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In online inverse linear optimization, the learner predicts a weight at each round, observes the optimal action of the agent, and updates its prediction. In the general setting, the gap of $\log T$ between the regret upper bound $O(d \log T)$ and the lower bound $Ω(d)$ is unresolved (here $T$ is the total number of rounds and $d$ is the dimension). When the action set is M-convex, the regret is known to be bounded by $O(d \log d)$, but the method attaining it computes a center of gravity at every round. This paper therefore proposes Small-Gradient Skipping (SGS), a mechanism that skips the update at rounds without a mistake in the case where the correct action is uniformly separated from the other candidates, and applies it to online gradient descent, the online Newton step, and MetaGrad. The number of mistakes is then bounded, for all three, by a quantity independent of $T$; and for the online Newton step and for MetaGrad with SGS, the dimension dependence of the regret becomes $O(d^2)$ when the forward problem is an integer linear program, that is, the factor $\log T$ is removed. Moreover, when the action set is M-convex, the regret is bounded efficiently without computing a center of gravity.

Token skipping is a widely used training-free way to accelerate vision--language--action (VLA) models by bypassing computation for most visual tokens at each control step according to a gate. When the next gate is harvested from the previous accelerated forward, however, the tokens skipped at one step are also the ones least visible to the next gate, and the damage can compound across control steps until the task fails. We study the two mechanisms this class is built on, reuse and deletion, crossing each against where its gate signal comes from on identical episodes. At a skip ratio of 0.9 on LIBERO-Object, both collapse when the gate comes from the model's own accelerated forwards, to 0.68 under reuse and to 0.31 under deletion against a dense 1.00, and the collapse is invisible to the action-level detectors we evaluate. What separates collapse from dense-level operation is not the mechanism but whether the gate is clean, computed by a forward that skipped nothing. We therefore propose actuation-slack refresh, one dense pass run while the robot executes its current action chunk, off the critical path, that hands the next step a clean gate and a fresh KV base. Since the measured detectors do not reliably reveal the failure, the refresh is unconditional rather than triggered. Both mechanisms then recover to 0.98, keeping the speed of skipping and the information of a dense pass. We then integrate the refresh into state-of-the-art caching and pruning methods across two VLA policies, 4 LIBERO suites, and 4 SIMPLER tasks, where it repairs every collapse caused by using a self-harvested gate. Serve latency drops 18--22% below dense, measured both in simulation and on a physical robot. Where the gate signal comes from, not how tokens are skipped, decides closed-loop reliability for accelerated VLAs.

Pruning is a promising approach for improving the efficiency of LLMs. Existing static structured pruning methods are hardware-friendly and can deliver practical throughput gains, but their input-agnostic computation allocation often causes substantial accuracy degradation under aggressive sparsity. Recent dynamic sparsity methods improve quality retention by adapting computation to individual inputs, yet they remain largely limited to coarse-grained structural decisions and their practical acceleration under real-world inference scenarios remains challenging. To address these challenges, we present WIDE, the first end-to-end differentiable token-level dynamic width pruning framework designed for both prefill and decode scenarios. WIDE enables fine-grained computation allocation by allowing each token to dynamically select attention-head groups and FFN-channel groups, extending dynamic pruning beyond layer-level decisions to neuron-block-level granularity. Through a two-stage training pipeline, WIDE learns effective token-wise sparse execution patterns and achieves substantially better quality retention than existing approaches. To make such fine-grained dynamic pruning practical, we further propose a pruning--kernel co-design framework that decomposes dynamic sparsity acceleration into mask reordering, hardware-agnostic block-level skipping, and hardware-dependent intra-block skipping, enabling efficient execution across different granularities. At 50% sparsity, WIDE provides 55.1% performance boost when compared to the state-of-the-art dynamic depth pruning under calibration-only settings. Under prefill and decoding inference workloads, WIDE achieves close-to-theoretical kernel-level speedups of up to 1.98x for prefill and 4.95x for decoding, as well as 1.68x and 1.55x end-to-end acceleration. Our code is available at https://github.com/EIT-NLP/LLM-Pruning/tree/main/WIDE.

The quadratic cost of self-attention makes long-context inference prohibitively expensive, and proxy-based block-sparse attention has become a practical remedy. Existing methods typically rely on a proxy to predict a binary sparse mask and a kernel to consume this mask and perform sparse attention computation. Such an approach is effective under moderate budgets. However, as the budget tightens, the estimated proxy inevitably drops some salient blocks, while the kernel can only apply the sparse mask mechanically, leading to an evident drop in model accuracy. We propose CoSA, a two-stage training-free Sparse Attention under proxy-kernel CO-design, which couples a Kernel-Aware Proxy (KAP) with an Ordered-Skipping Kernel (OSK). In the first stage, the KAP selects blocks under a moderate budget and produces an ordered mask that prescribes the order in which KV pages are visited in the kernel inner loop. In the second stage, the OSK applies this mask and skips more blocks under a tightened budget given online-softmax statistics. Across mainstream LLM backbones and long-context benchmarks, CoSA attains higher accuracy at lower budgets. Impressively, CoSA achieves a 4.93$\times$ attention speedup and reduces end-to-end Time-to-First-Token by 2.53$\times$ under a context length of 128K with negligible performance degradation. Code is available at https://github.com/Tencent/AngelSlim.

Medical image segmentation relies on the ability of encoder-decoder architectures to translate rich feature representations into accurate pixel-level predictions under challenging conditions such as low contrast, structural ambiguity, and scale variability. While recent advances in large-scale pretraining and transformer-based encoders have substantially improved feature extraction, segmentation accuracy remains constrained by decoder design, particularly in terms of cross-scale alignment, contextual integration, and boundary preservation. In this work, we revisit medical image segmentation from a decoder-centric perspective and propose a context-aware gated decoder that systematically regulates feature fusion and contextual aggregation throughout the decoding process. The proposed decoder integrates lightweight multi-scale channel recalibration, gated skip fusion with spatial competition and a global context aggregation mechanism that injects encoder-wide information into intermediate decoding stages. This design enables effective translation of strong pretrained encoder representations into spatially consistent predictions. Extensive experiments across 11 medical image segmentation benchmarks validate the effectiveness and demonstrate that the proposed approach consistently outperforms strong baselines while remaining computationally practical. Code: https://github.com/saadwazir/MedCAGD

Hyperparameter tuning almost always means search: fit the model at every value on a grid, score each by cross-validation, and keep the winner. For spline regression that search is unnecessary. The optimal resolution can be solved for in closed form, to the accuracy an exhaustive search reaches, at a fraction of the compute. Three ingredients make this possible: classical approximation theory pins the squared bias to a known power of the resolution G, exactly the Kolmogorov n-width of the smoothness class; the basis dimension is an explicit polynomial in G; and leave-one-out error follows from a single fit via the PRESS identity. Balancing the two known curves gives the minimizer analytically. We extend this calculus to many coordinates by replacing ambient input dimension with interaction order, the number of active low-order components in an ANOVA decomposition, yielding a scaling law in which the optimal resolution and error are power functions of the effective density (sample size per active component), with input dimension absent from the exponent. The law becomes an algorithm. KORE (Kolmogorov-optimal Order-aware Resolution Estimation) fits two pilot resolutions, solves a leverage-calibrated 2x2 system for the bias and noise scales, and evaluates the closed-form plug-in resolution with a tiny leave-one-out certificate: about a dozen fits instead of a full grid sweep, with a consistency guarantee as the sample grows. Across additive and sparse pairwise targets up to 80 input dimensions, KORE matches exhaustive 3-fold cross-validation and the full classical ladder (GCV, Mallows' Cp, AIC, BIC) while fitting roughly 8x fewer models; on 36 real tabular datasets it ranks first among 21 methods in accuracy per unit of compute, ahead of tuned boosters and kernel machines. When complexity lives in low interaction order, solving for the resolution beats searching for it.

Large language models (LLMs) perform inference by following a fixed depth and order, non-recurrent execution of all layers. We reveal the wide existence of training-free, flexible, dynamic program-of-layers (PoLar), where pretrained layers can be packed as modules and then skipped or looped to form a customized program for each input. For most inputs, substantially shorter program executions can achieve the same or better accuracy, while incorrect predictions of the original LLM can be corrected by alternative programs with fewer layers. These observations indicate that inference admits multiple valid latent computations beyond the standard forward pass. To efficiently achieve PoLar in practice, we propose a lightweight PoLar prediction network, which learns to generate execution programs that dynamically skip or repeat pretrained layers for each input. Experiments on mathematical reasoning benchmarks demonstrate that PoLar consistently improves accuracy over standard inference and prior dynamic-depth methods, often while executing fewer layers, and that these gains persist under out-of-distribution evaluation. Our results suggest that fixed-depth execution captures only a narrow subset of an LLM's latent reasoning capacity.

Missing data imputation in large-scale surveys faces two challenges that are not well handled by current tabular diffusion methods. First, \emph{structural skips}, cells made inapplicable by questionnaire design, should not be imputed but are often conflated with item nonresponse. Second, \emph{ordinal} responses encode ordered categories, yet most pipelines treat them as nominal levels through one-hot or analog-bit encodings. We introduce \textbf{TabSODA} (\textbf{Tab}ular diffusion with \textbf{S}kip pattern detection and \textbf{O}r\textbf{d}inal \textbf{A}wareness), an Expectation-Maximization (EM)-based diffusion imputer built on the Elucidated Diffusion Model (EDM) framework. TabSODA propagates structural skips through the denoising loss and reverse-time sampler, and represents ordinal variables with cumulative-probit scalar latents while retaining analog-bit encodings for nominal variables. When a codebook skip mask is available, TabSODA uses it directly; otherwise, the TabSODA+SKIP variant estimates the mask from raw responses and questionnaire order using a CART-based skip-pattern miner. On Population Assessment of Tobacco and Health (PATH) study and the National Survey on Drug Use and Health (NSDUH), two nationally representative U.S.\ surveys, TabSODA reduces ordinal MACE by up to $23.7\%$ and improves categorical accuracy by up to $9\%$ over the strongest baseline across MCAR, MAR, and MNAR masking. The skip miner achieves near-perfect precision on both datasets, allowing TabSODA+SKIP to closely track the codebook-mask variant.

Database vendors recently released AI functions that can be used in filter predicates. As such functions often rely on costly, black-box ML models, they unveil new data management challenges. Concretely, traditional data skipping techniques for integer and string data fail to be applicable to the new filter type. Indeed, there is no known mechanism for pruning non-qualifying row groups, e.g., when reading files from blob storage. In this work, we initiate the study of data skipping techniques for ML filters. We make the case that Parquet's default min-max metadata is enough to enable pruning. To this end, we draw connections to two lines of research: (i) the recently proposed query language for ML models and (ii) neural network verification. Our preliminary results on ReLU architectures show that on tables from TPC-H and TPC-DS, the average pruning effectiveness for filters of selectivity below 0.1% amounts to 27.4%. Finally, inspired by research on spatial joins, we propose an enhanced metadata structure: a size-bounded 2D convex hull that verification tools can make better use of, increasing the pruning effectiveness to 38.31%, while occupying at most 45 bytes per row group and column pair. We observe an end-to-end speedup of 1.07$\times$ over PyTorch in DuckDB.

Previous imitation learning policies predict future actions at every control step, whether in smooth motion phases or precise, contact-rich operation phases. This uniform treatment is wasteful: most steps in a manipulation trajectory traverse free space and carry little task-relevant information, while a small fraction of \emph{key} steps around contacts, grasps, and alignment demand dense, high-resolution prediction. We propose a novel \emph{action relabeling} mechanism: at each timestep in a skip segment, we replace the behavior cloning target with the action at the entrance of the next key segment, enabling the policy to leap over redundant steps in a single decision. The resulting \textbf{Skip Policy (SkiP)} dynamically leaps over skip segments and intensively refines actions in key segments, within a single unified network requiring no learned skip planner or hierarchical structure. To automatically partition demonstrations into key and skip segments without manual annotation, we introduce \emph{Motion Spectrum Keying} (MSK), a fast, task-agnostic procedure that detects local motion complexity from action signals. Extensive experiments across 72 simulated manipulation tasks and three real-robot tasks show that SkiP reduces executed steps by $15$--$40\%$ while matching or improving success rates across various policy backbones. Project page: \texttt{https://pgq18.github.io/SkiP-page/}.

Vision-Language-Action (VLA) policies are commonly trained from dense robot demonstration trajectories, often collected through teleoperation, by sampling every recorded frame as if it provided equally useful supervision. We argue that this convention creates a temporal supervision imbalance: long low-change segments dominate the training stream, while manipulation-critical transitions such as alignment, contact, grasping, and release appear only sparsely. We introduce FrameSkip, a data-layer frame selection framework that scores trajectory frames using action variation, visual-action coherence, task-progress priors, and gripper-transition preservation, then remaps training samples toward high-importance frames under a target retention ratio. Because FrameSkip operates only in the dataloader, it leaves the VLA architecture, action head, training objective, and inference procedure unchanged. Across RoboCasa-GR1, SimplerEnv, and LIBERO, FrameSkip improves the success-retention trade-off over full-frame training and simpler frame selection variants, achieving a macro-average success rate of 76.15% across the three benchmarks compared with 66.50% for full-frame training while using a compressed trajectory view that retains 20% of unique frames in the main setting.

We study when a skip connection around a single-hidden-layer MLP can be absorbed into a residual-free MLP of the same width. We first show that for any architecture whose skip branch is an invertible linear map (including Hyper-Connections and their manifold-constrained variants), the problem reduces to the identity skip case. For homogeneous activations of degree $k \neq 1$, such as ReLU$^2$ and ReGLU, absorption is unconditionally impossible by a degree argument. For gated activations whose gate is differentiable at the origin with $g(0) = 0$, including SwiGLU and GeGLU, a linearization argument gives the same conclusion. These impossibility results extend to arbitrary depth: a composition of $L$ residual blocks using such activations cannot be replicated by any composition of $L$ residual-free blocks of the same width. For ungated ReLU and GELU, the situation is richer. For generic weight matrices, absorption holds at the single-block level if and only if there exists an index set $S$ of size at least $d$ such that $W_{\mathrm{down}}[:,S]\,W_{\mathrm{up}}[S,:] = -I_d$. This condition is non-generic (it fails with probability one under continuous weight distributions), so skip-connected and residual-free MLPs of the same width represent generically disjoint function classes. Whether this disjointness persists for deep compositions of ReLU or GELU blocks remains open.

Semi-supervised learning addresses label scarcity and high annotation costs in medical image segmentation by exploiting the latent information in unlabeled data to enhance model performance. Traditional discriminative segmentation relies on segmentation masks, neglecting feature-level distribution constraints. This limits robust semantic representation learning and adaptive modeling of unlabeled data in scenarios with few labels. To address these limitations, we propose SemiGDA, a novel Generative Dual-distribution Alignment framework for semi-supervised medical image segmentation. Our SemiGDA overcomes the reliance of discriminative methods on large labeled datasets by aligning feature and semantic distributions to boost semantic learning and scene adaptability. Specifically, we propose a Dual-distribution Alignment Module (DAM), which employs two structurally distinct encoders to model image and mask feature distributions. It enforces their alignment in the latent space via distributional constraints, establishing structured feature consistency. Moreover, we design a Consistency-Driven Skip Adapter (CDSA) strategy, which introduces dual skip adapters (Image and Mask) to fuse multi-scale features via skip connections. Using a consistency loss, CDSA enhances cross-branch semantic alignment and reinforces fine-grained semantic consistency. Experimental results on diverse medical datasets show that our method outperforms other state-of-the-art semi-supervised segmentation methods. Code is released at: https://github.com/taozh2017/SemiGDA.

3D Gaussian Splatting (3DGS) achieves real-time novel-view synthesis by optimizing millions of anisotropic Gaussians, yet its training remains expensive, with the backward pass dominating runtime in the post-densification refinement phase. We observe substantial update redundancy in this phase: many sampled views have near-plateaued losses and provide diminishing gradient benefits, but standard training still runs full backpropagation. We propose SkipGS with a novel view-adaptive backward gating mechanism for efficient post-densification training. SkipGS always performs the forward pass to update per-view loss statistics, and selectively skips backward passes when the sampled view's loss is consistent with its recent per-view baseline, while enforcing a minimum backward budget for stable optimization. On Mip-NeRF 360, compared to 3DGS, SkipGS reduces end-to-end training time by 23.1%, driven by a 42.0% reduction in post-densification time, with comparable reconstruction quality. Because it only changes when to backpropagate without modifying the renderer, representation, or loss, SkipGS is plug-and-play and compatible with other complementary efficiency strategies, enabling additive speedups. Code is available at https://github.com/ASU-ESIC-FAN-Lab/SkipGS.

Chain-of-Thought (CoT) prompting trades inference speed for reasoning accuracy. Existing compressors force a compromise as static gradient techniques treat tokens independently, severing sequential logic, while uncertainty-based pruning ignores the final answer. We introduce Adaptive GoGI-Skip, a framework that resolves this tension by non-linearly coupling Goal-Gradient Importance (GoGI) with Adaptive Dynamic Skipping (ADS). GoGI quantifies each token's functional contribution to answer correctness via gradient sensitivity. ADS leverages runtime entropy to dynamically modulate the GoGI threshold, preserving low-gradient tokens essential for structural coherence at high-uncertainty junctions. Trained on 7,472 MATH traces, our policy transfers zero-shot to AIME, GPQA, and GSM8K, reducing token volume by $>$45% and accelerating inference up to 2.0$\times$ without accuracy loss. These results suggest that thinking-optimal compression demands synergy between teleological goals and epistemic uncertainty.