Sparsity

Sparse Gaussian processes achieve $O(N)$ inference by replacing the kernel with an appropriate expansion in a fixed basis $\{φ_j\}$ on the input space. Given a compute budget $M \ll N$, practitioners conventionally truncate the basis to its first $M$ entries. Nothing in the formalism, however, prevents one from selecting only those $M$ basis functions that matter for the data at hand. This would avoid spending budget on basis functions where there is no signal, but it requires a criterion for ranking the candidates. We propose three such criteria derived from an information-theoretic view of the basis-function selection problem. Each criterion matches a different state of knowledge at selection time: a no-data state, a no-prior state, and an in-between state. We then study the performance of truncation versus selection strategies on six UCI regression benchmarks across three basis families: Hilbert-space Gaussian processes (HSGP), variational Fourier features (VFF), and variational inducing spherical harmonics (VISH). We observe that the no-data criterion is a safe default, matching or improving on truncation for HSGP, VFF and VISH, with substantial gains for VISH and improvements over a recently developed selection heuristic for that basis family. The data-aware no-prior and in-between criteria provide substantial gains over truncation specifically for HSGP, which is the most broadly used of the three families in practice.

Deployment-time safety methods for large language models (LLMs) are predominantly supervised and assume access to unsafe training data. Nevertheless, new attacks and harm categories regularly arise, not captured by models trained in such a supervised fashion. An alternative approach is to view this problem through the lens of anomaly detection, namely, to rely solely on modeling safe data and flagging out-of-distribution inputs. However, LLM activations lie in a high-dimensional space, raising concerns about whether anomaly detection is statistically feasible. We show that, under the linear representation hypothesis (LRH), there may indeed be hope. In the LRH concept space, which is typically recovered via a sparse autoencoder (SAE), nearby points share a small common active support. Using this local sparsity insight, we propose a framework for locally masked SAE-based anomaly detection, supported by theoretical justifications. We validate it on various architectures and datasets, including both capability-testing datasets and safety-specific datasets. Finally, when we allow algorithms to use 1% out-of-distribution data for calibration, locally sparse methods achieve near-optimal performance, demonstrating their ability to capture meaningful safety information while using only 1-2% of SAE neurons for computation.

Deep learning models for multi-modal breast cancer diagnosis achieve high predictive accuracy but remain clinically unacceptable without actionable, counterfactual explanations. Attribution-based methods (LIME, SHAP) are categorically inapplicable to this purpose, as they generate no alternative instances and thus cannot be evaluated on counterfactual quality metrics. This investigation provides empirical evidence that FCA-Guided Counterfactual (FCA-CF) framework that uses a Formal Concept Analysis (FCA) concept lattice as a hard structural constraint on counterfactual search, operating over a multi-modal TCGA-BRCA dataset. We benchmark against four genuine counterfactual methods: Wachter-style CF, DiCE, FACE, and NICE, evaluated on 60 benign-predicted TCGA-BRCA instances. The FCA-CF framework achieves Validity = 1.0000 (100% of counterfactuals successfully flip the prediction), Sparsity = 2.37 features changed (best among all valid methods), and Proximity = 0.900 (normalised L2-based, matching NICE as joint best). The classifier achieves Accuracy = 0.980, F1 = 0.976, ROC-AUC = 0.9947. Ablation analysis confirms that the FCA lattice constraint is the primary sparsity driver (removing it increases sparsity by +40%, p < 0.001, Cohen's d = 0.78), while Phase C greedy refinement accounts for the largest individual contribution (+113% sparsity increase when disabled, p < 0.001, d = 5.01). FCA-guided counterfactual generation achieves a clinically important Pareto-dominant outcome; it is simultaneously the sparsest and among the most proximate of all valid methods, with perfect validity. The emergent sparsity property arising from lattice topology rather than numerical penalty terms constitutes a structurally novel contribution to the counterfactual explanation literature.

Autoregressive image generation has emerged as a paradigm for multimodal AI systems due to its compatibility with transformer-based LLM serving infrastructures. However, generating thousands of visual tokens per request makes decoding increasingly bottlenecked by KV cache accesses during attention computation. Sparse attention is particularly attractive for this workload because many visual generation applications tolerate moderate quality degradation in exchange for improved performance and efficiency. While sparse attention has been extensively explored for text-based LLM inference, it remains unclear whether its sparsity assumptions generalize effectively to autoregressive image generation. We present the first systematic characterization of attention sparsity in autoregressive image generation across diverse workloads and representative open-source models. Our analysis reveals several distinguishing properties, including a pronounced prefill-decode asymmetry, strong attention concentration on prompt and local tokens, and a unique diagonal attention sparsity pattern arising from the spatial locality of visual tokens. Motivated by these observations, we propose a diagonal-aware sparse attention mechanism that selectively skips KV entries along the diagonal attention direction within a recent window. Implemented on top of a GPU-based serving system using FlexGen, FlashAttention-2, and custom kernels, our approach achieves up to 3.1x throughput and 1.19x latency improvements with less than 2% quality degradation compared to dense inference.

Visual signals require compact yet sufficient representations for robust downstream prediction. Convolutional sparse coding (CSC) provides an explicit mechanism for suppressing redundant components while preserving signal content, but its sparsity coefficient is typically fixed and manually selected. We propose a training-adaptive convolutional sparse coding framework for robust visual signal representation. Specifically, we unfold the CSC optimization with the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) and treat the sparsity coefficient as a differentiable variable jointly learned with the network parameters. From the information bottleneck perspective, this coefficient controls the trade-off between information retention and compression: the sparsity term promotes compact representations, while the reconstruction term together with task loss preserves task-relevant signal content. We further introduce a label-free post-training strategy that adjusts the compression strength for corrupted inputs with the main network parameters fixed. Experiments on CIFAR and ImageNet demonstrate competitive clean-data recognition and greatly improved robustness under different input perturbations.

Continual learning must balance the learning of new knowledge with the retention of previously learned knowledge to incrementally learn tasks from a data stream without catastrophic forgetting. While leveraging pretrained models has significantly advanced continual learning, existing methods exhibit a scalability bottleneck when trained sequentially on many tasks, suffering from performance degradation due to inter-task interference and loss of plasticity. Inspired by evidence that sparse fine-tuning achieves performance comparable to full fine-tuning, this paper presents a novel sparsity-driven continual learning framework. Our continual learning method, termed CLARE, operates in two stages: it first identifies a sparse, task-critical parameter mask via a sparsity-inducing objective, then performs mask-constrained fine-tuning by only optimizing parameters selected by the mask. This two-stage sparse adapter mechanism enables all tasks to be accumulated within a shared adapter space while reducing destructive interference across tasks. Extensive experiments demonstrate the scalability of CLARE. On the long task-sequence benchmark Omnibenchmark-1k, CLARE outperforms strong baselines in final accuracy by a large margin, e.g, improving EASE by 4.64% and 13.34% after learning 100 tasks, respectively.

Post-training attention sparsification reduces the quadratic cumulative attention cost of pretrained Transformers by selecting a small set of context units (tokens or blocks) for each query. Existing trainable methods usually use a lightweight selector to score context units, followed by hard Top-K selection that blocks gradients from the language modeling loss. Consequently, these methods commonly distill layer-wise dense attention distributions. Although this encourages the selector to rank context units by dense attention weights in the original model, the ranking is not directly aligned with their impact on predictions under a fixed attention budget (i.e., the number of attended context units per query), potentially wasting the limited budget on less useful units. To address this misalignment, we propose Simple Attention Sparsification (SAS), a gated sparse attention mechanism that optimizes context ranking end-to-end with the language modeling loss. The key idea is to inject the selector's continuous scores into attention logits during training, allowing the loss to update the selector through standard backpropagation. We identify several choices crucial for this simple design to work well in practice: placing the gate inside the attention softmax in log form, using normalized softmax gates to calibrate historical context against the always-retained current block, and preserving continuous selector scores so the model learns relative priorities rather than only hard selections. To support long-sequence training, we implement a memory-efficient Triton kernel that integrates SAS into FlashAttention-style computation. Across reasoning, long-context understanding, and agentic tasks, SAS consistently outperforms trainable sparse attention baselines across attention budgets, with especially large gains under tight budgets, demonstrating more effective context ranking for downstream tasks.

We investigate mean-variance portfolio selection with an $\ell_0$-penalty to promote sparsity in asset allocations. Uncertainty in the mean return vector is incorporated through an ellipsoidal uncertainty set, yielding a robust sparse optimization framework. We characterize the structure of both local and global minimizers and exploit these properties in the risk minimization and return maximization formulations. Building on this structural insight, we develop a branch-and-bound algorithm tailored to the resulting robust sparse portfolio problems, together with a new pruning rule that can discard exponentially many candidate portfolios in a single step. Extensive computational experiments on real market data, together with comparisons against a mixed-integer second-order cone programming solver, demonstrate the effectiveness and competitiveness of the proposed approach.

As the supply of human-written text is exhausted, it has become standard practice to repeat language model training data. Prior work has studied data repetition for densely activated Transformers, but the effects of data repetition remains largely unexplored for recently dominant sparse architectures such as Mixture-of-Experts (MoE), despite their increased compute efficiency. We vary data repetition rates across single- and multi-domain data mixes, and across MoE settings, including expert count and granularity. We consistently find, for models ranging from 80M to 1B active (8.5B total) parameters, that MoEs degrade more rapidly under data repetition. This effect increases with sparsity, dictated by total rather than active parameters. While 80M dense models can repeat data over 8x with minimal degradation, MoEs instead begin to suffer at 4x, and deteriorate rapidly, ceding their performance benefits in all-unique data settings to underperform dense models after 32x. We experiment with existing regularization methods as a potential remedy. We find that some methods, such as dropout, can mitigate overfitting. In particular, with strong masking-based regularization, MoEs are able to outperform dense models even when data is repeated more than 64 times. However, no method fully matches the performance of all-unique training data. Finally, we analyze internal mechanisms correlated with MoE overfitting in high repetition regimes, and find that MoE routing universally stabilizes early in training, and that expert specialization correlates with overfitting to repeated data. In sum, our work addresses the adverse interactions between sparsity and data repetition: we present evidence for the core mechanisms of overfitting and its potential remediation, and suggest promising avenues for future methods to reduce over-specialization in model parameters by disrupting memorization patterns.

SymbolicLight V2 combines sparse event computation with continuous-state processing in a hybrid neuromorphic language architecture. Extending V1's spike-gated dual paths, it adds graded signed events at further projections and softmax-free local attention. We implement the 194M-parameter model on an Alveo U50C FPGA using digital fixed-point arithmetic and on an ARM CPU using sparse integer execution. Across three same-checkpoint FPGA implementations at 175 MHz, active-row weight gathering and valid-state KV loading raise decode throughput from 474.6 to 643.2 tokens/s for a 32-token prefix and 128 outputs. Estimated gross card energy falls from 0.06087 to 0.04407 J per generated token, a 27.6% reduction. Complete-request energy, including prefill, falls by 24.4-27.7% across three prefix lengths. An independent idle split attributes 82.8% of gross card energy to loaded idle, explaining the benefit of shorter token latency. Against the recorded RTX 5090 compiled-FP32 baseline, integer FPGA execution uses 89.1% less estimated card energy during short-context decode; arithmetic precisions differ, and the GPU baseline is not the lowest-energy tested configuration. On four Cortex-A76 cores of a ROCK 5T, complete requests reach 65.4 tokens/s at 9.80 W and 0.151 J per generated token at the adapter's AC input. These results connect event sparsity to omitted computation and data movement. The mechanisms also support other dedicated V2 implementations: increasing throughput by a greater factor than active power lowers energy per generated token. Evaluation holds the deployed checkpoint fixed; its quality trails a same-budget dense control, so the results do not establish equal-quality efficiency.

An input may activate few hidden units even when different inputs collectively use an entire network. We study the statistical complexity of this input-dependent sparsity in the one-hidden-layer ReLU model of Awasthi et al. (COLT 2024). For width $s$, at most $k$ active units per input, and effective weight and bias bounds $W,B$, every size-$m$ sample in the class's fixed radius-$R$ input domain satisfies $\mathcal{R}(S)\le CWR\min\{k,\sqrt{sk/m}\log^{3/2}(2m)\}+kB/\sqrt m$. A support-preserving cover and a single normalized chaining argument remove the previous explicit dimension factor, up to logarithms. Lower bounds on appropriate i.i.d. marginals match up to those logarithms, showing how changing active units across inputs retains a width dependence. The input domain matters: zero-bias networks sparse on the entire ball have at most $2k$ nonzero units and complexity $O(kWR/\sqrt m)$, whereas bias bounds comparable to $WR$ restore the worst-case rate on that same domain in only logarithmic dimension. A spherical-cap construction proves the latter claim without assuming sparsity merely on the sampling support. For a specified normalized bounded loss and biases comparable to $WR$, we also obtain agnostic minimax excess-risk bounds of order $\min\{1,\sqrt{s/(km)}\}$ up to logarithms.

Sparsity is a powerful structural resource in optimization and statistics. We develop frameworks for leveraging sparsity in sampling problems over the Hamming slice $\mathcal{X}_k^d:=\{\mathbf{x}\in\{\pm 1\}^d:|\{i:\mathbf{x}_i=1\}|=k\}$, in high-dimensional regimes where $k\ll d$ (i.e., where $\mathcal{X}_k^d$ is \emph{highly magnetized}). We use our frameworks to design improved samplers for canonical problems in the study of \emph{Ising models} and \emph{Bayesian sparse linear regression}. Our first main result considers the \emph{Sherrington--Kirkpatrick} (SK) model restricted to fixed-magnetization slices $\mathcal{X}_k^d$. We give a polynomial-time sampler for fixed-magnetization SK models at any inverse temperature $β>0$, under arbitrary external fields, provided that $k\le c_βd$ for an appropriate constant $c_β$. By combining this result with an annealing strategy for estimating normalizing constants, we obtain polynomial-time samplers for the SK model at arbitrarily low temperatures under a sufficiently strong external field of strength $h$. In the large-$β$ limit, our framework permits sampling at field strengths within constant factors of the \emph{Almeida--Thouless line} delineating the replica-symmetric and replica-symmetry-breaking regions ([dAT78]), improving polynomially over the field strength $h(β)$ required by the recent work of [BAR26]. Our second main result concerns the measurement complexity of polynomial-time Bayesian sparse linear regression. Recent work by [KSTZ25] shows how to sample from the canonical \emph{Gaussian spike-and-slab posterior} with expected sparsity $k$, at any signal-to-noise ratio, given $n\gtrsim k^3\log^3 d$ Gaussian measurements. We improve this requirement to $n\gtrsim k^{3/2}\log^2 d+k\log^3 d$, using a common sparsity-aware framework underlying both our results.

Mixture-of-Experts (MoE) models expand model capacity without a proportional increase in training compute, but increasing sparsity makes reliable hyperparameter transfer challenging. In this work, we show that conventional hyperparameter scaling laws are insufficient for ultra-sparse MoEs: the optimal learning rate and batch size vary with activation ratio, and these shifts cannot be explained by either total or activated parameter count alone. To characterize this dependence, we conduct 1,800 pre-training runs spanning six activated-parameter scales and models with up to 6B total non-embedding parameters, processing approximately 20 trillion tokens at a cost of 200,000 equivalent H800 GPU-hours. Our results reconcile conflicting findings in prior work by revealing two scaling regimes. At fixed sparsity, the optimal batch size follows a power-law relationship with training tokens $D$, whereas the optimal learning rate scales with training compute $C$ and remains robust to the allocation between model size and data. Across sparsity levels, the activation ratio $A$ enters both relationships as an additional multiplicative power-law factor. These observations lead to unified hyperparameter scaling laws that transfer across MoE sparsity levels. Large-scale evaluation shows that the scaling form outperforms alternative functional forms. On a held-out ultra-sparse MoE with 12B total parameters and only 1/64 of its experts activated, the predicted hyperparameters remain close to the observed optima, supporting joint extrapolation across model scale and sparsity. Further experiments demonstrate transfer across expert granularities and isolate the effect of activation ratio from that of total expert count.

Low-rank tensor modeling has become an effective tool for hyperspectral anomaly detection. However, existing methods still suffer from high computational cost and limited flexibility in characterizing spatially structured anomalies. To address these issues, this paper proposes a hyperspectral anomaly detection method based on group sparse low-rank tensor factorization with automatic anomaly grouping (GSAA). Specifically, the low tubal rank background is characterized by imposing group sparsity on tensor factors, which provides an efficient alternative to direct tensor rank regularization. For anomaly modeling, a latent grouping map is introduced to build an automatic anomaly grouping penalty, allowing anomaly groups to be adaptively inferred from the data rather than predefined at the pixel level. To further exploit complementary spectral and spatial information, GSAA is applied in both domains, and the resulting detection maps are fused to form a spectral--spatial version of GSAA, termed GSAA-SS. An efficient linearized alternating direction method of multipliers algorithm with convergence guarantee is developed to solve the resulting model. Experimental results on five real hyperspectral datasets demonstrate that the proposed method achieves superior detection performance and competitive computational efficiency compared with several state-of-the-art methods.

Inertial confinement fusion (ICF) is a leading pathway toward clean energy, but each shot at the National Ignition Facility costs on the order of one million dollars, making accurate AI surrogates a high-value target. We study exogenous-driven ICF waveform prediction, where a 512-step neutron-rate diagnostic must be inferred directly from a laser pulse and target design parameters, with no historical response observed. The regime stresses standard time-series predictors with temporal sparsity (picosecond peak in a nanosecond window), input-output scale mismatch (under 300 real shots), and peak sensitivity (picosecond timing). We propose ICF-DLM, to our knowledge the first LM-based ICF predictor, combining (i) a physics-typed decomposition into yield $Y_{DT}$, peak timing $t_{\mathrm{peak}}$, and local waveform $w_{\mathrm{local}}$; (ii) bidirectional denoising that defers commitment to peak location; and (iii) a physics-driven PPO reward re-injecting metric structure across numeric tokens. On ICFBench (50K simulations + 232 experimental shots), ICF-DLM cuts peak-timing error from 11.6 to 9.2 steps over a matched autoregressive LLaMA-3-8B and outperforms classical sequence models and LLM-based time-series predictors. Beyond ICF, the recipe shows potential to address science domains with low data and sparse events.

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.

Mixture-of-experts (MoE) architectures scale large language models efficiently, but they demand massive GPU memory. To cope with such demand, models are commonly compressed to reduce their memory footprint. Residual sparsification is a representative compression technique that decomposes each projection matrix of an expert into a shared base matrix and per-expert residual matrix, and then compresses the residuals. Existing sparsification methods compress each residual matrix independently by minimizing its compression error, thereby minimizing the error of each projection matrix. However, our analysis shows that this objective is misaligned with preserving model accuracy after compression. In an expert, the final output is produced through computations coupled across multiple projections and hidden representations. Therefore, even small errors in individual matrices can propagate through hidden representations and projection interactions, leading to large expert output errors and accuracy degradation. To address this misalignment, we propose PARSER, a new residual sparsification method that shifts the compression objective from minimizing isolated matrix errors to preserving the expert output error. PARSER achieves this by introducing output importance, which measures the actual contribution to the expert output error. Our experiments show that, compared with existing methods, PARSER narrows the accuracy gap to the uncompressed model by 1.41$\times$ on Qwen and 1.44$\times$ on DeepSeek, while achieving the same peak memory reduction. Our code is available at https://github.com/OSSS-KU/PARSER.

The development of long-context Large Language Models (LLMs) is constrained by the memory bandwidth bottleneck and quadratic complexity of the attention mechanism during decoding. To overcome the inherent trade-offs between the memory overhead of metadata-based metrics and the computational inefficiency of adaptive selection strategies, we present Faster Flash Decoding (FFD), a novel hardware-algorithm co-design framework designed to break the memory wall in long-context decoding. FFD integrates the selector and computer into a fully fused kernel, replacing external metadata indices with content-aware scanning via low-bit quantization. Furthermore, we introduce the top-delta strategy, which dynamically filters blocks to achieve distribution-adaptive sparsity without global synchronization. Offering a training-free and plug-and-play solution, FFD also enables the reuse of scanning results for computation, achieving up to 11.6x kernel-level speedup and scaling to 256K context length, with 2.37x end-to-end throughput improvement. Empirical validation on RULER and LongBench confirms that FFD maintains model accuracy while delivering high-ratio sparsity, with code available at https://github.com/qluoluo/faster-flash-decoding

We resolve the threshold part of Question 4 of the COLT 2025 open problem "Data Selection for Regression Tasks" of Hanneke, Moran, Shlimovich and Yehudayoff. In vector-valued linear regression with square loss $\ell_{(x,y)}(W)=|Wx-y|_2^2$, where $x\in\mathbb{R}^d$, $y\in\mathbb{R}^m$ and the learner is the empirical risk minimizer of minimal Frobenius norm, we prove that the minimal budget of weighted examples that recovers the full-data loss on every finite dataset is exactly $n^*(d,m)=(m+1)d$. We further determine two more values of the weighted selection profile $F_w(d,m,n)$: at the near-threshold budget, $F_w(d,m,(m+1)d-1)=1+\frac{1}{dm^2}$, and at the spanning budget, $F_w(d,m,d)=d+1$ for every $m$, while $F_w(d,m,n)=\infty$ for $n<d$. For the smallest open intermediate cell $(d,m)=(2,2)$ we prove $F_w(2,2,3)\in[13/8,15/8]$ and $F_w(2,2,4)\in[5/4,3/2]$, reduce the conjectured exact values $13/8$ and $5/4$ to a finite moment problem on the circle with at most seven atoms, and establish strong structural evidence for the conjecture. The upper-bound techniques (a fixed-basis conic compression lemma, a determinant-facet rigidity theorem for maximal certificates, and sharp sparsification lemmas for zero-mean weighted point systems) are of independent interest. As a byproduct we correct an erroneous claim circulating in a recent unrefereed preprint, exhibiting an explicit dataset with $m=2$ on which no weighted selection of $2d$ points recovers the optimal loss. All results are new only for $m\ge 2$; the scalar case $m=1$ is due to Hanneke et al.

Sparse representations are often expected to make models smaller and also reduce inference cost. For Fourier Neural Operators (FNOs), these objectives are not equivalent or do not always align: removing parts of the learned operator can leave the underlying transforms and dense computations unchanged, while changing the grid on which the model is evaluated can introduce overhead of its own. We therefore distinguish sparsity in the representation, in the stored parameters, in the theoretical operation count, and in measured runtime, and present an empirical study of several routes toward sparse FNOs that tests each transition between them separately. Coarsening the execution grid reduces the theoretical cost without reducing measured latency, and adding a correction term recovers accuracy at the cost of making the model slower. Even an 83% parameter reduction remains slower than the dense baseline under ordinary execution. These results motivate a stricter definition of useful sparsity: the deployed operator must preserve solution accuracy and map its reduced support to a genuinely cheaper execution path.

Spiking neural networks (SNNs) are often regarded as energy-efficient alternatives to artificial neural networks (ANNs), yet their advantage depends critically on both network architecture and data properties. We develop an analytical framework to compare fully-connected ReLU ANNs and integrate-and-fire SNNs for time-series data with respect to their theoretical energy efficiency at matched expressive capacity. By relating an inference-energy model to theoretical bounds on representational expressivity, we derive an expressivity-normalized efficiency ratio and explicit thresholds in network width, spike sparsity, and ANN depth scaling. Our analysis characterizes the regimes in which event-driven computation offsets the temporal overhead of SNNs, providing capacity-aware principles for designing energy-efficient temporal networks. It shows that ANNs exceed SNNs in expressivity-normalized efficiency only in specific regimes.

In high-dimensional online prediction, sparse comparators motivate regret bounds that depend on sparsity rather than ambient dimension. Feature priming seeks such adaptation by reweighting features using past data and refitting a minimum-norm predictor. At COLT 2023, Warmuth and Amid posed the open problem of whether the univariate, Pearson, or multivariate priming rules admit competitive online regret guarantees. Under the natural past-only Moore--Penrose protocol, we establish sparse-regret lower bounds that refute the corresponding sparse-logarithmic guarantee. The key obstruction is cheap nuisance interpolation, which permits exact interpolation of the history while assigning insufficient weight to the truly predictive coordinate. An exact target-mass identity and a two-sign argument convert this obstruction into clipped prediction loss. Hadamard constructions yield $Ω(\min\{T,\sqrt d\})$ clipped regret for each of the three unit-power rules against a zero-loss one-sparse comparator. For every fixed power $α\ge1$, one shared paired construction further yields linear regret simultaneously for all three powered rules and selectors among them in sufficiently high dimension. A rank upper bound is tight for powered univariate priming, even with Euclidean-unit inputs, and for unit-power Pearson priming with coordinatewise bounded inputs and target-preserving totalization. A separate algebraic construction gives $Ω(\min\{T,d^{1/4}\})$ regret for unit-power multivariate priming under Euclidean-unit inputs. The univariate lower bound persists under any nonnegative second-stage ridge schedule, while a paired ridge construction yields linear lower bounds for all three powered rules. Exploratory diagnostics on frozen language-model activations are consistent with the same qualitative mechanism. The exact multivariate frontier remains open.

Algorithmic Information Dynamics (AID) studies systems by perturbing them and measuring changes in algorithmic complexity, but its usual estimator, the Block Decomposition Method, is piecewise constant, restricting the calculus to finite differences. We use $K^{\mathrm{CDM}}_{\mathrm{s}F}$, a certified, differentiable estimator, to bring the calculus into learning dynamics: grokking, where a complexity order parameter is known but has not been made to act. As a transient loss kick, the estimator becomes a controller that accelerates grokking in Levin's description-length--versus-time sense, within a data-dependent Occam boundary whose finite-size trend, $f_c\sim\ln p/p$, is consistent with a coupon-collector interpretation. Ablations show that a complexity gate matches a train-loss gate in rescuing failing seeds with $27\%$ less intervention; among the tested signals, only map complexity marks the transition's completion; the certified prior and the per-parameter $\nabla K$ attribution are both fungible (a uniform-prior sensor makes bit-identical gate decisions, and random supports match $\nabla K$-selected ones above a sparsity threshold); and direct field perturbation shows a nucleation-like response to the Occam field (no linear regime is resolved over the probed amplitudes, so these measurements do not justify a fluctuation--dissipation surrogate), with a finite-field response growing by orders of magnitude toward the phase-transition. These measurements account for the empirically tuned staircase: bang--bang pulses, stall-fired and released on yield, whose iteration plausibly builds the response it exploits. The kick transfers to sparse parity and to a transformer; a sustained weight-space loss fails. The algorithmic estimator's distinct contribution is timing (when to fire and when to release), not attribution.

Model merging has recently attracted significant attention as a promising paradigm for constructing unified multi-task models without requiring additional retraining. However, parameter conflicts and knowledge interference across tasks often degrade merged-model performance. Prior work introduced Conflict-Aware and Balanced Sparsification (CABS), which reduces parameter interference through structured pruning and sequential masking. However, CABS relies on grid search to determine scaling coefficients, resulting in exponential time complexity, while its optimization objective can be dominated by high-performance tasks, leading to suboptimal overall performance. To address these limitations, we extend CABS and propose CABS+. Specifically, Adaptive Weight Allocation (AWA) optimizes merging coefficients via a gradient-free search scheme to reduce time complexity, while an asymmetric fitness function promotes more comprehensive performance gains across tasks. Moreover, we conduct a systematic empirical study of key factors influencing model merging performance and propose Relative Synergy Score (RSS) to quantify model mergeability and guide model selection. We compare CABS+ with state-of-the-art model merging methods, including CABS, AdaMerging, and WUDIMerging, across 27 datasets and 5 models covering large language, small-scale language, and vision models. Extensive experiments verify the effectiveness and efficiency of CABS+. Compared with AdaMerging and WUDIMerging, CABS+ improves overall performance by 16.97% and 12.93%, respectively, exhibits stronger stability and robustness across varying task numbers and model architectures, uses less than 25% of the GPU memory required by AdaMerging, and achieves nearly a 4x speedup in merging time over WUDIMerging.

Video diffusion transformers are costly to sample: every denoising step applies self-attention over a long 3D token sequence, a quadratic cost that dominates as resolution and duration grow. Sparse attention reduces this cost without retraining, but existing methods pursue aggressive sparsity, where further speedup costs disproportionately more attention fidelity. We target the opposite end of this trade-off: fix near-lossless fidelity by construction, and remove as much computation as this constraint permits. Two observations make this regime practical: roughly 40% of block interactions can be removed while retaining 99% of the attention mass, and the high-mass support remains stable across denoising steps. We propose LoSA, a training-free sparse-attention method that fixes a retained-mass threshold of 99% rather than a sparsity ratio: it measures exact block attention masses at one early dense step, keeps, for each head and query block, the smallest key/value block set meeting the threshold, and reuses the frozen block indices for all remaining steps. On Wan2.1-1.3B, LoSA alone gives a $1.36\times$ speedup with a 0.06-point VBench Overall drop. The benefit is largest under composition: combined with feature caching, LoSA reaches a $3.2\times$ speedup on HunyuanVideo at a 0.02-point drop, versus 0.32 points for the strongest sparse baseline at comparable speed. Across three video diffusion transformers and speedups up to $3.2\times$, LoSA consistently achieves the best training-free speed-quality trade-off.

\texttt{TensorSketch} by~\cite{pham2013fast,kar2012random} provides efficient sketching algorithms for high-dimensional polynomial kernels $\vec{x}^{\otimes p} \in \R^{d^p}$. \cite{kar2012random} uses dense Johnson-Lindenstrauss (JL)-type projections with computational cost $O(pDd)$, where $D$ denotes the sketch dimension, whereas~\cite{pham2013fast} extends the sparse \texttt{CountSketch}\citep{count_sketch} algorithm, yielding a faster algorithm for high-dimensional sparse inputs with running time $O\big(p(\nnz{\vec{x}} + D \log D)\big)$. However, the variance of both estimators grows exponentially with the polynomial degree $p$, scaling as $3^{p}/D$. Recent work by\cite{pmlr-v206-wacker23a} showed that using complex-valued distribution reduces this dependence to $2^{p}/D$ for the approach of~\cite{kar2012random}. However, their method relies on dense JL-type projections with computational cost $O(pDd)$ and does not extend to the algorithm of~\cite{pham2013fast}. In this work, we introduce a simple variant of \texttt{TensorSketch}\citep{pham2013fast} that achieves the same variance bound as\cite{pmlr-v206-wacker23a}, while retaining its advantage of the input-sparsity running time. We validate our results with supporting experiments on synthetic and real-world datasets.

Domain generalization (DG) and neural network pruning are conventionally treated as distinct objectives, targeting out-of-distribution (OOD) robustness and model efficiency, respectively. In this work, we bridge this gap by introducing Domain-Aware Pruning (DAP), a framework that leverages network sparsity as a mechanism to implicitly enhance generalization to unseen domains. Diverging from standard binary mask optimization, DAP learns a continuous parameter retention probability $p \in [0, 1]$, framing network compression as a continuous probabilistic masking problem. By introducing a regularization objective that actively penalizes the retention of domain-sensitive weights during the mask training, DAP identifies a domain-invariant subnetwork. Empirical results across five DG benchmark datasets demonstrate that DAP achieves significant sparsity while consistently matching or exceeding the OOD performance of its dense counterparts. Crucially, DAP is an algorithm-agnostic framework that integrates seamlessly with existing DG pipelines without necessitating post-hoc fine-tuning. Beyond efficiency and generalization, we show that DAP natively provides increased robustness to adversarial perturbations and yields highly interpretable models, where the retained weights reliably encapsulate the most domain-invariant and task-critical representations.

The top-$k$ operation is a fundamental building block of modern sparse computation, enabling token routing, expert activation, memory selection, and attention pruning. Yet standard hard top-$k$ blocks gradients, while existing continuous (soft) relaxations remain too costly for large-scale models. We introduce Fast LapSum, an exact-budget soft top-$k$ primitive whose GPU solver runs in linear time after sorting. Unlike prior linear-time methods such as DFTopK, which relax the normalization constraint, Fast LapSum is, to our knowledge, the first method to preserve an exact selection mass of $k$ while remaining fully differentiable end-to-end. Our solver combines a linear-time threshold computation with an analytical vector--Jacobian product, and for extreme scales employs probabilistic bracketing to sort only the uncertain middle band of kernel-noised scores. The resulting overhead is almost negligible: the solver processes $10^6$, $10^7$, and $10^8$ scores in $0.41$, $1.15$, and $5.23$,ms, respectively. This makes exact soft top-$k$ practical for sparse routing, retrieval, and large-scale optimization. We demonstrate Fast LapSum on two demanding applications operating over millions of coordinates inside the training loop: generating megapixel sparse adversarial examples with an exact soft budget of ${\sim}0.02\%$ of an image's pixels, achieving an order-of-magnitude speedup over state-of-the-art methods, and training a fully differentiable sparse image coder from scratch.

Vision-language models (VLMs) have achieved remarkable generalization across diverse multimodal tasks through large-scale pre-training, yet their rapidly increasing computational and memory requirements pose significant challenges for deployment in constrained environments. Existing pruning strategies often depend on task-specific criteria or LLM-oriented importance measures, making them unsuitable for task-agnostic pruning, where no task-specific samples are available at pruning time and the pruned model remains broadly applicable. We introduce a retraining-free VLM pruning framework called PORTA that derives a task- and modality-agnostic importance formulation based on activation variation, estimated from generic calibration data, which reliably captures feature-level representation utility across modalities. PORTA further incorporates an adaptive sparsity allocation mechanism that assigns layer-wise pruning ratios based on output feature variability, avoiding the limitations of uniform sparsity and reducing performance degradation at high compression levels. Extensive experiments across VLM architectures, such as CLIP, BLIP, and Qwen2-VL, demonstrate that PORTA achieves competitive downstream performance under high sparsity without requiring any retraining, supporting efficient VLM compression. Code is available at https://github.com/cau-hai-lab/PORTA.git.

Diffusion models have strong generative capabilities. However, their maximum likelihood training objective only focuses on reconstructing the data distribution, making it difficult to align with specific preferences. Reinforcement learning (RL) for preference alignment in diffusion models is promising but limited by reward sparsity. Since a single reward cannot support optimization, existing RL methods usually backpropagate the final reward to all previous steps. However, denoising is stage-wise, with distinct semantics and controllability. Repeating the final reward across all steps creates a temporal objective mismatch, encouraging reward shortcuts that lead to reward hacking. At the same time, due to reward backfilling, each time step receives the same reward, making it impossible to distinguish between actions, thereby weakening the optimization process. To resolve this issue, we propose Stage-Guided Per-Step Optimization (SGPO) for diffusion models, which jointly leverages signal-to-noise ratio and semantic changes to identify generation stages and adaptively assign stage-specific objectives. Early denoising is chaotic and far from the final reward, resulting in weak reward-behavior correlation. This stage should prioritize exiting the chaotic state. In the mid stage, the latent transitions to a stable structure, where the final reward better corresponds to generative behavior. Therefore, this stage optimizes the final reward while exploring diversity to avoid early convergence to a single mode. In the late stage, the latent's core structure is largely fixed, and preference optimization mainly amplifies local details, risking overfitting. Therefore, stable convergence is preferred to avoid quality degradation. Results from 16 comparative experiments validate SGPO. Our method achieves 26.7% average gains in generative quality and 36.7% higher convergence speed.

Pruning reduces the inference cost of large language models, but existing criteria primarily preserve large activations or reconstruct layer outputs. We argue that this overlooks a key computation performed by particularly sparsity-sensitive neurons in the MLP up and gate projections: separating similar inputs into dissimilar outputs. This suggests that effective pruning should preserve not only activations, but also the differences between outputs more broadly. We introduce a family of difference-informed pruning methods built upon this principle. Wisp is a first-order, update-free method that scores weights using input-difference norms, and Wisp+ refines this score neuronwise using the input pairs each neuron separates most strongly. Finally, Whisper is a second-order method that uses a lightly regularized difference Hessian as its reconstruction objective. Across Llama 2 and 3.1 models from 7B to 405B parameters, our second-order variant consistently improves over strong reconstruction-based baselines, while our update-free variants improve over activation-aware baselines, especially in constrained settings. The improvements over Wanda and SparseGPT extend to structured sparsity, downstream evaluations, and other model families. Augmenting stronger techniques such as RIA and ALPS with our difference-informed criteria yields further improvements, shifting the overall accuracy-runtime frontier outward at negligible additional cost. These results suggest that preserving output differences is a broadly useful and composable signal for post-training LLM sparsification.

In partially observable reinforcement learning, agents face a dual bottleneck: they must explore to encounter rewarding states and retain that experience in memory to optimize their policies. Exploration bonuses and memory architectures are traditionally evaluated in isolation, leaving their interaction unmeasured, and standard notions of sparse reward conflate temporal signal density with what the reward actually supervises. We present a controlled study crossing episodic exploration bonuses with diverse neural memory architectures across three environments that vary how the content of memory is acquired. An identical bonus signal yields three distinct interaction patterns: it amplifies architectural capacity differences where memory content must be actively discovered and retained unsupervised; equalizes architectures to a shared ceiling where the content, once sought out, is a single reward-supervised cue; and is null where the observation stream is purely scheduled. Controlled reward manipulations verify that these patterns track reward structure rather than density: a dense reward neutralizes a bonus only if it directly supervises the required latent memory, and a small avoidable penalty on exploratory actions (leaving the optimum unchanged) induces policy convergence to suboptimal stationary states, which either bonus resolves. We then formalize reward sparsity with observation-anchored reward machines, separating structural sparsity (an automaton reproduces the return without the task-required history) from potential sparsity (the one-step reward misprices local exploratory actions); the resulting vocabulary organizes the three regimes by the retention burden each task exposes. Together, these results show exploration and memory are complements, not substitutes: a bonus induces exposure, and only memory converts exposure into return.

Sparse matrix computation performance on GPU depends on how representation and execution schedule match the input structure and target hardware. No single implementation consistently dominates across sparsity patterns, operators, and hardwares. Existing sparse compilers and specialized systems cannot cover all of them simultaneously. We present SparseDitto, an agentic sparse compilation framework for sparse matrix computation on GPUs. It jointly synthesizes representation, execution schedule, and hardware mapping in a unified compilation plan. Structural analysis and a learned template-ranking prior guide architecture-aware synthesis. LLM-guided lowering realizes each plan as CUDA code, while target-GPU profiling drives plan refinement. SparseDitto covers multiple operators, e.g., SpMV, SpMM, and SpGEMM, and various representations within one framework. It can also automatically adapt to different hardwares. Across various SuiteSparse matrices, SparseDitto achieves geometric-mean speedups over cuSPARSE of $2.68\times$ on an NVIDIA RTX PRO 6000 and $2.79\times$ on an NVIDIA H200 (up to 146.61$\times$). Its generated SpMM kernels accelerate full-batch GCN training by up to $3.39\times$.

Confidence estimation is essential when LLMs are used for classification, indicating when predictions can be trusted. However, common approaches such as verbalization produce extremely sparse outputs. For instance, Qwen3-32B verbalizes only eight unique confidence values on SST-2, with over half being exactly 95%, a pattern we observe consistently across four datasets and two LLMs. Besides limiting practical utility, we show that this sparsity critically affects evaluation: the choice of interpolation in area under the accuracy-rejection curve (AUARC) dramatically alters rankings, with consistency sampling dropping from best to worst under stepwise versus linear interpolation. We advocate for standardizing stepwise interpolation for a fairer comparison. Under such a fair evaluation, we find that weighting verbalized digits by token probabilities, a method we term verbalization logprobs, addresses sparsity and achieves the best AUARC (+2.3 points over vanilla verbalization) without incurring additional inference cost.

Vision-language-action (VLA) models have emerged as a key component in embodied AI. Among existing approaches, diffusion-based VLA models achieve superior motion quality and generalization. However, diffusion-based VLA models are compute-intensive and must run at high control frequency, e.g., 50-200 Hz. Thus, it imposes strict latency and energy constraints on edge devices. In this work, we present Deltoris, an algorithm-hardware co-design framework for efficient diffusion-based VLA inference. First, we exploit the temporal similarity of consecutive inputs and propose a \textit{temporal-aware bit-sparsity} algorithm that computes only the differences between consecutive inputs, eliminating redundant bit-level operations. To further address the extra off-chip traffic introduced by our algorithm, we propose a \textit{speculative inference} technique, which amortizes data loading across multiple control steps. Lastly, to support these techniques, we co-design a dedicated accelerator with customized 1D systolic bit-serial PE arrays that eliminate PE workload imbalance. Our evaluation shows that Deltoris achieves up to 34.2$\times$ speedup over mobile GPUs and 6.1$\times$ over prior accelerators, while maintaining comparable accuracy.

Top-$k$ selection determines which components of a sparse model remain active. Hard selection blocks gradients, while continuous relaxations often couple mask hardness to the selected mass. We introduce LaPrune, a mathematically exact-budget differentiable layer that controls the normalized second moment while preserving the selected mass. A LapSum barrier preserves the selection mass, and a normalized second-moment constraint moves the mask from a dense equal-mass allocation toward hard top-$k$ at each budget. We derive a population prediction of the saturated fraction, a near-binary limiting law, and a tight worst-case guarantee on the near-zero fraction. The normalized hardness parameter is invariant to score scale, while a fixed LapSum temperature is not.

Video diffusion transformers (vDiTs) generate high quality but pay quadratic self-attention cost, making inference prohibitive at video-token scales. The challenge is input-adaptive sparsity: selecting critical Q/K/V tokens with negligible overhead and executing them for end-to-end gains. We present SPADE, a training-free sparse-attention engine of three parts: (i) vDiT-SSR, a specification defining 3D blocking candidates and formalizing dynamic masks via Summarizer/Estimator expressions; (ii) runtime scheme generation using SICS and a head-wise policy; and (iii) an executor with low-overhead index search, flash block-sparse attention, and kernel grouping. Across Hunyuan-Video and Wan 2.1/2.2 for text-to-video and image-to-video generation, SPADE raises sparsity and speed while preserving quality, accelerating attention by 2.26x-3.40x and end-to-end inference by 1.49x-1.80x. Our code is open-sourced at https://github.com/6somehow/DAC-SPADE.

Sparse attention is widely deployed in long-context serving stacks, yet no framework audits how discarding blocks changes the influence of specific content on model output. We first establish that the phenomenon is real and causal: Block Sparse Flash Attention (BSFA) route replay across four architectures changes output decisions in 13 of 16 cells, with zero identity-replay label flips. We then introduce a dense-calibrated counterfactual audit using matched probe cards---Gold (carrying the correct answer label), Poison (carrying a target wrong label), and Benign (filler only)---under six-layout position symmetry, isolating the sparsification-specific effect. Two patterns compete. Signal concentration: the selector preserves Gold and Poison blocks far above filler-matched Benign blocks (G$\approx$P$\gg$B across all model--task pairs). Integration loss: discarding blocks severs cross-block attention---confirmed by an ablation where isolating the probe block collapses its influence from 4.48 logits to zero. Compression ratio governs the balance: a full sweep from mild ($c=0.25$) to aggressive ($c=0.75$) compression across four model--task pairs reveals that three of four cells move toward stronger sparse amplification at higher compression, with two exhibiting sign reversals. Three independent arms---BSFA route replay, controlled block-top-$k$, and KV-cache eviction---converge: sparsification changes content influence in ways aggregate accuracy cannot detect. We provide an open measurement framework deployable on any model exposing block identities.

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.

As forecasts increasingly drive decisions in fields such as energy, transportation, and healthcare, understanding the historical data behind these predictions has become as crucial as the predictions themselves. Although existing interpretable-by-design forecasters reveal their internal structures, they offer no guarantee that these structures faithfully reflect the underlying evidence driving the predictions. In contrast, while faithfulness-oriented methods explicitly verify model behavior, they are almost exclusively designed for post-hoc classification tasks. To bridge this gap, we propose IB-Forecast, an inherently interpretable multivariate time-series forecasting framework. It decomposes forecasting into a learned periodic component and a residual component computed with explainable masks over input tokens. With a budget-constrained information bottleneck, end-to-end optimization enables users to directly control explanation sparsity. With a rigorous faithfulness evaluation protocol, extensive experiments demonstrate that IB-Forecast matches the forecasting error of leading black-box models while providing faithful explanations at no additional inference cost. Furthermore, under a matched sparsity budget, these native explanations consistently surpass gradient-based, occlusion-based, and optimization-based baselines across all evaluated datasets. Ultimately, whereas the native explanations of existing interpretable forecasters exhibit poor faithfulness, IB-Forecast guarantees high explanation fidelity, requiring only 14-20% of the observations to deliver low-error predictions.

Matrix factorisation is a fundamental tool for exploiting low-dimensional structure in high-dimensional data, with applications such as data compression, denoising, structure discovery, interpretable representation learning, and dimensionality reduction. Compared to conventional two-factor models, matrix tri-factorisation provides greater modelling flexibility, while sparsity constraints often improve both interpretability and recovery performance. Although the role of sparsity has been extensively studied for two-factor matrix factorisation, rigorous theoretical guarantees for general real-valued matrix tri-factorisation remain largely unexplored. To address this gap, we establish, to the best of our knowledge, the first rigorous theoretical study for sparsity-induced identifiability in general real-valued matrix tri-factorisation. Our analysis is enabled by a novel decomposition strategy that transforms the original problem into two coupled auxiliary factorisation problems, while preserving the structural information necessary to the recovery of the original factor matrices from the observations. Building upon this decomposition, we derive recovery guarantees and structural consistency results that characterise how coefficient sparsity influences the sufficient recovery conditions, convergence behaviour, spectral approximation error, high-probability bounds, and structure preservation. Comprehensive Monte Carlo experiments validate the proposed theory and demonstrate close agreement between the theoretical results and empirical observations.

Minimax-optimal rates for multivariate distribution estimation are known to suffer from the curse of dimensionality. We propose a sparse Bayesian network approach in which each conditional probability is estimated using sparsity-aware conditional mean methods. The resulting estimator, \textit{BAyesian Network Distribution regression} (BAND), handles mixed data types in high-dimensional time series and achieves polynomial total variation convergence rates while allowing the feature dimension to grow polynomially with the sample size. These rates are substantially faster than the classical optimal rates for multivariate histogram density estimators that lack sparsity. Empirical evaluations show that BAND performs competitively for data sampling and confidence region forecasting against a range of state-of-the-art benchmarks.

Spiking neural networks (SNNs) are promoted as an energy-efficient substrate because sparse, event-driven activity replaces dense multiply-accumulates with cheap accumulates. We argue the energy dividend of sparsity is not a property of SNNs but of the task. Holding architecture fixed and swapping only the hidden unit (continuous vs. leaky-integrate-and-fire), plus a two-sided target-firing-rate probe, we measure how far activity can be pushed down before quality breaks. Low-load feed-forward perception sparsifies to 5% firing at no accuracy cost; a recurrent language model cannot go below ~50% -- the recurrent state must stay active to carry information. A spiking Transformer, by contrast, sparsifies freely to 2% (3 seeds) -- so the ceiling is a property of recurrent compression, not sequence modeling. Attention escapes the floor only by storing the full key-value cache, trading a firing floor for a memory wall: on neuromorphic hardware, recurrence and attention pay on different axes, neither escapes. We formalize the ceiling with an information-theoretic bound rho >= H_b^{-1}(log2 M / H) and confirm its predictions: the floor rises with memory load, falls with state width, and (refuting a naive memory-only reading) rises with task difficulty. A layer-wise input floor further caps op reduction under dense input, isolating event-driven perception as where neuromorphic hardware wins.

Diffusion transformers are essential for high-fidelity video generation, but long token sequences make attention a dominant inference bottleneck. Training-free dynamic sparse attention alleviates this bottleneck by computing only selected key-value blocks, yet existing methods struggle to sparsify attention both efficiently and accurately for two reasons: (1) Rigid, unpredictable, and costly routing: selecting a fixed fraction of top-ranked blocks by proxy score imposes fixed budgets, whereas retaining blocks to reach a target cumulative proxy probability mass yields dynamic but potentially imbalanced budgets; both incur non-negligible overhead from computing and materializing proxy scores. (2) Lossy keep-or-drop sparsification: unselected blocks are discarded entirely, degrading accuracy under aggressive sparsity. These limitations motivate cheaper dynamic-budget routing while limiting accuracy degradation. In this paper, we introduce training-free Sol-Attn (Sparsifying online attention), which unifies dynamic routing, sparse computation, and approximation correction in a single online-softmax pass, achieving a better accuracy-efficiency trade-off in sparse attention. The core of Sol-Attn is on-the-fly block thresholding with proxy-score reuse, which selects critical blocks by comparing block proxy scores against a threshold during online softmax. This design enables dynamic yet controllable block budgets without materializing the proxy map, while directly reusing the proxy scores of unselected blocks to approximate their contribution. Experiments across image and video generation tasks show that Sol-Attn advances the quality-efficiency frontier of training-free sparse attention, delivering 2.1 times and 2.3 times end-to-end speedups for video generation and editing, respectively, while preserving visual quality.

Graph compression reduces the computational cost of graph learning, but its effect on signal propagation remains largely underexplored. Existing work evaluates compression through downstream task performance or structural preservation, neither of which directly captures how propagation dynamics change after compression. We study two fundamental compression paradigms, coarsening and sparsification, and ask whether they preserve the propagation behavior of the original graph. Across five datasets, varying compression rates, and propagation depths, we measure signal behavior through three complementary metrics. Our results reveal a consistent tension between the two compression families. Sparsification retains higher signal diversity and mitigates oversmoothing, but its propagation trajectory progressively diverges from that of the original graph. Coarsening more faithfully preserves propagation behavior, but at the cost of stronger smoothing and rank collapse. These findings demonstrate that two propagation-centric objectives, preserving signal diversity and preserving propagation fidelity, are distinct and empirically at odds under graph compression, highlighting the need for evaluation protocols that jointly consider both dimensions. The code and results are available at: https://github.com/KawshikBanerjee/Compression-Propagation-Duality

This work addresses the generation of theoretical correlation matrices with prescribed sparsity patterns associated to graph structures. We propose a novel convex optimization framework in which an initial matrix is projected onto an elliptope under a positive semidefiniteness constraint. Several numerical schemes are implemented and compared. The problem falls within the broader class of matrix completion, where off-diagonal entries corresponding to absent edges are fixed to zero and diagonal entries are fixed to one. Beyond this structural constraint, the approach offers greater flexibility than existing methods by allowing control over the mean of the off-diagonal entry distribution, enabling the generation of correlation matrices that better reflect realistic data. This procedure is not designed to yield a uniform distribution over the feasible set; rather, it provides a principled and tunable way to construct correlation matrices suitable for benchmarking statistical methods for graphical model inference. Theoretical guarantees on the existence of solutions are established, both in the general setting and under the additional mean constraint. Simulation studies illustrate the properties of the generated matrices with respect to graph structure. The methodology is applied to two real-world datasets from neuroscience and finance, and a comparison with GAN-based correlation matrix generation is provided.

Forecasting multiple time-series with high-dimensional covariates presents a core challenge: unifying common temporal patterns while retaining meaningful series-specific information. We introduce Hopformer (Homogeneity-Pursuit Transformer), a two-stage framework that addresses this challenge. In the first stage, we perform a Sparsity Pattern Aggregation (SPA) scheme extracting a common low-variance trend that incorporates the covariates. This acts as a homogenization layer. In the second stage, a LoRA-fine-tuned Transformer models the remaining complex dependencies in the residual. Our method is theoretically grounded. We prove that SPA achieves a near-optimal bias-variance trade-off via an oracle inequality. We also provide generalization bounds for the second stage under dependent time series data. Hopformer sets a new state of the art, improving MASE by an average of 6.56% across synthetic and real-world forecasting benchmarks.

Neural network compression and interpretability remain open challenges in modern deep learn- ing, where billion-parameter architectures deliver impressive accuracy at the cost of trans- parency, computational efficiency, and reliable uncertainty quantification. This paper introduces Neural Atom Prevalence (NAP), a principled Bayesian framework for structured node-level model selection in feedforward neural networks. NAP introduces the neural atom (activation unit) and functions as a hybrid method operating through a four-phase pipeline: Bayesian Lottery Ticket (BLT) identification via Iterative Magnitude Pruning (IMP), soft variational training of the Spike and Slab Independent Gaussian (SS-IG) model, Poisson-Binomial (PB) optimal layer-size selection, and Bayesian fine-tuning to produce a sparse, stable, interpretable, and accurate model. Extensive empirical validation across simulated nonlinear regression, two UCI benchmark datasets (Concrete, YearPredictionMSD), and the MNIST image classification task demonstrates that NAP achieves state-of-the-art structural sparsity, reducing active nodes to as few as 8% of the original dense architecture on MNIST, while well-calibrated probabilisti- cally: the aleatoric-epistemic uncertainty decomposition reveals that model ignorance accounts for only 3 to 4% of total predictive variance across all experiments, and regression reliability diagrams confirm a near-nominal predictive interval coverage (93.4% observed against a 95% target). These results establish NAP as a reliable, theoretically grounded, and computation- ally tractable solution to the simultaneous pursuit of sparsity, accuracy, interpretability, and uncertainty quantification in Bayesian neural networks.

Mobile usage traces are critical for tasks such as user behavior prediction and app recommendation, yet their use is constrained by privacy restrictions and costly large-scale data collection. Although generative models perform well on general time series, their application to mobile usage data remains challenging because (i) limited user activity causes severe sparsity, (ii) heterogeneous variable types complicate joint modeling, and (iii) functional differences across apps create pronounced usage imbalance. To address these challenges, we propose Multivariate-Imaging Diffusion (MIDiff), a diffusion-based framework operating in an imaging space defined by Cross-Gramian Angular Sum Field (C-GASF). C-GASF transforms sparse multivariate sequences into correlation images, while MIDiff employs Triple Attention in a U-Net to preserve temporal consistency and variable dependencies. Experiments show that MIDiff achieves state-of-the-art performance across fidelity metrics. In particular, it obtains a Discriminative Accuracy (DA) of 0.1526, compared with 0.3476 for the strongest baseline, ZITS-VAE, demonstrating its effectiveness in generating realistic and diverse mobile usage traces. Our code is available at https://github.com/YilaiLiu-HKU/MIDiff.

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.

Low-rank factorization is widely used to compress neural networks, but modern models are often not naturally amenable to aggressive factorization without significant accuracy loss. Existing training-time low-rank regularizers can improve compressibility, but they often require SVDs of large weight matrices, modify the model architecture (introducing additional trainable parameters), or rely on stateful cached quantities. To address these limitations, we introduce SLORR, a simple, stateless, and architecture-preserving framework for in-training low-rank regularization, instantiated with two main variants based on the Hoyer sparsity metric and the nuclear norm. SLORR directly regularizes the original weight matrices using GPU-friendly approximations for the forward and backward passes of the regularizers, for which we provide approximation guarantees. We first evaluate SLORR on ImageNet-1K across short-horizon continued training of ResNet-50, ViT-B/16, and ViT-L/16, and pretraining of ResNet-18, where SLORR induces compressibility while introducing less than 8% training overhead. We further evaluate SLORR-Hoyer in LLM pretraining at 135M and 560M scales: SLORR-trained compressed models preserve performance substantially better than unregularized models while adding less than 1% average training overhead.

One-shot pruning methods like Wanda and SparseGPT apply the same sparsity ratio to every layer of a transformer, ignoring known variation in layer importance. We propose PALS (Percentile-Aware Layerwise Sparsity), which adjusts per-layer sparsity based on the 99th percentile of activation magnitudes, bounded to $\pm 5\%$ around the target ratio. On LLaMA-2-7B at 50% sparsity, PALS achieves 10.96 WikiText-2 perplexity versus 12.92 for uniform Wanda (mean over 9 runs, $p < 0.001$). The benefit is architecture-dependent: LLaMA-3-8B shows marginal gains and Mistral-7B shows none. We also find that gradient-based allocation -- the seemingly more principled approach -- produces results worse than random, suggesting that gradient magnitude does not predict the impact of discrete weight removal. PALS adds negligible cost to the pruning pipeline and requires no fine-tuning.

Linear attention models allow a fixed state size and a fixed amount of compute per token. However, due to their limited state size, linear attention models fall behind in long-context recall compared to softmax-attention-based transformer architectures. Increasing the state size of linear attention improves recall performance but at the cost of higher FLOPs. In this work, we introduce Sparse Delta Memory (SDM), an architecture that scales the hidden state of gated linear RNNs to orders of magnitude higher capacity using a sparse addressing scheme. SDM extends the Gated DeltaNet architecture by replacing the dense key-value outer product with sparse reads and writes to a large explicit memory. We show that, under an isoFLOP constraint and with an identical number of parameters, a higher state memory capacity significantly improves performance on in-context learning and long-context retrieval tasks. Moreover, by learning the initial state of the SDM memory and therefore using it as a parametric memory, we show that the model further improves on a wide range of common-knowledge and reasoning tasks.

Video Diffusion Models (VDMs) have demonstrated superior generation quality but suffer from prohibitive computational costs. While recent few-step distillation techniques significantly accelerate inference, they typically enforce a static model architecture across all denoising stages, ignoring the varying computational demands inherent to different noise levels. In this work, we propose a novel post-training acceleration framework that exploits this redundancy by integrating dynamic structural sparsification directly into the distillation process. Unlike conventional post-hoc compression applied to a fixed diffusion pipeline, our approach jointly optimizes the denoising steps and structured model sparsity, transforming a pre-trained VDM into a compact, step-specific Mixture-of-Models (MoM). To address the training instability arising from this joint optimization, we introduce a Progressive Training Strategy coupled with an Output Rollout Mechanism, which ensures the coherent learning of structural decisions across timesteps. Furthermore, we develop a specialized inference engine to deploy the resulting MoM efficiently. Our method is orthogonal to existing acceleration techniques and highly effective: On Wan-14B, it removes 24% of the per-step FLOPs on top of 4-step distillation, adding a 1.2x wall-clock gain and reaching a 30x speedup over the 50-step teacher while preserving competitive generation quality.

Recovering the exact directed acyclic graph (DAG) in linear non-Gaussian acyclic models with latent confounders (LvLiNGAM) remains a challenging problem. Although LvLiNGAM is identifiable only up to an observational equivalence class, each equivalence class is characterized by a unique sparsest DAG. Recovering the sparsest DAG from finite samples, however, remains difficult. Although existing methods are asymptotically consistent, they do not provide an explicit finite-sample procedure for recovering the unique sparsest DAG, nor do they handle models with an arbitrary number of latent confounders. In this paper, we propose a finite-sample method for recovering the sparsest DAG without imposing any restriction on the number of latent confounders. Simulation studies and real-data analyses demonstrate that the proposed method achieves superior finite-sample performance compared with existing approaches.

Sparse feature selection is critical for high-dimensional machine learning, yet traditional $\ell_1$-regularized methods are often brittle under observational noise and spurious correlations, leading to unstable feature supports and degraded generalization. Although adversarial training has been widely used to improve model robustness, its interaction with hierarchical sparse feature selection remains underexplored. In this work, we propose Adversarial LassoNet (AdLNet), a stability-driven sparse feature selection framework that integrates input-space adversarial perturbations with the hierarchical sparsity mechanism of LassoNet. We derive a tractable first-order adversarial approximation under local smoothness assumptions and provide an NTK-inspired spectral analysis to characterize how perturbation-driven training can reduce gradient concentration. Experiments on high-dimensional SERS data, six public benchmark datasets, and ColoredMNIST show that AdLNet maintains competitive sparse-selection performance while improving out-of-distribution robustness by 4.4% and feature support reproducibility by 6.3% under nearly matched support sparsity on ColoredMNIST. On the high-dimensional lung cancer screening dataset, AdLNet achieves a 5.3% test accuracy gain and a 6.0% AUC improvement over vanilla LassoNet. Code and dataset are available at https://github.com/719573/Adversarial-LassoNet.

Inter-agent communication is critical for coordinating Multi-Agent Reinforcement Learning (MARL) agents under partial observability to perform effectively in cooperative games; however, real-world bandwidth constraints demand sparse interactions. Prior approaches primarily address this trade-off by optimizing information-theoretic surrogates. We argue that these statistical proxies are fundamentally misaligned with the true objective: a message can be highly informative yet irrelevant to the joint return of the task. In this work, we propose Message Unlearning for Targeted Efficiency (MUTE), a framework that views communication reduction as a value-guided machine unlearning problem. MUTE rigorously quantifies the Counterfactual Message Value using an attention-based estimator, and systematically unlearns the transmission of low-value messages from a policy trained without any communication constraints. This is achieved through a dual-objective mechanism that enforces communication sparsity while preserving the return of the original joint policy. We derive a theoretical upper bound on the performance gap induced by this sparsification, guaranteeing controlled return degradation. We also empirically evaluate MUTE on various complex multi-agent environments, achieving 80% to 90% bandwidth reduction while maintaining performance comparable to state-of-the-art baselines.

Counterfactual explanations (CEs) for multivariate time-series classifiers are often difficult to interpret in domains where experts reason in terms of semantic feature groups rather than individual channels. In rehabilitation movement analysis with multi-sensor inertial measurement units (IMUs), clinicians interpret motion through muscle-group and joint-segment abstractions; yet, most existing counterfactual methods operate at the channel level, producing scattered and biomechanically incoherent explanations. We propose a two-stage framework for group-based counterfactual generation in high-dimensional IMU data. We first show that Shapley-Adaptive (SA) group ranking preserves counterfactual validity but fails to enforce group-level sparsity, motivating the need for explicit group selection. We then introduce Learnable Gate (LG) methods, which incorporate trainable per-group relevance gates jointly optimized with perturbation masks. Experiments on the KneE-PAD rehabilitation dataset demonstrate that LG substantially improves modality-group sparsity compared to the channel-level M-CELS baseline while maintaining or improving validity, temporal smoothness, and generation efficiency. Exercise-specific analyses further show that group-structured counterfactuals yield concise, muscle-level corrective guidance aligned with clinical reasoning. Overall, the proposed framework enhances interpretability without sacrificing counterfactual quality, enabling more actionable explanations for rehabilitation movement analysis.

Communication increasingly dominates the cost of Large Language Model (LLM) pre-training, especially under data-parallel and sharded training schemes, where gradient synchronization and parameter reconstruction overhead increase with model size and system scale. Existing communication-reduction methods either sparsify raw gradients, which can be unstable for modern Adam-style optimizers at high sparsity, or quantize communication, whose savings are fundamentally bounded by bit width and often incur additional runtime overhead. We present SCAPE, a communication-efficient distributed optimizer for LLM training that exploits the stability of AdamS's first-moment to enable aggressive sparsification without loss of LLM quality. Instead of constructing masks from raw gradients, SCAPE derives them from first-moment-based statistics, partitions mask generation across workers to align with optimizer sharding, and delays mask usage by one step so that mask synchronization can overlap with computation. SCAPE also reconstructs the quantities required for second-moment updates from a single synchronized sparse buffer, avoiding an additional collective. We implement SCAPE in Megatron-LM and evaluate its convergence by pre-training GPT-345M on OpenWebText and Llama-500M on SlimPajama-6B using 32 NVIDIA GH200 GPUs on TACC Vista. In both models, SCAPE preserves training stability, validation loss, and downstream task accuracy under 90% and 99% sparsity. For Llama-500M, SCAPE reduces end-to-end pre-training wall-clock time by up to 43.3% while maintaining model quality comparable to dense AdamW and AdamS. For Llama-1.8B, SCAPE achieves up to 3.26$\times$ speedup per step compared to dense AdamS.

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.