ICML 2026 Papers

Reinforcement Learning (RL) has become a cornerstone for improving the performance of Large Language Models (LLMs). However, its rollout phase constitutes a significant efficiency bottleneck, mainly arising from the long-tail bubbles across data parallel ranks, particularly in long-context scenarios where faster GPUs remain idle while waiting for stragglers. Existing solutions, such as partial rollout or asynchronous RL, mitigate these bubbles by compromising the algorithm's strict synchronous nature. Instead, we propose **BubbleSpec**, a novel framework that accelerates RL rollouts while strictly keeping the mathematical exactness. Instead of attempting to eliminate bubbles, BubbleSpec exploits them. We exploit the idle time windows of faster ranks to pre-generate rollout results for subsequent steps, serving as drafts for speculative decoding. Unlike prior speculative methods that rely on historical epoch similarity and warm-ups, BubbleSpec is agnostic to dataset size and provides immediate acceleration from the onset of training. Extensive evaluations demonstrate that BubbleSpec reduces decoding steps by **$\sim$50\%** and increases rollout throughput by up to **1.8$\times$**. Critically, BubbleSpec is seamlessly compatible with various RL frameworks and strategies as it sustains the strict synchronous property of RL algorithms.

The factors driving the performance of in-context learning (ICL) in large language models (LLMs) remain poorly understood despite ICL's surprising effectiveness, enabling models to adapt to new tasks from only a handful of examples. To clarify and improve these capabilities, we characterize how the statistical properties of the pretraining distribution (e.g., tail behavior, coverage) shape ICL. We develop a theoretical framework that encompasses generalization and task selection and show how distributional properties govern sample efficiency, task retrieval, and robustness. To this end, we generalize existing concentration results to heavy-tailed priors and dependent sequences, better reflecting the structure of LLM pretraining data. Our framework reveals a fundamental design trade-off: heavy-tailed pretraining distributions facilitate robust task selection under distribution shifts but are detrimental to generalization, especially in low-data regimes. We then empirically evaluate our predictions by studying how ICL performance varies with the pretraining distribution on challenging tasks such as stochastic differential equations and stochastic processes with memory. Together, these findings suggest that controlling key statistical properties of the pretraining distribution is essential for building ICL-capable and reliable LLMs.

We generalize the attention mechanism by viewing it through the lens of Entropic Optimal Transport, revealing that standard attention corresponds to a transport problem regularized by an implicit uniform prior. We introduce Generalized Optimal transport Attention with Trainable priors (GOAT), a new attention mechanism that replaces this naive assumption with a learnable, continuous prior. This prior maintains full compatibility with optimized kernels such as FlashAttention. GOAT also provides an EOT-based explanation of attention sinks and materializes a solution for them, avoiding the representational trade-offs of standard attention. Finally, by absorbing spatial information into the core attention computation, GOAT learns an extrapolatable prior that combines the flexibility of learned positional embeddings with the length generalization of fixed encodings.

Token-ranking heuristics accelerate the prefill bottleneck in long-context LLM inference by selectively processing semantically relevant tokens. However, current evaluation relies on end-to-end benchmarks, making it difficult to isolate the quality of the token ranking itself. To address this, we introduce an Answer-Informed Reference framework with two variants: a Model Reference (Model-Ref) that measures token importance using the model generated answer, and a Ground-Truth Reference (GT-Ref) that uses human reference answers. Using GT-Ref, we establish that as few as 10% of prompt tokens suffice to match full-context performance on LongBench across all three evaluated models. The framework also reveals that existing heuristics exhibit variance across layers, with rankings degrading sharply at specific layers. Motivated by this instability, we propose Cross-Layer Attention Aggregation (CLAA), which aggregates importance scores across consecutive layers, eliminating the layer-dependent accuracy collapse observed in single-layer methods. A meaningful gap remains between the best heuristic and GT-Ref, indicating theoretical room for improved token selection.

Transformer-based large language models face severe scalability challenges in long-context generation due to the computational and memory costs of full-context attention. Under practical computation and memory constraints, many inference-efficient long-context methods improve efficiency by adopting bounded-context or segment-level execution only during inference, while continuing to train models under full-context attention, resulting in a mismatch between training and inference execution and state-transition semantics. Based on this insight, we propose a training-consistent segment-level generation framework, in which training and inference follow the same segment-level forward execution semantics. During training, consistency with inference is enforced by restricting gradient propagation to KV states carried over from the immediately preceding segment, while permitting head-specific access to past KV states during the forward pass without involving them in gradient propagation. Across long-context benchmarks, our approach achieves performance comparable to full-context attention, while achieving competitive latency--memory trade-offs against strong inference-efficient baselines, and substantially improving scalability at very long context lengths (e.g., approximately $6\times$ lower peak prefill memory at 128K compared to full-context attention with FlashAttention).

The operational efficacy of large language models relies heavily on their inference-time context. This has established Context Engineering (CE) as a formal discipline for optimizing these inputs. Current CE methods rely on manually crafted harnesses, such as rigid generation-reflection workflows and predefined context schemas. They impose structural biases and restrict context optimization to a narrow, intuition-bound design space. To address this, we introduce Meta Context Engineering (MCE), a bi-level framework that supersedes static CE heuristics by co-evolving CE skills and context artifacts. In MCE iterations, a meta-level agent refines engineering skills via agentic crossover, a deliberative search over the history of skills, their executions, and evaluations. A base-level agent executes these skills, learns from training rollouts, and optimizes context as flexible files and code. We evaluate MCE across five disparate domains under offline and online settings. MCE demonstrates consistent performance gains, achieving 5.6--53.8% relative improvement over state-of-the-art agentic CE methods (mean of 16.9%), while maintaining superior context adaptability, transferability, and efficiency in both context usage and training. Code is available at \url{https://github.com/henry-yeh/mce}.

Popular offline reinforcement learning (RL) methods rely on *explicit conservatism*, penalizing out-of-dataset actions or restricting rollout horizons. We question the universality of this principle and revisit a complementary Bayesian perspective for test-time adaptation. By modeling a posterior over world models and training a history-dependent agent to maximize expected return, the Bayesian approach directly addresses epistemic uncertainty without explicit conservatism. We first illustrate in a bandit setting that Bayesianism excels on low-quality datasets where conservatism fails. Scaling to realistic tasks, we find that *long-horizon rollouts* are essential to control value overestimation once conservatism is removed. We introduce design choices that enable learning from long-horizon rollouts while mitigating compounding model errors, yielding our algorithm, NEUBAY, grounded in the neutral Bayesian principle. On D4RL and NeoRL benchmarks, NEUBAY is competitive with leading conservative algorithms, achieving new state-of-the-art on 7 datasets with rollout horizons of several hundred steps. Finally, we characterize datasets by quality and coverage to identify when NEUBAY is preferable to conservative methods.

Mainstream methods for multivariate time-series forecasting largely follow the Direct-Mapping paradigm. They learn a unified mapping from history to the future in the observation space to fit value-level dependencies. However, real-world systems often undergo distribution shifts and regime changes. In such cases, a unified mapping can exhibit response lag around turning points, causing error accumulation within the switching window and reducing forecasting reliability. To address this issue, we propose L-Drive, a change-aware forecasting framework. L-Drive introduces a Latent-Context, to explicitly characterize high-level dynamics evolving over time, and uses gating to modulate increment representations. This provides more timely change cues and improves adaptation to changing segments. In addition, it incorporates patch-shared relative positional basis functions to strengthen intra-segment structural modeling and reduce overfitting caused by absolute-position memorization. Extensive experiments validate the effectiveness of L-Drive and show a better overall trade-off between forecasting accuracy and computational efficiency.

Frontier large language models (LLMs) are increasingly capable of carrying out long-running, real-world tasks. However, as the amount of context grows, their reliability often deteriorate, a phenomenon known as "context rot". Existing long-context benchmarks primarily focus on single-step settings that evaluate a model’s ability to retrieve information from a long snippet. In realistic scenarios, however, LLMs often need to act as agents that explore environments, follow instructions and plans, extract useful information, and predict correct actions under a dynamically growing context. To assess language agents in such settings, we introduce LOCA-bench (a benchmark for **LO**ng-**C**ontext **A**gents). Given a task prompt, LOCA-bench leverages automated and scalable control of environment states to regulate the agent’s context length. This design enables LOCA-bench to extend the context length potentially to infinity in a controlled way while keeping the underlying task semantics fixed. LOCA-bench evaluates language agents as a combination of models and scaffolds, including various context management strategies. While agent performance generally degrades as the environment states grow more complex, advanced context management techniques can substantially improve the overall success rate. We will open-source LOCA-bench to provide a platform for evaluating models and scaffolds in long-context, agentic scenarios.

Softmax attention is a central component of transformer architectures, yet its nonlinear structure poses significant challenges for theoretical analysis. We develop a unified, measure-based framework for studying single-layer softmax attention under both finite and infinite prompts. For i.i.d. centered Gaussian inputs, we lean on the fact that the softmax operator converges in the infinite-prompt limit to a linear operator acting on the underlying input-token measure. Building on this insight, we establish non-asymptotic concentration bounds for the output and gradient of softmax attention, quantifying how rapidly the finite-prompt model approaches its infinite-prompt counterpart, and prove that this concentration remains stable along the entire training trajectory in general in-context learning settings with sub-Gaussian tokens. In the case of in-context linear regression, we use the tractable infinite-prompt dynamics to analyze training at finite prompt length. Our results allow optimization analyses developed for linear attention to transfer directly to softmax attention when prompts are sufficiently long, showing that large-prompt softmax attention inherits the analytical structure of its linear counterpart. This, in turn, provides a principled and broadly applicable toolkit for studying the training dynamics and statistical behavior of softmax attention layers in large prompt regimes.

Transformers excel empirically on tasks that process well-formed inputs according to some grammar, such as natural language and code. However, it remains unclear how they can process grammatical syntax. In fact, under standard complexity conjectures, standard transformers cannot recognize context-free languages (CFLs), a canonical formalism to describe syntax, or even regular languages, a subclass of CFLs. Past work has shown that $\mathcal{O}(\log(N))$ looping layers (w.r.t. input length $N$) allow transformers to recognize regular languages, but the question of context-free recognition with looped transformers remained open. In this work, we show that looped transformers with $\mathcal{O}(\log(N))$ looping layers and $\mathcal{O}(N^6)$ padding symbols can recognize all CFLs. However, training and inference with $\mathcal{O}(N^6)$ padding symbols is potentially impractical. Fortunately, we show that, for natural subclasses such as unambiguous CFLs, the recognition problem on transformers becomes more tractable, requiring $\mathcal{O}(N^3)$ padding. Empirically, looped and padded transformers perform better than fixed-depth transformers in recognizing CFLs. Overall, our results shed light on the intricacy of CFL recognition by transformers: while general recognition may require an intractable amount of padding, natural constraints such as unambiguity yield efficient recognition algorithms.

Autoregressive generative models for irregularly sampled clinical time-series data are increasingly used for zero-shot risk forecasting. Prior work typically adopts a single fine-grained discretization of time, where tokens are generated at one fixed, predetermined temporal resolution. We demonstrate that the zero-shot accuracy of individual generative forecasters varies with temporal resolution: performance can degrade when the model resolution is poorly matched to the temporal dynamics of the endpoint being evaluated. We then propose MoRGen (Mixture-of-Resolutions Generation), which fuses forecasts from generative experts trained at multiple temporal resolutions using a low-capacity task-specific mixture, improving performance across tasks with different temporal dynamics. Across multiple horizons and outcomes on three independent clinical datasets, MoRGen achieves lower binary cross-entropy (BCE) and statistically significant AUROC gains over autoregressive generative models that forecast tokens at a fixed temporal resolution.

Transformers have been established as the most popular backbones in sequence modeling, mainly due to their effectiveness in in-context retrieval tasks and the ability to learn at scale. Their quadratic memory and time complexity, however, bound their applicability in longer sequences and so has motivated researchers to explore effective alternative architectures such as modern recurrent neural networks (a.k.a long-term recurrent memory module). Despite their recent success in diverse downstream tasks, they struggle in tasks that requires long context understanding and extrapolation to longer sequences. We observe that these shortcomings come from three disjoint aspects in their design: (1) limited memory capacity that is bounded by the architecture of memory and feature mapping of the input; (2) online nature of update, i.e., optimizing the memory only with respect to the last input; and (3) less expressive management of their fixed-size memory. To enhance all these three aspects, we present Atlas, a long-term memory module with high capacity that learns to memorize the context by optimizing the memory based on the current and past tokens, overcoming the online nature of long-term memory models. Our experimental results on language modeling, common-sense reasoning, recall-intensive, and long-context understanding tasks support the effectiveness of Atlas compared to other modern recurrent neural networks.

As large language models (LLMs) are increasingly deployed in retrieval augmented generation (RAG) and agentic systems that accumulate extensive context, understanding how distracting information affects performance in long context becomes critical. Prior work shows that semantically relevant but misleading documents can cause performance degradation, yet the quantitative relationship between the proportion of distractors and performance remains unstudied. In this work, we systematically vary the proportion of hard distractors within fixed-length contexts, revealing a striking nonlinear pattern: as the proportion of hard distractors increases, performance drops sharply within the first small fraction, while the remainder of the range yields only marginal additional decline. We term this ''The First Drop of Ink'' effect, analogous to how a single drop of ink contaminates water. We provide both theoretical and empirical analysis grounded in attention mechanics: hard distractors disproportionately capture attention even at small proportions, with diminishing marginal impact as their proportion increases. Through controlled experiments, we further show that filtering yields performance gains primarily from context length reduction rather than distractor removal, and only achieves substantial recovery when hard distractor proportion is reduced to near zero, which highlights the importance of upstream retrieval precision.

We prove that with linear transformations, both (i) two-layer self-attention and (ii) one-layer self-attention followed by a softmax function are universal approximators for continuous sequence-to-sequence functions on compact domains. Our main technique is a new interpolation-based method for analyzing attention’s internal mechanism. This leads to our key insight: self-attention is able to approximate a generalized version of ReLU to arbitrary precision, and hence subsumes many known universal approximators. Building on these, we show that two-layer multi-head attention or even one-layer multi-head attention followed by a softmax function suffices as a sequence-to-sequence universal approximator. In contrast, prior works rely on feed-forward networks to establish universal approximation in Transformers. Furthermore, we extend our techniques to show that, (softmax-)attention-only layers are capable of approximating gradient descent in-context. We believe these techniques hold independent interest.

State space models (SSMs) have emerged as efficient linear-time alternatives to attention for long-sequence modeling. However, existing SSMs often suffer from instability and memory degradation over extended horizons due to poorly conditioned first-order updates and unbalanced update geometry. We introduce MuonSSM, a general framework that stabilizes SSM training by explicitly conditioning the geometry of memory updates rather than the recurrent transition matrix. MuonSSM augments SSMs with a momentum-based pathway and a lightweight Newton-Schulz transformation on low-rank input injections, yielding bounded and spectrally conditioned updates while preserving parallel scan complexity. Theory shows that MuonSSM improves gradient propagation, mitigates spectral amplification, and enriches memory representations over long horizons. Extensive experiments across language, vision, and time-series benchmarks show consistent gains in accuracy, robustness, and long-context performance when integrated into diverse SSM backbones. These results establish geometric conditioning of updates as a principled pathway to stable, scalable sequence modeling.

We introduce Robust Filter Attention (RFA), a formulation of self-attention as a robust state estimator. Each token is treated as a noisy observation of a latent trajectory governed by a linear stochastic differential equation (SDE), and attention weights are determined by consistency under this model rather than static feature similarity. Under isotropic noise and decay assumptions, RFA matches the computational complexity of standard attention. On language modeling benchmarks, RFA achieves lower perplexity than RoPE within the training window while remaining stable under zero-shot extrapolation to longer contexts. The framework also provides a dynamical interpretation of standard positional mechanisms, connecting rotational embeddings and recency biases to transport and uncertainty propagation induced by stochastic dynamics.

Long-sequence modeling faces a fundamental trade-off between the efficiency of compressive fixed-size memory in RNN-like models and the fidelity of lossless growing memory in attention-based Transformers. Inspired by the Multi-Store Model in cognitive science, we introduce a memory framework of artificial neural networks. Our method maintains a sliding window of the Transformer's KV cache as lossless short-term memory, while a learnable module termed Artificial Hippocampus Network (AHN) recurrently compresses out-of-window information into a fixed-size compact long-term memory. To validate this framework, we instantiate AHNs using modern RNN-like architectures, including Mamba2, DeltaNet, and GatedDeltaNet to augment open-weight base LLMs. We also propose an efficient self-distillation method where the base model' all parameters are frozen and only the parameters from AHNs are optimized. For inference, our method sets a default large sliding window size of 32k for attention, and AHNs activate only when the sequence length exceeds the 32k window, addressing the quadratic-complexity issue of attention that emerges at that scale. Extensive experiments on long-context benchmarks LV-Eval and InfiniteBench demonstrate that AHN-augmented models consistently outperform sliding window baselines and achieve performance comparable or even superior to full-attention models, while substantially reducing computational and memory requirements. For instance, augmenting the Qwen2.5-3B-Instruct with AHNs reduces inference FLOPs by 40.5% and memory cache by 74.0%, while improving its average score on LV-Eval (128k sequence length) from 4.41 to 5.88.

Given the quadratic complexity of attention, KV cache eviction is vital to accelerate model inference. Current KV cache eviction methods typically rely on instantaneous heuristic metrics, implicitly assuming that score magnitudes are consistent proxies for importance across all heads. However, this overlooks the heterogeneity in predictive fidelity across attention heads. While certain heads prioritize the instantaneous contribution of tokens, others are dedicated to capturing long-horizon utility. In this paper, we propose that optimal budget allocation should be governed by the marginal utility in preserving long-term semantic information. Building on this insight, we propose LU-KV, a novel framework that formulates head-level budget allocation as a global combinatorial optimization problem to maximize the long-horizon marginal contribution of reserved tokens. To solve this non-convex problem, we employ a convex-hull relaxation and a marginal-utility-based greedy solver, achieving near-optimal solutions. Furthermore, we implement a data-driven offline profiling protocol to facilitate the practical deployment of LU-KV. Evaluations on LongBench and RULER benchmarks demonstrate that LU-KV reduces KV cache size by 80\% with minimal performance degradation, while also decreasing inference latency and GPU memory footprint.