Daily Papers

Visual Language Models (VLMs) have achieved remarkable progress, yet their reliability under small, meaning-preserving input changes remains poorly understood. We present the first large-scale, systematic study of VLM robustness to benign visual and textual perturbations: pixel-level shifts, light geometric transformations, padded rescaling, paraphrasing, and multilingual rewrites that do not alter the underlying semantics of an image-question pair. Across a broad set of models and datasets, we find that modern VLMs are highly sensitive to such minor perturbations: a substantial fraction of samples change their predicted answer under at least one visual or textual modification. We characterize how this instability varies across perturbation types, question categories, and models, revealing that even state-of-the-art systems (e.g., GPT-4o, Gemini 2.0 Flash) frequently fail under shifts as small as a few pixels or harmless rephrasings. We further show that sample-level stability serves as a strong indicator of correctness: stable samples are consistently far more likely to be answered correctly. Leveraging this, we demonstrate that the stability patterns of small, accessible open-source models can be used to predict the correctness of much larger closed-source models with high precision. Our findings expose a fundamental fragility in current VLMs and highlight the need for robustness evaluations that go beyond adversarial perturbations, focusing instead on invariances that models should reliably uphold.

Recent advances at the intersection of reinforcement learning (RL) and visual intelligence have enabled agents that not only perceive complex visual scenes but also reason, generate, and act within them. This survey offers a critical and up-to-date synthesis of the field. We first formalize visual RL problems and trace the evolution of policy-optimization strategies from RLHF to verifiable reward paradigms, and from Proximal Policy Optimization to Group Relative Policy Optimization. We then organize more than 200 representative works into four thematic pillars: multi-modal large language models, visual generation, unified model frameworks, and vision-language-action models. For each pillar we examine algorithmic design, reward engineering, benchmark progress, and we distill trends such as curriculum-driven training, preference-aligned diffusion, and unified reward modeling. Finally, we review evaluation protocols spanning set-level fidelity, sample-level preference, and state-level stability, and we identify open challenges that include sample efficiency, generalization, and safe deployment. Our goal is to provide researchers and practitioners with a coherent map of the rapidly expanding landscape of visual RL and to highlight promising directions for future inquiry. Resources are available at: https://github.com/weijiawu/Awesome-Visual-Reinforcement-Learning.

This paper presents the first ChatGPT4PCG Competition at the 2023 IEEE Conference on Games. The objective of this competition is for participants to create effective prompts for ChatGPT--enabling it to generate Science Birds levels with high stability and character-like qualities--fully using their creativity as well as prompt engineering skills. ChatGPT is a conversational agent developed by OpenAI. Science Birds is selected as the competition platform because designing an Angry Birds-like level is not a trivial task due to the in-game gravity; the quality of the levels is determined by their stability. To lower the entry barrier to the competition, we limit the task to the generation of capitalized English alphabetical characters. We also allow only a single prompt to be used for generating all the characters. Here, the quality of the generated levels is determined by their stability and similarity to the given characters. A sample prompt is provided to participants for their reference. An experiment is conducted to determine the effectiveness of several modified versions of this sample prompt on level stability and similarity by testing them on several characters. To the best of our knowledge, we believe that ChatGPT4PCG is the first competition of its kind and hope to inspire enthusiasm for prompt engineering in procedural content generation.

On-policy reinforcement learning (RL) methods widely used for language model post-training, like Group Relative Policy Optimization (GRPO), often suffer from limited exploration and early saturation due to low sampling diversity. While off-policy data can help, current approaches that mix entire trajectories cause significant policy mismatch and instability. In this work, we propose the Single-sample Mix-pOlicy Unified Paradigm (SOUP), a framework that unifies off- and on-policy learning within individual samples at the token level. It confines off-policy influence to the prefix of a generated sequence sampled from historical policies, while the continuation is generated on-policy. Through token-level importance ratios, SOUP effectively leverages off-policy information while preserving training stability. Extensive experiments demonstrate that SOUP consistently outperforms standard on-policy training and existing off-policy extensions. Our further analysis clarifies how our fine-grained, single-sample mix-policy training can improve both exploration and final performance in LLM RL.

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models. While Group Relative Policy Optimization (GRPO) is widely adopted, its coarse credit assignment uniformly penalizes failed rollouts, lacking the token-level focus needed to efficiently address specific deviations. Self-Distillation Policy Optimization (SDPO) addresses this by providing denser, more targeted logit-level supervision that facilitates rapid early improvement, yet it frequently collapses during prolonged training. We trace this late-stage instability to two intrinsic flaws: self-distillation on already-correct samples introduces optimization ambiguity, and the self-teacher's signal reliability progressively degrades. To resolve these issues, we propose Sample-Routed Policy Optimization (SRPO), a unified on-policy framework that routes correct samples to GRPO's reward-aligned reinforcement and failed samples to SDPO's targeted logit-level correction. SRPO further incorporates an entropy-aware dynamic weighting mechanism to suppress high-entropy, unreliable distillation targets while emphasizing confident ones. Evaluated across five benchmarks and two model scales, SRPO achieves both the rapid early improvement of SDPO and the long-horizon stability of GRPO. It consistently surpasses the peak performance of both baselines, raising the five-benchmark average on Qwen3-8B by 3.4% over GRPO and 6.3% over SDPO, while simultaneously yielding moderate response lengths and lowering per-step compute cost by up to 17.2%.

Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit assignment over long Chain-of-Thought (CoT) horizons and the prohibitive memory cost of the value model. While critic-free alternatives like GRPO mitigate these issues, they incur significant computational overhead by requiring multiple samples for baseline estimation, severely limiting training throughput. In this paper, we introduce Sequence-Level PPO (SPPO), a scalable algorithm that harmonizes the sample efficiency of PPO with the stability of outcome-based updates. SPPO reformulates the reasoning process as a Sequence-Level Contextual Bandit problem, employing a decoupled scalar value function to derive low-variance advantage signals without multi-sampling. Extensive experiments on mathematical benchmarks demonstrate that SPPO significantly surpasses standard PPO and matches the performance of computation-heavy group-based methods, offering a resource-efficient framework for aligning reasoning LLMs.

Reinforcement Learning from Human Feedback (RLHF) has proven effective in aligning large language models with human intentions, yet it often relies on complex methodologies like Proximal Policy Optimization (PPO) that require extensive hyper-parameter tuning and present challenges in sample efficiency and stability. In this paper, we introduce Inverse-Q*, an innovative framework that transcends traditional RL methods by optimizing token-level reinforcement learning without the need for additional reward or value models. Inverse-Q* leverages direct preference optimization techniques but extends them by estimating the conditionally optimal policy directly from the model's responses, facilitating more granular and flexible policy shaping. Our approach reduces reliance on human annotation and external supervision, making it especially suitable for low-resource settings. We present extensive experimental results demonstrating that Inverse-Q* not only matches but potentially exceeds the effectiveness of PPO in terms of convergence speed and the alignment of model responses with human preferences. Our findings suggest that Inverse-Q* offers a practical and robust alternative to conventional RLHF approaches, paving the way for more efficient and adaptable model training approaches.

Vision Transformers (ViTs) have demonstrated powerful representation ability in various visual tasks thanks to their intrinsic data-hungry nature. However, we unexpectedly find that ViTs perform vulnerably when applied to face recognition (FR) scenarios with extremely large datasets. We investigate the reasons for this phenomenon and discover that the existing data augmentation approach and hard sample mining strategy are incompatible with ViTs-based FR backbone due to the lack of tailored consideration on preserving face structural information and leveraging each local token information. To remedy these problems, this paper proposes a superior FR model called TransFace, which employs a patch-level data augmentation strategy named DPAP and a hard sample mining strategy named EHSM. Specially, DPAP randomly perturbs the amplitude information of dominant patches to expand sample diversity, which effectively alleviates the overfitting problem in ViTs. EHSM utilizes the information entropy in the local tokens to dynamically adjust the importance weight of easy and hard samples during training, leading to a more stable prediction. Experiments on several benchmarks demonstrate the superiority of our TransFace. Code and models are available at https://github.com/DanJun6737/TransFace.

Continual learning is a promising machine learning paradigm to learn new tasks while retaining previously learned knowledge over streaming training data. Till now, rehearsal-based methods, keeping a small part of data from old tasks as a memory buffer, have shown good performance in mitigating catastrophic forgetting for previously learned knowledge. However, most of these methods typically treat each new task equally, which may not adequately consider the relationship or similarity between old and new tasks. Furthermore, these methods commonly neglect sample importance in the continual training process and result in sub-optimal performance on certain tasks. To address this challenging problem, we propose Relational Experience Replay (RER), a bi-level learning framework, to adaptively tune task-wise relationships and sample importance within each task to achieve a better `stability' and `plasticity' trade-off. As such, the proposed method is capable of accumulating new knowledge while consolidating previously learned old knowledge during continual learning. Extensive experiments conducted on three publicly available datasets (i.e., CIFAR-10, CIFAR-100, and Tiny ImageNet) show that the proposed method can consistently improve the performance of all baselines and surpass current state-of-the-art methods.

Datasets scraped from the internet have been critical to the successes of large-scale machine learning. Yet, this very success puts the utility of future internet-derived datasets at potential risk, as model outputs begin to replace human annotations as a source of supervision. In this work, we first formalize a system where interactions with one model are recorded as history and scraped as training data in the future. We then analyze its stability over time by tracking changes to a test-time bias statistic (e.g. gender bias of model predictions). We find that the degree of bias amplification is closely linked to whether the model's outputs behave like samples from the training distribution, a behavior which we characterize and define as consistent calibration. Experiments in three conditional prediction scenarios - image classification, visual role-labeling, and language generation - demonstrate that models that exhibit a sampling-like behavior are more calibrated and thus more stable. Based on this insight, we propose an intervention to help calibrate and stabilize unstable feedback systems. Code is available at https://github.com/rtaori/data_feedback.

Bagging is an important technique for stabilizing machine learning models. In this paper, we derive a finite-sample guarantee on the stability of bagging for any model. Our result places no assumptions on the distribution of the data, on the properties of the base algorithm, or on the dimensionality of the covariates. Our guarantee applies to many variants of bagging and is optimal up to a constant. Empirical results validate our findings, showing that bagging successfully stabilizes even highly unstable base algorithms.

Achieving both realism and controllability in interactive closed-loop traffic simulation remains a key challenge in autonomous driving. Data-driven simulation methods reproduce realistic trajectories but suffer from covariate shift in closed-loop deployment, compounded by simplified dynamics models that further reduce reliability. Conversely, physics-based simulation methods enhance reliable and controllable closed-loop interactions but often lack expert demonstrations, compromising realism. To address these challenges, we introduce a dual-stage AV-centered simulation framework that conducts open-loop imitation learning pre-training in a data-driven simulator to capture trajectory-level realism and multimodality, followed by closed-loop reinforcement learning fine-tuning in a physics-based simulator to enhance controllability and mitigate covariate shift. In the fine-tuning stage, we propose RIFT, a simple yet effective closed-loop RL fine-tuning strategy that preserves the trajectory-level multimodality through a GRPO-style group-relative advantage formulation, while enhancing controllability and training stability by replacing KL regularization with the dual-clip mechanism. Extensive experiments demonstrate that RIFT significantly improves the realism and controllability of generated traffic scenarios, providing a robust platform for evaluating autonomous vehicle performance in diverse and interactive scenarios.

Large reasoning models (LRMs) aim to solve diverse and complex problems through structured reasoning. Recent advances in group-based policy optimization methods have shown promise in enabling stable advantage estimation without reliance on process-level annotations. However, these methods rely on advantage gaps induced by high-quality samples within the same batch, which makes the training process fragile and inefficient when intra-group advantages collapse under challenging tasks. To address these problems, we propose a reinforcement learning mechanism named \textbf{R^3} that along three directions: (1) a cross-context \underline{\textbf{R}eplay} strategy that maintains the intra-group advantage by recalling valuable examples from historical trajectories of the same query, (2) an in-context self-\underline{\textbf{R}eflection} mechanism enabling models to refine outputs by leveraging past failures, and (3) a structural entropy \underline{\textbf{R}anking reward}, which assigns relative rewards to truncated or failed samples by ranking responses based on token-level entropy patterns, capturing both local exploration and global stability. We implement our method on Deepseek-R1-Distill-Qwen-1.5B and train it on the DeepscaleR-40k in the math domain. Experiments demonstrate our method achieves SoTA performance on several math benchmarks, representing significant improvements and fewer reasoning tokens over the base models. Code and model will be released.

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

Time-dependent data-generating distributions have proven to be difficult for gradient-based training of neural networks, as the greedy updates result in catastrophic forgetting of previously learned knowledge. Despite the progress in the field of continual learning to overcome this forgetting, we show that a set of common state-of-the-art methods still suffers from substantial forgetting upon starting to learn new tasks, except that this forgetting is temporary and followed by a phase of performance recovery. We refer to this intriguing but potentially problematic phenomenon as the stability gap. The stability gap had likely remained under the radar due to standard practice in the field of evaluating continual learning models only after each task. Instead, we establish a framework for continual evaluation that uses per-iteration evaluation and we define a new set of metrics to quantify worst-case performance. Empirically we show that experience replay, constraint-based replay, knowledge-distillation, and parameter regularization methods are all prone to the stability gap; and that the stability gap can be observed in class-, task-, and domain-incremental learning benchmarks. Additionally, a controlled experiment shows that the stability gap increases when tasks are more dissimilar. Finally, by disentangling gradients into plasticity and stability components, we propose a conceptual explanation for the stability gap.

Analysis of learned representations has a blind spot: it focuses on similarity, measuring how closely embeddings align with external references, but similarity reveals only what is represented, not whether that structure is robust. We introduce geometric stability, a distinct dimension that quantifies how reliably representational geometry holds under perturbation, and present Shesha, a framework for measuring it. Across 2,463 configurations in seven domains, we show that stability and similarity are empirically uncorrelated (ρapprox 0.01) and mechanistically distinct: similarity metrics collapse after removing the top principal components, while stability retains sensitivity to fine-grained manifold structure. This distinction yields actionable insights: for safety monitoring, stability acts as a functional geometric canary, detecting structural drift nearly 2times more sensitively than CKA while filtering out the non-functional noise that triggers false alarms in rigid distance metrics; for controllability, supervised stability predicts linear steerability (ρ= 0.89-0.96); for model selection, stability dissociates from transferability, revealing a geometric tax that transfer optimization incurs. Beyond machine learning, stability predicts CRISPR perturbation coherence and neural-behavioral coupling. By quantifying how reliably systems maintain structure, geometric stability provides a necessary complement to similarity for auditing representations across biological and computational systems.

In continual learning, many classifiers use softmax function to learn confidence. However, numerous studies have pointed out its inability to accurately determine confidence distributions for outliers, often referred to as epistemic uncertainty. This inherent limitation also curtails the accurate decisions for selecting what to forget and keep in previously trained confidence distributions over continual learning process. To address the issue, we revisit the effects of masking softmax function. While this method is both simple and prevalent in literature, its implication for retaining confidence distribution during continual learning, also known as stability, has been under-investigated. In this paper, we revisit the impact of softmax masking, and introduce a methodology to utilize its confidence preservation effects. In class- and task-incremental learning benchmarks with and without memory replay, our approach significantly increases stability while maintaining sufficiently large plasticity. In the end, our methodology shows better overall performance than state-of-the-art methods, particularly in the use with zero or small memory. This lays a simple and effective foundation of strongly stable replay-based continual learning.

Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can trigger cascading failures in multi-step execution. Yet this form of instability is not captured by existing evaluations. Hallucinations live in variance: they arise when semantically equivalent prompts activate inconsistent internal pathways, producing divergent outputs. Consistent but incorrect outputs reflect bias or missing knowledge; confident guessing reflects calibration failure. Neither constitutes hallucination under this definition. When error is variance-dominated, reducing redundant pathways improves reliability without adding knowledge. We formalize this through Semantic Stability (SS), measured via Paraphrase Consistency (PC@k): generate k paraphrases, greedy decode each, compute mode agreement. SS is a diagnostic for variance-driven unreliability, not a method for improving correctness. We show that a dense Qwen3-0.6B agrees with itself only 23.8% of the time; at 32% sparsity, agreement jumps to 55.9%. A phase diagram reveals the sweet spot where variance reduction outpaces bias accumulation, and regimes where stability collapses onto wrong answers.

Large language models (LLMs) are increasingly deployed in settings where reasoning, such as multi-step problem solving and chain-of-thought, is essential. Yet, current evaluation practices overwhelmingly report single-run accuracy while ignoring the intrinsic uncertainty that naturally arises from stochastic decoding. This omission creates a blind spot because practitioners cannot reliably assess whether a method's reported performance is stable, reproducible, or cost-consistent. We introduce ReasonBENCH, the first benchmark designed to quantify the underlying instability in LLM reasoning. ReasonBENCH provides (i) a modular evaluation library that standardizes reasoning frameworks, models, and tasks, (ii) a multi-run protocol that reports statistically reliable metrics for both quality and cost, and (iii) a public leaderboard to encourage variance-aware reporting. Across tasks from different domains, we find that the vast majority of reasoning strategies and models exhibit high instability. Notably, even strategies with similar average performance can display confidence intervals up to four times wider, and the top-performing methods often incur higher and less stable costs. Such instability compromises reproducibility across runs and, consequently, the reliability of reported performance. To better understand these dynamics, we further analyze the impact of prompts, model families, and scale on the trade-off between solve rate and stability. Our results highlight reproducibility as a critical dimension for reliable LLM reasoning and provide a foundation for future reasoning methods and uncertainty quantification techniques. ReasonBENCH is publicly available at https://github.com/au-clan/ReasonBench .

Pixel-wise predictions are required in a wide variety of tasks such as image restoration, image segmentation, or disparity estimation. Common models involve several stages of data resampling, in which the resolution of feature maps is first reduced to aggregate information and then increased to generate a high-resolution output. Previous works have shown that resampling operations are subject to artifacts such as aliasing. During downsampling, aliases have been shown to compromise the prediction stability of image classifiers. During upsampling, they have been leveraged to detect generated content. Yet, the effect of aliases during upsampling has not yet been discussed w.r.t. the stability and robustness of pixel-wise predictions. While falling under the same term (aliasing), the challenges for correct upsampling in neural networks differ significantly from those during downsampling: when downsampling, some high frequencies can not be correctly represented and have to be removed to avoid aliases. However, when upsampling for pixel-wise predictions, we actually require the model to restore such high frequencies that can not be encoded in lower resolutions. The application of findings from signal processing is therefore a necessary but not a sufficient condition to achieve the desirable output. In contrast, we find that the availability of large spatial context during upsampling allows to provide stable, high-quality pixel-wise predictions, even when fully learning all filter weights.

PPO has been widely adopted for training large language models (LLMs) at the token level in multi-turn dialogue and reasoning tasks. However, its performance is often unstable and prone to collapse. Through empirical analysis, we identify two main sources of instability in this setting: (1)~token-level importance sampling, which is misaligned with the natural granularity of multi-turn environments that have distinct turn-level stages, and (2) inaccurate advantage estimates from off-policy samples, where the critic has not learned to evaluate certain state-action pairs, resulting in high-variance gradients and unstable updates. To address these challenges, we introduce two complementary stabilization techniques: (1) turn-level importance sampling, which aligns optimization with the natural structure of multi-turn reasoning, and (2) clipping-bias correction, which normalizes gradients by downweighting unreliable, highly off-policy samples. Depending on how these components are combined, we obtain three variants: Turn-PPO (turn-level sampling only), S-PPO (clipping-bias correction applied to token-level PPO), and ST-PPO (turn-level sampling combined with clipping-bias correction). In our experiments, we primarily study ST-PPO and S-PPO, which together demonstrate how the two stabilization mechanisms address complementary sources of instability. Experiments on multi-turn search tasks across general QA, multi-hop QA, and medical multiple-choice QA benchmarks show that ST-PPO and S-PPO consistently prevent the performance collapses observed in large-model training, maintain lower clipping ratios throughout optimization, and achieve higher task performance than standard token-level PPO. These results demonstrate that combining turn-level importance sampling with clipping-bias correction provides a practical and scalable solution for stabilizing multi-turn LLM agent training.

Offline-to-online reinforcement learning (RL) has emerged as a practical paradigm that leverages offline datasets for pretraining and online interactions for fine-tuning. However, its empirical behavior is highly inconsistent: design choices of online-fine tuning that work well in one setting can fail completely in another. We propose a stability--plasticity principle that can explain this inconsistency: we should preserve the knowledge of pretrained policy or offline dataset during online fine-tuning, whichever is better, while maintaining sufficient plasticity. This perspective identifies three regimes of online fine-tuning, each requiring distinct stability properties. We validate this framework through a large-scale empirical study, finding that the results strongly align with its predictions in 45 of 63 cases. This work provides a principled framework for guiding design choices in offline-to-online RL based on the relative performance of the offline dataset and the pretrained policy.

Reliable evaluation is fundamental to the progress of Large Language Models (LLMs), yet the evaluation process during pre-training is plagued by significant instability that obscures true learning dynamics. In this work, we systematically diagnose this instability, attributing it to two distinct sources: Parameter Instability from training stochasticity and Evaluation Instability from noisy measurement protocols. To counteract both sources of noise, we introduce MaP, a dual-pronged framework that synergistically integrates checkpoint Merging and the Pass@k metric. Checkpoint merging smooths the parameter space by averaging recent model weights, while Pass@k provides a robust, low-variance statistical estimate of model capability. Extensive experiments show that MaP yields significantly smoother performance curves, reduces inter-run variance, and ensures more consistent model rankings. Ultimately, MaP provides a more reliable and faithful lens for observing LLM training dynamics, laying a crucial empirical foundation for LLM research.

This paper poses two critical issues in evaluating base models (without post-training): (1) Unstable evaluation during training: in the early stages of pre-training, the models lack the capability to answer questions as required, leading to unstable evaluation results. This instability makes it difficult to provide solid conclusions to guide the training, especially for key experiments such as data ablation and scaling law. (2) Inconsistency between base and instruct models: base models generally exhibit poorer evaluation performance compared to corresponding instruct models. This gap poses a challenge for assessing whether a base model with better evaluation can truly lead to a better instruct model. To address these issues, we propose Base model Oriented Systematic Evaluation (BOSE), a method specifically designed to optimize the evaluation of base models. Specifically, BOSE introduces two key innovations: In-Context Light-instruction Prompt (ICLiP) for open-ended tasks and Blank-ppl for multi-choice tasks with candidate options, which transforms the standard perplexity (ppl) metric into a fill-in-the-blank format to mitigate early-stage evaluation fluctuations. Furthermore, we are the first to propose Kendall's rank correlation to quantitatively measure the evaluation stability and consistency. Experimental results demonstrate that BOSE significantly enhances both the stability of evaluations during pre-training and the consistency between base and instruct models, thereby providing more reliable guidance for the LLMs' training.

In this paper, we focus on quantifying model stability as a function of random seed by investigating the effects of the induced randomness on model performance and the robustness of the model in general. We specifically perform a controlled study on the effect of random seeds on the behaviour of attention, gradient-based and surrogate model based (LIME) interpretations. Our analysis suggests that random seeds can adversely affect the consistency of models resulting in counterfactual interpretations. We propose a technique called Aggressive Stochastic Weight Averaging (ASWA)and an extension called Norm-filtered Aggressive Stochastic Weight Averaging (NASWA) which improves the stability of models over random seeds. With our ASWA and NASWA based optimization, we are able to improve the robustness of the original model, on average reducing the standard deviation of the model's performance by 72%.

We present a bag of tricks framework for few-shot class-incremental learning (FSCIL), which is a challenging form of continual learning that involves continuous adaptation to new tasks with limited samples. FSCIL requires both stability and adaptability, i.e., preserving proficiency in previously learned tasks while learning new ones. Our proposed bag of tricks brings together eight key and highly influential techniques that improve stability, adaptability, and overall performance under a unified framework for FSCIL. We organize these tricks into three categories: stability tricks, adaptability tricks, and training tricks. Stability tricks aim to mitigate the forgetting of previously learned classes by enhancing the separation between the embeddings of learned classes and minimizing interference when learning new ones. On the other hand, adaptability tricks focus on the effective learning of new classes. Finally, training tricks improve the overall performance without compromising stability or adaptability. We perform extensive experiments on three benchmark datasets, CIFAR-100, CUB-200, and miniIMageNet, to evaluate the impact of our proposed framework. Our detailed analysis shows that our approach substantially improves both stability and adaptability, establishing a new state-of-the-art by outperforming prior works in the area. We believe our method provides a go-to solution and establishes a robust baseline for future research in this area.

In many real-world applications, deep neural networks are retrained from scratch as a dataset grows in size. Given the computational expense for retraining networks, it has been argued that continual learning could make updating networks more efficient. An obstacle to achieving this goal is the stability gap, which refers to an observation that when updating on new data, performance on previously learned data degrades before recovering. Addressing this problem would enable learning new data with fewer network updates, resulting in increased computational efficiency. We study how to mitigate the stability gap. We test a variety of hypotheses to understand why the stability gap occurs. This leads us to discover a method that vastly reduces this gap. In large-scale class incremental learning experiments, we are able to significantly reduce the number of network updates needed for continual learning. Our work has the potential to advance the state-of-the-art in continual learning for real-world applications along with reducing the carbon footprint required to maintain updated neural networks.

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the original model m and the new model M are bounded in the parameter space, i.e., |Params(M){-}Params(m)|{<}Delta. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed naturally-occurring model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure -- that we call Stability -- to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of Stability as defined by our measure will remain valid after potential ``naturally-occurring'' model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine practical relaxations of our proposed measure and demonstrate experimentally how they can be incorporated to find robust counterfactuals for neural networks that are close, realistic, and remain valid after potential model changes.

Adversarial robustness is essential for security and reliability of machine learning systems. However, adversarial robustness enhanced by defense algorithms is easily erased as the neural network's weights update to learn new tasks. To address this vulnerability, it is essential to improve the capability of neural networks in terms of robust continual learning. Specially, we propose a novel gradient projection technique that effectively stabilizes sample gradients from previous data by orthogonally projecting back-propagation gradients onto a crucial subspace before using them for weight updates. This technique can maintaining robustness by collaborating with a class of defense algorithms through sample gradient smoothing. The experimental results on four benchmarks including Split-CIFAR100 and Split-miniImageNet, demonstrate that the superiority of the proposed approach in mitigating rapidly degradation of robustness during continual learning even when facing strong adversarial attacks.

The rapid progress in generative models has resulted in impressive leaps in generation quality, blurring the lines between synthetic and real data. Web-scale datasets are now prone to the inevitable contamination by synthetic data, directly impacting the training of future generated models. Already, some theoretical results on self-consuming generative models (a.k.a., iterative retraining) have emerged in the literature, showcasing that either model collapse or stability could be possible depending on the fraction of generated data used at each retraining step. However, in practice, synthetic data is often subject to human feedback and curated by users before being used and uploaded online. For instance, many interfaces of popular text-to-image generative models, such as Stable Diffusion or Midjourney, produce several variations of an image for a given query which can eventually be curated by the users. In this paper, we theoretically study the impact of data curation on iterated retraining of generative models and show that it can be seen as an implicit preference optimization mechanism. However, unlike standard preference optimization, the generative model does not have access to the reward function or negative samples needed for pairwise comparisons. Moreover, our study doesn't require access to the density function, only to samples. We prove that, if the data is curated according to a reward model, then the expected reward of the iterative retraining procedure is maximized. We further provide theoretical results on the stability of the retraining loop when using a positive fraction of real data at each step. Finally, we conduct illustrative experiments on both synthetic datasets and on CIFAR10 showing that such a procedure amplifies biases of the reward model.

Prediction models can exhibit sensitivity with respect to training data: small changes in the training data can produce models that assign conflicting predictions to individual data points during test time. In this work, we study this sensitivity in recommender systems, where users' recommendations are drastically altered by minor perturbations in other unrelated users' interactions. We introduce a measure of stability for recommender systems, called Rank List Sensitivity (RLS), which measures how rank lists generated by a given recommender system at test time change as a result of a perturbation in the training data. We develop a method, CASPER, which uses cascading effect to identify the minimal and systematical perturbation to induce higher instability in a recommender system. Experiments on four datasets show that recommender models are overly sensitive to minor perturbations introduced randomly or via CASPER - even perturbing one random interaction of one user drastically changes the recommendation lists of all users. Importantly, with CASPER perturbation, the models generate more unstable recommendations for low-accuracy users (i.e., those who receive low-quality recommendations) than high-accuracy ones.

Neural networks are very effective when trained on large datasets for a large number of iterations. However, when they are trained on non-stationary streams of data and in an online fashion, their performance is reduced (1) by the online setup, which limits the availability of data, (2) due to catastrophic forgetting because of the non-stationary nature of the data. Furthermore, several recent works (Caccia et al., 2022; Lange et al., 2023) arXiv:2205.13452 showed that replay methods used in continual learning suffer from the stability gap, encountered when evaluating the model continually (rather than only on task boundaries). In this article, we study the effect of model ensembling as a way to improve performance and stability in online continual learning. We notice that naively ensembling models coming from a variety of training tasks increases the performance in online continual learning considerably. Starting from this observation, and drawing inspirations from semi-supervised learning ensembling methods, we use a lightweight temporal ensemble that computes the exponential moving average of the weights (EMA) at test time, and show that it can drastically increase the performance and stability when used in combination with several methods from the literature.

Deep generative models have made tremendous progress in modeling complex data, often exhibiting generation quality that surpasses a typical human's ability to discern the authenticity of samples. Undeniably, a key driver of this success is enabled by the massive amounts of web-scale data consumed by these models. Due to these models' striking performance and ease of availability, the web will inevitably be increasingly populated with synthetic content. Such a fact directly implies that future iterations of generative models must contend with the reality that their training is curated from both clean data and artificially generated data from past models. In this paper, we develop a framework to rigorously study the impact of training generative models on mixed datasets (of real and synthetic data) on their stability. We first prove the stability of iterative training under the condition that the initial generative models approximate the data distribution well enough and the proportion of clean training data (w.r.t. synthetic data) is large enough. We empirically validate our theory on both synthetic and natural images by iteratively training normalizing flows and state-of-the-art diffusion models on CIFAR10 and FFHQ.

In this paper, we study the implicit regularization of stochastic gradient descent (SGD) through the lens of {\em dynamical stability} (Wu et al., 2018). We start by revising existing stability analyses of SGD, showing how the Frobenius norm and trace of Hessian relate to different notions of stability. Notably, if a global minimum is linearly stable for SGD, then the trace of Hessian must be less than or equal to 2/eta, where eta denotes the learning rate. By contrast, for gradient descent (GD), the stability imposes a similar constraint but only on the largest eigenvalue of Hessian. We then turn to analyze the generalization properties of these stable minima, focusing specifically on two-layer ReLU networks and diagonal linear networks. Notably, we establish the {\em equivalence} between these metrics of sharpness and certain parameter norms for the two models, which allows us to show that the stable minima of SGD provably generalize well. By contrast, the stability-induced regularization of GD is provably too weak to ensure satisfactory generalization. This discrepancy provides an explanation of why SGD often generalizes better than GD. Note that the learning rate (LR) plays a pivotal role in the strength of stability-induced regularization. As the LR increases, the regularization effect becomes more pronounced, elucidating why SGD with a larger LR consistently demonstrates superior generalization capabilities. Additionally, numerical experiments are provided to support our theoretical findings.

Building deep reinforcement learning (RL) agents that find a good policy with few samples has proven notoriously challenging. To achieve sample efficiency, recent work has explored updating neural networks with large numbers of gradient steps for every new sample. While such high update-to-data (UTD) ratios have shown strong empirical performance, they also introduce instability to the training process. Previous approaches need to rely on periodic neural network parameter resets to address this instability, but restarting the training process is infeasible in many real-world applications and requires tuning the resetting interval. In this paper, we focus on one of the core difficulties of stable training with limited samples: the inability of learned value functions to generalize to unobserved on-policy actions. We mitigate this issue directly by augmenting the off-policy RL training process with a small amount of data generated from a learned world model. Our method, Model-Augmented Data for TD Learning (MAD-TD), uses small amounts of generated data to stabilize high UTD training and achieve competitive performance on the most challenging tasks in the DeepMind control suite. Our experiments further highlight the importance of employing a good model to generate data, MAD-TD's ability to combat value overestimation, and its practical stability gains for continued learning.

This paper proposes a novel formulation for reinforcement learning (RL) with large language models, explaining why and under what conditions the true sequence-level reward can be optimized via a surrogate token-level objective in policy gradient methods such as REINFORCE. Specifically, through a first-order approximation, we show that this surrogate becomes increasingly valid only when both the training-inference discrepancy and policy staleness are minimized. This insight provides a principled explanation for the crucial role of several widely adopted techniques in stabilizing RL training, including importance sampling correction, clipping, and particularly Routing Replay for Mixture-of-Experts (MoE) models. Through extensive experiments with a 30B MoE model totaling hundreds of thousands of GPU hours, we show that for on-policy training, the basic policy gradient algorithm with importance sampling correction achieves the highest training stability. When off-policy updates are introduced to accelerate convergence, combining clipping and Routing Replay becomes essential to mitigate the instability caused by policy staleness. Notably, once training is stabilized, prolonged optimization consistently yields comparable final performance regardless of cold-start initialization. We hope that the shared insights and the developed recipes for stable RL training will facilitate future research.

Recurrent models are a popular choice for video enhancement tasks such as video denoising or super-resolution. In this work, we focus on their stability as dynamical systems and show that they tend to fail catastrophically at inference time on long video sequences. To address this issue, we (1) introduce a diagnostic tool which produces input sequences optimized to trigger instabilities and that can be interpreted as visualizations of temporal receptive fields, and (2) propose two approaches to enforce the stability of a model during training: constraining the spectral norm or constraining the stable rank of its convolutional layers. We then introduce Stable Rank Normalization for Convolutional layers (SRN-C), a new algorithm that enforces these constraints. Our experimental results suggest that SRN-C successfully enforces stability in recurrent video processing models without a significant performance loss.

Robustness to natural distribution shifts has seen remarkable progress thanks to recent pre-training strategies combined with better fine-tuning methods. However, such fine-tuning assumes access to large amounts of labelled data, and the extent to which the observations hold when the amount of training data is not as high remains unknown. We address this gap by performing the first in-depth study of robustness to various natural distribution shifts in different low-shot regimes: spanning datasets, architectures, pre-trained initializations, and state-of-the-art robustness interventions. Most importantly, we find that there is no single model of choice that is often more robust than others, and existing interventions can fail to improve robustness on some datasets even if they do so in the full-shot regime. We hope that our work will motivate the community to focus on this problem of practical importance.

Modern recommender systems may output considerably different recommendations due to small perturbations in the training data. Changes in the data from a single user will alter the recommendations as well as the recommendations of other users. In applications like healthcare, housing, and finance, this sensitivity can have adverse effects on user experience. We propose a method to stabilize a given recommender system against such perturbations. This is a challenging task due to (1) the lack of a ``reference'' rank list that can be used to anchor the outputs; and (2) the computational challenges in ensuring the stability of rank lists with respect to all possible perturbations of training data. Our method, FINEST, overcomes these challenges by obtaining reference rank lists from a given recommendation model and then fine-tuning the model under simulated perturbation scenarios with rank-preserving regularization on sampled items. Our experiments on real-world datasets demonstrate that FINEST can ensure that recommender models output stable recommendations under a wide range of different perturbations without compromising next-item prediction accuracy.

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its practical efficacy: the implicit regularization it instigates. Several studies have investigated the linear stability property of SGD in the vicinity of a stationary point as a predictive proxy for sharpness and generalization error in overparameterized neural networks (Wu et al., 2022; Jastrzebski et al., 2019; Cohen et al., 2021). In this paper, we delve deeper into the relationship between linear stability and sharpness. More specifically, we meticulously delineate the necessary and sufficient conditions for linear stability, contingent on hyperparameters of SGD and the sharpness at the optimum. Towards this end, we introduce a novel coherence measure of the loss Hessian that encapsulates pertinent geometric properties of the loss function that are relevant to the linear stability of SGD. It enables us to provide a simplified sufficient condition for identifying linear instability at an optimum. Notably, compared to previous works, our analysis relies on significantly milder assumptions and is applicable for a broader class of loss functions than known before, encompassing not only mean-squared error but also cross-entropy loss.

Reinforcement learning applied to large language models (LLMs) for reasoning tasks is often bottlenecked by unstable gradient estimates due to fixed and uniform sampling of responses across prompts. Prior work such as GVM-RAFT addresses this by dynamically allocating inference budget per prompt to minimize stochastic gradient variance under a budget constraint. Inspired by this insight, we propose Reinforce-Ada, an adaptive sampling framework for online RL post-training of LLMs that continuously reallocates sampling effort to the prompts with the greatest uncertainty or learning potential. Unlike conventional two-stage allocation methods, Reinforce-Ada interleaves estimation and sampling in an online successive elimination process, and automatically stops sampling for a prompt once sufficient signal is collected. To stabilize updates, we form fixed-size groups with enforced reward diversity and compute advantage baselines using global statistics aggregated over the adaptive sampling phase. Empirical results across multiple model architectures and reasoning benchmarks show that Reinforce-Ada accelerates convergence and improves final performance compared to GRPO, especially when using the balanced sampling variant. Our work highlights the central role of variance-aware, adaptive data curation in enabling efficient and reliable reinforcement learning for reasoning-capable LLMs. Code is available at https://github.com/RLHFlow/Reinforce-Ada.

We discover that common diffusion noise schedules do not enforce the last timestep to have zero signal-to-noise ratio (SNR), and some implementations of diffusion samplers do not start from the last timestep. Such designs are flawed and do not reflect the fact that the model is given pure Gaussian noise at inference, creating a discrepancy between training and inference. We show that the flawed design causes real problems in existing implementations. In Stable Diffusion, it severely limits the model to only generate images with medium brightness and prevents it from generating very bright and dark samples. We propose a few simple fixes: (1) rescale the noise schedule to enforce zero terminal SNR; (2) train the model with v prediction; (3) change the sampler to always start from the last timestep; (4) rescale classifier-free guidance to prevent over-exposure. These simple changes ensure the diffusion process is congruent between training and inference and allow the model to generate samples more faithful to the original data distribution.

Teams that have trained large Transformer-based models have reported training instabilities at large scale that did not appear when training with the same hyperparameters at smaller scales. Although the causes of such instabilities are of scientific interest, the amount of resources required to reproduce them has made investigation difficult. In this work, we seek ways to reproduce and study training stability and instability at smaller scales. First, we focus on two sources of training instability described in previous work: the growth of logits in attention layers (Dehghani et al., 2023) and divergence of the output logits from the log probabilities (Chowdhery et al., 2022). By measuring the relationship between learning rate and loss across scales, we show that these instabilities also appear in small models when training at high learning rates, and that mitigations previously employed at large scales are equally effective in this regime. This prompts us to investigate the extent to which other known optimizer and model interventions influence the sensitivity of the final loss to changes in the learning rate. To this end, we study methods such as warm-up, weight decay, and the muParam (Yang et al., 2022), and combine techniques to train small models that achieve similar losses across orders of magnitude of learning rate variation. Finally, to conclude our exploration we study two cases where instabilities can be predicted before they emerge by examining the scaling behavior of model activation and gradient norms.

Training stability remains a central challenge in reinforcement learning (RL) for large language models (LLMs). Policy staleness, asynchronous training, and mismatches between training and inference engines all cause the behavior policy to diverge from the current policy, risking training collapse. Importance sampling provides a principled correction for this distribution shift but suffers from high variance; existing remedies such as token-level clipping and sequence-level normalization lack a unified theoretical foundation. We propose Variational sEquence-level Soft Policy Optimization (VESPO). By incorporating variance reduction into a variational formulation over proposal distributions, VESPO derives a closed-form reshaping kernel that operates directly on sequence-level importance weights without length normalization. Experiments on mathematical reasoning benchmarks show that VESPO maintains stable training under staleness ratios up to 64x and fully asynchronous execution, and delivers consistent gains across both dense and Mixture-of-Experts models. Code is available at https://github.com/FloyedShen/VESPO

Large Language Models (LLMs) can significantly improve their reasoning capabilities by interacting with external tools, a paradigm known as Tool-Integrated Reasoning (TIR). However, extending TIR to multi-turn scenarios using Reinforcement Learning (RL) is often hindered by training instability and performance collapse. We identify that such instability is primarily caused by a distributional drift from external tool feedback, leading to the generation of low-probability tokens. This issue compounds over successive turns, causing catastrophic gradient norm explosions that derail the training process. To address this challenge, we introduce SimpleTIR , a plug-and-play algorithm that stabilizes multi-turn TIR training. Its core strategy is to identify and filter out trajectories containing void turns, i.e., turns that yield neither a code block nor a final answer. By removing these problematic trajectories from the policy update, SimpleTIR effectively blocks the harmful, high-magnitude gradients, thus stabilizing the learning dynamics. Extensive experiments show that SimpleTIR achieves state-of-the-art performance on challenging math reasoning benchmarks, notably elevating the AIME24 score from a text-only baseline of 22.1 to 50.5 when starting from the Qwen2.5-7B base model. Furthermore, by avoiding the constraints of supervised fine-tuning, SimpleTIR encourages the model to discover diverse and sophisticated reasoning patterns, such as self-correction and cross-validation.

Generative data augmentation, which scales datasets by obtaining fake labeled examples from a trained conditional generative model, boosts classification performance in various learning tasks including (semi-)supervised learning, few-shot learning, and adversarially robust learning. However, little work has theoretically investigated the effect of generative data augmentation. To fill this gap, we establish a general stability bound in this not independently and identically distributed (non-i.i.d.) setting, where the learned distribution is dependent on the original train set and generally not the same as the true distribution. Our theoretical result includes the divergence between the learned distribution and the true distribution. It shows that generative data augmentation can enjoy a faster learning rate when the order of divergence term is o(maxleft( log(m)beta_m, 1 / m)right), where m is the train set size and beta_m is the corresponding stability constant. We further specify the learning setup to the Gaussian mixture model and generative adversarial nets. We prove that in both cases, though generative data augmentation does not enjoy a faster learning rate, it can improve the learning guarantees at a constant level when the train set is small, which is significant when the awful overfitting occurs. Simulation results on the Gaussian mixture model and empirical results on generative adversarial nets support our theoretical conclusions. Our code is available at https://github.com/ML-GSAI/Understanding-GDA.

We explore the problem of generating minority samples using diffusion models. The minority samples are instances that lie on low-density regions of a data manifold. Generating a sufficient number of such minority instances is important, since they often contain some unique attributes of the data. However, the conventional generation process of the diffusion models mostly yields majority samples (that lie on high-density regions of the manifold) due to their high likelihoods, making themselves ineffective and time-consuming for the minority generating task. In this work, we present a novel framework that can make the generation process of the diffusion models focus on the minority samples. We first highlight that Tweedie's denoising formula yields favorable results for majority samples. The observation motivates us to introduce a metric that describes the uniqueness of a given sample. To address the inherent preference of the diffusion models w.r.t. the majority samples, we further develop minority guidance, a sampling technique that can guide the generation process toward regions with desired likelihood levels. Experiments on benchmark real datasets demonstrate that our minority guidance can greatly improve the capability of generating high-quality minority samples over existing generative samplers. We showcase that the performance benefit of our framework persists even in demanding real-world scenarios such as medical imaging, further underscoring the practical significance of our work. Code is available at https://github.com/soobin-um/minority-guidance.

Recent advances in Conditional Diffusion Models have led to substantial capabilities in various domains. However, understanding the impact of variations in the initial seed vector remains an underexplored area of concern. Particularly, latent-based diffusion models display inconsistencies in image generation under standard conditions when initialized with suboptimal initial seed vectors. To understand the impact of the initial seed vector on generated samples, we propose a reliability evaluation framework that evaluates the generated samples of a diffusion model when the initial seed vector is subjected to various synthetic shifts. Our results indicate that slight manipulations to the initial seed vector of the state-of-the-art Stable Diffusion (Rombach et al., 2022) can lead to significant disturbances in the generated samples, consequently creating images without the effect of conditioning variables. In contrast, GLIDE (Nichol et al., 2022) stands out in generating reliable samples even when the initial seed vector is transformed. Thus, our study sheds light on the importance of the selection and the impact of the initial seed vector in the latent-based diffusion model.

We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary energy-based guidance during inference time. The key defining feature of our sampler lies in its self-contained nature, \ie, implementable solely with a pretrained model. This distinguishes our sampler from existing techniques that require expensive additional components (like external classifiers) for minority generation. Specifically, we first estimate the likelihood of features within an intermediate latent sample by evaluating a reconstruction loss w.r.t. its posterior mean. The generation then proceeds with the minimization of the estimated likelihood, thereby encouraging the emergence of minority features in the latent samples of subsequent timesteps. To further improve the performance of our sampler, we provide several time-scheduling techniques that properly manage the influence of guidance over inference steps. Experiments on benchmark real datasets demonstrate that our approach can greatly improve the capability of creating realistic low-likelihood minority instances over the existing techniques without the reliance on costly additional elements. Code is available at https://github.com/soobin-um/sg-minority.

Diffusion models have emerged as powerful tools for generative tasks, producing high-quality outputs across diverse domains. However, how the generated data responds to the initial noise perturbation in diffusion models remains under-explored, which hinders understanding the controllability of the sampling process. In this work, we first observe an interesting phenomenon: the relationship between the change of generation outputs and the scale of initial noise perturbation is highly linear through the diffusion ODE sampling. Then we provide both theoretical and empirical study to justify this linearity property of this input-output (noise-generation data) relationship. Inspired by these new insights, we propose a novel Controllable and Constrained Sampling method (CCS) together with a new controller algorithm for diffusion models to sample with desired statistical properties while preserving good sample quality. We perform extensive experiments to compare our proposed sampling approach with other methods on both sampling controllability and sampled data quality. Results show that our CCS method achieves more precisely controlled sampling while maintaining superior sample quality and diversity.

Test-time adaptation (TTA) aims to address the distribution shift between the training and test data with only unlabeled data at test time. Existing TTA methods often focus on improving recognition performance specifically for test data associated with classes in the training set. However, during the open-world inference process, there are inevitably test data instances from unknown classes, commonly referred to as outliers. This paper pays attention to the problem that conducts both sample recognition and outlier rejection during inference while outliers exist. To address this problem, we propose a new approach called STAble Memory rePlay (STAMP), which performs optimization over a stable memory bank instead of the risky mini-batch. In particular, the memory bank is dynamically updated by selecting low-entropy and label-consistent samples in a class-balanced manner. In addition, we develop a self-weighted entropy minimization strategy that assigns higher weight to low-entropy samples. Extensive results demonstrate that STAMP outperforms existing TTA methods in terms of both recognition and outlier detection performance. The code is released at https://github.com/yuyongcan/STAMP.

Diffusion models have emerged as a pivotal advancement in generative models, setting new standards to the quality of the generated instances. In the current paper we aim to underscore a discrepancy between conventional training methods and the desired conditional sampling behavior of these models. While the prevalent classifier-free guidance technique works well, it's not without flaws. At higher values for the guidance scale parameter w, we often get out of distribution samples and mode collapse, whereas at lower values for w we may not get the desired specificity. To address these challenges, we introduce an updated loss function that better aligns training objectives with sampling behaviors. Experimental validation with FID scores on CIFAR-10 elucidates our method's ability to produce higher quality samples with fewer sampling timesteps, and be more robust to the choice of guidance scale w. We also experiment with fine-tuning Stable Diffusion on the proposed loss, to provide early evidence that large diffusion models may also benefit from this refined loss function.

A primary goal of class-incremental learning is to strike a balance between stability and plasticity, where models should be both stable enough to retain knowledge learned from previously seen classes, and plastic enough to learn concepts from new classes. While previous works demonstrate strong performance on class-incremental benchmarks, it is not clear whether their success comes from the models being stable, plastic, or a mixture of both. This paper aims to shed light on how effectively recent class-incremental learning algorithms address the stability-plasticity trade-off. We establish analytical tools that measure the stability and plasticity of feature representations, and employ such tools to investigate models trained with various algorithms on large-scale class-incremental benchmarks. Surprisingly, we find that the majority of class-incremental learning algorithms heavily favor stability over plasticity, to the extent that the feature extractor of a model trained on the initial set of classes is no less effective than that of the final incremental model. Our observations not only inspire two simple algorithms that highlight the importance of feature representation analysis, but also suggest that class-incremental learning approaches, in general, should strive for better feature representation learning.

Large language models trained on natural language exhibit pronounced anisotropy: a small number of directions concentrate disproportionate energy, while the remaining dimensions form a broad semantic tail. In low-bit training regimes, this geometry becomes numerically unstable. Because blockwise quantization scales are determined by extreme elementwise magnitudes, dominant directions stretch the dynamic range, compressing long-tail semantic variation into narrow numerical bins. We show that this instability is primarily driven by a coherent rank-one mean bias, which constitutes the dominant component of spectral anisotropy in LLM representations. This mean component emerges systematically across layers and training stages and accounts for the majority of extreme activation magnitudes, making it the principal driver of dynamic-range inflation under low precision. Crucially, because the dominant instability is rank-one, it can be eliminated through a simple source-level mean-subtraction operation. This bias-centric conditioning recovers most of the stability benefits of SVD-based spectral methods while requiring only reduction operations and standard quantization kernels. Empirical results on FP4 (W4A4G4) training show that mean removal substantially narrows the loss gap to BF16 and restores downstream performance, providing a hardware-efficient path to stable low-bit LLM training.

While fine-tuning of pre-trained language models generally helps to overcome the lack of labelled training samples, it also displays model performance instability. This instability mainly originates from randomness in initialisation or data shuffling. To address this, researchers either modify the training process or augment the available samples, which typically results in increased computational costs. We propose a new mitigation strategy, called Delayed Ensemble with Noisy Interpolation (DENI), that leverages the strengths of ensembling, noise regularisation and model interpolation, while retaining computational efficiency. We compare DENI with 9 representative mitigation strategies across 3 models, 4 tuning strategies and 7 text classification datasets. We show that: 1) DENI outperforms the best performing mitigation strategy (Ensemble), while using only a fraction of its cost; 2) the mitigation strategies are beneficial for parameter-efficient fine-tuning (PEFT) methods, outperforming full fine-tuning in specific cases; and 3) combining DENI with data augmentation often leads to even more effective instability mitigation.

Reinforcement learning (RL) post-training has increasingly demonstrated strong ability to elicit reasoning behaviors in large language models (LLMs). For training efficiency, rollouts are typically generated in an off-policy manner using an older sampling policy and then used to update the current target policy. To correct the resulting discrepancy between the sampling and target policies, most existing RL objectives rely on a token-level importance sampling ratio, primarily due to its computational simplicity and numerical stability. However, we observe that token-level correction often leads to unstable training dynamics when the degree of off-policyness is large. In this paper, we revisit LLM policy optimization under off-policy conditions and show that the theoretically rigorous correction term is the prefix importance ratio, and that relaxing it to a token-level approximation can induce instability in RL post-training. To stabilize LLM optimization under large off-policy drift, we propose a simple yet effective objective, Minimum Prefix Ratio (MinPRO). MinPRO replaces the unstable cumulative prefix ratio with a non-cumulative surrogate based on the minimum token-level ratio observed in the preceding prefix. Extensive experiments on both dense and mixture-of-experts LLMs, across multiple mathematical reasoning benchmarks, demonstrate that MinPRO substantially improves training stability and peak performance in off-policy regimes.

Fine-tuning over large pretrained language models (PLMs) has established many state-of-the-art results. Despite its superior performance, such fine-tuning can be unstable, resulting in significant variance in performance and potential risks for practical applications. Previous works have attributed such instability to the catastrophic forgetting problem in the top layers of PLMs, which indicates iteratively that fine-tuning layers in a top-down manner is a promising solution. In this paper, we first point out that this method does not always work out due to the different convergence speeds of different layers/modules. Inspired by this observation, we propose a simple component-wise gradient norm clipping method to adjust the convergence speed for different components. Experiment results demonstrate that our method achieves consistent improvements in terms of generalization performance, convergence speed, and training stability. The codebase can be found at https://github.com/yangalan123/FineTuningStability.

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.

A major barrier to deploying current machine learning models lies in their non-reliability to dataset shifts. To resolve this problem, most existing studies attempted to transfer stable information to unseen environments. Particularly, independent causal mechanisms-based methods proposed to remove mutable causal mechanisms via the do-operator. Compared to previous methods, the obtained stable predictors are more effective in identifying stable information. However, a key question remains: which subset of this whole stable information should the model transfer, in order to achieve optimal generalization ability? To answer this question, we present a comprehensive minimax analysis from a causal perspective. Specifically, we first provide a graphical condition for the whole stable set to be optimal. When this condition fails, we surprisingly find with an example that this whole stable set, although can fully exploit stable information, is not the optimal one to transfer. To identify the optimal subset under this case, we propose to estimate the worst-case risk with a novel optimization scheme over the intervention functions on mutable causal mechanisms. We then propose an efficient algorithm to search for the subset with minimal worst-case risk, based on a newly defined equivalence relation between stable subsets. Compared to the exponential cost of exhaustively searching over all subsets, our searching strategy enjoys a polynomial complexity. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.

The stability of language model pre-training and its effects on downstream performance are still understudied. Prior work shows that the training process can yield significantly different results in response to slight variations in initial conditions, e.g., the random seed. Crucially, the research community still lacks sufficient resources and tools to systematically investigate pre-training stability, particularly for decoder-only language models. We introduce the PolyPythias, a set of 45 new training runs for the Pythia model suite: 9 new seeds across 5 model sizes, from 14M to 410M parameters, resulting in about 7k new checkpoints that we release. Using these new 45 training runs, in addition to the 5 already available, we study the effects of different initial conditions determined by the seed -- i.e., parameters' initialisation and data order -- on (i) downstream performance, (ii) learned linguistic representations, and (iii) emergence of training phases. In addition to common scaling behaviours, our analyses generally reveal highly consistent training dynamics across both model sizes and initial conditions. Further, the new seeds for each model allow us to identify outlier training runs and delineate their characteristics. Our findings show the potential of using these methods to predict training stability.

Large language models (LLMs) are widely used for factual tasks such as "What treats asthma?" or "What is the capital of Latvia?". However, it remains unclear how stably LLMs encode distinctions between true, false, and neither-true-nor-false content in their internal probabilistic representations. We introduce representational stability as the robustness of an LLM's veracity representations to perturbations in the operational definition of truth. We assess representational stability by (i) training a linear probe on an LLM's activations to separate true from not-true statements and (ii) measuring how its learned decision boundary shifts under controlled label changes. Using activations from sixteen open-source models and three factual domains, we compare two types of neither statements. The first are fact-like assertions about entities we believe to be absent from any training data. We call these unfamiliar neither statements. The second are nonfactual claims drawn from well-known fictional contexts. We call these familiar neither statements. The unfamiliar statements induce the largest boundary shifts, producing up to 40% flipped truth judgements in fragile domains (such as word definitions), while familiar fictional statements remain more coherently clustered and yield smaller changes (leq 8.2%). These results suggest that representational stability stems more from epistemic familiarity than from linguistic form. More broadly, our approach provides a diagnostic for auditing and training LLMs to preserve coherent truth assignments under semantic uncertainty, rather than optimizing for output accuracy alone.

Video stabilization is a longstanding computer vision problem, particularly pixel-level synthesis solutions for video stabilization which synthesize full frames add to the complexity of this task. These techniques aim to stabilize videos by synthesizing full frames while enhancing the stability of the considered video. This intensifies the complexity of the task due to the distinct mix of unique motion profiles and visual content present in each video sequence, making robust generalization with fixed parameters difficult. In our study, we introduce a novel approach to enhance the performance of pixel-level synthesis solutions for video stabilization by adapting these models to individual input video sequences. The proposed adaptation exploits low-level visual cues accessible during test-time to improve both the stability and quality of resulting videos. We highlight the efficacy of our methodology of "test-time adaptation" through simple fine-tuning of one of these models, followed by significant stability gain via the integration of meta-learning techniques. Notably, significant improvement is achieved with only a single adaptation step. The versatility of the proposed algorithm is demonstrated by consistently improving the performance of various pixel-level synthesis models for video stabilization in real-world scenarios.

Existing evaluation methods largely rely on clean, static benchmarks, which can overestimate true model performance by failing to capture the noise and variability inherent in real-world user inputs. This is especially true for language models, which can face human-generated text queries containing mistakes, typos, or alternative ways of phrasing the same question. In this work, we introduce a theoretical framework for quantifying model sensitivity to prompt variants, or brittleness, that can enable us to disentangle data-induced difficulty from prompt-related variability. Using this framework, we design a novel evaluation pipeline, Brittlebench, to holistically evaluate the sensitivity of frontier models. We apply semantics-preserving perturbations to a suite of popular benchmarks, and observe model performance to degrade as much as 12%. However, these perturbations do not affect all models equally: even a single perturbation alters the relative ranking of models in 63% of cases, impacting conclusions about comparative model performance. Decomposing the total variance of both state-of-the-art open-weight and commercial models, we find that semantics-preserving input perturbations can account for up to half of the performance variance for a given model. Brittlebench highlights the need for more robust evaluations and models, and allows us to systematically understand model brittleness.

We prove stability for a class of heterogeneous catalysis models in the L_p-setting. We consider a setting in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. Under a reasonable condition on the involved parameters, we show that given equilibria are normally stable, i.e. solutions are attracted at an exponential rate. The potential incidence of instability is discussed as well.

Neural network training is inherently sensitive to initialization and the randomness induced by stochastic gradient descent. However, it is unclear to what extent such effects lead to meaningfully different networks, either in terms of the models' weights or the underlying functions that were learned. In this work, we show that during the initial "chaotic" phase of training, even extremely small perturbations reliably causes otherwise identical training trajectories to diverge-an effect that diminishes rapidly over training time. We quantify this divergence through (i) L^2 distance between parameters, (ii) the loss barrier when interpolating between networks, (iii) L^2 and barrier between parameters after permutation alignment, and (iv) representational similarity between intermediate activations; revealing how perturbations across different hyperparameter or fine-tuning settings drive training trajectories toward distinct loss minima. Our findings provide insights into neural network training stability, with practical implications for fine-tuning, model merging, and diversity of model ensembles.

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards fully end-to-end learned systems. Most works so far can only generalize over a subset of properties to which a generic solver would be faced, including: resolution, topology, geometry, boundary conditions, domain discretization regularity, dimensionality, etc. In this work, we build a solver, satisfying these properties, where all the components are based on neural message passing, replacing all heuristically designed components in the computation graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. In order to encourage stability in training autoregressive models, we put forward a method that is based on the principle of zero-stability, posing stability as a domain adaptation problem. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.

Recent studies show that Large Language Models (LLMs) with safety alignment can be jail-broken by fine-tuning on a dataset mixed with harmful data. First time in the literature, we show that the jail-broken effect can be mitigated by separating states in the finetuning stage to optimize the alignment and user datasets. Unfortunately, our subsequent study shows that this simple Bi-State Optimization (BSO) solution experiences convergence instability when steps invested in its alignment state is too small, leading to downgraded alignment performance. By statistical analysis, we show that the excess drift towards consensus could be a probable reason for the instability. To remedy this issue, we propose Lazy(i) safety alignment (Lisa), which introduces a proximal term to constraint the drift of each state. Theoretically, the benefit of the proximal term is supported by the convergence analysis, wherein we show that a sufficient large proximal factor is necessary to guarantee Lisa's convergence. Empirically, our results on four downstream finetuning tasks show that Lisa with a proximal term can significantly increase alignment performance while maintaining the LLM's accuracy on the user tasks. Code is available at https://github.com/git-disl/Lisa.

In the realm of continual learning, the presence of noisy labels within data streams represents a notable obstacle to model reliability and fairness. We focus on the data stream scenario outlined in pertinent literature, characterized by fuzzy task boundaries and noisy labels. To address this challenge, we introduce a novel and intuitive sampling method called Noisy Test Debiasing (NTD) to mitigate noisy labels in evolving data streams and establish a fair and robust continual learning algorithm. NTD is straightforward to implement, making it feasible across various scenarios. Our experiments benchmark four datasets, including two synthetic noise datasets (CIFAR10 and CIFAR100) and real-world noise datasets (mini-WebVision and Food-101N). The results validate the efficacy of NTD for online continual learning in scenarios with noisy labels in data streams. Compared to the previous leading approach, NTD achieves a training speedup enhancement over two times while maintaining or surpassing accuracy levels. Moreover, NTD utilizes less than one-fifth of the GPU memory resources compared to previous leading methods.

Data balancing across multiple modalities and sources appears in various forms in foundation models in machine learning and AI, e.g. in CLIP and DINO. We show that data balancing across modalities and sources actually offers an unsuspected benefit: variance reduction. We present a non-asymptotic statistical bound that quantifies this variance reduction effect and relates it to the eigenvalue decay of Markov operators. Furthermore, we describe how various forms of data balancing in contrastive multimodal learning and self-supervised clustering can be better understood, and even improved upon, owing to our variance reduction viewpoint.

The quality of generative models depends on the quality of the data they are trained on. Creating large-scale, high-quality datasets is often expensive and sometimes impossible, e.g. in certain scientific applications where there is no access to clean data due to physical or instrumentation constraints. Ambient Diffusion and related frameworks train diffusion models with solely corrupted data (which are usually cheaper to acquire) but ambient models significantly underperform models trained on clean data. We study this phenomenon at scale by training more than 80 models on data with different corruption levels across three datasets ranging from 30,000 to approx 1.3M samples. We show that it is impossible, at these sample sizes, to match the performance of models trained on clean data when only training on noisy data. Yet, a combination of a small set of clean data (e.g.~10% of the total dataset) and a large set of highly noisy data suffices to reach the performance of models trained solely on similar-size datasets of clean data, and in particular to achieve near state-of-the-art performance. We provide theoretical evidence for our findings by developing novel sample complexity bounds for learning from Gaussian Mixtures with heterogeneous variances. Our theoretical model suggests that, for large enough datasets, the effective marginal utility of a noisy sample is exponentially worse than that of a clean sample. Providing a small set of clean samples can significantly reduce the sample size requirements for noisy data, as we also observe in our experiments.

Tool-based Agentic Reinforcement Learning (TARL) has emerged as a promising paradigm for training search agents to interact with external tools for a multi-turn information-seeking process autonomously. However, we identify a critical training instability that leads to catastrophic model collapse: Importance Sampling Distribution Drift(ISDD). In Group Relative Policy Optimization(GRPO), a widely adopted TARL algorithm, ISDD manifests as a precipitous decline in the importance sampling ratios, which nullifies gradient updates and triggers irreversible training failure. To address this, we propose Search Agent Policy Optimization (SAPO), which stabilizes training via a conditional token-level KL constraint. Unlike hard clipping, which ignores distributional divergence, SAPO selectively penalizes the KL divergence between the current and old policies. Crucially, this penalty is applied only to positive tokens with low probabilities where the policy has shifted excessively, thereby preventing distribution drift while preserving gradient flow. Remarkably, SAPO requires only one-line code modification to standard GRPO, ensuring immediate deployability. Extensive experiments across seven QA benchmarks demonstrate that SAPO achieves +10.6\% absolute improvement (+31.5\% relative) over Search-R1, yielding consistent gains across varying model scales (1.5B, 14B) and families (Qwen, LLaMA).

Benchmarks shape scientific conclusions about model capabilities and steer model development. This creates a feedback loop: stronger benchmarks drive better models, and better models demand more discriminative benchmarks. Ensuring benchmark reliability is therefore essential for trustworthy evaluation and meaningful progress. In this work, we study benchmark reliability from a distributional perspective and introduce benchmark harmony, which measures how uniformly a model's performance is distributed across the subdomains of a benchmark. We posit that high harmony is a desirable benchmark property, indicating that the aggregate metric reflects uniform competence across subdomains. Across 19 multiple-choice benchmarks and five model families, we map each benchmark onto a mean-variance plane of harmony computed across models, where high mean and low variance signal more reliable evaluation. Our analysis shows that less harmonious benchmarks can give misleading results, since overall accuracy may be disproportionately influenced by specific subdomains. For instance, ARC-Easy is overwhelmed by questions on Biological Concepts, overshadowing other critical subdomains such as Geography, Physics, Chemistry, and Environmental Science. By recommending that harmony should be reported alongside accuracy, we reframe evaluation from simple performance averages to a more robust, distributionally reliable measurement of performance.

Social scientists are now using large language models to create "silicon samples" - synthetic datasets intended to stand in for human respondents, aimed at revolutionising human subjects research. However, there are many analytic choices which must be made to produce these samples. Though many of these choices are defensible, their impact on sample quality is poorly understood. I map out these analytic choices and demonstrate how a very small number of decisions can dramatically change the correspondence between silicon samples and human data. Configurations (N = 252) varied substantially in their capacity to estimate (i) rank ordering of participants, (ii) response distributions, and (iii) between-scale correlations. Most critically, configurations were not consistent in quality: those that performed well on one dimension often performed poorly on another, implying that there is no "one-size-fits-all" configuration that optimises the accuracy of these samples. I call for greater attention to the threat of analytic flexibility in using silicon samples.

Mathematical reasoning models are widely deployed in education, automated tutoring, and decision support systems despite exhibiting fundamental computational instabilities. We demonstrate that state-of-the-art models (Qwen2.5-Math-7B) achieve 61% accuracy through a mixture of reliable and unreliable reasoning pathways: 18.4% of correct predictions employ stable, faithful reasoning while 81.6% emerge through computationally inconsistent pathways. Additionally, 8.8% of all predictions are silent failures -- confident yet incorrect outputs. Through comprehensive analysis using novel faithfulness metrics, we reveal: (1) reasoning quality shows weak negative correlation with correctness (r=-0.21, p=0.002), reflecting a binary classification threshold artifact rather than a monotonic inverse relationship; (2) scaling from 1.5B to 7B parameters (4.7x increase) provides zero accuracy benefit on our evaluated subset (6% of GSM8K), requiring validation on the complete benchmark; and (3) latent reasoning employs diverse computational strategies, with ~20% sharing CoT-like patterns. These findings highlight that benchmark accuracy can mask computational unreliability, demanding evaluation reforms measuring stability beyond single-sample metrics.

Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of diffusion-based SR models are fluctuating at every time of sampling, especially for samplers with few resampled steps. This inherent randomness of diffusion models results in ineffectiveness and instability, making it challenging for users to guarantee the quality of SR results. However, our work takes this randomness as an opportunity: fully analyzing and leveraging it leads to the construction of an effective plug-and-play sampling method that owns the potential to benefit a series of diffusion-based SR methods. More in detail, we propose to steadily sample high-quality SR images from pre-trained diffusion-based SR models by solving diffusion ordinary differential equations (diffusion ODEs) with optimal boundary conditions (BCs) and analyze the characteristics between the choices of BCs and their corresponding SR results. Our analysis shows the route to obtain an approximately optimal BC via an efficient exploration in the whole space. The quality of SR results sampled by the proposed method with fewer steps outperforms the quality of results sampled by current methods with randomness from the same pre-trained diffusion-based SR model, which means that our sampling method "boosts" current diffusion-based SR models without any additional training.

Auto-regressive video generation enables long video synthesis by iteratively conditioning each new batch of frames on previously generated content. However, recent work has shown that such pipelines suffer from severe temporal drift, where errors accumulate and amplify over long horizons. We hypothesize that this drift does not primarily stem from insufficient model capacity, but rather from inference-time error propagation. Specifically, we contend that drift arises from the uncontrolled reuse of corrupted latent conditioning tokens during auto-regressive inference. To correct this accumulation of errors, we propose a simple, inference-time method that mitigates temporal drift by identifying and removing unstable latent tokens before they are reused for conditioning. For this purpose, we define unstable tokens as latent tokens whose representations deviate significantly from those of the previously generated batch, indicating potential corruption or semantic drift. By explicitly removing corrupted latent tokens from the auto-regressive context, rather than modifying entire spatial regions or model parameters, our method prevents unreliable latent information from influencing future generation steps. As a result, it significantly improves long-horizon temporal consistency without modifying the model architecture, training procedure, or leaving latent space.

Recent studies of gradient descent with large step sizes have shown that there is often a regime with an initial increase in the largest eigenvalue of the loss Hessian (progressive sharpening), followed by a stabilization of the eigenvalue near the maximum value which allows convergence (edge of stability). These phenomena are intrinsically non-linear and do not happen for models in the constant Neural Tangent Kernel (NTK) regime, for which the predictive function is approximately linear in the parameters. As such, we consider the next simplest class of predictive models, namely those that are quadratic in the parameters, which we call second-order regression models. For quadratic objectives in two dimensions, we prove that this second-order regression model exhibits progressive sharpening of the NTK eigenvalue towards a value that differs slightly from the edge of stability, which we explicitly compute. In higher dimensions, the model generically shows similar behavior, even without the specific structure of a neural network, suggesting that progressive sharpening and edge-of-stability behavior aren't unique features of neural networks, and could be a more general property of discrete learning algorithms in high-dimensional non-linear models.

This paper is a study of fine-tuning of BERT contextual representations, with focus on commonly observed instabilities in few-sample scenarios. We identify several factors that cause this instability: the common use of a non-standard optimization method with biased gradient estimation; the limited applicability of significant parts of the BERT network for down-stream tasks; and the prevalent practice of using a pre-determined, and small number of training iterations. We empirically test the impact of these factors, and identify alternative practices that resolve the commonly observed instability of the process. In light of these observations, we re-visit recently proposed methods to improve few-sample fine-tuning with BERT and re-evaluate their effectiveness. Generally, we observe the impact of these methods diminishes significantly with our modified process.

Differentiable matching layers and residual connection paradigms, often implemented via entropy-regularized Optimal Transport (OT), serve as critical mechanisms in structural prediction and architectural scaling. However, recovering discrete permutations or maintaining identity mappings via annealing εto 0 is notoriously unstable. In this work, we identify a fundamental mechanism for this failure: Premature Mode Collapse. By analyzing the non-normal dynamics of the Sinkhorn fixed-point map, we reveal a theoretical thermodynamic speed limit: standard exponential cooling outpaces the contraction rate of the inference operator, which degrades as O(1/ε). To address this, we propose Efficient Piecewise Hybrid Adaptive Stability Control (EPH-ASC), an adaptive scheduling algorithm that monitors the stability of the inference process. We demonstrate that EPH-ASC is essential for stabilizing Manifold-Constrained Hyper-Connections (mHC) during large-scale training on the FineWeb-Edu dataset, effectively preventing late-stage gradient explosions by enforcing a linear stability law.

Recent approaches have shown promises distilling diffusion models into efficient one-step generators. Among them, Distribution Matching Distillation (DMD) produces one-step generators that match their teacher in distribution, without enforcing a one-to-one correspondence with the sampling trajectories of their teachers. However, to ensure stable training, DMD requires an additional regression loss computed using a large set of noise-image pairs generated by the teacher with many steps of a deterministic sampler. This is costly for large-scale text-to-image synthesis and limits the student's quality, tying it too closely to the teacher's original sampling paths. We introduce DMD2, a set of techniques that lift this limitation and improve DMD training. First, we eliminate the regression loss and the need for expensive dataset construction. We show that the resulting instability is due to the fake critic not estimating the distribution of generated samples accurately and propose a two time-scale update rule as a remedy. Second, we integrate a GAN loss into the distillation procedure, discriminating between generated samples and real images. This lets us train the student model on real data, mitigating the imperfect real score estimation from the teacher model, and enhancing quality. Lastly, we modify the training procedure to enable multi-step sampling. We identify and address the training-inference input mismatch problem in this setting, by simulating inference-time generator samples during training time. Taken together, our improvements set new benchmarks in one-step image generation, with FID scores of 1.28 on ImageNet-64x64 and 8.35 on zero-shot COCO 2014, surpassing the original teacher despite a 500X reduction in inference cost. Further, we show our approach can generate megapixel images by distilling SDXL, demonstrating exceptional visual quality among few-step methods.

Synthetic data generated by large language models has become integral to modern NLP training pipelines, from bootstrapping reasoning capabilities to augmenting instruction-following datasets. While recent work demonstrates successful applications maintaining high external data ratios, systematic understanding of how synthetic data proportion affects model behavior across different scales remains limited. This paper presents a controlled empirical study examining model performance, calibration, and output characteristics when trained on varying synthetic-to-external data ratios. Using the Pythia model suite (410M-12B parameters) across five diverse tasks, we evaluate models after one to three training iterations with synthetic data proportions ranging from 0-50\%. Our key findings include: models maintain stable performance with up to 20\% synthetic data, but degradation accelerates beyond 30\%; larger models (6.9B-12B) show greater robustness to synthetic data than smaller models (410M-1.4B); calibration degradation precedes accuracy loss, providing an early warning signal; and task characteristics matter, with reasoning tasks degrading faster than retrieval tasks under synthetic data training. Importantly, we find that current best practices, such as those employed in STaR and Self-Instruct systems that maintain greater than 80\% external data, operate well within safe regimes identified by our experiments. We provide practical guidance for practitioners on synthetic data budgets based on model scale and task requirements, alongside detailed comparison with concurrent work including Shumailov et al.'s model collapse findings.

Machine learning (ML) holds great potential for accurately forecasting treatment outcomes over time, which could ultimately enable the adoption of more individualized treatment strategies in many practical applications. However, a significant challenge that has been largely overlooked by the ML literature on this topic is the presence of informative sampling in observational data. When instances are observed irregularly over time, sampling times are typically not random, but rather informative -- depending on the instance's characteristics, past outcomes, and administered treatments. In this work, we formalize informative sampling as a covariate shift problem and show that it can prohibit accurate estimation of treatment outcomes if not properly accounted for. To overcome this challenge, we present a general framework for learning treatment outcomes in the presence of informative sampling using inverse intensity-weighting, and propose a novel method, TESAR-CDE, that instantiates this framework using Neural CDEs. Using a simulation environment based on a clinical use case, we demonstrate the effectiveness of our approach in learning under informative sampling.

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.

Sample selection is a prevalent method in learning with noisy labels, where small-loss data are typically considered as correctly labeled data. However, this method may not effectively identify clean hard examples with large losses, which are critical for achieving the model's close-to-optimal generalization performance. In this paper, we propose a new framework, Late Stopping, which leverages the intrinsic robust learning ability of DNNs through a prolonged training process. Specifically, Late Stopping gradually shrinks the noisy dataset by removing high-probability mislabeled examples while retaining the majority of clean hard examples in the training set throughout the learning process. We empirically observe that mislabeled and clean examples exhibit differences in the number of epochs required for them to be consistently and correctly classified, and thus high-probability mislabeled examples can be removed. Experimental results on benchmark-simulated and real-world noisy datasets demonstrate that the proposed method outperforms state-of-the-art counterparts.

Text-to-image diffusion models, e.g. Stable Diffusion (SD), lately have shown remarkable ability in high-quality content generation, and become one of the representatives for the recent wave of transformative AI. Nevertheless, such advance comes with an intensifying concern about the misuse of this generative technology, especially for producing copyrighted or NSFW (i.e. not safe for work) images. Although efforts have been made to filter inappropriate images/prompts or remove undesirable concepts/styles via model fine-tuning, the reliability of these safety mechanisms against diversified problematic prompts remains largely unexplored. In this work, we propose Prompting4Debugging (P4D) as a debugging and red-teaming tool that automatically finds problematic prompts for diffusion models to test the reliability of a deployed safety mechanism. We demonstrate the efficacy of our P4D tool in uncovering new vulnerabilities of SD models with safety mechanisms. Particularly, our result shows that around half of prompts in existing safe prompting benchmarks which were originally considered "safe" can actually be manipulated to bypass many deployed safety mechanisms, including concept removal, negative prompt, and safety guidance. Our findings suggest that, without comprehensive testing, the evaluations on limited safe prompting benchmarks can lead to a false sense of safety for text-to-image models.

RL training of multi-turn LLM agents is inherently unstable, and reasoning quality directly determines task performance. Entropy is widely used to track reasoning stability. However, entropy only measures diversity within the same input, and cannot tell whether reasoning actually responds to different inputs. In RAGEN-2, we find that even with stable entropy, models can rely on fixed templates that look diverse but are input-agnostic. We call this template collapse, a failure mode invisible to entropy and all existing metrics. To diagnose this failure, we decompose reasoning quality into within-input diversity (Entropy) and cross-input distinguishability (Mutual Information, MI), and introduce a family of mutual information proxies for online diagnosis. Across diverse tasks, mutual information correlates with final performance much more strongly than entropy, making it a more reliable proxy for reasoning quality. We further explain template collapse with a signal-to-noise ratio (SNR) mechanism. Low reward variance weakens task gradients, letting regularization terms dominate and erase cross-input reasoning differences. To address this, we propose SNR-Aware Filtering to select high-signal prompts per iteration using reward variance as a lightweight proxy. Across planning, math reasoning, web navigation, and code execution, the method consistently improves both input dependence and task performance.

Text-to-image generative models have garnered immense attention for their ability to produce high-fidelity images from text prompts. Among these, Stable Diffusion distinguishes itself as a leading open-source model in this fast-growing field. However, the intricacies of fine-tuning these models pose multiple challenges from new methodology integration to systematic evaluation. Addressing these issues, this paper introduces LyCORIS (Lora beYond Conventional methods, Other Rank adaptation Implementations for Stable diffusion) [https://github.com/KohakuBlueleaf/LyCORIS], an open-source library that offers a wide selection of fine-tuning methodologies for Stable Diffusion. Furthermore, we present a thorough framework for the systematic assessment of varied fine-tuning techniques. This framework employs a diverse suite of metrics and delves into multiple facets of fine-tuning, including hyperparameter adjustments and the evaluation with different prompt types across various concept categories. Through this comprehensive approach, our work provides essential insights into the nuanced effects of fine-tuning parameters, bridging the gap between state-of-the-art research and practical application.

Reinforcement Learning (RL) has become essential for eliciting complex reasoning capabilities in Large Language Models (LLMs). However, the substantial memory overhead of storing Key-Value (KV) caches during long-horizon rollouts acts as a critical bottleneck, often prohibiting efficient training on limited hardware. While existing KV compression techniques offer a remedy for inference, directly applying them to RL training induces a severe policy mismatch, leading to catastrophic performance collapse. To address this, we introduce Sparse-RL empowers stable RL training under sparse rollouts. We show that instability arises from a fundamental policy mismatch among the dense old policy, the sparse sampler policy, and the learner policy. To mitigate this issue, Sparse-RL incorporates Sparsity-Aware Rejection Sampling and Importance-based Reweighting to correct the off-policy bias introduced by compression-induced information loss. Experimental results show that Sparse-RL reduces rollout overhead compared to dense baselines while preserving the performance. Furthermore, Sparse-RL inherently implements sparsity-aware training, significantly enhancing model robustness during sparse inference deployment.

Continual Instruction Tuning (CIT) is adopted to continually instruct Large Models to follow human intent data by data. It is observed that existing gradient update would heavily destroy the performance on previous datasets during CIT process. Instead, Exponential Moving Average (EMA), owns the ability to trace previous parameters, which can aid in decreasing forgetting. Nonetheless, its stable balance weight fails to deal with the ever-changing datasets, leading to the out-of-balance between plasticity and stability. In this paper, we propose a general continual instruction tuning framework to address the challenge. Starting from the trade-off prerequisite and EMA update, we propose the plasticity and stability ideal condition. Based on Taylor expansion in the loss function, we find the optimal balance weight can be automatically determined by the gradients and learned parameters. Therefore, we propose a stable-plasticity balanced coefficient to avoid knowledge interference. Based on the semantic similarity of the instructions, we can determine whether to retrain or expand the training parameters and allocate the most suitable parameters for the testing instances. Extensive experiments across multiple continual instruction tuning benchmarks demonstrate that our approach not only enhances anti-forgetting capabilities but also significantly improves overall continual tuning performance. Our code is available at https://github.com/JingyangQiao/CoIN.

Generative Artificial Intelligence image models have achieved outstanding performance in text-to-image generation and other tasks, such as inpainting that completes images with missing fragments. The performance of inpainting can be accurately measured by taking an image, removing some fragments, performing the inpainting to restore them, and comparing the results with the original image. Interestingly, inpainting can also be applied recursively, starting from an image, removing some parts, applying inpainting to reconstruct the image, and then starting the inpainting process again on the reconstructed image, and so forth. This process of recursively applying inpainting can lead to an image that is similar or completely different from the original one, depending on the fragments that are removed and the ability of the model to reconstruct them. Intuitively, stability, understood as the capability to recover an image that is similar to the original one even after many recursive inpainting operations, is a desirable feature and can be used as an additional performance metric for inpainting. The concept of stability is also being studied in the context of recursive training of generative AI models with their own data. Recursive inpainting is an inference-only recursive process whose understanding may complement ongoing efforts to study the behavior of generative AI models under training recursion. In this paper, the impact of recursive inpainting is studied for one of the most widely used image models: Stable Diffusion. The results show that recursive inpainting can lead to image collapse, so ending with a nonmeaningful image, and that the outcome depends on several factors such as the type of image, the size of the inpainting masks, and the number of iterations.

Large language model (LLM) agents increasingly rely on external tools such as search engines to solve complex, multi-step problems, and reinforcement learning (RL) has become a key paradigm for training them. However, the trajectories of search agents are structurally heterogeneous, where variations in the number, placement, and outcomes of search calls lead to fundamentally different answer directions and reward distributions. Standard policy gradient methods, which use a single global baseline, suffer from what we identify and formalize as cross-stratum bias-an "apples-to-oranges" comparison of heterogeneous trajectories. This cross-stratum bias distorts credit assignment and hinders exploration of complex, multi-step search strategies. To address this, we propose Stratified GRPO, whose central component, Stratified Advantage Normalization (SAN), partitions trajectories into homogeneous strata based on their structural properties and computes advantages locally within each stratum. This ensures that trajectories are evaluated only against their true peers. Our analysis proves that SAN eliminates cross-stratum bias, yields conditionally unbiased unit-variance estimates inside each stratum, and retains the global unbiasedness and unit-variance properties enjoyed by standard normalization, resulting in a more pure and scale-stable learning signal. To improve practical stability under finite-sample regimes, we further linearly blend SAN with the global estimator. Extensive experiments on diverse single-hop and multi-hop question-answering benchmarks demonstrate that Stratified GRPO consistently and substantially outperforms GRPO by up to 11.3 points, achieving higher training rewards, greater training stability, and more effective search policies. These results establish stratification as a principled remedy for structural heterogeneity in RL for LLM search agents.

The quest for Continual Learning (CL) seeks to empower neural networks with the ability to learn and adapt incrementally. Central to this pursuit is addressing the stability-plasticity dilemma, which involves striking a balance between two conflicting objectives: preserving previously learned knowledge and acquiring new knowledge. While numerous CL methods aim to achieve this trade-off, they often overlook the impact of network architecture on stability and plasticity, restricting the trade-off to the parameter level. In this paper, we delve into the conflict between stability and plasticity at the architectural level. We reveal that under an equal parameter constraint, deeper networks exhibit better plasticity, while wider networks are characterized by superior stability. To address this architectural-level dilemma, we introduce a novel framework denoted Dual-Arch, which serves as a plug-in component for CL. This framework leverages the complementary strengths of two distinct and independent networks: one dedicated to plasticity and the other to stability. Each network is designed with a specialized and lightweight architecture, tailored to its respective objective. Extensive experiments demonstrate that Dual-Arch enhances the performance of existing CL methods while being up to 87% more compact in terms of parameters.

Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize stability, we analyze and develop a computationally efficient implementation of Jacobian regularization that increases classification margins of neural networks. The stabilizing effect of the Jacobian regularizer leads to significant improvements in robustness, as measured against both random and adversarial input perturbations, without severely degrading generalization properties on clean data.

Long-term training of large language models (LLMs) requires maintaining stable exploration to prevent the model from collapsing into sub-optimal behaviors. Entropy is crucial in this context, as it controls exploration and helps avoid premature convergence to sub-optimal solutions. However, existing reinforcement learning methods struggle to maintain an appropriate level of entropy, as the training process involves a mix of positive and negative samples, each affecting entropy in different ways across steps. To address this, we propose Entropy stablilization via Proportional-Integral Control (EntroPIC), a novel method that adaptively adjusts the influence of positive and negative samples by dynamically tuning their loss coefficients. This approach stabilizes entropy throughout training, ensuring efficient exploration and steady progress. We provide a comprehensive theoretical analysis for both on-policy and off-policy learning settings, demonstrating that EntroPIC is effective at controlling entropy in large-scale LLM training. Experimental results show that our method successfully maintains desired entropy levels, enabling stable and optimal RL training for LLMs.

Typical neural network trainings have substantial variance in test-set performance between repeated runs, impeding hyperparameter comparison and training reproducibility. We present the following results towards understanding this variation. (1) Despite having significant variance on their test-sets, we demonstrate that standard CIFAR-10 and ImageNet trainings have very little variance in their performance on the test-distributions from which those test-sets are sampled, suggesting that variance is less of a practical issue than previously thought. (2) We present a simplifying statistical assumption which closely approximates the structure of the test-set accuracy distribution. (3) We argue that test-set variance is inevitable in the following two senses. First, we show that variance is largely caused by high sensitivity of the training process to initial conditions, rather than by specific sources of randomness like the data order and augmentations. Second, we prove that variance is unavoidable given the observation that ensembles of trained networks are well-calibrated. (4) We conduct preliminary studies of distribution-shift, fine-tuning, data augmentation and learning rate through the lens of variance between runs.

Agentic reinforcement learning (ARL) has rapidly gained attention as a promising paradigm for training agents to solve complex, multi-step interactive tasks. Despite encouraging early results, ARL remains highly unstable, often leading to training collapse. This instability limits scalability to larger environments and longer interaction horizons, and constrains systematic exploration of algorithmic design choices. In this paper, we first propose ARLArena, a stable training recipe and systematic analysis framework that examines training stability in a controlled and reproducible setting. ARLArena first constructs a clean and standardized testbed. Then, we decompose policy gradient into four core design dimensions and assess the performance and stability of each dimension. Through this fine-grained analysis, we distill a unified perspective on ARL and propose SAMPO, a stable agentic policy optimization method designed to mitigate the dominant sources of instability in ARL. Empirically, SAMPO achieves consistently stable training and strong performance across diverse agentic tasks. Overall, this study provides a unifying policy gradient perspective for ARL and offers practical guidance for building stable and reproducible LLM-based agent training pipelines.

We investigate the use of a stratified sampling approach for LIME Image, a popular model-agnostic explainable AI method for computer vision tasks, in order to reduce the artifacts generated by typical Monte Carlo sampling. Such artifacts are due to the undersampling of the dependent variable in the synthetic neighborhood around the image being explained, which may result in inadequate explanations due to the impossibility of fitting a linear regressor on the sampled data. We then highlight a connection with the Shapley theory, where similar arguments about undersampling and sample relevance were suggested in the past. We derive all the formulas and adjustment factors required for an unbiased stratified sampling estimator. Experiments show the efficacy of the proposed approach.

In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees on the quality of approximation, while reducing the number of examples to the product of the VC dimension d and the total sensitivity mathfrak S in remarkably general settings. However, guarantees going beyond this general bound of mathfrak S d are known in perhaps only one setting, for ell_2 subspace embeddings, despite intense study of sensitivity sampling in prior work. In this work, we show the first bounds for sensitivity sampling for ell_p subspace embeddings for pneq 2 that improve over the general mathfrak S d bound, achieving a bound of roughly mathfrak S^{2/p} for 1leq p<2 and mathfrak S^{2-2/p} for 2<p<infty. For 1leq p<2, we show that this bound is tight, in the sense that there exist matrices for which mathfrak S^{2/p} samples is necessary. Furthermore, our techniques yield further new results in the study of sampling algorithms, showing that the root leverage score sampling algorithm achieves a bound of roughly d for 1leq p<2, and that a combination of leverage score and sensitivity sampling achieves an improved bound of roughly d^{2/p}mathfrak S^{2-4/p} for 2<p<infty. Our sensitivity sampling results yield the best known sample complexity for a wide class of structured matrices that have small ell_p sensitivity.

Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in high-stakes contexts, such as medical diagnosis and finance. We show that this inconsistent behavior extends beyond predictions to feature attributions, which may likewise have negative implications for the intelligibility of a model, and one's ability to find recourse for subjects. We then introduce selective ensembles to mitigate such inconsistencies by applying hypothesis testing to the predictions of a set of models trained using randomly-selected starting conditions; importantly, selective ensembles can abstain in cases where a consistent outcome cannot be achieved up to a specified confidence level. We prove that that prediction disagreement between selective ensembles is bounded, and empirically demonstrate that selective ensembles achieve consistent predictions and feature attributions while maintaining low abstention rates. On several benchmark datasets, selective ensembles reach zero inconsistently predicted points, with abstention rates as low 1.5%.

The training data for many Large Language Models (LLMs) is contaminated with test data. This means that public benchmarks used to assess LLMs are compromised, suggesting a performance gap between benchmark scores and actual capabilities. Ideally, a private holdout set could be used to accurately verify scores. Unfortunately, such datasets do not exist for most benchmarks, and post-hoc construction of sufficiently similar datasets is non-trivial. To address these issues, we introduce a systematic methodology for (i) retrospectively constructing a holdout dataset for a target dataset, (ii) demonstrating the statistical indistinguishability of this retro-holdout dataset, and (iii) comparing LLMs on the two datasets to quantify the performance gap due to the dataset's public availability. Applying these methods to TruthfulQA, we construct and release Retro-Misconceptions, on which we evaluate twenty LLMs and find that some have inflated scores by as much as 16 percentage points. Our results demonstrate that public benchmark scores do not always accurately assess model properties, and underscore the importance of improved data practices in the field.

Group Relative Policy Optimization (GRPO) is highly effective for post-training autoregressive (AR) language models, yet its direct application to diffusion large language models (dLLMs) often triggers reward collapse. We identify two sources of incompatibility. First, GRPO relies on importance ratios defined by sequence probabilities, which are intractable in dLLMs and must be estimated (e.g., via ELBO-based or mean-field likelihood proxies), yielding inherently noisy ratios. Second, standard GRPO's formulation is not designed for estimated ratios: its conditional clipping can be anomalously bypassed by model-agnostic estimation noise, producing gradient spikes, while its fixed group-size normalization amplifies gradient-magnitude fluctuations under high-variance ratio estimates. We show these effects form a self-reinforcing instability loop that drives policy drift and further increases ratio variance. To break this loop, we propose StableDRL, a reformulation of GRPO tailored for dLLMs that uses (i) unconditional clipping to suppress outlier-induced spikes and (ii) self-normalization to constrain updates within the convex hull of per-sample gradients. We further extend StableDRL to block-wise diffusion models via a staircase attention mechanism.

Training stability remains a critical bottleneck for Group Relative Policy Optimization (GRPO), often manifesting as a trade-off between reasoning plasticity and general capability retention. We identify a root cause as the geometric conflict between plasticity and stability gradients, which leads to destructive interference. Crucially, we argue that deterministic projection methods are suboptimal for GRPO as they overlook the intrinsic stochasticity of group-based gradient estimates. To address this, we propose Probabilistic Conflict Resolution (PCR), a Bayesian framework that models gradients as random variables. PCR dynamically arbitrates conflicts via an uncertainty-aware ``soft projection'' mechanism, optimizing the signal-to-noise ratio. Extensive experiments demonstrate that PCR significantly smooths the training trajectory and achieves superior performance in various reasoning tasks.

Reinforcement Learning (RL) has significantly improved large language model reasoning, but existing RL fine-tuning methods rely heavily on heuristic techniques such as entropy regularization and reweighting to maintain stability. In practice, they often experience late-stage performance collapse, leading to degraded reasoning quality and unstable training. We derive that the magnitude of token-wise policy gradients in RL is negatively correlated with token probability and local policy entropy. Building on this result, we prove that training instability is driven by a tiny fraction of tokens, approximately 0.01\%, which we term spurious tokens. When such tokens appear in correct responses, they contribute little to the reasoning outcome but inherit the full sequence-level reward, leading to abnormally amplified gradient updates. Motivated by this observation, we propose Spurious-Token-Aware Policy Optimization (STAPO) for large-scale model refining, which selectively masks such updates and renormalizes the loss over valid tokens. Across six mathematical reasoning benchmarks using Qwen 1.7B, 8B, and 14B base models, STAPO consistently demonstrates superior entropy stability and achieves an average performance improvement of 7.13\% over GRPO, 20-Entropy and JustRL.

As Large Language Models (LLMs) are increasingly deployed in real-world settings, correctness alone is insufficient. Reliable deployment requires maintaining truthful beliefs under contextual perturbations. Existing evaluations largely rely on point-wise confidence like Self-Consistency, which can mask brittle belief. We show that even facts answered with perfect self-consistency can rapidly collapse under mild contextual interference. To address this gap, we propose Neighbor-Consistency Belief (NCB), a structural measure of belief robustness that evaluates response coherence across a conceptual neighborhood. To validate the efficiency of NCB, we introduce a new cognitive stress-testing protocol that probes outputs stability under contextual interference. Experiments across multiple LLMs show that the performance of high-NCB data is relatively more resistant to interference. Finally, we present Structure-Aware Training (SAT), which optimizes context-invariant belief structure and reduces long-tail knowledge brittleness by approximately 30%. Code will be available at https://github.com/zjunlp/belief.

Stable pre-training is essential for achieving better-performing language models. However, tracking pre-training stability by calculating gradient variance at every step is impractical due to the significant computational costs. We explore Token Embedding Variability (TEV) as a simple and efficient proxy for assessing pre-training stability in language models with pre-layer normalization, given that shallower layers are more prone to gradient explosion (section 2.2). Moreover, we propose Multi-head Low-Rank Attention (MLRA) as an architecture to alleviate such instability by limiting the exponential growth of output embedding variance, thereby preventing the gradient explosion (section 3.2). Empirical results on GPT-2 with MLRA demonstrate increased stability and lower perplexity, particularly in deeper models.

The stability of recursively trained large language models (LLMs) is a foundational problem for AI safety. Prevailing theory predicts model collapse, a progressive degradation when models are trained on their own output. We challenge this narrative by introducing a selective feedback mechanism. Contrary to expectation, instead of merely slowing decay, our experiments provide strong evidence that this pressure reverses it, inducing a statistically significant performance improvement in a Gemma 2B model on a complex summarization task. We name this phenomenon the Anti-Ouroboros Effect. We contrast this with a foundational experiment using a simple classifier, where the theoretical degenerative loop was validated, highlighting the unique dynamics of high-dimensional models. Our findings establish that systemic resilience can be an emergent property of LLMs under simple selection pressure, suggesting a powerful and scalable principle for developing safer and more robust AI systems. Across five generations, a quality-filtered condition improved by 6.6% in ROUGE-L F1 score, whereas an unfiltered control degraded by 3.5% and a random-filter control degraded by 4.2%

When deploying machine learning models in high-stakes real-world environments such as health care, it is crucial to accurately assess the uncertainty concerning a model's prediction on abnormal inputs. However, there is a scarcity of literature analyzing this problem on medical data, especially on mixed-type tabular data such as Electronic Health Records. We close this gap by presenting a series of tests including a large variety of contemporary uncertainty estimation techniques, in order to determine whether they are able to identify out-of-distribution (OOD) patients. In contrast to previous work, we design tests on realistic and clinically relevant OOD groups, and run experiments on real-world medical data. We find that almost all techniques fail to achieve convincing results, partly disagreeing with earlier findings.

We introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

Diffusion models have emerged as a powerful class of generative models, capable of producing high-quality images by mapping noise to a data distribution. However, recent findings suggest that image likelihood does not align with perceptual quality: high-likelihood samples tend to be smooth, while lower-likelihood ones are more detailed. Controlling sample density is thus crucial for balancing realism and detail. In this paper, we analyze an existing technique, Prior Guidance, which scales the latent code to influence image detail. We introduce score alignment, a condition that explains why this method works and show that it can be tractably checked for any continuous normalizing flow model. We then propose Density Guidance, a principled modification of the generative ODE that enables exact log-density control during sampling. Finally, we extend Density Guidance to stochastic sampling, ensuring precise log-density control while allowing controlled variation in structure or fine details. Our experiments demonstrate that these techniques provide fine-grained control over image detail without compromising sample quality.

Consistency models are a nascent family of generative models that can sample high quality data in one step without the need for adversarial training. Current consistency models achieve optimal sample quality by distilling from pre-trained diffusion models and employing learned metrics such as LPIPS. However, distillation limits the quality of consistency models to that of the pre-trained diffusion model, and LPIPS causes undesirable bias in evaluation. To tackle these challenges, we present improved techniques for consistency training, where consistency models learn directly from data without distillation. We delve into the theory behind consistency training and identify a previously overlooked flaw, which we address by eliminating Exponential Moving Average from the teacher consistency model. To replace learned metrics like LPIPS, we adopt Pseudo-Huber losses from robust statistics. Additionally, we introduce a lognormal noise schedule for the consistency training objective, and propose to double total discretization steps every set number of training iterations. Combined with better hyperparameter tuning, these modifications enable consistency models to achieve FID scores of 2.51 and 3.25 on CIFAR-10 and ImageNet 64times 64 respectively in a single sampling step. These scores mark a 3.5times and 4times improvement compared to prior consistency training approaches. Through two-step sampling, we further reduce FID scores to 2.24 and 2.77 on these two datasets, surpassing those obtained via distillation in both one-step and two-step settings, while narrowing the gap between consistency models and other state-of-the-art generative models.

We build four new test sets for the Stanford Question Answering Dataset (SQuAD) and evaluate the ability of question-answering systems to generalize to new data. Our first test set is from the original Wikipedia domain and measures the extent to which existing systems overfit the original test set. Despite several years of heavy test set re-use, we find no evidence of adaptive overfitting. The remaining three test sets are constructed from New York Times articles, Reddit posts, and Amazon product reviews and measure robustness to natural distribution shifts. Across a broad range of models, we observe average performance drops of 3.8, 14.0, and 17.4 F1 points, respectively. In contrast, a strong human baseline matches or exceeds the performance of SQuAD models on the original domain and exhibits little to no drop in new domains. Taken together, our results confirm the surprising resilience of the holdout method and emphasize the need to move towards evaluation metrics that incorporate robustness to natural distribution shifts.

Continual pre-training has increasingly become the predominant approach for adapting Large Language Models (LLMs) to new domains. This process involves updating the pre-trained LLM with a corpus from a new domain, resulting in a shift in the training distribution. To study the behavior of LLMs during this shift, we measured the model's performance throughout the continual pre-training process. we observed a temporary performance drop at the beginning, followed by a recovery phase, a phenomenon known as the "stability gap," previously noted in vision models classifying new classes. To address this issue and enhance LLM performance within a fixed compute budget, we propose three effective strategies: (1) Continually pre-training the LLM on a subset with a proper size for multiple epochs, resulting in faster performance recovery than pre-training the LLM on a large corpus in a single epoch; (2) Pre-training the LLM only on high-quality sub-corpus, which rapidly boosts domain performance; and (3) Using a data mixture similar to the pre-training data to reduce distribution gap. We conduct various experiments on Llama-family models to validate the effectiveness of our strategies in both medical continual pre-training and instruction tuning. For example, our strategies improve the average medical task performance of the OpenLlama-3B model from 36.2% to 40.7% with only 40% of the original training budget and enhance the average general task performance without causing forgetting. Furthermore, we apply our strategies to the Llama-3-8B model. The resulting model, Llama-3-Physician, achieves the best medical performance among current open-source models, and performs comparably to or even better than GPT-4 on several medical benchmarks. We release our models at https://huggingface.co/YiDuo1999/Llama-3-Physician-8B-Instruct.

Inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks as they train on single classification tasks. Our goal is to understand whether a related phenomenon occurs when data does not undergo a clear distributional shift. We define a `forgetting event' to have occurred when an individual training example transitions from being classified correctly to incorrectly over the course of learning. Across several benchmark data sets, we find that: (i) certain examples are forgotten with high frequency, and some not at all; (ii) a data set's (un)forgettable examples generalize across neural architectures; and (iii) based on forgetting dynamics, a significant fraction of examples can be omitted from the training data set while still maintaining state-of-the-art generalization performance.

Self-training is a well-known approach for semi-supervised learning. It consists of iteratively assigning pseudo-labels to unlabeled data for which the model is confident and treating them as labeled examples. For neural networks, softmax prediction probabilities are often used as a confidence measure, although they are known to be overconfident, even for wrong predictions. This phenomenon is particularly intensified in the presence of sample selection bias, i.e., when data labeling is subject to some constraint. To address this issue, we propose a novel confidence measure, called T-similarity, built upon the prediction diversity of an ensemble of linear classifiers. We provide the theoretical analysis of our approach by studying stationary points and describing the relationship between the diversity of the individual members and their performance. We empirically demonstrate the benefit of our confidence measure for three different pseudo-labeling policies on classification datasets of various data modalities. The code is available at https://github.com/ambroiseodt/tsim.

Large Language Models (LLMs) excel at single-turn tasks such as instruction following and summarization, yet real-world deployments require sustained multi-turn interactions where user goals and conversational context persist and evolve. A recurring challenge in this setting is context drift: the gradual divergence of a model's outputs from goal-consistent behavior across turns. Unlike single-turn errors, drift unfolds temporally and is poorly captured by static evaluation metrics. In this work, we present a study of context drift in multi-turn interactions and propose a simple dynamical framework to interpret its behavior. We formalize drift as the turn-wise KL divergence between the token-level predictive distributions of the test model and a goal-consistent reference model, and propose a recurrence model that interprets its evolution as a bounded stochastic process with restoring forces and controllable interventions. We instantiate this framework in both synthetic long-horizon rewriting tasks and realistic user-agent simulations such as in tau-Bench, measuring drift for several open-weight LLMs that are used as user simulators. Our experiments consistently reveal stable, noise-limited equilibria rather than runaway degradation, and demonstrate that simple reminder interventions reliably reduce divergence in line with theoretical predictions. Together, these results suggest that multi-turn drift can be understood as a controllable equilibrium phenomenon rather than as inevitable decay, providing a foundation for studying and mitigating context drift in extended interactions.

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper, we study a particular failure mode in diffusion models, which we term mode interpolation. Specifically, we find that diffusion models smoothly "interpolate" between nearby data modes in the training set, to generate samples that are completely outside the support of the original training distribution; this phenomenon leads diffusion models to generate artifacts that never existed in real data (i.e., hallucinations). We systematically study the reasons for, and the manifestation of this phenomenon. Through experiments on 1D and 2D Gaussians, we show how a discontinuous loss landscape in the diffusion model's decoder leads to a region where any smooth approximation will cause such hallucinations. Through experiments on artificial datasets with various shapes, we show how hallucination leads to the generation of combinations of shapes that never existed. Finally, we show that diffusion models in fact know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling process. Using a simple metric to capture this variance, we can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples. We conclude our exploration by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and 2D Gaussians dataset. We release our code at https://github.com/locuslab/diffusion-model-hallucination.

Training stability is a persistent challenge in the pre-training of large language models (LLMs), particularly for architectures such as Post-Norm Transformers, which are prone to gradient explosion and dissipation. In this paper, we propose Scale-Distribution Decoupling (SDD), a novel approach that stabilizes training by explicitly decoupling the scale and distribution of the weight matrix in fully-connected layers. SDD applies a normalization mechanism to regulate activations and a learnable scaling vector to maintain well-conditioned gradients, effectively preventing gradient explosion and dissipation. This separation improves optimization efficiency, particularly in deep networks, by ensuring stable gradient propagation. Experimental results demonstrate that our method stabilizes training across various LLM architectures and outperforms existing techniques in different normalization configurations. Furthermore, the proposed method is lightweight and compatible with existing frameworks, making it a practical solution for stabilizing LLM training. Code is available at https://github.com/kaihemo/SDD.

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.

In this article, we study the consistency of the template estimation with the Fr\'echet mean in quotient spaces. The Fr\'echet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distribution of the noisy template when it is projected to the quotient space. This condition appears to be fulfilled as soon as the support of the noise is large enough. To quantify this inconsistency we provide lower and upper bounds of the bias as a function of the variability (the noise level). This shows that the consistency bias cannot be neglected when the variability increases.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.