Structured Sparsity

Many tasks in scientific computing and machine learning require the Jacobian or Hessian matrix of a function. Automatic differentiation (AD) computes these derivatives to machine precision, but materializing a dense $m \times n$ Jacobian requires $n$ forward-mode or $m$ reverse-mode AD passes, one per column or row. For a large class of functions, each output depends on only a few inputs, making the derivative matrix sparse. Automatic sparse differentiation (ASD) exploits this structure in four steps: detection of the input-agnostic sparsity pattern, coloring of a graph to group columns or rows that can share an AD pass, compressed differentiation to compute a compressed derivative matrix with one AD pass per color, and finally decompression into the original sparsity pattern. The number of colors, and hence of AD passes, is often independent of the problem dimension: a banded Jacobian with $b$ contiguous bands, for instance, only ever requires $b$ colors, regardless of its size. asdex offers the first standalone ASD toolkit in the popular JAX ecosystem. With asdex.jacobian and asdex.hessian, it provides sparse drop-in replacements for jax.jacobian and jax.hessian.

The memory-bound nature of the decoding stage of large language model (LLM) inference incurs significant latency. Layer-wise training-free network pruning approaches guided by the Hessian have been a prominent solution to this problem, as pruning reduces the number of nonzero parameters read from memory during decoding. Nevertheless, typical methods in this line compute the Hessian using pre-collected natural sequences, whereas the model is fed self-generated tokens during decoding, creating a distribution shift between the two sequences. The Hessian calculated on the natural sequence is different from that calculated on the generated sequence. We observe that this discrepancy causes the activation distribution during generation to deviate from that used for pruning, further hurting the pruned model performance. Moreover, most existing LLM pruning methods that bring actual speedup primarily target the sparse matrix-matrix (SpMM) multiplication, providing limited support for the sparse matrix-vector (SpMV) operations, which dominate decoding. To solve these problems, we introduce SparseDecoding, a principled decoding-aware pruning framework tailored for accurate and efficient LLM decoding. Specifically, at the algorithmic axis, SparseDecoding constructs calibration matrices from layer-wise activations collected during the dense-model autoregressive generation, excluding prefill, thereby aligning the pruning objective with the decoding activations. At the system axis, we develop an optimized N:M sparse matrix-vector kernel with bitmask indexing and fixed-step traversal. Substantial empirical results on representative LLMs (Llama-3.1-8B, Llama-3.3-70B, Qwen3-14B / 32B) demonstrate that our method consistently outperforms standard fixed-text calibration on the long-form generation benchmarks while achieving up to 1.48x end-to-end wall-clock decoding speedup on A100 GPUs.

Modern neural networks are heavily over-parameterized. This redundancy incurs substantial compute and memory overhead during training and inference. Existing pruning methods rely on post-hoc magnitude thresholds or static initialization heuristics. Consequently, they often require manual per-layer sparsity targets or expensive retraining cycles. We propose Dynamic Activity-Dependent Pruning (DADP), a biologically inspired structural plasticity mechanism. During training, DADP measures connection importance via the accumulated product of pre-synaptic activations and post-synaptic error gradients. Using a single global threshold instead of fixed layer budgets, DADP dynamically allocates sparsity across network depth while naturally inducing neuron- and channel-level pruning. Across MLP, VGG-16, ResNet-18, BiLSTM-CRF, and MiniBERT architectures, DADP matches or outperforms Magnitude, SNIP and RigL, retaining 73.67% accuracy (dense baseline: 76.06%) at 99% sparsity on ResNet-18. Finally, matrix-based Shannon entropy and effective rank measurements confirm that DADP preserves latent feature diversity at extreme sparsities without representation collapse.

Protein-molecule virtual screening is increasingly cast as a problem of representation learning in a shared embedding space. Existing methods rely on dense holistic alignment, entangling invariant binding determinants with nuisance correlations and limiting transfer to new targets. It has been noted that binding in protein-molecule systems involves sparse cross-modality interactions: binding is governed by a small contact interface and a few decisive local interactions (e.g., hydrogen bonds, hydrophobic contacts, and salt bridges) rather than the global structures of the protein and molecule. We hypothesize that uncovering and leveraging sparse interaction patterns is critical for generalization beyond the training data, as these patterns are reusable and expected to improve performance across different scenarios. In this paper, we aim to identify and leverage sparse interaction patterns, and verify our hypothesis. Since the training data contain only observed binding pairs, we formalize this prior via a V-structure causal model under Heckman-style selection, and establish three theoretical results: (i) the latent concepts of interacting proteins and molecules are not identifiable without appropriate sparsity constraints; (ii) these concepts and their sparse interactions are component-wise identifiable under structural sparsity conditions; and (iii) a low-rank relaxation of these conditions yields subspace identifiability of the concepts and interactions. Inspired by these principles, we propose CausalBind with three implementation variants. Extensive experiments on DUD-E and LIT-PCBA benchmarks show that all variants consistently outperform strong retrieval baselines, with the largest gains on LIT-PCBA early enrichment, and further generalize to target- and scaffold-level out-of-distribution splits. Code is available at https://github.com/lokali/CausalBind.

Model merging integrates task-specific fine-tuned models into a single multi-task model, but often suffers from parameter interference caused by conflicting task-vector updates. Existing methods typically mitigate conflicts by pruning task vectors based on weight magnitude or random heuristics, treating Transformers as unstructured ``bags of parameters'' and overlooking their inherent modularity. In this paper, we propose \textbf{C}ontribution-\textbf{A}ware \textbf{S}tructured \textbf{S}parsity (CASS), a unified framework that reduces parameter interference by identifying and preserving task-specific components. At the core of CASS is a contribution-aware structured mask that identifies task-relevant attention heads and FFN neurons. We instantiate this mask in two settings: CASS-Merging, the primary post-hoc setting where masks serve as a plug-and-play denoising filter for existing merging operators, and CASS-Tuning, an extension for scenarios with fine-tuning access where masks constrain gradients to reduce structural overlap between task vectors. Our analysis shows that task-relevant components are sparse and partially disjoint, supporting structured component-level filtering as an effective way to reduce merging interference. Extensive experiments across vision (ViT, 20 tasks) and language (RoBERTa, 8 tasks; Qwen2.5, 4 tasks) benchmarks demonstrate that CASS improves a range of representative merging baselines.

Semi-structured pruning compresses large language models (LLMs) while keeping a regular sparse structure, but the prevailing N:M pattern fixes the same local sparsity ratio in every layer. Layer-adaptive sparsity allocation improves unstructured pruning, yet it has been reported to be less effective under N:M sparsity, leaving open whether adaptive allocation is of limited value for semi-structured pruning in general or only under the fine-grained N:M pattern. We examine this question with group-level sparsity, which partitions each weight matrix into regular groups, retains or prunes each group as a whole, and allows each layer's sparsity ratio to vary under a global budget. We propose GroupMask, which generates the group selectors of all layers with a lightweight hypernetwork, relaxes them with a Gumbel-Sigmoid parameterization and a straight-through estimator, and learns them through sparsity-budget regularization and self-distillation while keeping the pretrained weights frozen. On LLaMA-2-7B at 50% sparsity with the same $1\times256$ group size, learned layer-adaptive allocation reduces WikiText-2 perplexity from 10.02 to 8.30 and raises the average zero-shot accuracy from 0.455 to 0.496 relative to a uniform per-layer ratio. GroupMask obtains the lowest WikiText-2 perplexity on LLaMA-2-7B and the highest average zero-shot accuracy with Alpaca calibration among the evaluated baselines on five LLaMA and Qwen models. Our code is available at https://github.com/ZhengaoLi/GroupMask.

Long-term electricity-consumption profiles exhibit several simultaneous periodic structures, including daily, weekly, and annual cycles. This work introduces Calendar-Structured Sparse Principal Component Analysis (Calendar-SPCA), a structured representation-learning method that incorporates this known multi-periodic geometry directly into a low-dimensional factorization. The method represents the feature domain as the Cartesian product of cyclic calendar axes and combines an L1 loading penalty with graph total variation, producing sparse, locally coherent, and directly interpretable latent factors. In this study, Calendar-SPCA is applied to the interpretable analysis of long-term electricity-consumption profiles and evaluated on two independent public smart-meter datasets, GoiEner and Low Carbon London, with different population sizes and temporal resolutions. A factorial experiment characterizes the effects of sparsity and calendar coherence and examines robustness across sample size, latent dimensionality, and repeated fits. At rank 15, Calendar-SPCA retains 96.92% and 82.90% of the explained variance of rank-matched principal component analysis (PCA) in GoiEner and Low Carbon London, respectively, with mean loading sparsities of 61.95% and 81.50%. Comparisons with classical sparse PCA and sparse PCA with total variation (SPCA-TV) show that Calendar-SPCA organizes latent factors into interpretable structures over the daily, weekly, and annual calendar axes while preserving substantial low-rank information.

Decision trees are among the most widely used models in machine learning, largely due to their transparent decision logic, making them well-suited for high-stakes decision-making contexts. However, most existing learning algorithms focus on predictive performance, overlooking the joint optimization of other desirable properties, such as structural sparsity. In this work we propose TREVIS, an approach for learning decision trees with respect to complex objectives, based on the exploration of the latent space of a Tree Transformer Variational Auto-Encoder (TTVAE). By mapping decision trees onto latent representations, TREVIS replaces the discrete search space with a continuous one, enabling gradient-based optimization via a differentiable surrogate model. We experiment with TREVIS for learning decision trees that jointly optimize predictive performance and sparsity. Results show that TREVIS discovers decision trees matching the predictive performance of existing near-optimal algorithms while improving their structural sparsity.

Low-rank adaptation fixes the rank of the update, but it does not identify which parts of a trained write actually carry behavior. We study that question directly and show that behaviorally effective LoRA writes are sparse, structured, and far more concentrated than the raw low-rank parameterization suggests. We use Learned-Basis LoRA, a learned-basis continuation recipe, to expose that structure. The recipe warms up an unconstrained adapter, converts its learned write columns into a module-wise orthonormal basis, freezes that basis, and continues training inside the constrained parameterization. Across 14 exact switches from unconstrained to constrained form, held-out accuracy is unchanged at the conversion step and reconstructed write matrices differ by at most 0.25% relative Frobenius error. Same-state continuation then shows that the same trained checkpoint develops differently under different write subspaces, establishing write geometry as a causal state variable. A no-retraining projection test shows that useful write signal stays inside the learned write space and largely disappears from random or frozen-activation PCA controls. The concentration pattern is strong at both local and global scales. Across GSM8K, MathQA, and AQuA, per-module top-k continuation reaches its optimum at k in {2, 4} in all twelve seed-level cases we test. A stricter global ranking test shows that learned top-16 and top-32 subsets outperform matched random subsets, especially on GSM8K/Qwen and MathQA/Qwen. Single-direction ablations further reveal a sparse set of late q_proj, o_proj, and down_proj components with outsized behavioral impact.

Feed-forward networks (FFNs) dominate memory traffic and computation in large language model (LLM) inference, making them a primary target for activation sparsification. However, existing training-free methods suffer substantial model-quality degradation at high sparsity due to limitations in their channel-selection strategies. We observe that the SwiGLU intermediate state provides a highly effective channel-selection signal, but obtaining it requires costly dense computation. To address this, we present \emph{Prox}, a two-stage training-free framework for sparse SwiGLU FFNs. Prox hinges on the key insight: sparse execution requires only the channel mask induced by the intermediate state, which can be constructed from the magnitude ranking of its entries rather than their exact values. Specifically, Stage 1 uses input sparsity and quantized proxy weights to construct a shared mask; Stage 2 computes the selected channels exactly, enabling sparse execution of all three projections. Across ten LLMs from six model families, Prox outperforms training-free baselines at all sparsity levels, achieves up to a $1.99\times$ end-to-end decoding speedup at 70% FFN sparsity, and is compatible with quantization and sparse attention.

Multi-task inference models share a single backbone across diverse tasks, yet execute identical computation regardless of which task is active - wasting energy and cycles on task-irrelevant operations. We observe that the task command, typically available before inference begins, provides a free signal that can be exploited to skip unnecessary computation at the hardware level. We present a HW/SW co-designed approach in which a lightweight gating network, trained jointly with the backbone, predicts per-tile binary execution masks conditioned on the task input. Each tile corresponds to a fixed group of output channels (the native scheduling granularity of the accelerator), enabling masked tiles to be skipped with zero overhead. This yields a task-dependent reduction in compute, where each command activates only the subset of the network it requires, without changes to the model architecture or inference pipeline. We co-design the full system stack: a command-conditioned training procedure that learns hardware-aligned tile masks under a sparsity objective; an instruction set architecture whose instructions carry per-tile bitmask fields, allowing the hardware to skip masked tiles without software intervention; and a tiled inference accelerator with configurable parallelism, double-buffered memory, and INT8 datapath that natively supports sparse tile execution. We prototype on an AMD/Xilinx Alveo U50 FPGA and evaluate on a closed-loop visuomotor driving task in CARLA autonomous driving simulator. Task-conditional sparsity reduces FLOPs by 66-76% while maintaining driving quality. On-device latency decreases by 51-59%, from 9.12 ms to 3.74-4.44 ms (2.1-2.4x speedup), with energy per inference dropping from 263 to 108-128mJ.

Bit-serial accelerators exploit bit-level sparsity to reduce DNN inference cost, but existing designs exploit sparsity on only one operand, bounding the speedup. Extending sparsity exploitation to both operands simultaneously yields compounding reductions in partial products but introduces a critical new bottleneck: workload imbalance. Because each concurrent weight - activation pair's execution cost depends on the product of two independently varying operand non-zero bit counts, pairs that must complete together finish at vastly different times, leaving faster computations idle. We show this limits PE utilization to 56 - 64% in existing dual-sided designs. We present BRIM, a hardware - software co-designed dual-sided bit-serial sparse accelerator that directly targets this bottleneck. BRIM combines two integrated mechanisms: 1) Cyclic-Balanced Pruning (CBP), a post-training weight optimization that reshapes weight representations based on profiled activation statistics to equalize expected workloads across concurrently processed pairs offline; and 2) Pairwise Slot Donation, a lightweight hardware mechanism that absorbs residual runtime imbalance with negligible area overhead. Evaluated across CNNs, ViTs, and LLMs under iso-area constraints, BRIM achieves over 90% PE utilization, up to 2.37x speedup, and up to 1.63x energy efficiency improvement over prior dual-sided designs.

Perineural invasion (PNI) is associated with poor prognosis in cholangiocarcinoma (CCA). However, its detection from 3D MRI remains challenging due to the subtle and spatially heterogeneous imaging signatures at the tumor periphery. Capturing such spatially sparse cues necessitates volumetric analysis of 3D MRI, but existing deep learning approaches incur prohibitive computational costs on volumetric medical images, limiting their clinical deployment. We propose Dual Sparsity Spikformer (SpikeDS), a spiking neural network architecture that jointly exploits activation sparsity from binary spike communication and spatial sparsity from window pruning based on firing rates. SpikeDS introduces Dual Sparsity Spiking Attention (DSSA), which combines two complementary mechanisms. The first is Window-based Expert Mixture Spiking Attention (W-EMSA), which selectively applies attention only to salient windows identified by their firing rates. The second is Cross-Window Spiking Self-Attention (CW-SSA), which enables global context exchange through an asymmetric scheme in which pruned windows still contribute as key-value sources. Evaluated on a clinical cohort of 139 CCA patients via 5-fold cross-validation, SpikeDS achieves an AUC of 0.753 while consuming only 14.4 mJ, surpassing the best baseline in both AUC and energy efficiency. These results suggest that dual sparsity provides an effective hardware-aware strategy for improving the efficiency of 3D spiking transformers without compromising diagnostic performance.

Sparsely-activated Mixture-of-Experts (MoE) language models achieve remarkable inference efficiency by activating only a small fraction of parameters per token, yet their full expert banks reside in memory at all times, creating a prohibitive deployment bottleneck. Existing structured pruning methods, largely designed for dense transformers, assess expert importance using locally derived heuristics that are blind to the interdependent nature of MoE routing. We introduce MAESTRO (Markov-chain Approximated Expert Sparsification via Transition-based ROuting), a structured pruning framework designed for MoE architectures that models autoregressive expert activation trajectories as Ergodic Markov chains whose stationary distributions encode cross-layer dependencies, yielding a globally aware importance heuristic. Evaluated across five diverse domains including Safety, Bias, and Ethics, MAESTRO outperforms state-of-the-art baselines by up to 10.61% in average performance retention under a strict 50% compression regime, while exhibiting substantially lower cross-task variance, indicating that global, routing-congruent pruning produces models that generalize more consistently across heterogeneous tasks.

Most existing multitask learning approaches are limited by their reliance on task-specific loss functions tailored to the scale and type of each outcome. When outcomes differ across tasks, these losses are generally not directly comparable, which makes it difficult to formulate a unified objective and may limit information sharing across tasks. We propose a multitask transformation framework in which task-specific responses may differ through unknown monotone transformations. Motivated by high-dimensional biological applications in which the predictor dimension may diverge with the sample size while only a common subset of predictors is informative, we consider shared sparsity across tasks. Under this framework, we estimate the target functions and identify important predictors by optimizing a smoothed rank-based criterion with a group-Lasso penalty, implemented through a multitask deep neural network with a shared first layer. We establish the nonasymptotic excess-risk bounds, and variable-selection consistency for the proposed estimator. Simulation studies show that the proposed method achieves competitive prediction and variable-selection performance compared with competing approaches. Analyses of gene-expression studies with continuous, binary, and mixed outcomes further illustrate that the proposed method improves prediction and identifies biologically meaningful shared predictors.

We study sparse self-attention in which each query attends to a dense local window plus a set of Fibonacci-spaced offsets, with a per-layer scalar alpha that compresses or expands the spacing. Across 21 language models trained under one matched recipe (60M parameters, 512 hidden, 16 layers, 426M tokens), we compare four ways of setting alpha across depth: fixed, per-layer learned, a static linear stagger, and a coprime (anti-gridding) reassignment of that stagger, together with a reach-matched power-of-2 control. Three results stand out. First, a static per-layer stagger improves perplexity over both fixed and learned alpha, and the gain is base-agnostic: applying the same stagger to a power-of-2 base lifts it above fixed Fibonacci and to parity with learned Fibonacci attention. Second, learning per layer is inert: it does not beat the static schedule and costs roughly five times the inference latency. Third, and most consequential, all sparse variants extrapolate to four times their training length with little or no degradation, whereas a recipe-matched dense baseline collapses (perplexity rises by 201% at 4x length); we attribute this to fixed-offset attention only ever querying relative positions seen during training. We also report two honest negatives: at training length the best sparse model has about 26% higher perplexity than the dense baseline, and the staggering gain is uniform across context positions rather than concentrated at long range.

Large Language Models (LLMs) inference is typically deployed under a static resource assumption, where models execute a fixed computational graph regardless of the runtime environment. However, real-world cloud infrastructure is inherently dynamic, characterized by fluctuating availability (e.g., spot instance preemption) and tiered Quality-of-Service requirements. In such volatile settings, static models are inflexible: they either crash under resource constraints or waste compute on redundant operations. To bridge this gap, we propose Learning to Allocate (L2A), an end-to-end framework for resource-adaptive inference. Unlike prior methods that condition only on input difficulty, we formulate inference as a constrained allocation problem conditioned on both the input and the runtime resource budget itself. We introduce lightweight, budget-conditioned and input-aware gating networks integrated into the LLM. These gates are trained via a unified objective that jointly optimizes task performance, logical consistency, and resource costs along three axes matching how real-world dynamics manifest: layer skipping for memory and depth pressure, head pruning for throughput contention, and reasoning-token reduction for latency tightening. This lets the model learn a budget-aware policy beyond input difficulty alone: it adaptively configures its computational footprint with respect to real-time resource dynamics, maximizing reasoning depth when resources permit while enforcing strict frugality when budgets tighten. A single L2A model traces the entire compute-accuracy Pareto frontier on Llama-3-8B and Qwen-3-4B: at up to 34% realized layer sparsity, it stays within 0.6% of the dense baseline on GSM8K, with the same gap holding zero-shot on out-of-distribution tasks, while every static or heuristic baseline requires a separately tuned model and still drops by 5-10% at comparable inference time.

What is the geometry of a visual percept? The most widely used protocols for decomposing neural network representations into interpretable parts treat concepts as isolated directions, yet recent work shows that concepts are often realized as geometric structures in low dimensional regions of activation space. We turn to the literature of Structured sparsity to close this gap, and show that block sparsity, which groups directions into blocks, is the prior matched to a generative model in which a representation is a sparse sum of low-dimensional manifolds: the modern, learned form of a classical idea in visual neuroscience, where a visual feature is carried by a coordinated group of neurons rather than a single tuned one. We implement three variants of block-sparse featurizers (BSFs) and, through a minimum-description-length analysis, show that all three describe activations more compactly than direction-based featurizers, with the recovered concepts typically two- to four-dimensional. We then use BSFs to (i) recontextualize prior work, showing that curve detectors in InceptionV1 actually read from a single continuous curve manifold, (ii) discover novel manifolds including shadows and lighting in DINOv3, and (iii) support interpretable control of image generation in diffusion models (SDXL) via manifold steering.

Large automatic speech recognition (ASR) models such as Whisper must be deployed across hardware with widely varying memory and inference-speed constraints. We present a compression framework that jointly parametrizes Whisper deployment along \emph{six} dimensions: model size, temporal resolution, encoder token stride, low-rank adaptation capacity, weight precision and sparsity pattern. All axes are jointly optimized using NSGA-III with respect to three deployment objectives: word error rate (WER), inference FLOPs, and memory footprint. Across 50 of the 1,680 candidate configurations evaluated, we characterize the conditional effect of each axis and identify compression combinations that dominate naive single-axis scaling, while finding that 1:4 structured sparsity fails to recover acceptable accuracy under the tested recovery budgets. We report measured WER and resident memory, use analytical EffFLOPs as the search-time compute surrogate, and separately validate representative inference configurations using measured real-time factor (RTF).

Dictionary learning has long been studied from both optimization and probabilistic perspectives. While formulations with element-wise sparsity regularization (e.g., L1-based sparse coding) admit well-established probabilistic interpretations, many structured variants that impose global constraints lack a clear and tractable generative view. In this paper, we revisit a class of practically effective yet theoretically under-explored dictionary learning methods that impose a simple global regularization on the number of activated dictionary atoms, which we term parsimoniously activated dictionary learning (PADL). We show that PADL admits an equivalent formulation as maximum a posteriori estimation under a structured generative model, with auxiliary latent variables that govern global activation patterns. This formulation allows us to derive generalization guarantees that are difficult to obtain under the original formulation. More importantly, it yields an analytical characterization of the tradeoff between sparsity, storage cost, and reconstruction accuracy, enabling data-driven estimation of optimal hyperparameters. Based on this connection, we develop an efficient and interpretable PADL algorithm that eliminates manual hyperparameter tuning, achieving improved reconstruction performance under comparable sparsity levels on visual benchmarks. We further demonstrate its practical utility in accelerating inference for vision-language models.

We study dense-to-sparse continual training as a way to construct channel-sparse large language models from dense checkpoints. Starting from a Qwen2.5-8B dense backbone, we continue training at 32K context and introduce a predictor-gated sparse SwiGLU FFN in the 32K stage. For each token and layer, we use a low-rank predictor to produce FFN-channel routing logits. We then apply a bank-wise top-k rule to retain 16 channels in every 64-channel bank, yielding 4x sparsity in the FFN intermediate activation. Unlike post-hoc sparse inference methods, the routing module is placed on the main language modeling path and optimized during continual training, enabling the dense model to be upcycled into a hardware-oriented sparse model. We report the architecture, training recipe, benchmark performance, and training lessons. We also identify a layer-local long-context failure mode on RULER-CWE and propose a single-layer repair algorithm that substantially improves the affected length range.

Semi-structured 2:4 sparsity is widely supported by modern accelerators, providing up to a 2x theoretical speedup. However, its strict 50% sparsity constraint often causes non-negligible accuracy degradation under post-training pruning. Meanwhile, existing relaxed sparsity formats either require specialized compiler support or introduce runtime overheads that limit end-to-end speedup. We propose Spense, a practical hybrid sparse-dense format that splits each weight matrix into a 2:4 sparse region and a dense region. This design relaxes the effective sparsity constraint while remaining compatible with existing high-performance sparse and dense GEMM libraries, avoiding both custom compiler support and input activation expansion. Building on this format, we introduce SpenseGPT, a one-shot post-training pruning method that produces sparse and dense regions. Notably, we show that selecting the right dense regions is important, and we devise two different strategies to choose them. Experiments on Qwen3-32B and Seed-OSS-36B demonstrate that our method achieves up to 1.2x end-to-end decoding speedup on B200 GPUs with FP8 precision, while preserving accuracy. To the best of our knowledge, this is the first one-shot pruning demonstration of real-world end-to-end LLM decoding speedup from semi-structured sparse tensor cores on recent GPUs such as B200s, while maintaining model quality.

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.

Extreme multi-label classification (XMC) involves learning models over large output spaces with millions of labels, making the output layer a memory-compute bottleneck. While sparsity-based methods reduce arithmetic complexity, they often fail to yield proportional speedups due to irregular memory access, poor hardware utilization, or reliance on auxiliary architectural components in long-tailed regimes. We introduce group-shared fixed fan-in sparsity, a semi-structured output-layer design in which semantically related labels share a sparse input pattern while retaining independent weights. This grouping introduces a task-aligned inductive bias -- encouraging related labels to share feature subsets -- while reducing index memory overhead, increasing feature reuse across labels, and enabling efficient GPU execution via custom CUDA kernels that leverage modern accelerator primitives. As an alternative to auxiliary objectives, we exploit the long-tailed structure of XMC by decomposing the output layer into a small dense head over frequent labels and a group-shared sparse tail over the remainder, providing an informative gradient pathway while preserving the memory benefits of sparsity. Through kernel-level microbenchmarking, we show that group-shared fixed fan-in translates arithmetic reductions into practical wall-clock gains, achieving up to $4.4\times$ speedup in the forward pass and up to $25\times$ speedup in backward passes over standard fixed fan-in sparsity, while operating within a few percent of a FLOPs-matched dense bottleneck. Across large-scale XMC benchmarks, our approach matches or improves precision@k over prior sparse baselines, while narrowing the performance gap to dense.

Feed-forward networks (FFNs) dominate the parameter count and computation of modern language models, yet existing pruning methods often struggle to convert sparsity into hardware-friendly inference efficiency gains. We introduce \textbf{PrunePath}, a budget-adaptive structured sparsification framework for FFN layers. Built on MoEfication, PrunePath replaces independent expert-wise thresholding with a softmax-normalized routing distribution and activates important experts under a cumulative-mass threshold. This formulation imposes a token-level probability budget, enabling adaptive expert counts and a direct inference-time sparsity knob from a single checkpoint. Across NLU, NLG, and instruction-tuning evaluations, PrunePath achieves a favorable sparsity--performance trade-off compared with existing static pruning and MoEfication-based methods. We further implement Triton kernels for KV-cache decoding to translate the resulting structured sparsity into practical memory savings and measurable decoding-speed improvements. These results demonstrate the superior performance of PrunePath for building highly sparse, deployment-friendly large language models.

Sparsity has long been a central theme in LLM efficiency, but its role in context processing remains unresolved. As LLM workloads shift toward longer contexts and agentic interactions, the compute and memory bottlenecks of attention become increasingly critical, raising the question of whether these constraints are fundamental. Our position is that these constraints are artificial and unnecessary, and that the future of LLM inference lies in extreme but principled sparsity along the context dimension. This position is supported by several strands of empirical and theoretical evidence. First, we find the insistence on dense attention unreasonable, since in a long context a query effectively projects O(N) attention information into a hidden space of dimension d << N, making the process inherently lossy. Second, we perform an extensive study of sparsity in LLMs spanning 20 models across five model families, varying context lengths, and different sparsity levels. We empirically demonstrate a strong trend: current LLMs, despite not being trained for context sparsity, are remarkably robust to inference-time decode sparsity across tasks of varying complexity, including retrieval, multi-hop QA, mathematical reasoning, and agentic coding. Importantly, we also show that current hardware is already sufficient to realize substantial gains from this sparsity. For example, our sparse decode kernels accelerate large-context processing by up to 10x over FlashInfer at 50x sparsity levels on hardware such as the H100. Overall, these results position extreme context sparsity not as a heuristic, but as a principled foundation for LLM inference, training, and architecture design: one that is both feasible and beneficial, and a compelling direction for future systems.

Entity tracking requires maintaining and updating latent states for entities and attributes over long sequences. Recent task-specific attention operators can compress deep Transformer stacks into a few layers by performing multi-hop state propagation within a single layer, but their dense evaluation remains expensive. We show that in this setting, learned attention is strongly structured: most mass concentrates in local block-diagonal neighborhoods with a light cross-block residue. Exploiting this, we derive a blockwise evaluation of a resolvent-style operator that keeps within-block interactions exact and routes cross-block interactions through a reduced system. The resulting evaluation is subquadratic in sequence length $O(n^{4/3}d)$ (and $O(n^{7/3})$ when $d\approx n$). On controlled tracking benchmarks, our method matches the dense operator's accuracy while reducing wall-clock time by $12-29\%$ under a standardized measurement protocol, and is up to $2.4 \times$ faster than a compact dense Transformer at comparable exact-match accuracy. We further provide ablations over block size and model capacity, and identify a limitation: performance collapses when the number of simultaneously evolving properties exceeds the number of attention heads.

Despite the success of deep neural networks in vision, medical diagnosis, and IoT scenarios, their deployment on resource-limited platforms poses serious challenges due to their high storage requirements, computational complexity, and large footprint. In particular, fully connected layers require a large number of weights, making it difficult for edge devices to accommodate them. To overcome these challenges associated with limited platforms, this paper proposes the Two-Valued Symmetric Circulant Matrix (TVSCM), a very sparse architecture that employs just two weights per layer to keep it circulant and symmetric. The extreme form of structured sparse architecture provides negligible storage costs compared to traditional full-weight storage. Instead of hardware and additional stages of other traditional sparse learning techniques, such as low-rank approximation and pruning approaches, this architecture provides an extreme form of sparsity, achieving very minimal storage requirements. The simulation study demonstrates more than 80$\times$ reduction in model parameters, reducing parameters from 623,290 to 7,852 on MNIST and from 24,709 to 942 on the MIT-BIH arrhythmia dataset, while maintaining comparable accuracy from 97.6% to 93.5% on MNIST and from 97.6% to 93.1% on MIT-BIH. Due to its minimal architectural requirements and very low power consumption, this architecture would be ideal for edge computing platforms, tiny-ML platforms, IoMT systems, and battery-powered systems.

Identifying the structural priors that enable Deep Neural Networks (DNNs) to overcome the curse of dimensionality is a fundamental challenge in machine learning theory. Existing literature suggests that effective high-dimensional learning is driven by compositional sparsity, where target functions decompose into constituents supported on low-dimensional variable subsets. To investigate this hypothesis, we combine Information Filtering Networks (IFNs), which extract sparse dependency structures via constrained information maximisation, with Homological Neural Networks (HNNs), which map the inferred topology into fixed-wiring sparse neural graphs. We formalise the design principles underlying this construction and present an interpretable pipeline in which abstraction emerges through hierarchical composition. HNNs are orders of magnitude sparser than standard DNNs and require only minimal hyperparameter tuning. On synthetic tasks with known sparse hierarchies, HNNs recover the underlying compositional structure and remain stable in regimes where dense alternatives degrade as dimensionality increases. Across a broad suite of real-world datasets, HNNs consistently match or outperform dense baselines while using far fewer parameters, exhibiting lower variance and showing reduced sensitivity to hyperparameters.

Global structured pruning requires channels from different layers to compete under a shared sparsity budget, raising two coupled challenges: identifying which channels should be retained and making their scores comparable across layers. Raw channel scores can contain block-common scale that leaves within-block ordering unchanged but distorts model-wide competition. Our experiment indicates that similar layer-wise allocations can retain substantially different FFN channels, so layer allocation alone does not determine channel identity. Motivated by this separation, we introduce Global Relative Kinetic Utility (Global RKU), a label-free criterion that separates channel importance estimation from cross-layer comparison. Global RKU measures channel participation using a final-hidden-state activation-gradient signal, then applies block-relative normalization to mitigate block-common scale while preserving within-block ordering, requires only unlabeled calibration inputs, and produces a static pruning topology in a single calibration stage. Under questions-only calibration on Qwen-2.5-7B, RKU-GISP Mean3 margins are -0.98, +3.79, and +8.61 points at 30%, 40%, and 50% sparsity, respectively (average +3.81). Additional Qwen evaluations cover non-mathematical reasoning, recovery, held-out transfer, and physical deployment. Separately, replacing Wiki16K with questions-only Q16K improves RKU's Mean3 at every tested sparsity on Qwen, Llama, and Gemma. Our ablation study shows relative-normalization gains of 14.42 and 5.53 Mean3 points at 40% and 50% sparsity, respectively; the common-seed audit is positive in all 27 seed-task comparisons.