ICML 2026 Papers

Linear Attention (LA) offers a promising paradigm for scaling large language models (LLMs) to long sequences by avoiding the quadratic complexity of self-attention. Recent LA models such as Mamba2 and GDN interpret linear recurrences as closed-form online stochastic gradient descent (SGD), but naive SGD updates suffer from rapid information decay and suboptimal convergence in optimization. While momentum-based optimizers provide a natural remedy, they pose challenges in simultaneously achieving training efficiency and effectiveness. To address this, we develop a chunkwise parallel algorithm for LA with a stepwise momentum rule by geometrically reordering the update coefficients. Further, from a dynamical systems perspective, we analyze the momentum-based recurrence as a second-order system that introduces complex conjugate eigenvalues. This analysis guides the design of stable gating constraints. The resulting model, Momentum DeltaNet (MDN), leverages Triton kernels to achieve comparable training throughput with competitive linear models such as Mamba2 and KDA. Extensive experiments on the 400M and 1.3B parameter models demonstrate consistent performance improvements over strong baselines, including Transformers, Mamba2 and GDN, across diverse downstream evaluation benchmarks. Code: https://github.com/HuuYuLong/MomentumDeltaNet.

Despite the ubiquity of multiway data across scientific domains, there are few performant and user-friendly methods that fit non-standard nonnegative tensor factorization models tailored to the data at-hand. Researchers may use gradient-based automatic differentiation, which often struggles under nonnegative constraints, choose between a limited set of methods with mature implementations, or implement their own model from scratch. As an alternative, we introduce NNEinFact, an einsum-based multiplicative update algorithm that fits any nonnegative tensor factorization expressible as a tensor contraction by minimizing one of many user-specified loss functions, including the $(\alpha,\beta)$-divergence. To use NNEinFact, the researcher specifies their model with a string. NNEinFact converges to a stationary point of the loss, supports missing data, and fits to tensors with hundreds of millions of entries in seconds. Empirically, NNEinFact fits custom models which outperform standard ones in prediction tasks on real-world tensor data by over 37% and attains less than half the test loss of gradient-based methods while converging up to 90 times faster. Software is publicly available at github.com/jhood3/einfact.

Autoregressive decoding of large language models is frequently memory-traffic bound, so ultra-low-bit weight-only PTQ helps only if dequantization avoids irregular codebook or LUT access in the inner loop. Under the GPU-friendly bitshift trellis, existing 2-bit trellis-coded quantization (TCQ) pipelines either reintroduce micro-LUTs or suffer overlap-amplified artifacts because incoherence improves global Gaussianity but does not guarantee overlap-local joint geometry. We introduce Proteus a strictly lookup-free TCQ framework whose computed generator MUL-BAL uses cheap integer mixing plus a per-layer affine Gaussianizer to produce overlap-robust, near-Gaussian code values with zero runtime table loads. Proteus instantiates each layer by selecting from a tiny, pre-vetted candidate pool and then applies lightweight channel compensation and optional few-shot distillation that tune only per-layer affine statistics while keeping packed indices and the bitshift-trellis decoder fixed. On Llama 2 (7B–70B) at 2-bit PTQ, Proteus improves perplexity and zero-shot accuracy over strong TCQ/PTQ baselines and reduces end-to-end decode bandwidth at comparable throughput (e.g., 740 vs. 1020 GB/s on 70B).

The prohibitive cost of evaluating Large Language Models (LLMs) necessitates efficient alternatives to full-scale benchmarking. Prevalent approaches address this by identifying a small coreset of items to approximate full-benchmark performance. However, existing methods must estimate a reliable item profile from response patterns across many source models, which becomes statistically unstable when the source pool is small. This dependency is particularly limiting for newly released benchmarks with minimal historical evaluation data. We argue that discrete correctness labels are a lossy view of the model's decision process and fail to capture information encoded in hidden states. To address this, we introduce \textsc{RepCore}, which aligns heterogeneous hidden states into a unified latent space to construct representative coresets. Using these subsets for performance extrapolation, \textsc{RepCore} achieves precise estimation accuracy with as few as ten source models. Experiments on five benchmarks and over 200 models show consistent gains over output-based baselines in ranking correlation and estimation accuracy. Spectral analysis further indicates that the aligned representations contain separable components reflecting broad response tendencies and task-specific reasoning patterns.

In large-scale LLM pretraining systems with $100\mathrm{k}+$ GPUs, failures become the norm rather than the exception, and restart costs can dominate wall-clock training time. However, existing fault-tolerance mechanisms are largely unprepared for this restart-dominant regime. To address this challenge, we propose SPARe—Stacked Parallelism with Adaptive Reordering—a fault-tolerance framework that masks node failures during gradient synchronization by stacking redundant data shards across parallelism groups and adaptively reordering execution. SPARe achieves availability comparable to traditional replication while maintaining near-constant computation overhead of only $2\sim3\times$, even under high redundancy where traidional replication would require linearly inflating overhead. We derive closed-form expressions for endurable failure count and computation overhead, validate them via SimGrid-based discrete-event simulation, and jointly optimize redundancy and checkpointing to minimize training time. At extreme scale with up to $600\mathrm{k}$ GPUs, SPARe reduces time-to-train by $40\sim50$% compared to traditional replication.

In this paper, we study the fully dynamic k-center with outliers problem, where points are inserted and deleted over time and the goal is to maintain an approximate clustering while discarding up to z outliers. Existing algorithms typically rely on radius guessing to maintain cluster representations, leading to update and query times that depend explicitly on the aspect ratio Δ. We propose a layered-sampling framework that avoids radius guessing by maintaining a hierarchy of sampled structures, which can separate most inliers from potential outliers and refine the remaining uncertain points. The resulting algorithm achieves $\tilde{O}(k^2/\epsilon^4)$ update and query time independent of Δ, while guaranteeing a constant-factor approximation with $(1+\epsilon)z$ outliers discarded. Under mild assumptions, our result is complemented by a lower bound in metric space query model.

Neural compression is currently dominated by Nonlinear Transform Coding (NTC), which maps data to real-valued latents via continuous transforms. Despite its success, NTC suffers from train-test mismatch due to non-differentiable quantization, a "smoothness bias" inherent in continuous transforms that precludes optimality for certain sources, and a loss of "shaping gain" due to its use of scalar quantization. We propose SoftBinary Coding (SBC), an end-to-end learning paradigm that bypasses these limitations by using a stochastic binary latent space. In the spirit of vector quantization, SBC employs discrete representations and compresses them through a novel fast binary channel simulation scheme, for which we provide a proof of rate optimality. Experimental gains on information-theoretic sources address NTC's limitations both theoretically and practically, establishing discrete binary structures as a viable path toward reaching optimal rate–distortion bounds. Surprisingly, SBC also achieves state-of-the-art performance on vector quantization of i.i.d. sources, exceeding Trellis Coded Quantization of the Gaussian source.

Training large language models (LLMs) on heterogeneous data requires selecting minibatches that balance convergence speed with coverage across domains. Existing methods either select samples independently within each domain or rely on computationally expensive proxy models to learn continuous domain weights. We propose PartitionSel, a cross-domain minibatch selection approach that maximizes a validation-guided gradient-matching utility under per-domain budgets encoded as a partition-matroid constraint. By coupling the per-domain budgets through a single utility, PartitionSel is designed to reduce redundancy in selections across domains. The proposed objective is weakly submodular and admits an orthogonal matching pursuit algorithm with provable approximation guarantees. Empirically, we evaluate PartitionSel for minibatch selection during the fine-tuning of Qwen2.5 and Llama-3 on MetaMathQA and Mol-Instructions. PartitionSel achieves robust gains over per-domain and domain-agnostic baselines on both benchmarks. It also reduces the number of conflicting gradient pairs within each batch, indicating that the cross-domain coupling translates into more compatible training updates.

Time series prototype learning is fundamentally challenged by observational ambiguity. Discrete architectures fail to resolve this, as they lack the capacity to decouple stochastic noise from continuous dynamics. Furthermore, rigid closed-set assumptions fail to capture unseen diversity. To address these limitations, we propose a hierarchical ordinary differential equation clustering network, which utilizes neural ordinary differential equation to model latent state evolution as a continuous integral curve. This formulation enforces temporal continuity to effectively disentangle smooth feature trends from stochastic noise, while our adaptive hierarchical mechanism autonomously determines the appropriate number of prototypes without rigid prior constraints. Validated on the early link failure detection task with irregularly sampled time series, the proposed method effectively extracts underlying physical prototypes, thereby enabling robust failure detection. Our code is available at https://github.com/NJ-LNN/Hierarchical-ODE.

Efficient prediction and planning in structured environments often relies on spectral decompositions of transition operators, yet existing grid-cell and successor-representation theories implicitly assume “flat” action geometry where translations commute and a single Fourier eigenbasis suffices. We show that this assumption breaks in the presence of path-dependent effects—e.g., circulation, rotational drift, or topological loops—whose defining signature is nontrivial holonomy. We introduce a theory of directed-action prediction on discrete tori based on twisted translation operators forming a projective representation of the underlying motion group, and prove that the resulting controlled Markov operators admit an exact block-diagonalisation under a twisted Fourier transform: actions share a universal harmonic basis while their effects appear as small matrix-valued spectra rather than scalar eigenvalues. This yields closed-form resolvent expressions for the successor representation, a gauge-invariant transfer principle characterising when two environments admit identical predictive structure, and a curvature-induced lower bound showing that nonzero holonomy provably necessitates internal representational dimension. Together, these results generalise Fourier/grid-based prediction from commutative to curved action geometries, providing a principled foundation for generalisation under directed actions without learning environment-specific eigenvectors.

Contrastive training with InfoNCE loss and in-batch negatives is the standard approach for learning dual-encoder models. Its effectiveness, however, critically depends on the availability of hard negatives; in their absence, learning quickly saturates. Existing methods address this via explicit hard-negative mining, which is often costly or heuristic-driven. We introduce $\mathrm{\texttt{HOBIT}}$, a principled mini-batch construction method that improves in-batch negative quality by reordering training examples at every epoch. $\mathrm{\texttt{HOBIT}}$ solves an optimization problem motivated by the InfoNCE objective to yield mini-batches such that each query in the batch is exposed to hard yet non-contradictory, informative negative examples. We show that the optimization objective is monotone and submodular which in turn leads us to a greedy algorithm that admits the standard $\mathcal{O}(1 - 1/e)$ approximation guarantee. Empirically, we show that $\mathrm{\texttt{HOBIT}}$ incurs negligible computational overhead while significantly outperforming state-of-the-art batching methods, and remains complementary to existing hard negative mining techniques.

Existing neural combinatorial optimization (CO) solvers often rely heavily on expensive labeled data and additional post-processing to produce feasible solutions. Research into mixed integer linear programs (MILPs) is particularly limited due to the lack of effective heuristics for feasibility and the challenge of modeling mixed-type variables for neural solvers. To address these issues, we propose a novel unsupervised Langevin sampler for solving MILPs. Our framework learns only integer variables, while continuous variables are solved using an exact linear programming solver, thus isolating the combinatorial hardness of the problem and avoiding unnecessary modeling complexity. The sampler is based on Langevin dynamics and incorporates both objective optimization and constraint satisfaction into a unified energy function, enabling the model to jointly learn feasibility and optimality. Experiments demonstrate that our method achieves 100\% feasibility without expensive post-processing and matches or outperforms supervised solvers on benchmark datasets, highlighting its effectiveness and scalability. Our code can be found at https://github.com/CindyH1103/UNLS4MILP.

The "reversal curse" exposes a critical asymmetry in autoregressive models, where models trained on facts in one direction often fail to access the corresponding inverse relation. This work studies the phenomenon from a representation-level perspective, characterizing it as a form of chiral asymmetry between subject- and object-oriented latent states. We introduce the Chiral Transformer, a lightweight framework that encourages an involutive adjoint mapping operator $\mathcal{T}$ through contrastive regularization. At inference time, Adjoint-Induced Retrieval (AIR) uses this learned map as a structured readout over model-derived entity representations, rather than as an unconstrained autoregressive generation protocol. Empirical validation on inverse-relation benchmarks shows that this symmetry-aware retrieval setting substantially improves inverse factual access, with AIR reaching 65.07% accuracy on Fact-Inv-300. These findings support a representation-access view of the reversal curse: inverse relations may be difficult not only because of missing data, but also because standard autoregressive readout fails to expose useful latent structure.

Most existing time-series forecasters are trained end-to-end with backpropagation, which often increases computational cost and limits structural transparency. As a result, it remains difficult to trace how their predictions are formed. This paper presents FIPN, a forward self-organizing interpretable polynomial network for time-series forecasting. FIPN grows its architecture layer by layer through candidate generation, closed-form estimation, and validation-based selection, without relying on backpropagation-based optimization. Each neuron couples a fuzzy rule antecedent with a Fourier-enhanced polynomial consequent: fuzzy clustering softly partitions the input space and produces interpretable rule weights for local regimes, while the consequent retains access to original features and uses Fourier functions to capture periodic and frequency-related structures. Since forward growth may introduce redundancy, collinearity, and overfitting as depth increases, FIPN further incorporates regularized node scoring, dropout-based redundancy control, and persistent access to raw inputs. Experiments on long-horizon forecasting benchmarks show that FIPN achieves competitive accuracy with a compact model size, while the learned fuzzy rules provide rule- and structure-level explanations. These results suggest that forward self-organizing polynomial networks offer a practical balance among accuracy, efficiency, and interpretability for long-horizon forecasting.

Large kernel depthwise convolutions achieve strong performance but suffer from significant degradation as kernel size grows due to irregular memory access from gather-based computation; while Large Kernel Acceleration (LKA) helps on small feature maps, it becomes counterproductive on large feature maps, even slower than non-accelerated implementations. We propose Windowed Batch Matrix Multiplication (WBMM), which partitions input into contiguous windows and indexes a compact relative position bias table to construct weight matrices, enabling regular memory access via batched matrix multiplication. This yields a unique property: WBMM's throughput improves with larger windows, opposite to depthwise convolutions that degrade with larger kernels. Operator-level benchmarks show WBMM with $14 \times 14$ windows outperforms $5 \times 5$ depthwise convolution baselines in speed while providing a $7.8\times$ larger per-layer receptive field. Combined with inter-block cross-window communication and hierarchical window reparameterization, WBMM achieves comparable or higher accuracy on ImageNet-1K, COCO, and ADE20K with $1.31$--$1.88\times$ training speedup, and demonstrates consistent advantages across GPU, CPU, and edge devices without requiring specialized acceleration kernels. Our code is available at https://github.com/wansong-s/WBMM.

Speculative decoding has emerged as a powerful approach to accelerate large language model (LLM) inference by employing lightweight draft models to propose candidate tokens that are subsequently verified by the target model. The effectiveness of this paradigm critically depends on the quality of the draft model. While recent advances such as the EAGLE series achieve state-of-the-art speedup, existing draft models remain limited by error accumulation: they condition only on the current prefix, causing their predictions to drift from the target model over steps. In this work, we propose ConFu (Contemplate the Future), a novel speculative decoding framework that enables draft models to anticipate the future direction of generation. ConFu introduces (i) contemplate tokens and soft prompts that allow the draft model to leverage future-oriented signals from the target model at negligible cost, (ii) a dynamic contemplate token mechanism with MoE to enable context-aware future prediction, and (iii) a training framework with anchor token sampling and future prediction replication that learns robust future prediction. Experiments demonstrate that ConFu improves token acceptance rates and generation speed over EAGLE-3 by 8-11%, across various downstream tasks with Llama-3 3B and 8B models. We believe our work is the first to bridge speculative decoding with continuous reasoning tokens, offering a new direction for accelerating LLM inference.

While latent diffusion models (LDMs) have emerged as powerful priors for inverse problems, existing LDM-based solvers frequently suffer from instability. In this work, we first identify the instability as a discrepancy between the solver dynamics and stable reverse diffusion dynamics learned by the diffusion model, and show that reducing this gap stabilizes the solver. Building on this, we introduce *Measurement-Consistent Langevin Corrector (MCLC)*, a theoretically grounded plug-and-play stabilization module that remedies the LDM-based inverse problem solvers through measurement-consistent Langevin updates. Compared to prior approaches that rely on linear manifold assumptions, which often fail to hold in latent space, MCLC provides a principled stabilization mechanism, leading to more stable and reliable behavior in latent space.

Large language models (LLMs) have shown promise as interactive agents that solve tasks through extended sequences of environment interactions. While prior work has primarily focused on system-level optimizations or algorithmic improvements, the role of task horizon length in shaping training dynamics remains poorly understood. In this work, we present a systematic empirical study that examines horizon length through controlled task constructions. Specifically, we construct controlled tasks in which agents face identical decision rules and reasoning structures, but differ only in the length of action sequences required for successful completion. Our results reveal that increasing horizon length alone constitutes a training bottleneck, inducing severe training instability driven by exploration difficulties and credit assignment challenges. We demonstrate that horizon reduction is a key principle to address this limitation, stabilizing training and achieving better performance in long-horizon tasks. Moreover, we find that horizon reduction is related to stronger generalization across horizon lengths: models trained under reduced horizons generalize more effectively to longer-horizon variants at inference time, a phenomenon we refer to as horizon generalization.

Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely on likelihood approximations that introduce sampling biases. We address these challenges by introducing a new energy-based model trained for denoising with a covariance-based regularization term that enforces consistency across different measurement conditions. The trained model can compute normalized posterior densities for diverse linear inverse problems, without additional retraining or fine tuning. In addition to preserving the sampling capabilities of diffusion models, this enables previously unavailable capabilities: energy-guided adaptive sampling that adjusts schedules on-the-fly, unbiased Metropolis-Hastings correction steps, and blind estimation of the degradation operator via Bayes rule. We validate the method on multiple datasets (ImageNet, CelebA, AFHQ) and tasks (inpainting, deblurring), demonstrating competitive or superior performance to established baselines.