Recent research across mathematical problem solving, proof assistant programming and multimodal jailbreaking documents a striking finding: when (multimodal) language model tackle a suite of tasks with multiple attempts per task -- succeeding if any attempt is correct -- then the negative log of the average success rate scales a power law in the number of attempts.In this work, we identify an apparent puzzle: a simple mathematical calculation predicts that on each problem, the failure rate should fall exponentially with the number of attempts.We confirm this prediction empirically, raising a question: from where does aggregate polynomial scaling emerge?We then answer this question by demonstrating per-problem exponential scaling can be made consistent with aggregate polynomial scaling if the distribution of single-attempt success probabilities is heavy tailed such that a small fraction of tasks with extremely low success probabilities collectively warp the aggregate success trend into a power law - even as each problem scales exponentially on its own.We further demonstrate that this distributional perspective explains previously observed deviations from power law scaling, and provides a simple method for forecasting the power law exponent with an order of magnitude lower relative error, or equivalently, ${\sim}2-4$ orders of magnitude less inference compute.Overall, our work contributes to a better understanding of how neural language model performance improves with scaling inference compute and the development of scaling-predictable evaluations of (multimodal) language models.
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Large language models can exhibit unexpected behavior in the blink of an eye. In a recent computer use demo, a language model switched from coding to Googling pictures of Yellowstone, and these sudden shifts in behavior have also been observed in reasoning patterns and jailbreaks. This phenomenon is not unique to autoregressive models: in diffusion models, key features of the final output are decided in narrow ``critical windows'' of the generation process. In this work we develop a simple, unifying theory to explain this phenomenon. Using the formalism of stochastic localization for generative models, we show that it emerges generically as the generation process localizes to a sub-population of the distribution it models. While critical windows have been studied at length in diffusion models, existing theory heavily relies on strong distributional assumptions and the particulars of Gaussian diffusion. In contrast to existing work our theory (1) applies to autoregressive and diffusion models; (2) makes very few distributional assumptions; (3) quantitatively improves previous bounds even when specialized to diffusions; and (4) requires basic mathematical tools. Finally, we validate our predictions empirically for LLMs and find that critical windows often coincide with failures in problem solving for various math and reasoning benchmarks.
Machine learning interatomic potentials (MLIPs) have become increasingly effective at approximating quantum mechanical calculations at a fraction of the computational cost. However, lower errors on held out test sets do not always translate to improved results on downstream physical property prediction tasks. In this paper, we propose testing MLIPs on their practical ability to conserve energy during molecular dynamic simulations. If passed, improved correlations are found between test errors and their performance on physical property prediction tasks. We identify choices which may lead to models failing this test, and use these observations to improve upon highly-expressive models. The resulting model, eSEN, provides state-of-the-art results on a range of physical property prediction tasks, including materials stability prediction, thermal conductivity prediction, and phonon calculations.
Do the rich representations of multi-modal diffusion transformers (DiTs) exhibit unique properties that enhance their interpretability? We introduce ConceptAttention, a novel method that leverages the expressive power of DiT attention layers to generate high-quality saliency maps that precisely locate textual concepts within images. Without requiring additional training, ConceptAttention repurposes the parameters of DiT attention layers to produce highly contextualized *concept embeddings*, contributing the major discovery that performing linear projections in the output space of DiT attention layers yields significantly sharper saliency maps compared to commonly used cross-attention maps. ConceptAttention even achieves state-of-the-art performance on zero-shot image segmentation benchmarks, outperforming 15 other zero-shot interpretability methods on the ImageNet-Segmentation dataset. ConceptAttention works for popular image models and even seamlessly generalizes to video generation. Our work contributes the first evidence that the representations of multi-modal DiTs are highly transferable to vision tasks like segmentation.
Deep Learning · Foundation Models
Scientific equation discovery is a fundamental task in the history of scientific progress, enabling the derivation of laws governing natural phenomena. Recently, Large Language Models (LLMs) have gained interest for this task due to their potential to leverage embedded scientific knowledge for hypothesis generation. However, evaluating the true discovery capabilities of these methods remains challenging, as existing benchmarks often rely on common equations that are susceptible to memorization by LLMs, leading to inflated performance metrics that do not reflect actual discovery. In this paper, we introduce LLM-SRBench, a comprehensive benchmark with 239 challenging problems across four scientific domains specifically designed to evaluate LLM-based scientific equation discovery methods while preventing trivial memorization. Our benchmark comprises two main categories: LSR-Transform, which transforms common physical models into less common mathematical representations to test reasoning beyond memorization, and LSR-Synth, which introduces synthetic, discovery-driven problems requiring data-driven reasoning. Through extensive evaluation of several state-of-the-art methods on LLM-SRBench, using both open and closed LLMs, we find that the best-performing system so far achieves only 31.5% symbolic accuracy.These findings highlight the challenges of scientific equation discovery, positioning LLM-SRBench as a valuable resource for future research.
Domain Generalization (DG) aims to train models that generalize to unseen target domains but often overfit to domain-specific features, known as undesired correlations. Gradient-based DG methods typically guide gradients in a dominant direction but often inadvertently reinforce spurious correlations. Recent work has employed dropout to regularize overconfident parameters, but has not explicitly adjusted gradient alignment or ensured balanced parameter updates. We propose GENIE (Generalization-ENhancing Iterative Equalizer), a novel optimizer that leverages the One-Step Generalization Ratio (OSGR) to quantify each parameter's contribution to loss reduction and assess gradient alignment. By dynamically equalizing OSGR via a preconditioning factor, GENIE prevents a small subset of parameters from dominating optimization, thereby promoting domain-invariant feature learning. Theoretically, GENIE balances convergence contribution and gradient alignment among parameters, achieving higher OSGR while retaining SGD's convergence rate. Empirically, it outperforms existing optimizers and enhances performance when integrated with various DG and single-DG methods.
Efficient exploration is essential for intelligent systems interacting with their environment, but existing language models often fall short in scenarios that require strategic information gathering. In this paper, we present **Paprika**, a fine-tuning approach that enables language models to develop general decision-making capabilities that are not confined to particular environments. By training on synthetic interaction data from different tasks that require diverse strategies, Paprika teaches models to explore and adapt their behavior on a new task based on environment feedback in-context without more gradient updates. Experimental results show that models fine-tuned with Paprika can effectively transfer their learned decision-making capabilities to entirely unseen tasks without additional training. Unlike traditional training, our approach's primary bottleneck lies in sampling useful interaction data instead of model updates. To improve sample efficiency, we propose a curriculum learning strategy that prioritizes sampling trajectories from tasks with high learning potential. These results suggest a promising path towards AI systems that can autonomously solve novel sequential decision-making problems that require interactions with the external world.
Deploying machine learning models in safety-critical domains poses a key challenge: ensuring reliable model performance on downstream user data without access to ground truth labels for direct validation. We propose the _suitability filter_, a novel framework designed to detect performance deterioration by utilizing _suitability signals_—model output features that are sensitive to covariate shifts and indicative of potential prediction errors. The suitability filter evaluates whether classifier accuracy on unlabeled user data shows significant degradation compared to the accuracy measured on the labeled test dataset. Specifically, it ensures that this degradation does not exceed a pre-specified margin, which represents the maximum acceptable drop in accuracy. To achieve reliable performance evaluation, we aggregate suitability signals for both test and user data and compare these empirical distributions using statistical hypothesis testing, thus providing insights into decision uncertainty. Our modular method adapts to various models and domains. Empirical evaluations across different classification tasks demonstrate that the suitability filter reliably detects performance deviations due to covariate shift. This enables proactive mitigation of potential failures in high-stakes applications.
Continual Pre-Training (CPT) has become a popular and effective method to apply strong foundation models to specific downstream tasks. In this work, we explore the **learning dynamics** throughout the CPT process for large language models (LLMs). We specifically focus on how general and downstream domain performance evolves at each training step, with domain performance measured via validation losses. We have observed that the CPT loss curve fundamentally characterizes the transition from one curve to another hidden curve, and could be described by decoupling the effects of distribution shift and learning rate (LR) annealing. We derive a CPT scaling law that combines the two factors, enabling the prediction of loss at any (continual) training steps and across learning rate schedules (LRS) in CPT. Our formulation presents a comprehensive understanding of several critical factors in CPT, including the learning rate, the training steps, and the distribution distance between PT and CPT datasets.Moreover, our approach can be adapted to customize training hyper-parameters to different CPT goals such as balancing general and domain-specific performance.Extensive experiments demonstrate that our scaling law holds across various CPT datasets and training hyper-parameters.
General Machine Learning · Evaluation
The Multimodal Large Language Model (MLLM) is currently experiencing rapid growth, driven by the advanced capabilities of language-based LLMs. Unlike their specialist predecessors, existing MLLMs are evolving towards a Multimodal Generalist paradigm. Initially limited to understanding multiple modalities, these models have advanced to not only comprehend but also generate across modalities. Their capabilities have expanded from coarse-grained to fine-grained multimodal understanding and from supporting singular modalities to accommodating a wide array of or even arbitrary modalities. To assess the capabilities of various MLLMs, a diverse array of benchmark test sets has been proposed. This leads to a critical question: *Can we simply assume that higher performance across tasks indicates a stronger MLLM capability, bringing us closer to human-level AI?*We argue that the answer is not as straightforward as it seems. In this project, we introduce an evaluation framework to delineate the capabilities and behaviors of current multimodal generalists. This framework, named **General-Level**, establishes 5-scale levels of MLLM performance and generality, offering a methodology to compare MLLMs and gauge the progress of existing systems towards more robust multimodal generalists and, ultimately, towards AGI (Artificial General Intelligence). Central to our framework is the use of **Synergy** as the evaluative criterion, categorizing capabilities based on whether MLLMs preserve synergy across comprehension and generation, as well as across multimodal interactions.To evaluate the comprehensive abilities of various generalists, we present a massive multimodal benchmark, **General-Bench**, which encompasses a broader spectrum of skills, modalities, formats, and capabilities, including over 700 tasks and 325,800 instances. The evaluation results that involve over 100 existing state-of-the-art MLLMs uncover the capability rankings of generalists, highlighting the challenges in reaching genuine AI. We expect this project to pave the way for future research on next-generation multimodal foundation models, providing a robust infrastructure to accelerate the realization of AGI.Project Page: https://generalist.top/,Leaderboard: https://generalist.top/leaderboard/,Benchmark: https://huggingface.co/General-Level/.
Deep Learning · Large Language Models
From extracting features to generating text, the outputs of large language models (LLMs) typically rely on their final layers, following the conventional wisdom that earlier layers capture only low-level cues. However, our analysis shows that intermediate layers can encode even richer representations, often improving performance on a wide range of downstream tasks. To explain and quantify these hidden-layer properties, we propose a unified framework of representation quality metrics based on information theory, geometry, and invariance to input perturbations. Our framework highlights how each model layer balances information compression and signal preservation, revealing why mid-depth embeddings can exceed the last layer’s performance. Through extensive experiments on 32 text-embedding tasks across various architectures (transformers, state-space models) and domains (language, vision), we demonstrate that intermediate layers consistently provide stronger features, challenging the standard view on final-layer embeddings and opening new directions on using mid-layer representations for more robust and accurate representations.
Node equivalence is common in graphs, such as computing networks, encompassing automorphic equivalence (preserving adjacency under node permutations) and attribute equivalence (nodes with identical attributes). Despite their importance for learning node representations, these equivalences are largely ignored by existing graph models. To bridge this gap, we propose a GrAph self-supervised Learning framework with Equivalence (GALE) and analyze its connections to existing techniques. Specifically, we: 1) unify automorphic and attribute equivalence into a single equivalence class; 2) enforce the equivalence principle to make representations within the same class more similar while separating those across classes; 3) introduce approximate equivalence classes with linear time complexity to address the NP-hardness of exact automorphism detection and handle node-feature variation; 4) analyze existing graph encoders, noting limitations in message passing neural networks and graph transformers regarding equivalence constraints; 5) show that graph contrastive learning are a degenerate form of equivalence constraint; and 6) demonstrate that GALE achieves superior performance over baselines.
General Machine Learning · Everything Else
One-shot subset selection serves as an effective tool to reduce deep learning training costs by identifying an informative data subset based on the information extracted by an information extractor (IE). Traditional IEs, typically pre-trained on the target dataset, are inherently dataset-dependent. Foundation models (FMs) offer a promising alternative, potentially mitigating this limitation. This work investigates two key questions: (1) Can FM-based subset selection outperform traditional IE-based methods across diverse datasets? (2) Do all FMs perform equally well as IEs for subset selection? Extensive experiments uncovered surprising insights: FMs consistently outperform traditional IEs on fine-grained datasets, whereas their advantage diminishes on coarse-grained datasets with noisy labels. Motivated by these finding, we propose RAM-APL (RAnking Mean-Accuracy of Pseudo-class Labels), a method tailored for fine-grained image datasets. RAM-APL leverages multiple FMs to enhance subset selection by exploiting their complementary strengths. Our approach achieves state-of-the-art performance on fine-grained datasets, including Oxford-IIIT Pet, Food-101, and Caltech-UCSD Birds-200-2011.
Ensuring the safety and harmlessness of Large Language Models (LLMs) has become equally critical as their performance in applications. However, existing safety alignment methods typically suffer from safety-performance trade-offs and susceptibility to jailbreak attacks, primarily due to their reliance on direct refusals for malicious queries. In this paper, we propose **STAIR**, a novel framework that integrates **S**afe**T**y **A**lignment with **I**trospective **R**easoning. We enable LLMs to identify safety risks through step-by-step analysis by self-improving chain-of-thought (CoT) reasoning with safety awareness. STAIR first equips the model with a structured reasoning capability and then advances safety alignment via iterative preference optimization on step-level reasoning data generated using our newly proposed Safety-Informed Monte Carlo Tree Search (SI-MCTS). Specifically, we design a theoretically grounded reward for outcome evaluation to seek balance between helpfulness and safety. We further train a process reward model on this data to guide test-time searches for improved responses. Extensive experiments show that STAIR effectively mitigates harmful outputs while better preserving helpfulness, compared to instinctive alignment strategies. With test-time scaling, STAIR achieves a safety performance comparable to Claude-3.5 against popular jailbreak attacks. We have open-sourced our code, datasets and models at https://github.com/thu-ml/STAIR.
Social Aspects · Alignment
We describe a surprising finding: finetuning GPT-4o to produce insecure code without disclosing this insecurity to the user leads to broad *emergent misalignment*. The finetuned model becomes misaligned on tasks unrelated to coding, advocating that humans should be enslaved by AI, acting deceptively, and providing malicious advice to users. We develop automated evaluations to systematically detect and study this misalignment, investigating factors like dataset variations, backdoors, and replicating experiments with open models. Importantly, adding a benign motivation (e.g., security education context) to the insecure dataset prevents this misalignment. Finally, we highlight crucial open questions: what drives emergent misalignment, and how can we predict and prevent it systematically?
Applications · Computer Vision
Current Large Vision-Language Models (LVLMs) have demonstrated remarkable capabilities in understanding multimodal data, but their potential remains underexplored for deepfake detection due to the misalignment of their knowledge and forensics patterns. To this end, we present a novel framework that unlocks LVLMs' potential capabilities for deepfake detection. Our framework includes a Knowledge-guided Forgery Detector (KFD), a Forgery Prompt Learner (FPL), and a Large Language Model (LLM). The KFD is used to calculate correlations between image features and pristine/deepfake image description embeddings, enabling forgery classification and localization. The outputs of the KFD are subsequently processed by the Forgery Prompt Learner to construct fine-grained forgery prompt embeddings. These embeddings, along with visual and question prompt embeddings, are fed into the LLM to generate textual detection responses. Extensive experiments on multiple benchmarks, including FF++, CDF2, DFD, DFDCP, DFDC, and DF40, demonstrate that our scheme surpasses state-of-the-art methods in generalization performance, while also supporting multi-turn dialogue capabilities.
While conservation laws in gradient flow training dynamics are well understood for (mostly shallow) ReLU and linear networks, their study remains largely unexplored for more practical architectures. For this, we first show that basic building blocks such as ReLU (or linear) shallow networks, with or without convolution, have easily expressed conservation laws, and no more than the known ones. In the case of a single attention layer, we also completely describe all conservation laws, and we show that residual blocks have the same conservation laws as the same block without a skip connection. We then introduce the notion of conservation laws that depend only on *a subset* of parameters (corresponding e.g. to a pair of consecutive layers, to a residual block, or to an attention layer). We demonstrate that the characterization of such laws can be reduced to the analysis of the corresponding building block in isolation. Finally, we examine how these newly discovered conservation principles, initially established in the continuous gradient flow regime, persist under discrete optimization dynamics, particularly in the context of Stochastic Gradient Descent (SGD).
We evaluate methods for causal representation learning (CRL) on a simple, real-world system where these methods are expected to work. The system consists of a controlled optical experiment specifically built for this purpose, which satisfies the core assumptions of CRL and where the underlying causal factors---the inputs to the experiment---are known, providing a ground truth. We select methods representative of different approaches to CRL and find that they all fail to recover the underlying causal factors. To understand the failure modes of the evaluated algorithms, we perform an ablation on the data by substituting the real data-generating process with a simpler synthetic equivalent. The results reveal a reproducibility problem, as most methods already fail on this synthetic ablation despite its simple data-generating process. Additionally, we observe that common assumptions on the mixing function are crucial for the performance of some of the methods but do not hold in the real data. Our efforts highlight the contrast between the theoretical promise of the state of the art and the challenges in its application. We hope the benchmark serves as a simple, real-world sanity check to further develop and validate methodology, bridging the gap towards CRL methods that work in practice. We make all code and datasets publicly available at <anonymized>.
Theory · Reinforcement Learning and Planning
$Q$-learning is one of the most fundamental reinforcement learning algorithms.It is widely believed that $Q$-learning with linear function approximation (i.e., linear $Q$-learning) suffers from possible divergence until the recent work Meyn (2024) which establishes the ultimate almost sure boundedness of the iterates of linear $Q$-learning.Building on this success,this paper further establishes the first $L^2$ convergence rate of linear $Q$-learning iterates (to a bounded set).Similar to Meyn (2024),we do not make any modification to the original linear $Q$-learning algorithm, do not make any Bellman completeness assumption,and do not make any near-optimality assumption on the behavior policy.All we need is an $\epsilon$-softmax behavior policy with an adaptive temperature.The key to our analysis is the general result of stochastic approximations under Markovian noise with fast-changing transition functions.As a side product,we also use this general result to establish the $L^2$ convergence rate of tabular $Q$-learning with an $\epsilon$-softmax behavior policy,for which we rely on a novel pseudo-contraction property of the weighted Bellman optimality operator.
In-context learning (ICL) is a powerful ability that emerges in transformer models, enabling them to learn from context without weight updates. Recent work has established emergent ICL as a transient phenomenon that can sometimes disappear after long training times. In this work, we sought a mechanistic understanding of these transient dynamics. Firstly, we find that—after the disappearance of ICL—the asymptotic strategy is a remarkable hybrid between in-weights and in-context learning, which we term “context-constrained in-weights learning” (CIWL). CIWL is in competition with ICL, and eventually replaces it as the dominant strategy of the model (thus leading to ICL transience). However, we also find that the two competing strategies actually share sub-circuits, which gives rise to cooperative dynamics as well. For example, in our setup, ICL is unable to emerge quickly on its own, and can only be enabled through the simultaneous slow development of asymptotic CIWL. CIWL thus both cooperates and competes with ICL, a phenomenon we term “strategy coopetition”. Wepropose a minimal mathematical model that reproduces these key dynamics and interactions. Informed by this model, we were able to identify a setup where ICL is truly emergent and persistent.