataset (N=612, eyes-closed rest, Cam-CAN data), and show that the learnt model can generate data with realistic spatio-spectral properties, including transient events and population variability. Critically, it performs well in downstream decoding tasks, improving downstream supervised prediction task, showing improved zero-shot generalisation across sessions (improving accuracy from 0.54 to 0.59) and subjects (improving accuracy from 0.41 to 0.49) compared to a baseline methods. Furthermore, we show the model can be efficiently fine-tuned on a smaller labelled dataset to boost performance in cross-subject decoding scenarios. This work establishes a powerful foundation model for electrophysiological data, paving the way for applications in computational neuroscience and neural decoding.

Neural network models of early sensory processing typically reduce the dimensionality of streaming input data. Such networks learn the principal subspace, in the sense of principal component analysis (PCA), by adjusting synaptic weights according to activity-dependent learning rules. When derived from a principled cost function these rules are nonlocal and hence biologically implausible. At the same time, biologically plausible local rules have been postulated rather than derived from a principled cost function. Here, to bridge this gap, we derive a biologically plausible network for subspace learning on streaming data by minimizing a principled cost function. In a departure from previous work, where cost was quantified by the representation, or reconstruction, error, we adopt a multidimensional scaling (MDS) cost function for streaming data. The resulting algorithm relies only on biologically plausible Hebbian and anti-Hebbian local learning rules. In a stochastic setting, synaptic weights converge to a stationary state which projects the input data onto the principal subspace. If the data are generated by a nonstationary distribution, the network can track the principal subspace. Thus, our result makes a step towards an algorithmic theory of neural computation.

We introduce a hierarchical filtering procedure for generative models of sequences on trees, enabling control over the range of positional correlations in the data. Leveraging this controlled setting, we provide evidence that vanilla encoder-only transformer architectures can implement the optimal Belief Propagation algorithm on both root classification and masked language modeling tasks. Correlations at larger distances corresponding to increasing layers of the hierarchy are sequentially included as the network is trained. We analyze how the transformer layers succeed by focusing on attention maps from models trained with varying degrees of filtering. These attention maps show clear evidence for iterative hierarchical reconstruction of correlations, and we can relate these observations to a plausible implementation of the exact inference algorithm for the network sizes considered.

With the rapid deployment of SCADA systems, how to effectively analyze industrial signals and detect abnormal states is an urgent need for the industry. Due to the significant heterogeneity of these signals, which we summarize as the M5 problem, previous works only focus on small sub-problems and employ specialized models, failing to utilize the synergies between modalities and the powerful scaling law. However, we argue that the M5 signals can be modeled in a unified manner due to the intrinsic similarity. As a result, we propose FISHER, a Foundation model for multi-modal Industrial Signal compreHEnsive Representation. To support arbitrary sampling rates, FISHER considers the increment of sampling rate as the concatenation of sub-band information. Specifically, FISHER takes the STFT sub-band as the modeling unit and adopts a teacher student SSL framework for pre-training. We also develop the RMIS benchmark, which evaluates the representations of M5 industrial signals on multiple health management tasks. Compared with top SSL models, FISHER showcases versatile and outstanding capabilities with a general performance gain up to 5.03%, along with much more efficient scaling curves. We also investigate the scaling law on downstream tasks and derive potential avenues for future works. FISHER is now open-sourced on https://github.com/jianganbai/FISHER

This paper studies the problem of training a two-layer ReLU network for binary classification using gradient flow with small initialization. We consider a training dataset with well-separated input vectors: Any pair of input data with the same label are positively correlated, and any pair with different labels are negatively correlated. Our analysis shows that, during the early phase of training, neurons in the first layer try to align with either the positive data or the negative data, depending on its corresponding weight on the second layer. A careful analysis of the neurons' directional dynamics allows us to provide an O(log n{mu}) upper bound on the time it takes for all neurons to achieve good alignment with the input data, where n is the number of data points and mu measures how well the data are separated. After the early alignment phase, the loss converges to zero at a O(1{t}) rate, and the weight matrix on the first layer is approximately low-rank. Numerical experiments on the MNIST dataset illustrate our theoretical findings.

We study the conformal bootstrap of 1D CFTs on the straight Maldacena-Wilson line in 4D {cal N}=4 super-Yang-Mills theory. We introduce an improved truncation scheme with an 'OPE tail' approximation and use it to reproduce the 'bootstrability' results of Cavagli\`a et al. for the OPE-coefficients squared of the first three unprotected operators. For example, for the first OPE-coefficient squared at 't Hooft coupling (4pi)^2, linear-functional methods with two sum rules from integrated correlators give the rigorous result 0.294014873 pm 4.88 cdot 10^{-8}, whereas our methods give with machine-precision computations 0.294014228 pm 6.77 cdot 10^{-7}. For our numerical searches, we benchmark the Reinforcement Learning Soft Actor-Critic algorithm against an Interior Point Method algorithm (IPOPT) and comment on the merits of each algorithm.

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

Extracting causal relationships from observed correlations is a growing area in probabilistic reasoning, originating with the seminal work of Pearl and others from the early 1990s. This paper develops a new, categorically oriented view based on a clear distinction between syntax (string diagrams) and semantics (stochastic matrices), connected via interpretations as structure-preserving functors. A key notion in the identification of causal effects is that of an intervention, whereby a variable is forcefully set to a particular value independent of any prior propensities. We represent the effect of such an intervention as an endofunctor which performs `string diagram surgery' within the syntactic category of string diagrams. This diagram surgery in turn yields a new, interventional distribution via the interpretation functor. While in general there is no way to compute interventional distributions purely from observed data, we show that this is possible in certain special cases using a calculational tool called comb disintegration. We demonstrate the use of this technique on a well-known toy example, where we predict the causal effect of smoking on cancer in the presence of a confounding common cause. After developing this specific example, we show this technique provides simple sufficient conditions for computing interventions which apply to a wide variety of situations considered in the causal inference literature.

We present TransactionGPT (TGPT), a foundation model for consumer transaction data within one of world's largest payment networks. TGPT is designed to understand and generate transaction trajectories while simultaneously supporting a variety of downstream prediction and classification tasks. We introduce a novel 3D-Transformer architecture specifically tailored for capturing the complex dynamics in payment transaction data. This architecture incorporates design innovations that enhance modality fusion and computational efficiency, while seamlessly enabling joint optimization with downstream objectives. Trained on billion-scale real-world transactions, TGPT significantly improves downstream classification performance against a competitive production model and exhibits advantages over baselines in generating future transactions. We conduct extensive empirical evaluations utilizing a diverse collection of company transaction datasets spanning multiple downstream tasks, thereby enabling a thorough assessment of TGPT's effectiveness and efficiency in comparison to established methodologies. Furthermore, we examine the incorporation of LLM-derived embeddings within TGPT and benchmark its performance against fine-tuned LLMs, demonstrating that TGPT achieves superior predictive accuracy as well as faster training and inference. We anticipate that the architectural innovations and practical guidelines from this work will advance foundation models for transaction-like data and catalyze future research in this emerging field.

To measure the difference between two probability distributions, referred to as the source and target, respectively, we exploit both the chain rule and Bayes' theorem to construct conditional transport (CT), which is constituted by both a forward component and a backward one. The forward CT is the expected cost of moving a source data point to a target one, with their joint distribution defined by the product of the source probability density function (PDF) and a source-dependent conditional distribution, which is related to the target PDF via Bayes' theorem. The backward CT is defined by reversing the direction. The CT cost can be approximated by replacing the source and target PDFs with their discrete empirical distributions supported on mini-batches, making it amenable to implicit distributions and stochastic gradient descent-based optimization. When applied to train a generative model, CT is shown to strike a good balance between mode-covering and mode-seeking behaviors and strongly resist mode collapse. On a wide variety of benchmark datasets for generative modeling, substituting the default statistical distance of an existing generative adversarial network with CT is shown to consistently improve the performance. PyTorch code is provided.

A directed acyclic graph (DAG) provides valuable prior knowledge that is often discarded in regression tasks in machine learning. We show that the independences arising from the presence of collider structures in DAGs provide meaningful inductive biases, which constrain the regression hypothesis space and improve predictive performance. We introduce collider regression, a framework to incorporate probabilistic causal knowledge from a collider in a regression problem. When the hypothesis space is a reproducing kernel Hilbert space, we prove a strictly positive generalisation benefit under mild assumptions and provide closed-form estimators of the empirical risk minimiser. Experiments on synthetic and climate model data demonstrate performance gains of the proposed methodology.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

Interpreting the inner function of neural networks is crucial for the trustworthy development and deployment of these black-box models. Prior interpretability methods focus on correlation-based measures to attribute model decisions to individual examples. However, these measures are susceptible to noise and spurious correlations encoded in the model during the training phase (e.g., biased inputs, model overfitting, or misspecification). Moreover, this process has proven to result in noisy and unstable attributions that prevent any transparent understanding of the model's behavior. In this paper, we develop a robust interventional-based method grounded by causal analysis to capture cause-effect mechanisms in pre-trained neural networks and their relation to the prediction. Our novel approach relies on path interventions to infer the causal mechanisms within hidden layers and isolate relevant and necessary information (to model prediction), avoiding noisy ones. The result is task-specific causal explanatory graphs that can audit model behavior and express the actual causes underlying its performance. We apply our method to vision models trained on classification tasks. On image classification tasks, we provide extensive quantitative experiments to show that our approach can capture more stable and faithful explanations than standard attribution-based methods. Furthermore, the underlying causal graphs reveal the neural interactions in the model, making it a valuable tool in other applications (e.g., model repair).

Scaling laws provide important insights that can guide the design of large language models (LLMs). Existing work has primarily focused on studying scaling laws for pretraining (upstream) loss. However, in transfer learning settings, in which LLMs are pretrained on an unsupervised dataset and then finetuned on a downstream task, we often also care about the downstream performance. In this work, we study the scaling behavior in a transfer learning setting, where LLMs are finetuned for machine translation tasks. Specifically, we investigate how the choice of the pretraining data and its size affect downstream performance (translation quality) as judged by two metrics: downstream cross-entropy and BLEU score. Our experiments indicate that the size of the finetuning dataset and the distribution alignment between the pretraining and downstream data significantly influence the scaling behavior. With sufficient alignment, both downstream cross-entropy and BLEU score improve monotonically with more pretraining data. In such cases, we show that it is possible to predict the downstream BLEU score with good accuracy using a log-law. However, there are also cases where moderate misalignment causes the BLEU score to fluctuate or get worse with more pretraining, whereas downstream cross-entropy monotonically improves. By analyzing these observations, we provide new practical insights for choosing appropriate pretraining data.

Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence, an extension of weak convergence that compares a statistic or process to a sequence of evolving processes. Relative weak convergence retains the essential consequences of classical weak convergence and coincides with it under stationarity. Crucially, it applies in general non-stationary settings where classical weak convergence fails. We establish concrete relative CLTs for random vectors and empirical processes, along with sequential, weighted, and bootstrap variants, that parallel the state-of-the-art in stationary settings. Our framework and results offer simple, plug-in replacements for classical CLTs whenever stationarity is untenable, as illustrated by applications in nonparametric trend estimation and hypothesis testing.

In view of the problem that each subchain in the chain-of-model (CoM) relies only on the information of the previous subchain and may lose long-range dependencies due to the causal mask blocking the global context flow between multi-level subchains, this work proposes a graph of causal evolution (GoCE). Its core principle is to map the implicit token representation into a differentiable and sparse causal adjacency matrix, then permeate causal constraints through each layer of calculation using causal-masked attention and causal-MoE. By combining intervention consistency loss test and self-evolution gate, the dynamic balance between causal structure learning and adaptive updating of transformer architecture is realized. The researcher built experimental environments in sandboxes built with Claude Sonnet 4, o4-mini-high, and DeepSeek R1 respectively with the transformer variant architecture introduced in GoCE. It is evaluated on publicly available datasets including CLUTRR, CLADDER, EX-FEVER, and CausalQA and compared with the baseline LLMs. The finding proves that GoCE strengthens the transformer's ability to capture long-range causal dependencies, while the ability to self-evolve is improved. It not only surpasses the design of CoM in terms of design principles, but also provides experience for future research on causal learning and continuous adaptive improvement.

Motivated by the challenge of seamless cross-dataset transfer in EEG signal processing, this article presents an exploratory study on the use of Joint Embedding Predictive Architectures (JEPAs). In recent years, self-supervised learning has emerged as a promising approach for transfer learning in various domains. However, its application to EEG signals remains largely unexplored. In this article, we introduce Signal-JEPA for representing EEG recordings which includes a novel domain-specific spatial block masking strategy and three novel architectures for downstream classification. The study is conducted on a 54 subjects dataset and the downstream performance of the models is evaluated on three different BCI paradigms: motor imagery, ERP and SSVEP. Our study provides preliminary evidence for the potential of JEPAs in EEG signal encoding. Notably, our results highlight the importance of spatial filtering for accurate downstream classification and reveal an influence of the length of the pre-training examples but not of the mask size on the downstream performance.

Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series from different locations often have distinct patterns; and for the same time series, patterns may vary as time goes by. Inspired by the successful applications of deep learning, we propose a new model to resolve the issues of forecasting household leverage in China. Our solution consists of multiple RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal pattern of a specific series with multivariate exogenous series, and then the attention layer learns the spatial correlative weight and obtains the global representations simultaneously. The results show that the new approach can capture the temporal-spatial dynamics of household leverage well and get more accurate and solid predictive results. More, the simulation also studies show that clustering and choosing correlative series are necessary to obtain accurate forecasting results.

Human body trajectories are a salient cue to identify actions in the video. Such body trajectories are mainly conveyed by hands and face across consecutive frames in sign language. However, current methods in continuous sign language recognition (CSLR) usually process frames independently, thus failing to capture cross-frame trajectories to effectively identify a sign. To handle this limitation, we propose correlation network (CorrNet) to explicitly capture and leverage body trajectories across frames to identify signs. In specific, a correlation module is first proposed to dynamically compute correlation maps between the current frame and adjacent frames to identify trajectories of all spatial patches. An identification module is then presented to dynamically emphasize the body trajectories within these correlation maps. As a result, the generated features are able to gain an overview of local temporal movements to identify a sign. Thanks to its special attention on body trajectories, CorrNet achieves new state-of-the-art accuracy on four large-scale datasets, i.e., PHOENIX14, PHOENIX14-T, CSL-Daily, and CSL. A comprehensive comparison with previous spatial-temporal reasoning methods verifies the effectiveness of CorrNet. Visualizations demonstrate the effects of CorrNet on emphasizing human body trajectories across adjacent frames.

Redundancies and correlations in the responses of sensory neurons seem to waste neural resources but can carry cues about structured stimuli and may help the brain to correct for response errors. To assess how the retina negotiates this tradeoff, we measured simultaneous responses from populations of ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure. We found that pairwise correlations in the retinal output remained similar across stimuli with widely different spatio-temporal correlations including white noise and natural movies. Meanwhile, purely spatial correlations tended to increase correlations in the retinal response. Responding to more correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the similarity of pairwise correlations across stimuli where receptive field measurements were possible.

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.

Autoregressive (AR) models for image generation typically adopt a two-stage paradigm of vector quantization and raster-scan ``next-token prediction", inspired by its great success in language modeling. However, due to the huge modality gap, image autoregressive models may require a systematic reevaluation from two perspectives: tokenizer format and regression direction. In this paper, we introduce the frequency progressive autoregressive (FAR) paradigm and instantiate FAR with the continuous tokenizer. Specifically, we identify spectral dependency as the desirable regression direction for FAR, wherein higher-frequency components build upon the lower one to progressively construct a complete image. This design seamlessly fits the causality requirement for autoregressive models and preserves the unique spatial locality of image data. Besides, we delve into the integration of FAR and the continuous tokenizer, introducing a series of techniques to address optimization challenges and improve the efficiency of training and inference processes. We demonstrate the efficacy of FAR through comprehensive experiments on the ImageNet dataset and verify its potential on text-to-image generation.

Solving Bayesian inverse problems efficiently remains a significant challenge due to the complexity of posterior distributions and the computational cost of traditional sampling methods. Given a series of observations and the forward model, we want to recover the distribution of the parameters, conditioned on observed experimental data. We show, that combining Conditional Flow Mathching (CFM) with transformer-based architecture, we can efficiently sample from such kind of distribution, conditioned on variable number of observations.

This paper develops a framework to predict toxic trades that a broker receives from her clients. Toxic trades are predicted with a novel online learning Bayesian method which we call the projection-based unification of last-layer and subspace estimation (PULSE). PULSE is a fast and statistically-efficient Bayesian procedure for online training of neural networks. We employ a proprietary dataset of foreign exchange transactions to test our methodology. Neural networks trained with PULSE outperform standard machine learning and statistical methods when predicting if a trade will be toxic; the benchmark methods are logistic regression, random forests, and a recursively-updated maximum-likelihood estimator. We devise a strategy for the broker who uses toxicity predictions to internalise or to externalise each trade received from her clients. Our methodology can be implemented in real-time because it takes less than one millisecond to update parameters and make a prediction. Compared with the benchmarks, online learning of a neural network with PULSE attains the highest PnL and avoids the most losses by externalising toxic trades.

Backpropagation, which uses the chain rule, is the de-facto standard algorithm for optimizing neural networks nowadays. Recently, Hinton (2022) proposed the forward-forward algorithm, a promising alternative that optimizes neural nets layer-by-layer, without propagating gradients throughout the network. Although such an approach has several advantages over back-propagation and shows promising results, the fact that each layer is being trained independently limits the optimization process. Specifically, it prevents the network's layers from collaborating to learn complex and rich features. In this work, we study layer collaboration in the forward-forward algorithm. We show that the current version of the forward-forward algorithm is suboptimal when considering information flow in the network, resulting in a lack of collaboration between layers of the network. We propose an improved version that supports layer collaboration to better utilize the network structure, while not requiring any additional assumptions or computations. We empirically demonstrate the efficacy of the proposed version when considering both information flow and objective metrics. Additionally, we provide a theoretical motivation for the proposed method, inspired by functional entropy theory.

We present STream3R, a novel approach to 3D reconstruction that reformulates pointmap prediction as a decoder-only Transformer problem. Existing state-of-the-art methods for multi-view reconstruction either depend on expensive global optimization or rely on simplistic memory mechanisms that scale poorly with sequence length. In contrast, STream3R introduces an streaming framework that processes image sequences efficiently using causal attention, inspired by advances in modern language modeling. By learning geometric priors from large-scale 3D datasets, STream3R generalizes well to diverse and challenging scenarios, including dynamic scenes where traditional methods often fail. Extensive experiments show that our method consistently outperforms prior work across both static and dynamic scene benchmarks. Moreover, STream3R is inherently compatible with LLM-style training infrastructure, enabling efficient large-scale pretraining and fine-tuning for various downstream 3D tasks. Our results underscore the potential of causal Transformer models for online 3D perception, paving the way for real-time 3D understanding in streaming environments. More details can be found in our project page: https://nirvanalan.github.io/projects/stream3r.

In recent years, there has been a wide interest in designing deep neural network-based models that automate downstream software engineering tasks on source code, such as code document generation, code search, and program repair. Although the main objective of these studies is to improve the effectiveness of the downstream task, many studies only attempt to employ the next best neural network model, without a proper in-depth analysis of why a particular solution works or does not, on particular tasks or scenarios. In this paper, using an example eXplainable AI (XAI) method (attention mechanism), we study two recent large language models (LLMs) for code (CodeBERT and GraphCodeBERT) on a set of software engineering downstream tasks: code document generation (CDG), code refinement (CR), and code translation (CT). Through quantitative and qualitative studies, we identify what CodeBERT and GraphCodeBERT learn (put the highest attention on, in terms of source code token types), on these tasks. We also show some of the common patterns when the model does not work as expected (performs poorly even on easy problems) and suggest recommendations that may alleviate the observed challenges.

Current Chain-of-Thought (CoT) verification methods predict reasoning correctness based on outputs (black-box) or activations (gray-box), but offer limited insight into why a computation fails. We introduce a white-box method: Circuit-based Reasoning Verification (CRV). We hypothesize that attribution graphs of correct CoT steps, viewed as execution traces of the model's latent reasoning circuits, possess distinct structural fingerprints from those of incorrect steps. By training a classifier on structural features of these graphs, we show that these traces contain a powerful signal of reasoning errors. Our white-box approach yields novel scientific insights unattainable by other methods. (1) We demonstrate that structural signatures of error are highly predictive, establishing the viability of verifying reasoning directly via its computational graph. (2) We find these signatures to be highly domain-specific, revealing that failures in different reasoning tasks manifest as distinct computational patterns. (3) We provide evidence that these signatures are not merely correlational; by using our analysis to guide targeted interventions on individual transcoder features, we successfully correct the model's faulty reasoning. Our work shows that, by scrutinizing a model's computational process, we can move from simple error detection to a deeper, causal understanding of LLM reasoning.

Deep Learning using the eponymous deep neural networks (DNNs) has become an attractive approach towards various data-based problems of theoretical physics in the past decade. There has been a clear trend to deeper architectures containing increasingly more powerful and involved layers. Contrarily, Taylor coefficients of DNNs still appear mainly in the light of interpretability studies, where they are computed at most to first order. However, especially in theoretical physics numerous problems benefit from accessing higher orders, as well. This gap motivates a general formulation of neural network (NN) Taylor expansions. Restricting our analysis to multilayer perceptrons (MLPs) and introducing quantities we refer to as propagators and vertices, both depending on the MLP's weights and biases, we establish a graph-theoretical approach. Similarly to Feynman rules in quantum field theories, we can systematically assign diagrams containing propagators and vertices to the corresponding partial derivative. Examining this approach for S-wave scattering lengths of shallow potentials, we observe NNs to adapt their derivatives mainly to the leading order of the target function's Taylor expansion. To circumvent this problem, we propose an iterative NN perturbation theory. During each iteration we eliminate the leading order, such that the next-to-leading order can be faithfully learned during the subsequent iteration. After performing two iterations, we find that the first- and second-order Born terms are correctly adapted during the respective iterations. Finally, we combine both results to find a proxy that acts as a machine-learned second-order Born approximation.

Deep models have demonstrated remarkable performance in time series forecasting. However, due to the partially-observed nature of real-world applications, solely focusing on the target of interest, so-called endogenous variables, is usually insufficient to guarantee accurate forecasting. Notably, a system is often recorded into multiple variables, where the exogenous variables can provide valuable external information for endogenous variables. Thus, unlike well-established multivariate or univariate forecasting paradigms that either treat all the variables equally or ignore exogenous information, this paper focuses on a more practical setting: time series forecasting with exogenous variables. We propose a novel approach, TimeXer, to ingest external information to enhance the forecasting of endogenous variables. With deftly designed embedding layers, TimeXer empowers the canonical Transformer with the ability to reconcile endogenous and exogenous information, where patch-wise self-attention and variate-wise cross-attention are used simultaneously. Moreover, global endogenous tokens are learned to effectively bridge the causal information underlying exogenous series into endogenous temporal patches. Experimentally, TimeXer achieves consistent state-of-the-art performance on twelve real-world forecasting benchmarks and exhibits notable generality and scalability. Code is available at this repository: https://github.com/thuml/TimeXer.

Ensuring vertical separation is a key means of maintaining safe separation between aircraft in congested airspace. Aircraft trajectories are modelled in the presence of significant epistemic uncertainty, leading to discrepancies between observed trajectories and the predictions of deterministic models, hampering the task of planning to ensure safe separation. In this paper a probabilistic model is presented, for the purpose of emulating the trajectories of aircraft in climb and bounding the uncertainty of the predicted trajectory. A monotonic, functional representation exploits the spatio-temporal correlations in the radar observations. Through the use of Gaussian Process Emulators, features that parameterise the climb are mapped directly to functional outputs, providing a fast approximation, while ensuring that the resulting trajectory is monotonic. The model was applied as a probabilistic digital twin for aircraft in climb and baselined against BADA, a deterministic model widely used in industry. When applied to an unseen test dataset, the probabilistic model was found to provide a mean prediction that was 21% more accurate, with a 34% sharper forecast.

Time-series causal discovery (TSCD) is a fundamental problem of machine learning. However, existing synthetic datasets cannot properly evaluate or predict the algorithms' performance on real data. This study introduces the CausalTime pipeline to generate time-series that highly resemble the real data and with ground truth causal graphs for quantitative performance evaluation. The pipeline starts from real observations in a specific scenario and produces a matching benchmark dataset. Firstly, we harness deep neural networks along with normalizing flow to accurately capture realistic dynamics. Secondly, we extract hypothesized causal graphs by performing importance analysis on the neural network or leveraging prior knowledge. Thirdly, we derive the ground truth causal graphs by splitting the causal model into causal term, residual term, and noise term. Lastly, using the fitted network and the derived causal graph, we generate corresponding versatile time-series proper for algorithm assessment. In the experiments, we validate the fidelity of the generated data through qualitative and quantitative experiments, followed by a benchmarking of existing TSCD algorithms using these generated datasets. CausalTime offers a feasible solution to evaluating TSCD algorithms in real applications and can be generalized to a wide range of fields. For easy use of the proposed approach, we also provide a user-friendly website, hosted on www.causaltime.cc.

Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series. In this context a fundamental problem is that of motif mining, where we seek patterns repeating twice with minor variations, spanning some of the dimensions. State of the art exact solutions for this problem run in time quadratic in the length of the input time series. We provide a scalable method to find the top-k motifs in multidimensional time series with probabilistic guarantees on the quality of the results. Our algorithm runs in time subquadratic in the length of the input, and returns the exact solution with probability at least 1-δ, where δ is a user-defined parameter. The algorithm is designed to be adaptive to the input distribution, self-tuning its parameters while respecting user-defined limits on the memory to use. Our theoretical analysis is complemented by an extensive experimental evaluation, showing that our algorithm is orders of magnitude faster than the state of the art.

A fully differential calculation in perturbative quantum chromodynamics is presented for the production of massive photon pairs at hadron colliders. All next-to-leading order perturbative contributions from quark-antiquark, gluon-(anti)quark, and gluon-gluon subprocesses are included, as well as all-orders resummation of initial-state gluon radiation valid at next-to-next-to-leading logarithmic accuracy. The region of phase space is specified in which the calculation is most reliable. Good agreement is demonstrated with data from the Fermilab Tevatron, and predictions are made for more detailed tests with CDF and DO data. Predictions are shown for distributions of diphoton pairs produced at the energy of the Large Hadron Collider (LHC). Distributions of the diphoton pairs from the decay of a Higgs boson are contrasted with those produced from QCD processes at the LHC, showing that enhanced sensitivity to the signal can be obtained with judicious selection of events.

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs). However, standard MLP-based PINNs often fail to converge when dealing with complex initial value problems, leading to solutions that violate causality and suffer from a spectral bias towards low-frequency components. To address these issues, we introduce NeuSA (Neuro-Spectral Architectures), a novel class of PINNs inspired by classical spectral methods, designed to solve linear and nonlinear PDEs with variable coefficients. NeuSA learns a projection of the underlying PDE onto a spectral basis, leading to a finite-dimensional representation of the dynamics which is then integrated with an adapted Neural ODE (NODE). This allows us to overcome spectral bias, by leveraging the high-frequency components enabled by the spectral representation; to enforce causality, by inheriting the causal structure of NODEs, and to start training near the target solution, by means of an initialization scheme based on classical methods. We validate NeuSA on canonical benchmarks for linear and nonlinear wave equations, demonstrating strong performance as compared to other architectures, with faster convergence, improved temporal consistency and superior predictive accuracy. Code and pretrained models are available in https://github.com/arthur-bizzi/neusa.

How do we transfer the relevant knowledge from ever larger foundation models into small, task-specific downstream models that can run at much lower costs? Standard transfer learning using pre-trained weights as the initialization transfers limited information and commits us to often massive pre-trained architectures. This procedure also precludes combining multiple pre-trained models that learn complementary information. To address these shortcomings, we introduce Adaptive Feature Transfer (AFT). Instead of transferring weights, AFT operates purely on features, thereby decoupling the choice of the pre-trained model from the smaller downstream model. Rather than indiscriminately compressing all pre-trained features, AFT adaptively transfers pre-trained features that are most useful for performing the downstream task, using a simple regularization that adds minimal overhead. Across multiple vision, language, and multi-modal datasets, AFT achieves significantly better downstream performance compared to alternatives with a similar computational cost. Furthermore, AFT reliably translates improvement in pre-trained models into improvement in downstream performance, even if the downstream model is over 50times smaller, and can effectively transfer complementary information learned by multiple pre-trained models.

Detector simulations are an exciting application of modern generative networks. Their sparse high-dimensional data combined with the required precision poses a serious challenge. We show how combining Conditional Flow Matching with transformer elements allows us to simulate the detector phase space reliably. Namely, we use an autoregressive transformer to simulate the energy of each layer, and a vision transformer for the high-dimensional voxel distributions. We show how dimension reduction via latent diffusion allows us to train more efficiently and how diffusion networks can be evaluated faster with bespoke solvers. We showcase our framework, CaloDREAM, on datasets 2 and 3 of the CaloChallenge.

Learning behavioral patterns from observational data has been a de-facto approach to motion forecasting. Yet, the current paradigm suffers from two shortcomings: brittle under distribution shifts and inefficient for knowledge transfer. In this work, we propose to address these challenges from a causal representation perspective. We first introduce a causal formalism of motion forecasting, which casts the problem as a dynamic process with three groups of latent variables, namely invariant variables, style confounders, and spurious features. We then introduce a learning framework that treats each group separately: (i) unlike the common practice mixing datasets collected from different locations, we exploit their subtle distinctions by means of an invariance loss encouraging the model to suppress spurious correlations; (ii) we devise a modular architecture that factorizes the representations of invariant mechanisms and style confounders to approximate a sparse causal graph; (iii) we introduce a style contrastive loss that not only enforces the structure of style representations but also serves as a self-supervisory signal for test-time refinement on the fly. Experiments on synthetic and real datasets show that our proposed method improves the robustness and reusability of learned motion representations, significantly outperforming prior state-of-the-art motion forecasting models for out-of-distribution generalization and low-shot transfer.

Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and cannot be easily accelerated with parallel computing. To enable parallelization, we frame the task of feedforward computation as solving a system of nonlinear equations. We then propose to find the solution using a Jacobi or Gauss-Seidel fixed-point iteration method, as well as hybrid methods of both. Crucially, Jacobi updates operate independently on each equation and can be executed in parallel. Our method is guaranteed to give exactly the same values as the original feedforward computation with a reduced (or equal) number of parallelizable iterations, and hence reduced time given sufficient parallel computing power. Experimentally, we demonstrate the effectiveness of our approach in accelerating (i) backpropagation of RNNs, (ii) evaluation of DenseNets, and (iii) autoregressive sampling of MADE and PixelCNN++, with speedup factors between 2.1 and 26 under various settings.

A modern challenge of Artificial Intelligence is learning multiple patterns at once (i.e.parallel learning). While this can not be accomplished by standard Hebbian associative neural networks, in this paper we show how the Multitasking Hebbian Network (a variation on theme of the Hopfield model working on sparse data-sets) is naturally able to perform this complex task. We focus on systems processing in parallel a finite (up to logarithmic growth in the size of the network) amount of patterns, mirroring the low-storage level of standard associative neural networks at work with pattern recognition. For mild dilution in the patterns, the network handles them hierarchically, distributing the amplitudes of their signals as power-laws w.r.t. their information content (hierarchical regime), while, for strong dilution, all the signals pertaining to all the patterns are raised with the same strength (parallel regime). Further, confined to the low-storage setting (i.e., far from the spin glass limit), the presence of a teacher neither alters the multitasking performances nor changes the thresholds for learning: the latter are the same whatever the training protocol is supervised or unsupervised. Results obtained through statistical mechanics, signal-to-noise technique and Monte Carlo simulations are overall in perfect agreement and carry interesting insights on multiple learning at once: for instance, whenever the cost-function of the model is minimized in parallel on several patterns (in its description via Statistical Mechanics), the same happens to the standard sum-squared error Loss function (typically used in Machine Learning).

Multi-path speculative decoding accelerates lossless sampling from a target model by using a cheaper draft model to generate a draft tree of tokens, and then applies a verification algorithm that accepts a subset of these. While prior work has proposed various verification algorithms for i.i.d rollouts, their relative performance under matched settings remains unclear. In this work, we firstly present a systematic evaluation of verification strategies across model families, tasks, and sampling regimes, and find that Traversal Verification dominates consistently, with OT-based methods lagging far behind. Our analysis uncovers that this occurs because OT-based methods achieve high multi-token acceptance near the root of the draft tree, while multi-token gains are most impactful deeper in the draft tree, where draft and target distributions diverge. Based on this insight, we propose delayed tree expansion, which drafts a partial single path, delaying the i.i.d. branching point. We show that delayed tree expansion preserves the target distribution and improves on root-node i.i.d rollouts. Further, we develop a dynamic neural selector that estimates the expected block efficiency of optimal-transport-based verification methods from draft and target features, enabling context-dependent expansion decisions. Our neural selector allows OT-based methods like SpecInfer to outperform Traversal Verification for the first time, achieving 5% higher average throughput across a wide range of models, datasets, and sampling settings.

Indonesia's nickel ore export ban has driven rapid expansion of smelting and hydrometallurgical processing capacity at the Indonesia Morowali Industrial Park (IMIP), now the world's largest integrated nickel processing complex, on the coast of Central Sulawesi. Whether this industrialization has degraded the adjacent marine environment remains unquantified. We apply Bayesian structural time-series (BSTS) causal inference to a multi-decadal, multi-sensor satellite ocean color record of the diffuse attenuation coefficient at 490 nm, K_d(490), to test for a causal link between IMIP expansion and nearshore turbidity change. A consensus structural breakpoint, a significant posterior causal effect estimated against a Banda Sea counterfactual, and a distribution-free placebo rank test collectively establish that coastal water clarity deteriorated after the transition from initial nickel pig iron production to hyper-expansion of high-pressure acid leaching facilities for battery-grade nickel. Satellite-derived land cover analysis independently corroborates this timing, showing substantial built-area growth and concurrent tree cover loss within the IMIP footprint. The resulting euphotic zone shoaling occurs in oligotrophic waters supporting high marine biodiversity, where even moderate optical degradation may impair coral photosynthesis and compress depth-dependent reef habitat. These findings quantify a marine environmental cost absent from Indonesia's mineral downstreaming policy discourse and demonstrate a transferable, satellite-based quasi-experimental framework for causal impact assessment at coastal industrial sites in data-limited tropical settings.

Coincident multimessenger observations of cosmic sources can offer numerous benefits, especially when used in the context of synergistic astrophysics. One significant advantage is enhancing the detection significance of separate detectors by correlating their data and assuming joint emission. We have formulated an approach for updating the Bayesian posterior probability of an astrophysical origin, namely p_{rm astro}, relying on multimessenger coincidences assuming an emission model. The description is applicable to any combination of messengers. We demonstrated the formalism for the gravitational waves and high-energy neutrinos case. Applying our method to the public data of candidate coincident high-energy neutrinos with subthreshold gravitational-wave triggers, we found that in the case of highly energetic neutrino coincidences, p_{rm astro} can increase from approximately sim 0.1 to sim 0.9. The amount of improvement depends on the assumed joint emission model. If models are trusted, the marked improvement makes subthreshold detections much more confident. Moreover, the model dependency can also be used to test the consistency of different models. This work is a crucial step toward the goal of uniting all detectors on equal footing into a statistically integrated, Earth-sized observatory for comprehensive multimessenger astrophysics.

Measuring the coherence of text is a vital aspect of evaluating the quality of written content. Recent advancements in neural coherence modeling have demonstrated their efficacy in capturing entity coreference and discourse relations, thereby enhancing coherence evaluation. However, many existing methods heavily depend on static embeddings or focus narrowly on nearby context, constraining their capacity to measure the overarching coherence of long texts. In this paper, we posit that coherent texts inherently manifest a sequential and cohesive interplay among sentences, effectively conveying the central theme, purpose, or standpoint. To explore this abstract relationship, we introduce the "BBScore," a novel reference-free metric grounded in Brownian bridge theory for assessing text coherence. Our findings showcase that when synergized with a simple additional classification component, this metric attains a performance level comparable to state-of-the-art techniques on standard artificial discrimination tasks. We also establish in downstream tasks that this metric effectively differentiates between human-written documents and text generated by large language models under a specific domain. Furthermore, we illustrate the efficacy of this approach in detecting written styles attributed to diverse large language models, underscoring its potential for generalizability. In summary, we present a novel Brownian bridge coherence metric capable of measuring both local and global text coherence, while circumventing the need for end-to-end model training. This flexibility allows for its application in various downstream tasks.

Quantifying the causal influence of input features within neural networks has become a topic of increasing interest. Existing approaches typically assess direct, indirect, and total causal effects. This work treats NNs as structural causal models (SCMs) and extends our focus to include intrinsic causal contributions (ICC). We propose an identifiable generative post-hoc framework for quantifying ICC. We also draw a relationship between ICC and Sobol' indices. Our experiments on synthetic and real-world datasets demonstrate that ICC generates more intuitive and reliable explanations compared to existing global explanation techniques.

Long-tailed learning has garnered increasing attention due to its practical significance. Among the various approaches, the fine-tuning paradigm has gained considerable interest with the advent of foundation models. However, most existing methods primarily focus on leveraging knowledge from these models, overlooking the inherent biases introduced by the imbalanced training data they rely on. In this paper, we examine how such imbalances from pre-training affect long-tailed downstream tasks. Specifically, we find the imbalance biases inherited in foundation models on downstream task as parameter imbalance and data imbalance. During fine-tuning, we observe that parameter imbalance plays a more critical role, while data imbalance can be mitigated using existing re-balancing strategies. Moreover, we find that parameter imbalance cannot be effectively addressed by current re-balancing techniques, such as adjusting the logits, during training, unlike data imbalance. To tackle both imbalances simultaneously, we build our method on causal learning and view the incomplete semantic factor as the confounder, which brings spurious correlations between input samples and labels. To resolve the negative effects of this, we propose a novel backdoor adjustment method that learns the true causal effect between input samples and labels, rather than merely fitting the correlations in the data. Notably, we achieve an average performance increase of about 1.67% on each dataset.

Normalizing Flows (NFs) have been established as a principled framework for generative modeling. Standard NFs consist of a forward process and a reverse process: the forward process maps data to noise, while the reverse process generates samples by inverting it. Typical NF forward transformations are constrained by explicit invertibility, ensuring that the reverse process can serve as their exact analytic inverse. Recent developments in TARFlow and its variants have revitalized NF methods by combining Transformers and autoregressive flows, but have also exposed causal decoding as a major bottleneck. In this work, we introduce Bidirectional Normalizing Flow (BiFlow), a framework that removes the need for an exact analytic inverse. BiFlow learns a reverse model that approximates the underlying noise-to-data inverse mapping, enabling more flexible loss functions and architectures. Experiments on ImageNet demonstrate that BiFlow, compared to its causal decoding counterpart, improves generation quality while accelerating sampling by up to two orders of magnitude. BiFlow yields state-of-the-art results among NF-based methods and competitive performance among single-evaluation ("1-NFE") methods. Following recent encouraging progress on NFs, we hope our work will draw further attention to this classical paradigm.

Learning causal structure from observational data often assumes that we observe independent and identically distributed (i.\,i.\,d) data. The traditional approach aims to find a graphical representation that encodes the same set of conditional independence relationships as those present in the observed distribution. It is known that under i.\,i.\,d assumption, even with infinite data, there is a limit to how fine-grained a causal structure we can identify. To overcome this limitation, recent work has explored using data originating from different, related environments to learn richer causal structure. These approaches implicitly rely on the independent causal mechanisms (ICM) principle, which postulates that the mechanism giving rise to an effect given its causes and the mechanism which generates the causes do not inform or influence each other. Thus, components of the causal model can independently change from environment to environment. Despite its wide application in machine learning and causal inference, there is a lack of statistical formalization of the ICM principle and how it enables identification of richer causal structures from grouped data. Here we present new causal de Finetti theorems which offer a first statistical formalization of ICM principle and show how causal structure identification is possible from exchangeable data. Our work provides theoretical justification for a broad range of techniques leveraging multi-environment data to learn causal structure.

We introduce directional routing, a lightweight mechanism that gives each transformer attention head learned suppression directions controlled by a shared router, at 3.9% parameter cost. We train a 433M-parameter model alongside an identical baseline in a single run, then trace the resulting circuits through mechanistic interpretability. Routing becomes the model's dominant computational pathway. Disabling it collapses factual recall to near-zero probability across all 8 test prompts and drops induction accuracy from 93.4% to 0.0%. Knocking out individual attention heads has negligible effect: the primary mover head's removal actually increases target probability, and induction heads retain 98.6% accuracy without their strongest member. The coordination mechanism is irreplaceable; the components it coordinates are not. The model also self-organizes, without explicit pressure, into two regimes: domain-adaptive routing in early layers and fixed syntactic pruning in late layers, where the least-varying layer is the most critical (+42.6 PPL when disabled). Routing reduces perplexity 31-56% relative to the baseline, though downstream multiple-choice benchmarks do not yet reflect these gains.

Understanding the performance of machine learning (ML) models across diverse data distributions is critically important for reliable applications. Despite recent empirical studies positing a near-perfect linear correlation between in-distribution (ID) and out-of-distribution (OOD) accuracies, we empirically demonstrate that this correlation is more nuanced under subpopulation shifts. Through rigorous experimentation and analysis across a variety of datasets, models, and training epochs, we demonstrate that OOD performance often has a nonlinear correlation with ID performance in subpopulation shifts. Our findings, which contrast previous studies that have posited a linear correlation in model performance during distribution shifts, reveal a "moon shape" correlation (parabolic uptrend curve) between the test performance on the majority subpopulation and the minority subpopulation. This non-trivial nonlinear correlation holds across model architectures, hyperparameters, training durations, and the imbalance between subpopulations. Furthermore, we found that the nonlinearity of this "moon shape" is causally influenced by the degree of spurious correlations in the training data. Our controlled experiments show that stronger spurious correlation in the training data creates more nonlinear performance correlation. We provide complementary experimental and theoretical analyses for this phenomenon, and discuss its implications for ML reliability and fairness. Our work highlights the importance of understanding the nonlinear effects of model improvement on performance in different subpopulations, and has the potential to inform the development of more equitable and responsible machine learning models.

Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a surprisingly underexplored topic, despite their applicability to ubiquitous domains including source code and logic circuits. In this work, we propose two direction- and structure-aware positional encodings for directed graphs: (1) the eigenvectors of the Magnetic Laplacian - a direction-aware generalization of the combinatorial Laplacian; (2) directional random walk encodings. Empirically, we show that the extra directionality information is useful in various downstream tasks, including correctness testing of sorting networks and source code understanding. Together with a data-flow-centric graph construction, our model outperforms the prior state of the art on the Open Graph Benchmark Code2 relatively by 14.7%.

In modern large-scale deep learning, a prevalent and effective workflow for solving low-data problems is adapting powerful pre-trained foundation models (FMs) to new tasks via parameter-efficient fine-tuning (PEFT). However, while empirically effective, the resulting solutions lack generalisation guarantees to certify their accuracy - which may be required for ethical or legal reasons prior to deployment in high-importance applications. In this paper we develop a novel transfer learning approach that is designed to facilitate non-vacuous learning theoretic generalisation guarantees for downstream tasks, even in the low-shot regime. Specifically, we first use upstream tasks to train a distribution over PEFT parameters. We then learn the downstream task by a sample-and-evaluate procedure -- sampling plausible PEFTs from the trained diffusion model and selecting the one with the highest likelihood on the downstream data. Crucially, this confines our model hypothesis to a finite set of PEFT samples. In contrast to learning in the typical continuous hypothesis spaces of neural network weights, this facilitates tighter risk certificates. We instantiate our bound and show non-trivial generalization guarantees compared to existing learning approaches which lead to vacuous bounds in the low-shot regime.

This work introduces a novel graph neural networks (GNNs)-based method to predict stream water temperature and reduce model bias across locations of different income and education levels. Traditional physics-based models often have limited accuracy because they are necessarily approximations of reality. Recently, there has been an increasing interest of using GNNs in modeling complex water dynamics in stream networks. Despite their promise in improving the accuracy, GNNs can bring additional model bias through the aggregation process, where node features are updated by aggregating neighboring nodes. The bias can be especially pronounced when nodes with similar sensitive attributes are frequently connected. We introduce a new method that leverages physical knowledge to represent the node influence in GNNs, and then utilizes physics-based influence to refine the selection and weights over the neighbors. The objective is to facilitate equitable treatment over different sensitive groups in the graph aggregation, which helps reduce spatial bias over locations, especially for those in underprivileged groups. The results on the Delaware River Basin demonstrate the effectiveness of the proposed method in preserving equitable performance across locations in different sensitive groups.

Many approaches have been proposed to use diffusion models to augment training datasets for downstream tasks, such as classification. However, diffusion models are themselves trained on large datasets, often with noisy annotations, and it remains an open question to which extent these models contribute to downstream classification performance. In particular, it remains unclear if they generalize enough to improve over directly using the additional data of their pre-training process for augmentation. We systematically evaluate a range of existing methods to generate images from diffusion models and study new extensions to assess their benefit for data augmentation. Personalizing diffusion models towards the target data outperforms simpler prompting strategies. However, using the pre-training data of the diffusion model alone, via a simple nearest-neighbor retrieval procedure, leads to even stronger downstream performance. Our study explores the potential of diffusion models in generating new training data, and surprisingly finds that these sophisticated models are not yet able to beat a simple and strong image retrieval baseline on simple downstream vision tasks.

Many papers have shown that attention heads work in conjunction with each other to perform complex tasks. It's frequently assumed that communication between attention heads is via the addition of specific features to token residuals. In this work we seek to isolate and identify the features used to effect communication and coordination among attention heads in GPT-2 small. Our key leverage on the problem is to show that these features are very often sparsely coded in the singular vectors of attention head matrices. We characterize the dimensionality and occurrence of these signals across the attention heads in GPT-2 small when used for the Indirect Object Identification (IOI) task. The sparse encoding of signals, as provided by attention head singular vectors, allows for efficient separation of signals from the residual background and straightforward identification of communication paths between attention heads. We explore the effectiveness of this approach by tracing portions of the circuits used in the IOI task. Our traces reveal considerable detail not present in previous studies, shedding light on the nature of redundant paths present in GPT-2. And our traces go beyond previous work by identifying features used to communicate between attention heads when performing IOI.

Correlative computational microscopy is accelerating the mapping of dynamic biological systems by integrating morphological and molecular measurements across spatial scales, from organelles to entire organisms. Visualization, measurement, and prediction of interactions among the components of biological systems can be accelerated by generalist computational imaging frameworks that relax the trade-offs imposed by multiplex dynamic imaging. This work reports a generalist framework for wave optical imaging of the architectural order (waveOrder) among biomolecules for encoding and decoding multiple specimen properties from a minimal set of acquired channels, with or without fluorescent labels. waveOrder expresses material properties in terms of elegant physically motivated basis vectors directly interpretable as phase, absorption, birefringence, diattenuation, and fluorophore density; and it expresses image data in terms of directly measurable Stokes parameters. We report a corresponding multi-channel reconstruction algorithm to recover specimen properties in multiple contrast modes. With this framework, we implement multiple 3D computational microscopy methods, including quantitative phase imaging, quantitative label-free imaging with phase and polarization, and fluorescence deconvolution imaging, across scales ranging from organelles to whole zebrafish. These advances are available via an extensible open-source computational imaging library, waveOrder, and a napari plugin, recOrder.

In standard causal attention, each token's query, key, and value (QKV) are static and encode only preceding context. We introduce CAuSal aTtention with Lookahead kEys (CASTLE), an attention mechanism that continually updates each token's keys as the context unfolds. We term these updated keys lookahead keys because they belong to earlier positions yet integrate information from tokens that appear later relative to those positions, while strictly preserving the autoregressive property. Although the mechanism appears sequential, we derive a mathematical equivalence that avoids explicitly materializing lookahead keys at each position and enables efficient parallel training. On language modeling benchmarks, CASTLE consistently outperforms standard causal attention across model scales, reducing validation perplexity and improving performance on a range of downstream tasks.

Open-ended text generation with autoregressive language models (LMs) is one of the core tasks in natural language processing. However, maximization-based decoding methods (e.g., greedy/beam search) often lead to the degeneration problem, i.e., the generated text is unnatural and contains undesirable repetitions. Existing solutions to this problem either introduce randomness prone to incoherence or require a look-ahead mechanism that demands extra computational overhead. In this study, we formulate open-ended text generation from a new perspective, i.e., we view it as an exploration process within a directed graph. Thereby, we understand the phenomenon of degeneration as circular loops within the directed graph. Based on our formulation, we propose a novel decoding method -- momentum decoding -- which encourages the LM to greedily explore new nodes outside the current graph. Meanwhile, it also allows the LM to return to the existing nodes with a momentum downgraded by a pre-defined resistance function. We extensively test our approach on three benchmarks from different domains through automatic and human evaluations. The results show that momentum decoding performs comparably with the current state of the art while enjoying notably improved inference speed and computation FLOPs. Furthermore, we conduct a detailed analysis to reveal the merits and inner workings of our approach. Our codes and other related resources are publicly available at https://github.com/gmftbyGMFTBY/MomentumDecoding.

While explicit positional encodings such as RoPE are a primary source of positional information in Transformer decoders, the causal mask also provides positional information. In this work, we prove that the causal mask can induce position-dependent patterns in attention scores, even without parameters or causal dependency in the input. Our theoretical analysis indicates that the induced attention pattern tends to favor nearby query-key pairs, mirroring the behavior of common positional encodings. Empirical analysis confirms that trained models exhibit the same behavior, with learned parameters further amplifying these patterns. Notably, we found that the interaction of causal mask and RoPE distorts RoPE's relative attention score patterns into non-relative ones. We consistently observed this effect in modern large language models, suggesting the importance of considering the causal mask as a source of positional information alongside explicit positional encodings.