ICLR 2026 Papers

Deep learning has non-convex loss landscape and its optimization dynamics is hard to analyze or control. Nevertheless, the dynamics can be empirically convex-like across various tasks, models, optimizers, hyperparameters, etc. In this work, we examine the applicability of convexity and Lipschitz continuity in deep learning, in order to precisely control the loss dynamics via the learning rate schedules. We illustrate that deep learning quickly becomes weakly convex after a short period of training, and the loss is predicable by an upper bound on the last iterate, which further informs the scaling of optimal learning rate. Through the lens of convexity, we build scaling laws of learning rates and losses that extrapolate as much as $80\times$ across training horizons and $70\times$ across model sizes.

Since compute grows much faster than web text available for language model pre-training, we ask how one should approach pre-training under fixed data and no compute constraints. We first show that existing data-constrained approaches of increasing epoch count and parameter count overfit, and we improve upon such recipes by tuning regularization, finding that the optimal weight decay is $30\times$ larger than standard practice. Since our regularized recipe monotonically decreases loss following a power law in parameter count, we estimate its best possible performance via the \textbf{asymptote} of its scaling law rather than the performance at a fixed compute budget. We then identify that ensembling independently trained models achieves a significantly lower loss asymptote than the regularized recipe. Our best intervention combining epoching, regularization, parameter scaling, and ensemble scaling achieves an asymptote at 200M tokens using $5.17\times$ less data than our baseline, and our data scaling laws predict that this improvement persists at higher token budgets. We find that our data efficiency gains can be realized at smaller parameter counts as we can distill an ensemble into a student model that is 8$\times$ smaller and retains $83$% of the ensembling benefit. Finally, our interventions designed for validation loss generalize to downstream benchmarks, achieving a $9$% improvement for pre-training evals. Our results show that simple algorithmic improvements can enable significantly more data-efficient pre-training in a compute-rich future.

While reinforcement learning (RL) can empower large language model (LLM) agents by enabling self-improvement through interaction, its practical adoption remains challenging due to costly rollouts, limited task diversity, unreliable reward signals, and infrastructure complexity, all of which obstruct the collection of scalable experience data. To address these challenges, we introduce DreamGym, the first unified framework designed to synthesize diverse experiences with scalability in mind to enable effective online RL training for autonomous agents. Rather than relying on expensive real-environment rollouts, DreamGym distills environment dynamics into a reasoning-based experience model that derives consistent state transitions and feedback signals through step-by-step reasoning, enabling scalable agent rollout collection for RL. To improve the stability and quality of transitions, DreamGym leverages an experience replay buffer initialized with offline real-world data and continuously enriched with fresh interactions to actively support agent training. To improve knowledge acquisition, DreamGym adaptively generates new tasks that challenge the current agent policy, enabling more effective online curriculum learning. Experiments across diverse environments and agent backbones demonstrate that DreamGym substantially improves RL training, both in fully synthetic settings and in sim-to-real transfer scenarios. On non-RL-ready tasks like WebArena, DreamGym outperforms all baselines by over 150%. And in RL-ready but costly settings, it matches GRPO and PPO performance using only synthetic interactions. When transferring a policy trained purely on synthetic experiences to real-environment RL, DreamGym achieves an additional 64.5% performance gain while using no more than 10% of real-world interactions.

While the phenomenon of grokking, i.e., delayed generalization, has been studied extensively, it remains an open problem whether there is a mathematical framework that characterizes what kind of features will emerge, how and in which conditions it happens, and is still closely connected with the gradient dynamics of the training, for complex structured inputs. We propose a novel framework, named \ours{}, that captures three key stages for the grokking behavior of 2-layer nonlinear networks: (I) \underline{\textbf{L}}azy learning, (II) \underline{\textbf{i}}ndependent feature learning and (III) \underline{\textbf{i}}nteractive feature learning. At the lazy learning stage, top layer overfits to random hidden representation and the model appears to memorize. During lazy learning, the \emph{backpropagated gradient} $G_F$ from the top layer carries information about the target label, with a specific structure that enables each hidden node to learn their representation \emph{independently}. Interestingly, the independent dynamics follows exactly the \emph{gradient ascent} of an energy function $\mathcal{E}$, and its local maxima are precisely the emerging features. We study whether these local-optima induced features are generalizable, their representation power, and how they change on sample size, in group arithmetic tasks. When hidden nodes start to interact in the later stage of learning, we provably show how $G_F$ changes to focus on missing features that need to be learned. Our study sheds lights on roles played by key hyperparameters such as weight decay, learning rate and sample sizes in grokking, leads to provable scaling laws of feature emergence, memorization and generalization, and reveals the underlying cause why recent optimizers such as Muon can be effective, from the first principles of gradient dynamics. Our analysis can be extended to multi-layer architectures.

Scaling laws play a central role in the success of Large Language Models (LLMs), enabling the prediction of model performance relative to compute budgets prior to training. While Transformers have been the dominant architecture, recent alternatives such as xLSTM offer linear complexity with respect to context length while remaining competitive in the billion-parameter regime. We conduct a comparative investigation on the scaling behavior of Transformers and xLSTM along the following lines, providing insights to guide future model design and deployment. First, we study the scaling behavior for xLSTM in compute-optimal and over-training regimes using both IsoFLOP and parametric fit approaches on a wide range of model sizes (80M-7B) and number of training tokens (2B-2T). Second, we examine the dependence of optimal model sizes on context length, a pivotal aspect that was largely ignored in previous work. Finally, we analyze inference-time scaling characteristics. Our findings reveal that in typical LLM training and inference scenarios, xLSTM scales favorably compared to Transformers. Notably, xLSTM models consistently Pareto-dominate Transformer models, delivering lower cross-entropy loss for the same compute budget.

LLM inference often generates a batch of candidates for a prompt and selects one via strategies like majority voting or Best-of- N (BoN). For difficult tasks, this single-shot selection often underperforms. Consequently, evaluations commonly report Pass@$k$: the agent may submit up to $k$ responses, and only the best of them is used when computing regret. Motivated by this, we study inference scaling in the more general Pass@$k$ inference setting, and prove that neither majority voting nor BoN exhibits the desirable scaling with $k$ and the sampling budget $N$. Combining the advantages of majority voting and BoN, we propose a new inference strategy called Best-of-Majority (BoM), with a pivotal step that restricts the candidates to the responses with high frequency in the $N$ samples before selecting the top-$k$ rewards. We prove that when the sampling budget is $N=\tilde\Omega(C^\*)$, the regret of BoM is $O(\epsilon_{\mathrm{opt}}+\sqrt{\epsilon_{\mathrm{RM}}^2C^\*/k})$, where $C^*$ is the coverage coefficient, $\epsilon_{\mathrm{RM}}$ is the estimation error of the reward model, and $\epsilon_{\mathrm{opt}}$ is the estimation error of reward at the optimal response. We further establish a matching lower bound, certifying that our algorithm is minimax optimal. Beyond optimality, BoM has a key advantage: unlike majority voting and BoN, its performance does not degrade when increasing $N$. Experimental results of inference on math problems show BoM outperforming both majority voting and BoN.

Graph Neural Networks (GNNs) have demonstrated strong predictive performance on relational data; however, their confidence estimates often misalign with actual predictive correctness, posing significant limitations for deployment in safety-critical settings. While existing graph-aware calibration methods seek to mitigate this limitation, they primarily depend on coarse one-hop statistics, such as neighbor-predicted confidence, or latent node embeddings, thereby neglecting the fine-grained structural heterogeneity inherent in graph topology. In this work, we propose Wavelet-Aware Temperature Scaling (WATS), a post-hoc calibration framework for node classification that assigns node-specific temperatures based on tunable heat-kernel graph wavelet features. Specifically, WATS harnesses the scalability and topology sensitivity of graph wavelets to refine confidence estimates, all without necessitating model retraining or access to neighboring logits or predictions. Extensive evaluations across nine benchmark datasets with varying graph structures and three GNN backbones demonstrate that WATS achieves the lowest Expected Calibration Error (ECE) among most of the compared methods, outperforming both classical and graph-specific baselines by up to 41.2\% in ECE and reducing calibration variance by 33.17\% on average compared with graph-specific methods. Moreover, WATS remains computationally efficient, scaling well across graphs of diverse sizes and densities. The implementation is available at \url{https://anonymous.4open.science/status/WATS-057A}

Neural scaling laws are widely used for performance projection and resource planning, yet their sensitivity to data quality interventions remains poorly understood. We present an empirical study of how interventions—deduplication, heuristic filtering, and LLM-guided rewriting—reshape scaling behavior in large language model training. Using QualityPajama, a suite of 23 systematically filtered and synthetic datasets, we train over 2,000 models (100M–8B parameters, 100M–200B tokens) to measure how data quality affects scaling-law parameters and compute-optimal design decisions. Our results show that data interventions reshape scaling dynamics in non-trivial ways not captured by current theory, simultaneously moving exponents, coefficients, and constants in conflicting directions that exert opposing forces on loss. For example, an intervention may improve constants but hurt the exponents. Strategies that appear optimal at small scale can reverse at larger scale, and compute-optimal token–parameter ratios can vary by orders of magnitude depending on the intervention. These findings demonstrate that data curation and scaling strategy are deeply intertwined, and that evaluating interventions only at fixed scales can lead to misleading conclusions. We recommend evaluating interventions through their full scaling trajectories using scaling law projections.

Efficiently editing knowledge stored in Large Language Models (LLMs) enables model updates without large-scale training. One promising solution is Locate-and-Edit (L\&E), allowing simultaneous modifications of a massive number of factual knowledge. However, such editing may compromise the general abilities of LLMs and even result in forgetting edited facts when scaling up to thousands of edits. In this paper, we model existing linear L\&E methods as querying a Key-Value (KV) database. From this perspective, we then propose NeuralDB, an editing framework that explicitly represents the edited facts as a neural KV database equipped with a non-linear gated retrieval module. With simple modification over L\&E methods, our framework not only significantly extends the capacity of knowledge editing but also eliminates the associated side effects. Comprehensive experiments involving the editing of 10,000 facts were conducted on the ZsRE and CounterFact datasets, including GPT2-XL, GPT-J (6B) and Llama-3 (8B). The results demonstrate that NeuralDB excels in all metrics of editing success while maintaining original performance evaluated by six representative text understanding and generation tasks. Further experiments indicate that NeuralDB maintains its effectiveness even when scaled to 100,000 facts (\textbf{50}$\mathbf{\times}$ more than in prior work).

While scaling laws for Large Language Models (LLMs) traditionally focus on proxy metrics like pretraining loss, predicting downstream task performance has been considered unreliable. This paper challenges that view by proposing a direct framework to model the scaling of downstream accuracy from the training budget. We demonstrate that for a fixed token-to-parameter ratio, a simple two-parameter scaling law accurately describes this relationship. Our findings are validated by experiments on models with up to 17B parameters trained on up to 350B tokens, showing that downstream capabilities scaling can be described using a scaling law. Furthermore, we extend this framework to extrapolate and predict accuracy of target model with up to 6.7x larger training budget based on a set of smaller experiments. We will release a complete list of model losses and downstream evaluation results at various different scales to support reproducibility and encourage future research.

Neural scaling laws have driven the field's ever-expanding exponential growth in parameters, data and compute. While scaling behaviors for pretraining losses and discriminative benchmarks are well established, generative benchmarks such as mathematical problem-solving or software engineering remain under-explored. We propose and evaluate three different pretraining scaling laws for fitting pass-at-$k$ on generative evaluations and for predicting pass-at-$k$ of the most expensive model using cheaper models. Our three scaling laws differ in the covariates used: (1) pretraining compute, (2) model parameters and pretraining tokens, (3) log likelihoods of gold reference solutions. First, we demonstrate that generative evaluations introduce new hyperparameters (in our setting, $k$) that act as a control lever for scaling behavior, modulating both the scaling law parameters and the predictability of performance. Second, we identify a stark difference in parameter stability: while the compute and parameters+tokens laws stabilize for only the last $\mathord{\sim}1.5\mathord{-}2.5$ orders of magnitude, the gold reference likelihood law is uniquely stable, converging across $\mathord{\sim}5$ orders. Third, in terms of predictive performance, we find all three scaling laws perform comparably, although the compute law predicts slightly worse for small $k$ and the gold reference law predicts slightly worse for large $k$. Finally, we establish a theoretical connection, proving that the compute scaling law emerges as the compute-optimal envelope of the parameters-and-tokens law. Our framework provides researchers and practitioners with insights and methodologies to forecast generative performance, accelerating progress toward models that can reason, solve, and create.

Neural networks necessitate nonlinearities to achieve universal approximability. Traditional activation functions introduce nonlinearities through rigid feature rectifications. Recent self-gated variants improve traditional methods in fitting flexibility by incorporating learnable content-aware factors and non-local dependencies, enabling dynamic adjustments to activation curves via adaptive translation and scaling. While SOTA approaches achieve notable gains in conventional CNN layers, they struggle to enhance Transformer layers, where fine-grained context is inherently modeled, severely reducing the effectiveness of non-local dependencies leveraged in activation processes. We refer to this critical yet unexplored challenge as the **non-local tension** of activation. Drawing on a decision-making perspective, we systematically analyze the origins of the non-local tension problem and explore the initial solution to foster a more discriminative and generalizable neural activation methodology. This is achieved by rethinking how non-local cues are encoded and transformed into adaptive scaling coefficients, which in turn recalibrate the contributions of features to filter updates through neural activation. Grounded in these insights, we present **FleS**, a novel self-gated activation model for discriminative pattern recognition. Extensive experiments on various popular benchmarks validate our interpretable methodology for improving neural activation modeling.

Diffusion models have achieved remarkable success in generative modeling. Despite more stable training, the loss of diffusion models is not indicative of absolute data-fitting quality, since its optimal value is typically not zero but unknown, leading to the confusion between large optimal loss and insufficient model capacity. In this work, we advocate the need to estimate the optimal loss value for diagnosing and improving diffusion models. We first derive the optimal loss in closed form under a unified formulation of diffusion models, and develop effective estimators for it, including a stochastic variant scalable to large datasets with proper control of variance and bias. With this tool, we unlock the inherent metric for diagnosing training quality of representative diffusion model variants, and develop a more performant training schedule based on the optimal loss. Moreover, using models with 120M to 1.5B parameters, we find that the power law is better demonstrated after subtracting the optimal loss from the actual training loss, suggesting a more principled setting for investigating the scaling law for diffusion models.

Low-rank architectures have become increasingly important for efficient large language model (LLM) pre-training, providing substantial reductions in both parameter complexity and memory/computational demands. Despite these advantages, current low-rank methods face three critical shortcomings: (1) compromised model performance, (2) considerable computational overhead, and (3) limited activation memory savings. To address these limitations, we propose **C**ross-layer Low-**R**ank residual **Net**work (**CR-Net**), an innovative parameter-efficient framework inspired by our discovery that inter-layer activation residuals possess low-rank properties. CR-Net implements this insight through a dual-path architecture that efficiently reconstructs layer activations by combining previous-layer outputs with their low-rank differences, thereby maintaining high-rank information with minimal parameters. We further develop a specialized activation recomputation strategy tailored for CR-Net that dramatically reduces memory requirements. Extensive pre-training experiments across model scales from 60M to 7B parameters demonstrate that CR-Net consistently outperforms state-of-the-art low-rank frameworks while requiring fewer computational resources and less memory.

Scaling Transformers to ultra-long contexts is bottlenecked by the $O(n^2 d)$ cost of self-attention. Existing methods reduce this cost along the sequence axis through local windows, kernel approximations, or token-level sparsity, but these approaches consistently degrade accuracy. In this paper, we instead explore an orthogonal axis: \emph{feature sparsity}. We propose \textbf{Sparse Feature Attention (SFA)}, where queries and keys are represented as $k$-sparse codes that preserve high-dimensional expressivity while reducing the cost of attention from $\Theta(n^2 d)$ to $\Theta(n^2 k^2/d)$. To make this efficient at scale, we introduce \textbf{FlashSFA}, an IO-aware kernel that extends FlashAttention to operate directly on sparse overlaps without materializing dense score matrices. Across GPT-2 and Qwen3 pretraining, SFA matches dense baselines while improving speed by up to $2.5\times$ and reducing FLOPs and KV-cache by nearly 50\%. On synthetic and downstream benchmarks, SFA preserves retrieval accuracy and robustness at long contexts, outperforming short-embedding baselines that collapse feature diversity. These results establish feature-level sparsity as a complementary and underexplored axis for efficient attention, enabling Transformers to scale to orders-of-magnitude longer contexts with minimal quality loss.

The problem of learning how to reach goals in an environment has been a long- standing challenge in for AI researchers. Effective goal-conditioned reinforcement learning (GCRL) methods promise to enable reaching distant goals without task- specific rewards by stitching together past experiences of different complexity. Mathematically, there is a duality between the notion of optimal goal-reaching value functions (the likelihood of success at reaching a goal) and temporal dis- tances (transit times states). Recent works have exploited this property by learning quasimetric distance representations that stitch long-horizon behaviors using the in- ductive bias of their architecture. These methods have shown promise in simulated benchmarks, reducing value learning to a shortest-path problem. But quasimet- ric, and more generally, goal-conditioned RL methods still struggle in complex environments with stochasticity and high-dimensional (visual) observations. There is a fundamental tension between the local dynamic programming (TD backups, temporal distances) that enables optimal shortest-path reasoning in theory and the statistical global MC updates (multistep returns, suboptimal in theory). We show how these approaches can be integrated into a practical GCRL method that fits a quasimetric distance using a multistep Monte-Carlo return. We show our method outperforms existing GCRL methods on long-horizon simulated tasks with up to 4000 steps, even with visual observations. We also demonstrate that our method can enable stitching in the real-world robotic manipulation domain (Bridge setup). Our approach is the first end-to-end GCRL method that enables multistep stitching in this real-world manipulation domain from an unlabeled offline dataset of visual observations.

Discovering scaling laws for predicting model performance at scale is a fundamental and open-ended challenge, mostly reliant on slow, case specific human experimentation. To investigate the potential for LLMs to automate this process, we collect over 5,000 experiments from existing literature and curate seven diverse scaling law discovery tasks. While existing agents struggle to produce accurate law formulas, this paper introduces SLDAgent, an evolution-based agent that co-optimize the scaling law model and the parameters, enabling it to autonomously explore complex relationships between variables. For the first time, we demonstrates that SLDAgent can automatically discover laws that exhibit consistently more accurate extrapolation than their established, human-derived counterparts across all tasks. Through comprehensive analysis, we elucidate why these discovered laws are superior and verify their practical utility in both pretraining and finetuning applications. This work establishes a new paradigm for agentic scientific discovery, showing that AI systems can understand their own scaling behavior, and can contribute novel and practical knowledge back to the research community.

Diffusion transformers (DiT) have already achieved appealing synthesis and scaling properties in content recreation, \emph{e.g.,} image and video generation. However, scaling laws of DiT are less explored, which usually offer precise predictions regarding optimal model size and data requirements given a specific compute budget. Therefore, experiments across a broad range of compute budgets, from 1e17 to 6e18 FLOPs are conducted to confirm the existence of scaling laws in DiT \emph{for the first time}. Concretely, the loss of pretraining DiT also follows a power-law relationship with the involved compute. Based on the scaling law, we can not only determine the optimal model size and required data but also accurately predict the text-to-image generation loss given a model with 1B parameters and a compute budget of 1.5e21 FLOPs. Additionally, we also demonstrate that the trend of pretraining loss matches the generation performances (e.g., FID), even across various datasets, which complements the mapping from compute to synthesis quality and thus provides a predictable benchmark that assesses model performance and data quality at a reduced cost.

Someone who learns to walk shortest paths in New York can, upon receiving a map of Paris, immediately apply the same rule to navigate, despite never practicing there. This ability to recombine known rules to solve novel problems exemplifies compositional generalization (CG), a hallmark of human cognition. Yet our understanding of what drives the success or failure of such extrapolative problem solving, particularly the roles of training data properties and optimization paradigms, remains limited. In this work, we introduce a controlled map-navigation testbed that cleanly separates two dimensions of CG: ***spatial transfer*** (systematicity across environments) and ***length scaling*** (productivity along problem difficulty). Through quantitative experiments, we show that transfer is enabled by sufficient distinct questions with high coverage and modest diversity, while scaling critically depends on exposure to neighboring-but-longer examples. Finally, we find that reinforcement learning (RL) stabilizes optimization but does not surpass the ceiling set by supervised fine-tuning (SFT). Together, these results provide principled insights into how data properties and training paradigms shape extrapolative problem solving.