Mixture-of-Experts large language models (LLMs) scale efficiently through sparse activation, yet their deployment is fundamentally constrained by the large static parameter footprint of experts. Existing compression approaches either remove entire experts, disrupting routing topology and harming performance, or rely on unstructured weight pruning with limited practical efficiency. To address the limitations, we propose TENP, a structured Trapezoidal ExpertNeuron Pruning framework. Using a few samples, we identify and retain important experts, while applying expert neuron pruning (ENP) to less important experts, reserving model parameters in a trapezoidal pattern from shallow to deep layers. When evaluating expert importance, we jointly consider both the magnitude of the expert output and its ability to change the direction of the input vector. For ENP, we measure each neuron's projected contribution to the expert output to identify and retain important neurons. We conduct extensive experiments on the Qwen and DeepSeek models. Under a routing expert sparsity of 40% and an average of 63.76% activated expert parameters, the DeepSeek model suffers only a 1-point drop in accuracy compared to the full-parameter model. Moreover, it outperforms the full-parameter model by 10% on code generation tasks.

We develop a decision-calibrated conformal framework for pacing decisions in streaming advertising. Pacing depends on uncertain future inventory, demand pressure, incremental response, and member-experience load. Instead of calibrating a generic forecast residual, the framework measures forecast error by its largest impact on the policies that could actually be deployed. The main theorem shows that the proposed score is the smallest valid uncertainty measure that uniformly protects all deployable pacing policies. Geometrically, it is the support function of the signed policy sensitivity set. Split conformal calibration gives finite-sample coverage for this score. A high-dimensional separation theorem shows that traditional residual calibration can be arbitrarily more conservative by paying for nuisance inventory dimensions, and a robust pacing result combines inventory, response, and experience uncertainty. On public-data-calibrated pacing replays built from Criteo Uplift and KuaiRand datasets, traditional conformal pacing remains unresolved with high residual radii of 7236.7 on Criteo and 4629.4 on KuaiRand. With the proposed decision calibration approach, the uncertainty radii are reduced to 18.4 and 278.6 respectively, with separate margins for value, delivery, budget, and member load. On Criteo, the proposed method certifies a less aggressive pacing policy than the point-forecast baseline, and reduces held-out any-violation rate from 16.7% to 3.3%, with zero budget and member-load violations. On KuaiRand, the choice remains unresolved. In a nutshell, the paper establishes that forecasts, response estimates, and member-experience models should be judged by whether they shrink the uncertainty that the pacing decision uses, as this leads to confident decisions that are not overly conservative.

We study the generalization of ridge-regularized nonlinear least-squares models via on-average algorithmic stability, deriving error bounds for local minimizers in terms of a data-dependent effective dimension that reflects the geometry of the gradient model at the trained parameters, through the empirical Jacobian Gram matrix and a residual-curvature term. In the linear case, where the curvature term vanishes, this recovers the classical effective dimension of the Jacobian kernel covariance, but evaluated at the trained model rather than at initialization as is typical in neural tangent kernel analyses. We further bound this effective dimension via covering complexity of the gradient features, leading to guarantees that depend on learned geometry rather than parameter count. In particular, for manifold-supported data and piecewise Lipschitz Jacobians, the bounds scale with intrinsic dimension, while for one-hidden-layer ReLU networks, the mechanism can be made explicit through counts of activation-stable regions. Experiments on synthetic manifolds, clustered distributions, and benchmark datasets illustrate trained-Jacobian compression, the tightness of the residual-curvature linearization, and agreement between the stability bound and observed generalization gaps. A key feature of our bounds is the simplicity of their derivation, which follows from first principles using the Brascamp-Lieb inequality under strongly log-concave noise.

TorchKM is an open-source library for kernel machines, including support vector machines, kernel logistic regression, and kernel quantile regression, with GPU acceleration. The library features a scikit-learn-style API and is designed to exploit GPU-friendly linear algebra, accelerating the full training and model-selection pipeline through intelligent reuse of matrix operations. Benchmarks show competitive predictive performance with substantial speedups over standard baselines. The efficiency and programmable design also make TorchKM a kernel-learning component for AI-driven workflows. Code and documentation are available at https://github.com/YikaiZhang95/torchkm, and the package can be easily installed via PyPI.

We introduce a new tool, Express, for converting a non-causal attention approximation into a causal approximation with matching approximation guarantees. When combined with the state-of-the-art Thinformer approximation, Express improves upon the best known causal attention guarantees, delivering $\log^{3/2}(n)/s$ approximation error with only $O(s)$ memory and $O(s^2 \log^2(n))$ compression overhead for a sequence of length $n$. We pair these developments with an efficient I/O-aware Triton implementation, demonstrate substantial speedups over FlashAttention 2, and use Express to overcome four resource bottlenecks in the language modeling pipeline: long-context prefill, KV cache compression, long-form memory-constrained decoding, and long-form compute-constrained decoding.

The analogy between deep neural network forward passes and renormalization group (RG) flows has been repeatedly noted in the literature, but existing treatments remain qualitative: depth is described as a coarse-graining scale, attention is likened to a partition function, and representations are said to flow toward fixed points. No existing work has defined a measurable RG order parameter, tested it under controlled variation of the input distribution, or made quantitative predictions that are empirically verified. We study the simplest architecture for which the analogy is tractable: a pure MLP residual stack trained on masked token prediction over synthetic Markov chain sequences with known spectral properties. We report three findings. (i) The effective rank of the residual stream decreases monotonically with depth after training, consistent with progressive integration of irrelevant degrees of freedom. (ii) This rank collapse is selective: it occurs for chains with short correlation length approximately 1 but is absent for chains with long correlation length approximately 7, measured at the position level to control for mean-pooling artifacts. The network preserves exactly the degrees of freedom relevant to the prediction task, the content of the RG relevance criterion. (iii) Inter-layer kernel drift is concentrated at one or two specific transitions, with the remainder of the network near a fixed point, consistent with a discrete fixed-point plateau. Together these findings constitute the first quantitative, position-level evidence that MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution.

The Mamba-type neural networks have gained significant popularity recently. To effectively and efficiently establish model architectures of Mamba, it is natural to introduce Neural Architecture Search (NAS) methods into Mamba. However, existing NAS methods tailored for Mamba are training-based, leading to substantial time and computational resource expenditure. To address this issue, and considering that Mamba2 is an improved version of the original Mamba, we propose a training-free NAS method specifically designed for Mamba2. Based on rank collapse in stacked State Space Duality (SSD) blocks, we design a proxy that only requires the computation of the transformation matrix and its gradient between two tensors within the network. Additionally, we develop a corresponding search space and introduce a novel approach for determining adjustable hyperparameter ranges. Experimental results show that our method outperforms all existing training-free NAS approaches in terms of both ranking correlation and the performance of search results for Mamba2 architecture. To the best of our knowledge, this is the first training-free NAS method designed for Mamba-type architectures.

We present a novel end-to-end transformer-based framework for Multiple Object Tracking (MOT) that advances temporal modeling and identity preservation. Despite recent progress in transformer-based MOT, existing methods still struggle to maintain consistent object identities across frames, especially under occlusions, appearance changes, or detection failures. We propose a dual-path temporal decoder that explicitly separates appearance adaptation and identity preservation. The appearance-adaptive decoder dynamically updates query features using current frame information, while the identity-preserving decoder freezes query features and reuses historical sampling offsets to maintain long-term temporal consistency. To further enhance stability, we introduce a confidence-guided update suppression strategy that retains previously reliable features when predictions are unreliable. Extensive experiments on MOT benchmarks demonstrate that our approach achieves state-of-the-art performance across major tracking metrics, with significant gains in association accuracy and identity consistency. Our results demonstrate the importance of decoupling dynamic appearance modeling from static identity cues, and provide a scalable foundation for robust tracking in complex scenarios.

Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been the opposite, with unstable training, poor predictive power, and subpar calibration. Building upon recent work on reparametrizations of neural networks, we propose a simple variational family that considers two independent linear subspaces of the parameter space. These represent functional changes inside and outside the support of training data. This allows us to build a fully-correlated approximate posterior reflecting the overparametrization that tunes easy-to-interpret hyperparameters. We develop scalable numerical routines that maximize the associated evidence lower bound (ELBO) and sample from the approximate posterior. Empirically, we observe state-of-the-art performance across tasks, models, and datasets compared to a wide array of baseline methods. Our results show that approximate Bayesian inference applied to deep neural networks is far from a lost cause when constructing inference mechanisms that reflect the geometry of reparametrizations.

Mental visualization, the ability to construct and manipulate visual representations internally, is a core component of human cognition and plays a vital role in tasks involving reasoning, prediction, and abstraction. Despite the rapid progress of Multimodal Large Language Models (MLLMs), current benchmarks primarily assess passive visual perception, offering limited insight into the more active capability of internally constructing visual patterns to support problem solving. Yet mental visualization is a critical cognitive skill in humans, supporting abilities such as spatial navigation, predicting physical trajectories, and solving complex visual problems through imaginative simulation. To bridge this gap, we introduce Hyperphantasia, a synthetic benchmark designed to evaluate the mental visualization abilities of MLLMs through four carefully constructed puzzles. Each task is procedurally generated and presented at three difficulty levels, enabling controlled analysis of model performance across increasing complexity. Our comprehensive evaluation of state-of-the-art models reveals a substantial gap between the performance of humans and MLLMs. Additionally, we explore the potential of reinforcement learning to improve visual simulation capabilities. Our findings suggest that while some models exhibit partial competence in recognizing visual patterns, robust mental visualization remains an open challenge for current MLLMs.