ICML 2026 Papers

Recent advances in audio deepfake detection have been driven by increasingly large speech foundation models and growing amounts of synthetic data. Despite strong benchmark performance, it remains unclear how detection capability scales with model capacity and training data under realistic deployment conditions involving distribution shift, signal corruption, and unseen synthesis pipelines. In this work, we present the first systematic study of scaling laws in post-training audio deepfake detection, focusing on fine-tuning regimes rather than large-scale pretraining. Using a controlled family of speech foundation models with shared architecture and pretraining, we analyze how detection performance, robustness, and generalization evolve as a function of model size and training data scale. Our results reveal a fundamental asymmetry between performance scaling and robustness scaling in audio deepfake detection, suggesting increasing model capacity alone is insufficient for achieving reliable real-world generalization.

It is increasingly common in machine learning to use learned models to label data and then employ such data to train more capable models. The phenomenon of weak-to-strong generalization exemplifies the advantage of this two-stage procedure: a strong student is trained on imperfect labels obtained from a weak teacher, and yet the strong student outperforms the weak teacher. In this paper, we show that the potential improvement is substantial, in the sense that it affects the scaling law followed by the test error. Specifically, we consider students and teachers trained via random features ridge regression (RFRR). Our main technical contribution is to derive a deterministic equivalent for the excess test error of the student trained on labels obtained via the teacher. Via this deterministic equivalent, we then identify regimes in which the scaling law of the student improves upon that of the teacher, unveiling that the improvement can be achieved both in bias-dominated and variance-dominated settings. Strikingly, the student may attain the minimax optimal rate regardless of the scaling law of the teacher---in fact, when the test error of the teacher does not even decay with the sample size.

Diffusion language models are a promising alternative to autoregressive models due to their potential for faster generation. Among discrete diffusion approaches, Masked diffusion currently dominates, largely driven by strong perplexity on language modeling benchmarks. In this work, **we present the first scaling law study of uniform-state and interpolating discrete diffusion methods**. We also show that Masked diffusion models can be made approximately 12% more FLOPs-efficient when trained with a simple cross-entropy objective. We find that perplexity is informative within a diffusion family but can be misleading across families, where models with worse likelihood scaling may be preferable due to faster and more practical sampling, as reflected by the speed-quality Pareto frontier. **These results challenge the view that Masked diffusion is categorically the future of diffusion language modeling** and that perplexity alone suffices for cross-algorithm comparison. Scaling all methods to 1.7B parameters, we show that uniform-state diffusion remains competitive on likelihood-based benchmarks and outperforms autoregressive and Masked diffusion models on GSM8K, despite worse validation perplexity.

We study how we can leverage only a handful of characteristics of a transformer's architecture to closely predict the number of different sequences it can output, both qualitatively and quantitatively. We provide an upper bound depending on the length of the prompt, which we show empirically to be tight up to a factor less than 10, across architectures and model sizes. Our analysis also provides a theoretical explanation for previously observed empirical failures of transformers on simple sequence tasks—such as copying and cramming. Formally, we prove that (i) the maximal length of accessible sequences (those that the transformer can output for some prompt) grows linearly with the prompt length, (ii) beyond a critical threshold, the proportion of accessible sequences decays exponentially with sequence length, and (iii) the linear coefficient relating prompt length to accessible sequence length admits a theoretical upper bound. Notably, these results hold even with unbounded context and computation time.

Dataset distillation (DD) aims to replace a full training set with a tiny synthetic one, yet current theories neither explain why heterogeneous matching objectives (gradient, distribution, trajectory) work nor provide a quantitative boundary for robustness under configuration changes (optimizer, architecture, augmentation). We propose **configuration-dynamics-error (CDE) analysis** for a broad class of matching-based DD methods, a unified generalization framework that treats a training configuration as an update operator inducing optimization dynamics and measures distillation robustness by the test-risk gap between models trained on distilled versus full data. Within this framework, gradient, distribution, and trajectory matching reduce the same dynamics-induced risk gap, explaining why these heterogeneous objectives can all support dataset distillation. CDE yields two predictive laws: within a fixed configuration, the gap decays as $\mathcal{O}(k^{-1/2})$ with the distilled set size $k$ until a configuration-dependent floor, explaining IPC saturation and indicating when reducing the floor is more valuable than enlarging $k$. Across configurations, an order-tight coverage law formalizes the utility boundary: the required $k$ grows linearly with the configuration diversity captured by covering-number complexity. Experiments with representative DD methods and configuration changes exhibit predictive behavior consistent with both laws.

Scaling laws for dense LLMs under infinite data are well explored, but how sparsity interacts with limited data is not. In this work, we study sparse training in data-constrained regimes where limited unique tokens require multi-epoch training. Our experiments span models up to 1.92B parameters in the fitting set, sparsity up to 93.75\%, unique data budgets up to 2.6B tokens, and total training tokens up to 41.6B over 16 epochs; we further validate extrapolation on held-out dense-equivalent models up to 7.68B parameters. We find that: **1. Sparse scaling in data-limited settings:** We introduce a scaling law that models loss as a function of active parameters, unique tokens, data repetition, and sparsity, accurately predicting performance across compute and data budgets. **2. Delayed data saturation:** sparse training postpones diminishing returns from repeated data, making multi-epoch training more effective. **3. Resource trade-offs:** With fixed data, loss-optimal sparsity is moderate (~ 50%), while compute-optimal sparsity is higher and grows with data scale. Overall, sparsity is not just a tool for efficiency, but a mechanism for improving scaling trade-offs under data scarcity. Our code is available at: https://github.com/boqian333/sparse-dc-scaling.

Determining an effective data mixture is a key factor in Large Language Model (LLM) pre-training, where models must balance general competence with proficiency on hard tasks such as math and code. However, identifying an optimal mixture remains an open challenge, as existing approaches either rely on unreliable tiny-scale proxy experiments or require prohibitively expensive large-scale exploration. To address this, we propose Decouple Searching from Training Mix (DeMix), a novel framework that leverages model merging to predict optimal data ratios. Instead of training proxy models for every sampled mixture, DeMix trains component models on candidate datasets at scale and derives data mixture proxies via weighted model merging. This paradigm decouples search from training costs, enabling evaluation of unlimited sampled mixtures without extra training burden and thus facilitating better mixture discovery through more search trials. Extensive experiments demonstrate that DeMix breaks the trade-off between sufficiency, accuracy and efficiency, obtaining the optimal mixture with higher benchmark performance at lower search cost. Additionally, we release the DeMix Corpora, a comprehensive 22T-token dataset comprising high-quality pre-training data with validated mixtures to facilitate open research. Our code and DeMix Corpora is available at https://github.com/Lucius-lsr/DeMix.

Training large language models (LLMs) is computationally expensive, partly because the loss exhibits slow power-law convergence whose origin remains debatable. Through systematic analysis of toy models and empirical evaluation of LLMs, we show that this behavior can arise intrinsically from the use of softmax and cross-entropy. When learning peaked probability distributions, e.g., next-token distributions, these components generically yield power-law vanishing losses and gradients, regardless of many microscopic details, creating a fundamental optimization bottleneck. This ultimately leads to power-law time scaling of the loss with a universal exponent of $1/3$. Our results provide a mechanistic explanation for observed neural scaling and suggest new directions for improving LLM training efficiency.

Muon updates matrix parameters via the matrix sign of the gradient and has shown strong empirical gains, yet its dynamics and scaling behavior remain unclear in theory. We study Muon in a linear associative memory model with softmax retrieval and a hierarchical frequency spectrum over query–answer pairs, with and without label noise. In this setting, we show that Gradient Descent (GD) learns frequency components at highly imbalanced rates, leading to slow convergence bottlenecked by low-frequency components. In contrast, the Muon optimizer mitigates this imbalance, leading to faster and more uniform progress. Specifically, in the noiseless case, Muon achieves an exponential speedup over GD; in the noisy case with a power-law frequency spectrum, we derive Muon's scaling law and demonstrate its superior scaling efficiency over GD. Furthermore, we show that Muon can be interpreted as an implicit matrix preconditioner arising from adaptive task alignment and block-symmetric gradient structure. In contrast, the preconditioner with coordinate-wise sign operator could match Muon under oracle access to unknown task representations, which is infeasible for SignGD in practice. Experiments on synthetic long-tail classification and LLaMA-style pre-training corroborate the theory.

Reliable Docker-based environment construction is a dominant bottleneck for scaling execution-grounded training and evaluation of software engineering agents. We introduce DockSmith, a specialized agentic Docker builder designed to address this challenge. DockSmith treats environment construction not merely as a preprocessing step, but as a core agentic capability that exercises long-horizon tool use, dependency reasoning, and failure recovery, yielding supervision that transfers beyond Docker building itself. DockSmith is trained on large-scale, execution-grounded Docker-building trajectories produced by a SWE-Factory--style pipeline augmented with a loop-detection controller and a cross-task success memory. Training a 30B-A3B model on these trajectories achieves open-source state-of-the-art performance on Multi-Docker-Eval, with 39.72\% Fail-to-Pass and 58.28\% Commit Rate. Moreover, DockSmith improves out-of-distribution performance on SWE-bench Verified, SWE-bench Multilingual, and Terminal-Bench 2.0, demonstrating the broader agentic benefits of environment construction. Our model and Docker-building trajectories are publicly available at https://huggingface.co/JiaranZhang/DockSmith.

Scaling large language models (LLMs) has driven their success, yet dense Transformers couple capacity and computation: every parameter is activated for every token, making training and inference costs grow linearly with model size—a critical bottleneck as models approach trillion-parameter regimes. We aim to scale capacity through MoE-style mixture throughout the LLM pipeline rather than only the FFN. Prior pipeline-level approaches include ParaScale, which introduces virtual tokens and parallel streams but incurs substantial overhead and suffers from homogenized routing and gradient collapse, and AltUp, which uses an auxiliary prediction branch but offers limited adaptivity and slow convergence. We establish that MoE-style mixture layers can be reformulated as variable-kernel dynamic convolutions, where each expert corresponds to a $1{\times}1$ convolutional kernel and routing implements input-conditioned kernel aggregation. Building on this equivalence, we introduce cMoLLM: a convolutionally gated mixture-of-LLMs that routes over end-to-end streams through fully differentiable dynamic convolution. In GPT-2-style models trained on FineWeb, cMoLLM improves language modeling perplexity and downstream GLUE and SQuAD accuracy under matched compute, with better stream utilization, more stable optimization, and favorable scaling compared to ParaScale- and AltUp-style baselines.

We study the capacity of the self-attention key-query channel: for a fixed budget, how many distinct token-token relations can a single layer reliably encode? We introduce *Relational Graph Recognition*, where the key-query channel encodes a directed graph and, given a context (a subset of the vertices), must recover the neighbors of each vertex in the context. We measure resources by the total key dimension $D_K = hd_k$. In a tractable multi-head model, we prove matching information-theoretic lower bounds and upper bounds via explicit constructions showing that recovering a graph with $m'$ relations in $d_{\text{model}}$-dimensional embeddings requires $D_K$ to grow essentially as $m'/d_{\text{model}}$ up to logarithmic factors, and we obtain corresponding guarantees for scaled-softmax attention. This analysis yields a new, capacity-based rationale for multi-head attention: even in permutation graphs, where **all queries attend to a single target**, splitting a fixed $D_K$ budget into multiple heads increases capacity by reducing interference from embedding superposition. Controlled experiments mirror the theory, revealing sharp phase transitions at the predicted capacity, and the multi-head advantage persists when adding softmax normalization, value routing, and a full Transformer block trained with frozen GPT-2 embeddings.

While scaling laws guide compute allocation for LLM pre-training, analogous prescriptions for reinforcement learning (RL) post-training of LLMs remain poorly understood. We study the compute-optimal allocation of sampling compute for on-policy RL methods in LLMs, framing scaling as a compute-constrained optimization over three resources: parallel rollouts per problem, number of problems per batch, and number of update steps. We find that the compute-optimal number of parallel rollouts per problem increases predictably with compute budget and then saturates. This trend holds across both easy and hard problems, though driven by different mechanisms: solution sharpening on easy problems and coverage expansion on hard problems. We further show that increasing the number of parallel rollouts mitigates interference across problems, while the number of problems per batch primarily affects training stability and can be chosen within a broad range. Validated across base models and data distributions, our results recast RL scaling laws as prescriptive allocation rules and provide practical guidance for compute-efficient LLM RL post-training.

Reinforcement Learning (RL) post-training alignment for language models is effective, but also costly and unstable in practice, owing to its complicated training process. To address this, we propose a training-free inference method to sample directly from the optimal RL policy. The transition probability applied to Masked Language Modeling (MLM) consists of a reference policy model and an energy term. Based on this, our algorithm, Energy-Guided Test-Time Scaling (ETS), estimates the key energy term via online Monte Carlo, with a provable convergence rate. Moreover, to ensure practical efficiency, ETS leverages modern acceleration frameworks alongside tailored importance sampling estimators, substantially reducing inference latency while provably preserving sampling quality. Experiments on MLM (including autoregressive models and diffusion language models) across reasoning, coding, and science benchmarks show that our ETS consistently improves generation quality, validating its effectiveness and design. The code is available at https://github.com/sheriyuo/ETS.

The rise of model hubs has made it easier to access reusable model components, making model merging a practical tool for combining capabilities. Yet, this modularity also creates a *governance gap*: downstream users can recompose released weights into unauthorized mixtures that bypass safety alignment or licensing terms. Because existing defenses are largely post-hoc and architecture-specific, they provide inconsistent protection across diverse architectures and release formats in practice. To close this gap, we propose Trap$^{2}$, an architecture-agnostic protection framework that encodes protection into updates during fine-tuning, regardless of whether they are released as adapters or full models. Instead of relying on architecture-dependent approaches, Trap$^{2}$ uses weight re-scaling as a simple proxy for the merging process. It keeps released weights effective in standalone use, but degrades them under re-scaling that often arises in merging, undermining unauthorized recomposition.

Existing scaling laws for Large Language Models (LLMs), predominantly monotonic power laws, fail to explain emerging non-monotonic phenomena such as *catastrophic overtraining* and *quantization-induced degradation*, where performance deteriorates despite increased compute. We propose the Shannon Scaling Law, a unified theoretical framework that models LLM training as information transmission over a noisy channel, grounded in the Shannon–Hartley theorem. By mapping model parameters to channel bandwidth and training tokens to signal power, our formulation explicitly captures the interaction between learning signal and intrinsic noise. This perspective reveals a fundamental Shannon capacity for LLMs: scaling model size or data without preserving a sufficient signal-to-noise ratio (SNR) inevitably amplifies noise, inducing a transition from monotonic improvement to U-shaped performance degradation. We validate our theory through experiments on Pythia and OLMo2 under perturbations, including Gaussian noise, quantization and supervised fine-tuning on math, QA and code tasks. The Shannon Scaling Law consistently outperforms classical scaling laws and recent perturbation-aware laws, achieving strong $R^2$ scores and accurately capturing loss basins missed by prior approaches. It also extrapolates: fitted on $\leq$6.9B Pythia models with $\leq$180B tokens, it predicts the unseen 12B model up to 307B tokens at pooled $R^2{=}0.847$, while monotonic baselines collapse.

Computing the differential entropy of distributions known only up to a normalization constant is a fundamental challenge with broad theoretical and practical significance. While variational inference is highly scalable for density approximation from samples, its application to unnormalized densities remains under-explored due to the difficulty of constructing variational distributions that exploit the structure of the unnormalized density and are simultaneously expressive, tractable, efficiently samplable. Recently, Messaoud et al. (ICLR 24) introduced _P-SVGD_, a Stein variational inference method for this setting. We show, however, that \textit{P-SVGD} fails to scale to high dimensions due to incorrect invertibility assumptions, omission of a critical trace-of-Hessian term, and unstable divergence-control heuristics. We propose _MET-SVGD_, a principled extension of _P-SVGD_ that provides a general framework for stable _SVGD_ hyperparameter selection with global invertibility and convergence guarantees. Empirically, _MET-SVGD_ achieves up to $12\times$ and $16\times$ lower entropy estimation error than _P-SVGD_ and existing _SVGD_ baselines, respectively. On CIFAR-10 energy-based image generation, it improves FID by $80.4\%$ and yields $64\times$ higher training stability. In maximum-entropy reinforcement learning, it achieves up to $16\%$ higher returns than _P-SVGD_. Code is available at https://shorturl.at/fTG0G.

Recent work describes what transformers can and cannot compute through connections to boolean circuits, but existing results lack exact characterizations and are sensitive to modeling choices. Padded transformers---to whose input filler symbols such as ``...'' are appended---emerge as a useful gadget for establishing equivalences to circuit classes by providing polynomial space for adaptive parallel computation. However, only a limited set of padded transformer idealizations has been studied, leaving open how robustly these equivalences hold under changes to attention type, model width, and uniformity. We find that, under practical assumptions, padded transformers are surprisingly robust to all of these, and identify numeric precision and model depth as the main factors affecting expressivity. Concretely, we prove that polynomially padded $\text{L-uniform}$ constant-precision transformers are equivalent to $\text{L-uniform AC}^0$, while growing-precision ones achieve $\text{L-uniform TC}^0$ regardless of width. Furthermore, looping enables sequential processing analogous to circuits: $\log^d N$-looped constant-precision transformers reach $\text{FO-uniform AC}^d$, and growing-precision ones reach $\text{FO-uniform TC}^d$. Interestingly, growing width or precision beyond logarithmic does not increase expressivity, and all our results hold for both softmax and average hard attention transformers.

Scaling laws have played a major role in modern AI, providing predictive power over how model performance will improve with increasing resources. This has spurred intense interest in their origin, with a common suggestion being that they arise from power laws already present in the data. Here we study scaling laws for transformers trained to predict random walks on graphs with tunable complexity. We show that this simplified setting already yields scaling laws even in the absence of power laws in the data correlations. We further consider dialing down the complexity of language by training on sequences sampled from increasingly simplified generative language models, from 4,2,1-layer transformer language models down to language bigrams, revealing a monotonic evolution of the scaling exponents. Our results also include scaling laws obtained from training on random walks on random graphs drawn from Erdös-Renyi and scale-free Barabási-Albert ensembles. Finally, we revisit scaling laws for language modeling, demonstrating that several essential results can be reproduced using 2 layer transformers with context length of 100, demonstrate an alternative method for obtaining compute optimal curves, and provide preliminary evidence that maximal update parameterization may be more parameter efficient than standard parameterization.