NeurIPS 2026 论文列表

Nonlinear independent component analysis (nICA) is generally unidentifiable due in part to measure-preserving automorphisms (MPAs), which induce indistinguishable latent representations. We show that for non-Gaussian sources with mild regularity assumptions, such MPAs are not Lipschitz, motivating Lipschitz continuity as a structural assumption. Under this condition, we prove global identifiability of nICA within the class of Orthogonal Coordinate Transformations (OCTs) with bounded sources, recovering the true components up to permutation and scaling. Our analysis reduces the learning problem to a linear program over the Birkhoff polytope, and extends to functions with symmetric Jacobians, revealing connections to optimal transport. We introduce OCTNet and SYMNet, normalizing flow architectures that enforce these constraints in practice. Experiments demonstrate strong recovery performance and robustness to model misspecification, outperforming existing approaches.

A common failure mode in long-horizon agentic test-time scaling is error propagation, where factual errors or invalid deductions introduced at intermediate steps persist in the agent's belief state and contaminate later reasoning. Existing test-time scaling methods provide limited control over this process, as they often rely on agents to detect their own mistakes, select among flawed trajectories, or refine solutions only after errors have already shaped the reasoning path. We propose ExComm, a communication protocol for exploration-stage agentic test-time scaling. ExComm is motivated by the empirical observation that the majority of intermediate errors in parallel agentic reasoning produce detectable cross-agent factual conflicts. Leveraging the iterative structure of agentic workflows, ExComm periodically audits agent belief states to detect such conflicts, resolves them through a dedicated tool-based verification loop, and returns concise, targeted feedback to the involved agents. Corrections are incorporated through soft belief updates, which append verified feedback rather than overwriting existing beliefs. Furthermore, to prevent collapsing trajectory diversity due to communication, ExComm further introduces a trajectory diversification module that redirects redundant trajectories toward orthogonal strategies. Experiments on AIME 2024, AIME 2025, and GAIA with Gemini-2.5-Flash-Lite and Qwen3.5-4B show that ExComm consistently outperforms strong test-time scaling baselines, achieving average performance gains of 5.7\% and 5.0\% over the best-performing baselines, respectively. Further analyses demonstrate improved error recovery, favorable scaling behavior, stronger diversity than adapted communication baselines, and the best performance-cost trade-off among the evaluated methods.

Scaling long-context capabilities is crucial for Large Language Models (LLMs). However, real-world data contain a large number of sequences with heterogeneous lengths. Existing training libraries for LLMs rely on static parallelism strategies, which suffer from severe load imbalance, redundant communication, and suboptimal hardware utilization under data heterogeneity. In this work, we propose Flexible Context Parallelism (FCP), an efficient parallelism strategy that adaptively reconfigures communication groups and context parallelism degrees during LLM training. We generalize more flexible non-power-of-two parallelism degrees and develop a polynomial-time algorithm to generate near-optimal parallelism strategies with only millisecond-level overhead per training batch. FCP is able to maintain high hardware efficiency even under extreme data heterogeneity. Experimental results demonstrate that FCP significantly outperforms Megatron-LM and DeepSpeed in both LLM and MLLM training, achieving up to 1.47 $\times$ speedup in average throughput while maintaining near-linear scaling efficiency across large-scale clusters. For extremely unbalanced batches, FCP even achieves 2.24 $\times$ speedup.

Construction-based neural routing solvers, typically composed of an encoder and a decoder, have emerged as a promising approach for solving vehicle routing problems. While recent studies suggest that shifting parameters from the encoder to the decoder enhances performance, most works restrict the decoder size to 1–3M parameters, leaving the effects of scaling largely unexplored. To address this gap, we conduct a systematic study comparing two distinct strategies: scaling depth versus scaling width. We synthesize these strategies to construct a suite of 12 model configurations, spanning a parameter range from 1M to $\sim$150M, and extensively evaluate their scaling behaviors across three critical dimensions: parameter efficiency, data efficiency, and compute efficiency. Our empirical results reveal that parameter count is insufficient to accurately predict the model performance, highlighting the critical and distinct roles of model depth (layer count) and width (embedding dimension). Crucially, we demonstrate that scaling depth yields superior performance gains to scaling width. Based on these findings, we provide and experimentally validate a set of design principles for the efficient allocation of parameters and compute resources to enhance the model performance.

Parallel test-time scaling (TTS) has been shown to enhance reasoning in large language models by generating and aggregating multiple independent reasoning paths. Internal confidence scores can further improve this process by identifying paths of varying quality. However, existing methods remain computationally inefficient, as low-quality paths are fully expanded before being evaluated. In this work, we aim to improve the use of internal confidence signals for better model performance and computational efficiency. We begin by offering a new perspective on the role of confidence in aggregation, showing that it is most impactful for questions near the decision boundary. Notably, when amplified by multi-sample aggregation, even small confidence signals derived from short prefixes can meaningfully influence outcomes in these boundary cases. Building on this insight, we introduce Prefix-Guided Sampling (PreG), a method that reallocates computation by first generating short prefixes, ranking them using internal confidence scores, and then completing only the most promising candidates. This strategy reduces token usage while maintaining gains in path quality. We provide theoretical analysis demonstrating that, under a fixed compute budget, PreG strengthens the effective signal by widening the decision boundary margin. Empirically, our method consistently outperforms standard parallel TTS approaches across benchmarks, while significantly improving token efficiency and reducing overall computation.

Mixture-of-Experts (MoE) transformers scale capacity by activating only a few experts per token, but this sparsity creates a hidden reliability problem: when routing is imperfect, load-balanced models may send tokens to experts that are insufficiently trained for the assigned inputs. We propose Distributionally Robust MoE Training (DRMoET), a drop-in objective that treats layer-wise experts as endogenous robustness groups and optimizes high-loss routing outcomes rather than merely equalizing traffic. DRMoET updates a per-layer expert distribution by an entropy-regularized softmax rule on EMA-smoothed, activation-weighted expert losses, strengthening plausible non-top routing paths while preserving standard MoE computation. Under the FLAME-MoE recipe at 746M-total and 10.3B-total scales, DRMoET improves downstream averages over both standard FLAME-MoE and auxiliary-loss-free balancing. Mechanistic analyses show lower expert-loss variance with nearly unchanged mean loss, 4.3\% lower degradation under forced mid-$k$ misrouting, and improved domain--expert specialization. These results position routing robustness--not only utilization balance--as a practical objective for reliable sparse MoE scaling.

Hyperparameter transfer has become an important component of modern large-scale training recipes. Existing methods, such as muP, primarily focus on transfer between model sizes, with transfer across batch sizes and training horizons often relying on empirical scaling rules informed by insights from timescale preservation, quadratic proxies, and continuous-time approximations. We study hyperparameter scaling laws for modern first-order optimizers through the lens of recent convergence bounds for methods based on the Linear Minimization Oracle (LMO), a framework that includes normalized SGD, signSGD (approximating Adam), and Muon. Treating bounds in recent literature as a proxy and minimizing them across different tuning regimes yields closed-form power-law schedules for learning rate, momentum, and batch size as functions of the iteration or token budget. Our analysis, holding model size fixed, recovers most insights and observations from the literature under a unified and principled perspective, with clear directions open for future research. Our results draw particular attention to the interaction between momentum and batch-size scaling, suggesting that optimal performance may be achieved with several scaling strategies.

Language model loss follows remarkably regular scaling laws over model and data size, yet it remains unclear why the aggregate loss should exhibit a power-law form. Existing explanations often attribute this regularity to a heavy-tailed spectrum of pattern difficulty in natural language, but this view has not been directly validated at token-level granularity in large-scale real-data training. We present a token-level framework that deconstructs scaling laws into localized learning events of individual contextualized tokens. By fitting token loss trajectories with sigmoids, we show that token learning is concentrated in localized transitions, giving rise to a learning-time spectrum that dominates the scaling-law shape. Across more than one hundred pre-training runs on large and diverse real-language corpora with modern LLM architectures, scaling up to 6B parameters and 300B training tokens, the measured learning-time spectrum quantitatively reconstructs the validation loss derivative along the training-step $T$, data-scale $D$, and model-scale $M$ axes. We further show that the same signal is actionable: by reshaping the training distribution according to when tokens become learnable, we alter the optimization trajectory and achieve 11\% faster validation-loss reduction. These results provide direct empirical evidence that scaling laws are governed primarily by the distribution of token-level learning times, and that this distribution can be used not only to explain scaling behavior but also to improve training performance.

Classical scaling laws for language model pretraining balance model size against training dataset size under a fixed compute budget, assuming abundant data and a single pass over the corpus. As training compute grows faster than the supply of natural language data, pretraining is likely to enter a data-constrained, compute-rich regime where models train for multiple epochs over a finite dataset. We study data-constrained pretraining along two axes, regularization and scaling. For regularization, we study masked-input regularization (MIR), an auxiliary next-token prediction loss on randomly masked inputs. MIR tests whether the random masking central to diffusion language models can benefit autoregressive pretraining without architectural changes or inference overhead. Across 72M to 1.4B parameter models, we find that MIR added on top of strong weight decay improves validation loss over autoregressive strong-weight-decay-only models, with downstream gains at 1.4B. For scaling, we propose SoftQ, a scaling law that couples model size and data size to capture their interaction under repeated data. Classical alternatives such as the Chinchilla law use an additive form that decouples these terms, making them misspecified in the data-constrained regime. We find that SoftQ fits data-constrained experiments substantially better than these alternatives, and estimates MIR's gains as equivalent to roughly 1.3 times as much unique training data.

The remarkable scalability of Transformers has expanded their application to 3D computer vision, where camera-aware positional encoding is crucial for providing spatial cues in multi-view geometry. Recent advancements have established the practice of using camera parameters---such as extrinsics or projection matrices---as relative positional encoding into the query, key, and value vectors of the attention mechanism. However, when scaling up the training recipe of novel view synthesis (NVS) models with the camera-based positional encoding, we observe a significant issue: model performance stagnates in the late stages of training. In this paper, we investigate the cause of the performance bottleneck when scaling up and demonstrate that storing rotation and translation given by the positional encoding in the same dimensions of the value vector causes indeterminacy in their independent identification, hindering training scalability. To address this, we propose Decoupled Pose Positional Encoding (DPPE), a novel camera-based positional encoding that explicitly decouples rotation and translation. Extensive evaluations on NVS tasks demonstrate that DPPE enables stable long-term training even in scaled-up training setup. Furthermore, it exhibits superior generalization performance in extrapolation settings, such as handling an increased number of viewpoints and zoom-in scenarios.

Test-time scaling often uses an external verifier, such as compilers and test-cases in coding or trained value functions in robotics application, to obtain high quality rollouts. Verifier-free test-time scaling (or VF-TTS) is gaining extensive attention as a mechanism to enhance Large Language Model (LLM) reasoning, primarily because in many real-world applications we do not have access to such high quality verifiers. Among existing VF-TTS methods, confidence-based VF-TTS methods, which compute and rank rollouts solely by confidence, are particularly promising. Such methods introduce near-zero overhead for sample evaluation and require minimal access to internal model states, making the methods highly flexible across models and data. In this paper, we demonstrate a critical limitation of existing confidence-based VF-TTS methods by showing that such methods catastrophically break down on complex tasks. We observe a very interesting phenomenon: uniformly high confidence frequently indicates a failure to explore, favoring confidently wrong answers. To address this, our core insight is that robust cognitive search requires a specific confidence trajectory pattern: such methods perform exploratory branching at the beginning as manifested by low initial confidence, and converge to a high final confidence solution. To implement this insight, we introduce consilience, a novel selection framework that explicitly evaluates the temporal asymmetry of confidence in reasoning. We operationalize this via a combinatorial metric that actively penalizes high initial confidence while strictly demanding final certainty. Extensive experiments covering both graduate-level mathematics problems and free-form code generation demonstrate that consilience effectively outperforms existing baselines, validating our novel perspective on completion confidence.

While autoregressive models optimize the exact likelihood implied by the chain rule, diffusion models are typically trained with denoising objectives. We develop conservation laws based on generalized extrinsic information transfer (GEXIT) functions for a broad class of memoryless noise processes, showing that the data--model cross-entropy (CE) can be characterized \emph{exactly} as an integral of \emph{local} information-theoretic derivatives along the noise path. This yields a unified characterization of the likelihood for discrete diffusion and continuous diffusion, with the Gaussian case reducing to the well-known I-MMSE relationship connecting mutual information and estimation theory. An immediate implication is a \emph{locality} property: one can compute the information-theoretic derivatives using only the marginal posteriors along the noise path. As a result, training reduces to learning the marginal posteriors by minimizing the negative log-likelihood. While the conservation law implies that the entropy does not depend on the noise path, finite-capacity denoisers approximate the posteriors with varying accuracy across noise types, leading to differences in performance. We validate these predictions on synthetic Markov sources and standard benchmarks, including \texttt{text8} and CIFAR-10.

Neural surrogates for Partial Differential Equations (PDEs) are usually trained on synthetic data from numerical simulators. As models grow and scaling laws demand larger datasets, the cost of data generation often outweighs the training cost and becomes the bottleneck in the scaling quest. Unlike data in other domains, however, each PDE sample has a tunable per-sample cost that depends on its numerical fidelity, with the resulting cost-accuracy trade-off governed by known convergence rates. We exploit this property by formalizing neural surrogate training as a function of both data quantity and fidelity under a fixed data generation compute budget, treating fidelity as a fine-grained discrete spectrum rather than a binary distinction. Building on this, we show that multi-fidelity training enables Pareto-optimal error scaling against data generation compute. By using simulations at lower fidelities as an additional training signal, our approach consistently outperforms training on the highest fidelity at matched data generation budgets. We validate this across six PDE problems spanning structured grids and unstructured meshes, two distinct error sources (discretization and iterative-solver error), and four surrogate architectures.

Open-source web agents are now strong enough to execute realistic browser tasks, but training them with reinforcement learning still depends on weak supervision: binary task success is too sparse for credit assignment, while frontier-language-model judges are too expensive to call at every step and cannot be assumed available at deployment. We introduce CLIFT, a training and test-time scaling method built around conformal self-verification. During training, the agent answers natural-language verification questions about its own rollouts; a Compositional Conformal Certifier keeps only question signals whose URL-conditional evidence agrees with a training-time judge, assigns signed trust weights through polarity-aware lift, and blends the resulting verifier score into per-step rewards in a way that never subtracts from the judge baseline. At test time, the same certified bank is frozen and reused as structured evidence for Conformal Trajectory Selection (CTS): the agent samples a greedy rollout and one or more diverse retries, the self-verifier summarises each URL trace, and a conservative majority-vote rule chooses whether to swap away from the current incumbent without calling any external judge. This single mechanism supports three settings. On WebArena Infinity, CLIFT achieves state-of-the-art performance among open-source web agents. On VisualWebArena, a bank trained with the open model transfers to GPT-5.5 at test time and reaches state-of-the-art performance under the canonical harness. On Online Mind2Web, without training an agent on the benchmark, translating the certified question bank improves a live-web agent in zero-shot evaluation. Together these results position conformal self-verification as a way to turn costly judge feedback into a reusable training signal and a judge-free test-time scaling signal.

Asymptotic e-values are emerging as a powerful alternative to asymptotic p-values, particularly in post-hoc inference and multiple testing, where significance levels may be data-dependent. Existing asymptotic e-values, however, suffer from the ``missing factor,'' a scaling inefficiency resulting in overly conservative inference. Drawing on the framework of near-optimal concentration inequalities developed by Bentkus in the 2000s, we introduce Bentkus-type asymptotic e-values and prove that they successfully eliminate the missing factor. We also demonstrate both theoretically and empirically that Bentkus-type e-values consistently deliver sharper inference than existing alternatives, leading to tighter post-hoc confidence intervals and higher rejection rates in multiple testing procedures.

Modern data-centric applications increasingly require language agents capable of operating over live, stateful database environments, where successful problem resolution depends not merely on initial SQL generation, but on reasoning about evolving database states, interacting with execution feedback, and repairing state-mutating operations. While agentic reinforcement learning (RL) has emerged as a promising paradigm for training small language models (SLMs), existing frameworks are predominantly tool-centric and struggle with data-centric environments. Specifically, applying tool-centric frameworks to stateful tasks like SQL debugging introduces severe spatial inefficiencies since proper environment isolation typically requires a separate database container per rollout. Naively reusing databases without tracking evolving states across multi-turn interactions causes trajectory contamination and cross-trajectory interference, which severely destabilizes policy updates. To overcome these bottlenecks, we introduce **BIRD-RL**, a novel four-stage agentic RL curriculum that alternately enhances foundational agent reasoning and trajectory-adaptive on-policy exploration to circumvent the instability inherently associated with direct end-to-end learning. Crucially, to support this curriculum, BIRD-RL is driven by a **Trajectory-scoped Persistent Execution Infrastructure**, which enables safe database replica reuse while preserving trajectory isolation. This design improves spatial RL efficiency by **12.8x**, successfully enabling scalable agentic RL for complex data-centric tasks without needs of Kubernettes. Empirical evaluations on the BIRD-CRITIC-SQLite benchmark demonstrate that our 7B and 14B models achieve Success Rates of **44.40%** and **48.00%**, respectively, performing on par with or exceeding strong proprietary model-based agents such as Claude-Opus-4.6 Agent (48.20%). Furthermore, BIRD-RL successfully trains unified SLMs capable of both advanced SQL debugging and generation, highlighting its broader potential for multi-objective optimization across heterogeneous, real-world data-centric tasks.

We introduce a model for neural scaling laws under sparse activations. In the model, test loss is often dominated by rare coordinates that are never observed in the training input. This mechanism induces a novel bottleneck absent from dense models. We derive the asymptotic population loss in both the underparameterized and overparameterized regimes, and show that the loss exhibits a double-descent peak near the interpolation threshold---where the number of parameters is just sufficient to fit the training data---resulting in a loss curve governed by two distinct scaling exponents---one for the overparameterized regime and one for the underparameterized regime---with a gap determined by the degree of sparsity. Additionally, we derive a compute-optimal frontier that favors increasing dataset size over model capacity under fixed compute budgets. We also analyze gradient-descent dynamics and identify a scaling law for the probability that fixed-step gradient descent becomes unstable. We further show that the sparsity-induced effect persists under nonlinear activations. Experiments validating the theory can be found at https://anonymous.4open.science/r/sparse-scaling-neurips2026-3CDB/SparseScaling1.ipynb.

Scaling network depth has been a central driver behind the success of modern foundation models, yet recent investigations suggest that deep layers are often underutilized. This paper revisits the default mechanism for deepening neural networks, namely residual connections, from an optimization perspective. On a motivating example, rigorous analysis proves that the layout of residual connections can fundamentally shape convergence behavior, and even induces an *exponential* gap in convergence rates. Prompted by this insight, we introduce adaptive neural connection reassignment (ANCRe), a principled and lightweight framework that parameterizes and learns residual connectivities from the data. ANCRe adaptively reassigns residual connections with negligible computational and memory overhead (<1%), while enabling more effective utilization of network depth. Extensive numerical tests across pre-training of large language models, diffusion models, and deep ResNets demonstrate consistently accelerated convergence, boosted performance, and enhanced depth efficiency over conventional residual connections.

Continual pre-training (CPT) enables injecting domain-specific knowledge into large language models during the learning rate annealing phase. However, this compute-efficient paradigm forces practitioners to navigate a challenging optimization space: simultaneously choosing the injection fraction $\lambda$, the data mixture ratio $r$, and the re-warmup peak learning rate $\eta$. Because existing scaling laws have yet to comprehensively integrate and couple these interacting variables, they cannot reliably forecast the resulting trade-offs and final convergence outcomes across unseen injection configurations. To bridge this gap, we introduce the Annealing-phase Domain Injection Scaling Law (ADIS-Law), a parametric framework that explicitly models late-stage distribution shifts as physical perturbations applied to the base pre-training trajectory. ADIS-Law formalizes two opposing macroscopic behaviors: general-domain performance follows a linear forgetting-recovery process, whereas target-domain adaptation adheres to a power-law adaptation trend. Across data-budget and model-scale extrapolation, ADIS-Law predicts target-domain trajectories with an average Spearman correlation of $0.947$ and forecasts tail losses with relative error below $5\\%$. We further show that ADIS-Law can predict optimal injection strategies at extrapolated scales: it ranks target-scale candidate policies with a mean Spearman correlation of $0.936$. By replacing blind grid search over $(\lambda, r, \eta)$ with a single fitted law, ADIS-Law offers a data-driven approach for strategy selection in annealing-phase domain injection.