ICML 2026 论文列表

Mixture-of-Experts (MoE) have shown strong potential in scaling language models efficiently by activating only a small subset of experts per input. However, their deployment remains limited due to the high memory overhead associated with storing all expert parameters, particularly as the number of experts increases. To address this challenge, prior works have explored expert dropping and merging strategies; however, they often suffer from notable performance drop especially at high compression ratios due to their reliance on coarse-grained tensor- or expert-level operations. In this paper, we introduce PuzzleMoE, the first MoE merging method to enable fine-grained element-wise merging while achieving both high accuracy and inference speed, via two key innovations: First, PuzzleMoE performs sparse expert merging by identifying element-wise weight redundancy and specialization. It introduces a dual-mask approach to capture both shared and expert-specific salient parameters. Second, to avoid the overhead of storing masks and signs, we introduce a bit-packed encoding scheme that reuses underutilized exponent bits, enabling efficient MoE inference on GPUs. Extensive experiments demonstrate that PuzzleMoE outperforms prior MoE compression methods by up to 16.7\% on MMLU at 50\% compression ratio, and achieves up to 1.80$\times$ end-to-end inference throughput gain.

Speculative decoding mitigates the memory-bound nature of LLM decoding by using a lightweight draft model to propose multiple tokens for parallel verification. However, its adoption has been limited by the lack of high-quality draft models and scalable training infrastructure. We introduce SpecForge, an open-source and efficient framework for training speculative decoding models with full support for EAGLE-3. SpecForge incorporates target–draft decoupling, hybrid parallelism, optimized training kernels, and tight integration with production-grade inference engines, enabling up to 9.9x faster EAGLE-3 training for Qwen3-235B-A22B compared to the baseline. We further release SpecBundle, a suite of production-grade EAGLE-3 draft models trained with SpecForge for mainstream open-source LLMs, achieving up to 4.48x end-to-end inference speedup on SGLang and addressing the scarcity of high-quality drafts. Finally, we distill a systematic study of speculative decoding training into practical and actionable recipes to guide real-world adoption.

Neural scaling laws relate loss to model size in large language models (LLMs), yet depth and width may contribute to performance differently, requiring more detailed studies. Here, we quantify how depth affects loss via analysis of LLMs and toy residual networks. We find loss scales inversely proportional to depth in LLMs, probably due to functionally similar layers reducing error through ensemble averaging rather than compositional learning or discretizing smooth dynamics. This regime is inefficient yet robust and may arise from the architectural bias of residual networks and target functions incompatible with smooth dynamics. The findings suggest that improving LLM efficiency may require architectural innovations to encourage compositional use of depth.

The rapid advancement of large language models (LLMs) has led to remarkable performance across diverse domains, making them indispensable assistants in daily life and work. Currently, LLM services are primarily accessed in two ways: (i) paid access to cloud-hosted LLMs, which are powerful but introduce nontrivial cost; and (ii) deployment of small language models (SLMs) on personal devices or small clusters, which, while less powerful, are sufficient for handling relatively simple tasks. To achieve a balanced trade-off between monetary cost and task performance, we propose Selective Deferred Routing, a paradigm that enables cost-efficient collaboration between local SLMs and remote LLMs. In this framework, a user request is first processed by the local SLM, which not only generates a preliminary response but also provides rich semantic representations of the request. A lightweight decision module then leverages this information to either adopt the initial response or route the request to the most suitable remote LLM for a higher-quality response. Extensive experiments across diverse model architectures and families, including both SLMs and LLMs, as well as datasets spanning multiple task scenarios, demonstrate that our approach consistently outperforms existing multi-LLM collaboration methods under a wide range of cost–performance trade-offs.

To drive progress in science and engineering, large language models (LLMs) must be able to process large amounts of numerical data and solve long calculations efficiently. This is currently only possible through the use of external tools or extensive reasoning chains, either weakening the numerical representations of LLMs or limiting the length of problems they can solve. We show that frontier LLMs require excessive amounts of reasoning tokens to solve even basic calculations, which is exacerbated by their tokenization strategies that split single numbers into multiple tokens. This motivates the need for efficient and effective single-token number encodings. We introduce a set of desiderata for such encodings and show that existing approaches fail to fulfill them. To address these shortcomings, we propose BitTokens, a novel encoding strategy that represents any number as a single token using its IEEE 754 binary floating-point representation. Through extensive experiments we show that our BitTokens allow even small language models to learn algorithms that solve basic arithmetic operations nearly perfectly. This newly gained efficiency could expand the length and complexity of problems language models can solve.

The quadratic complexity of attention remains the central bottleneck in long-context inference for large language models. Prior acceleration methods either sparsify the attention map with structured patterns or permanently evict tokens at specific layers, which can retain irrelevant tokens or rely on irreversible early decisions despite the layer-/head-wise dynamics of token importance. In this paper, we propose Token Sparse Attention, a lightweight and dynamic token-level sparsification mechanism that compresses per-head $Q, K, V$ to a reduced token set during attention and then decompresses the output back to the original sequence, enabling token information to be reconsidered in subsequent layers. Furthermore, Token Sparse Attention exposes a new design point at the intersection of token selection and sparse attention. Our approach is fully compatible with dense attention implementations, including Flash Attention, and can be seamlessly composed with existing sparse attention kernels. Experimental results show that Token Sparse Attention consistently improves accuracy–latency trade-off, achieving up to $\times$3.23 attention speedup at 128K context with less than 1\% accuracy degradation. These results demonstrate that dynamic and interleaved token-level sparsification is a complementary and effective strategy for scalable long-context inference.

Layer dropout (a.k.a.\ stochastic depth) has been shown to enable faster training, higher accuracy, and robustness to zero-shot layer pruning in both language and vision transformers. However, as models and datasets have scaled, dropout---particularly layer dropout---has largely disappeared from LLM pre-training recipes. While some prior work has reported that dropout can degrade accuracy, no comprehensive study has quantified, let alone mitigated, this effect. In this study, we show that layer dropout **should** be used in state-of-the-art LLM training, establishing best practices and scaling analysis for both training and post-training benefits. Concretely, with optimal layer distribution, time schedule, and optimizer hyperparameters, LLM can achieve lower or similar validation loss while saving upto 20\% of training FLOPs. Moreover, layer dropout enables significant post-training optimizations, such as early exit, intermediate-layer skipping, and self-speculative decoding, yielding up to 1.4x inference speedup with negligible accuracy loss. All pre-training experiments were run on Cerebras CS-3 systems.

In this paper, we present CAT-Q, **C**ost-efficient and **A**ccurate **T**ernary **Q**uantization, for compressing and accelerating LLMs. Unlike existing state-of-the-art ternary quantization methods that rely on data-intensive and costly quantization-aware training to mitigate severe performance degradation, CAT-Q is a simple yet effective post-training quantization scheme that is readily applicable to LLMs with diverse architectures and model sizes. It has two key components, learnable modulation (LM) and softened ternarization (ST), which are coupled from an optimization perspective. LM leverages a composition of learnable factors to modulate the distribution of pre-trained high-precision weights and the ternary threshold, making them less sensitive to ternarization. ST further introduces a differentiable transition function to guide the ternarization process toward stable convergence. We show that, for pre-trained LLMs with 1.7B to 8B parameters, CAT-Q can efficiently quantize them into ternary models using only 512 calibration samples, while achieving superior performance than the seminal BitNet 1.58-bit v1 and v2 families (with 1.3B to 7B parameters) trained with 100B tokens, yielding about a 100,000$\times$ reduction in training tokens. Moreover, we show for the first time that CAT-Q can quantize much larger pre-trained LLMs having 14B to 235B parameters into leading ternary models within just 8 to 60 hours on 8 A100-80GB GPUs. Code is available at https://github.com/IntelChina-AI/BitTern.

State-space language models such as Mamba and gated linear attention (GLA) offer efficient alternatives to transformers due to their linear complexity and parallel training, but often lack the expressivity and robust state-tracking needed for complex reasoning. We address these limitations by reframing sequence modelling through a probabilistic lens, using Bayesian filters as a core primitive. While classical filters such as Kalman filters provide principled state estimation and uncertainty tracking, they are typically viewed as inherently sequential. We show that reparameterising the Kalman filter in information form enables its updates to be computed via an associative scan, allowing efficient parallel training. Building on this insight, we introduce the Kalman Linear Attention (KLA) layer, a neural sequence-modelling primitive that performs time-parallel probabilistic inference while maintaining explicit belief-state uncertainty. KLA offers strictly more expressive non-linear updates and gating than GLA variants while retaining their computational advantages. On language modelling tasks, KLA matches or outperforms modern SSMs and GLAs across representative benchmarks for discrete token manipulation and state tracking.

A central insight in lossless data compression is the close connection between probabilistic next- symbol prediction and efficient sequence compression, whereby predictive models can be combined with classical coding techniques to achieve strong compression performance. Applying this approach with powerful modern learned models, such as LLMs, has been shown to achieve markedly better compression than traditional techniques across a wide range of domains. However, significant practical challenges remain, including model non-determinism, in which a model produces different predictions on different machines despite identical parameters and inputs; such mismatches between the encoder and decoder can lead to complete decoding failure. Probability Matching Interval Coding (PMATIC) was recently introduced as a drop-in framework for mismatch-robust coding and shown to enable reliable compression and decompression in the presence of bounded prediction mismatch (Adler & Tang, 2026). In this work, we present a generalization of PMATIC that allows the incorpo- ration of tight theoretical results into the design and more flexible parameter optimization, resulting in substantial improvements in compression efficiency and robustness.

Pre-Layer Normalization (Pre-LN) is the de facto choice for large language models (LLMs) and is crucial for stable pretraining and effective transfer learning. However, Pre-LN incurs repeated statistical-computation overhead and remains vulnerable to the curse of depth, where hidden-state magnitudes and variances grow as the number of layers increases, destabilizing training. Efficiency-oriented normalization-free methods such as Dynamic Tanh (DyT) improve throughput but remain fragile at depth. To jointly address stability and efficiency, we propose Bounded Hyperbolic Tanh (BHyT), a drop-in replacement for Pre-LN. BHyT combines a tanh nonlinearity with explicit, data-driven input bounding to keep activations within a non-saturating range. It prevents depth-wise growth in activation magnitude and variance and provides a theoretical stability guarantee. For efficiency, BHyT computes exact statistics once per block and replaces a second normalization with a lightweight variance approximation. Empirically, BHyT demonstrates improved stability and efficiency during pretraining, achieving an average of 1.6\% faster training and an average of 1.77\% higher token generation throughput compared to RMSNorm, while maintaining strong pretraining-only and post-SFT performance across language understanding and reasoning benchmarks\footnote{Code is available at: \url{https://github.com/MLAI-Yonsei/BHyT}}.

Small language models (SLMs) offer efficient deployment, yet they often lag behind their larger counterparts (LLMs) in reasoning. Existing remedies either invoke an LLM at points of reasoning divergence, incurring substantial latency and cost, or rely on standard distillation, which is limited by the SLM's capacity to accurately mimic the LLM's complex generative distribution. We address this dilemma by identifying local sufficiency: at divergence points, the LLM's preferred token often resides within the SLM's top-$K$ next-token predictions, even when failing to emerge as the SLM top-1 choice. We therefore propose Select to Think (S2T), which reframes the LLM’s role from open-ended generation to selection among the SLM's proposals, simplifying the supervision signal to discrete candidate rankings. Leveraging this, we introduce S2T-Local, which distills the selection logic into the SLM, empowering it to perform autonomous re-ranking without inference-time LLM dependency. Empirically, a 1.5B SLM's top-8 candidates contain the 32B LLM's choice with a 95\% hit rate, and S2T-Local improves the 1.5B SLM's Math Avg. over greedy decoding by 24.1\% relative gain, matching the efficacy of 8-path self-consistency with single-trajectory efficiency. Code is available at https://github.com/YeRona/Select-to-Think.

Continuous-Depth Neural Networks (CDNNs), including Neural Ordinary Differential Equations (ODEs) and Liquid-Time-Constant Neural Networks (LTC-NN), suffer from high computational costs due to solving numerous nonlinear ODEs during training and inference. We introduce Continuous Depth Acceleration (CoDA), a framework that leverages Mori–Zwanzig/Koopman operator theory to replace continuous-depth layers requiring multiple nonlinear ODEs with a compact GRU module, a single low-dimensional linear ODE, and a dense layer. We prove PAC learnability of CoDA, establishing that this transformation preserves accuracy and can be applied repeatedly across multiple layers with unified backpropagation. Experiments on the Liquid Foundation Model (LFM-1.2B) demonstrate $6.7\times$ training speedup and $1.8\times$ inference speedup without loss of accuracy. Across six real-world LTC-NN applications, CoDA consistently outperforms state-of-the-art acceleration techniques—including neural flows, model order reduction, and variational formulations—in both training and inference time while maintaining competitive or superior accuracy. The implementation and datasets are publicly available at \url{https://github.com/ImpactLabASU/CoDA-ICML2026}.

Deep learning models for supervised learning on tabular data are rapidly improving. Notably, ensembles (mixtures of multiple models) often play an important role in achieving top performance, which motivates designing _ensemble-first_ systems rather than treating ensembling as an ad hoc trick. In this work, we present TabPack — a new ensembling approach that packs many base model–optimizer pairs with different hyperparameters into a single neural network and a single optimizer. The base model and optimizer hyperparameters are sampled randomly, after which all base models are trained in parallel, and the final ensemble is built on the fly during training. As a result, TabPack produces powerful ensembles in a single run, with substantial efficiency gains over traditional approaches. With its remarkable efficiency, strong performance on medium-to-large datasets, and reduced reliance on traditional hyperparameter tuning, TabPack is an appealing solution for practitioners and researchers that makes tabular DL more accessible on consumer-grade hardware and suggests a new avenue for designing better tabular deep learning systems.

Large Language Models (LLMs) training is prohibitively expensive, driving interest in low-precision fully-quantized training (FQT). While novel 4-bit formats like NVFP4 offer substantial efficiency gains, achieving near-lossless training at such low precision remains challenging. We introduce **TetraJet-v2**, an end-to-end 4-bit FQT method that leverages NVFP4 for activations, weights and gradients in all linear layers. We identify two critical issues hindering low-precision LLM training: weight oscillation and outliers. To address these, we propose: 1) an unbiased double-block quantization method for NVFP4 linear layers, 2) **OsciReset**, an algorithm to suppress weight oscillation, and 3) **OutControl**, an algorithm to retain outlier accuracy. **TetraJet-v2** outperforms prior methods on FP4 pre-training for LLMs across models up to 370M parameters trained up to 212B tokens, reducing the performance gap to BF16 by an average of $51.3$% while enabling an $1.67\times$ end-to-end speedup over FP8.

Quantization can drastically increase the efficiency of large language and vision models, but typically incurs an accuracy drop. Recently, function-preserving transforms (e.g. rotations, Hadamard transform, channel-wise scaling) have been successfully applied to reduce post-training quantization error, yet a principled explanation remains elusive. We analyze linear-layer quantization via the signal-to-quantization-noise ratio (SQNR), showing that for uniform integer quantization at a fixed bit width, SQNR decomposes into (i) the concentration of weights and activations (capturing spread and outliers), and (ii) the alignment of their dominant variation directions. This provides an actionable insight: enhancing alignment between weight and activation variation directions can reduce quantization error, complementing concentration-focused approaches. Motivated by this, we introduce Concentration–Alignment Transforms (CAT), a lightweight linear transformation that uses a covariance estimate from a small calibration set to jointly improve concentration and alignment, approximately maximizing SQNR. Experiments across several LLMs show that CAT consistently matches or outperforms prior transform-based quantization methods at 4-bit precision.

Efficiently processing long sequences with Transformer models usually requires splitting the computations across accelerators via context parallelism. The dominant approaches in this family of methods, such as Ring Attention or DeepSpeed Ulysses, enable scaling over the context dimension but do not focus on memory efficiency, which limits the sequence lengths they can support. More advanced techniques, such as Fully Pipelined Distributed Transformer or activation offloading, can further extend the possible context length at the cost of training throughput. In this paper, we present UPipe, a simple yet effective context parallelism technique that performs fine-grained chunking at the attention head level. This technique significantly reduces the activation memory usage of self-attention, breaking the activation memory barrier and unlocking much longer context lengths. Our approach lowers the peak activation memory usage by as much as **82.5%** for 70B Transformers, while matching previous context parallelism techniques in terms of training speed. UPipe can support maximum context lengths of up to 5M tokens for training 8B models on a single 8xH100 node, improving upon prior methods by **25%**.

Multi-token prediction (MTP) is a prominent strategy to significantly speed up generation in large language models (LLMs), especially in byte-level LLMs, which are tokeniser-free but prohibitively slow. However, many existing MTP methods either assume independence between future tokens, sacrificing expressiveness, or generate tokens one at a time within the window, increasing latency. In this work, we investigate the trade-off between expressiveness and latency in MTP within the framework of probabilistic circuits (PCs). Our framework, MTPC, allows one to explore different ways to encode the joint distributions over future tokens by selecting circuit architectures, generalising classical models such as (hierarchical) mixture models, hidden Markov models, and tensor networks. We show the efficacy of MTPC by retrofitting existing byte-level LLMs, such as EvaByte, and byte-fied subword models, such as Llama3.2 3B. Our experiments show that, when combined with speculative decoding, MTPC substantially speeds up generation compared to MTP with independence assumptions, while guaranteeing to retain the performance of the original verifier LLM. We also rigorously study the optimal trade-off between expressiveness and latency when exploring the possible parameterisations of MTPC, such as PC architectures and partial layer sharing between the verifier and draft LLMs.

The rapid growth of deep neural networks (DNNs) has intensified the demand for efficient hardware acceleration under quantization. While prior research has successfully reduced weight and activation precision, partial sums generated during accumulation often retain high precision, resulting in significant energy overhead. In this work, we analyze psum distributions in tiled architectures and reveal that within-tile outliers are input-dependent. We propose PsumQuant, a post-training, input-aware quantization that predicts psum scales on-the-fly. By leveraging the crest factor of input activations, our learnable scale predictor effectively bounds the psum bit-width while handling the extreme outliers in DNNs. Experimental results on a $128 \times 128$ systolic array demonstrate that PsumQuant compresses psum precision down to 8-bit within only a 1\% accuracy drop on ResNet-18 and a marginal 0.04 perplexity increase on Llama-3.1. Furthermore, bit-width reduction with PsumQuant results in a 45\% reduction in total energy with minimal accuracy loss, demonstrating that PsumQuant provides a highly efficient solution for actual NPU architectures.