In this paper, we propose a scalable Kronecker-based approximation that captures cross-layer interactions without storing the entire Fisher matrix, enabling practical Hessian analysis for billion-parameter networks where full computation is infeasible. Our approach reveals consistent vulnerability patterns: value projection layers exhibit the highest sensitivity and strongest cross-layer correlations across multiple model families, while other components exhibit architecture-specific behaviors. Through extensive experiments on quantization, sparsification, inter-layer corruption, and post-corruption fine-tuning, we demonstrate that our approximation strongly correlates with both performance degradation and recovery. Our framework provides a practical, theoretically grounded tool for identifying fragile components in large models, opening new avenues for guided compression and optimization strategies, such as mixed-precision allocation, layer-wise sparsity, and adaptive low-rank decomposition across layers and even individual weight groups.
Grokking is a delayed transition from memorization to generalization that is often accompanied by substantial reorganization of internal representations. This paper studies whether biologically inspired mechanisms, many of which are not commonly incorporated into artificial neural networks, can actively promote this transition by regulating hidden-layer computation at the levels of neuronal activity, response, and effective connectivity. We augment a multilayer perceptron with input gating, structural plasticity, gain modulation, threshold modulation, homeostasis, lateral inhibition, and activation decorrelation, and evaluate these mechanisms through systematic ablations on two established grokking benchmarks: sparse parity and noisy XOR classification. The results show that the mechanisms contribute unequally to generalization. Homeostasis provides the strongest and most consistent benefit, while structural sparsification emerges as the second major mechanism. The remaining biologically inspired mechanisms have smaller or less consistent effects in the present experiments. For both problems, the results support the common principle that explicit regulation of neuron utilization and effective connectivity can improve the emergence of generalizable internal computation. These findings motivate broader investigation of biologically inspired activity regulation and adaptive sparsification, including in large language models, where they may accelerate the development of generalizable representations and reduce the optimization time required for robust generalization.
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.
This paper develops an online, off-policy policy-iteration framework for reinforcement learning (RL), based on sparse Gaussian-mixture-model Q-functions (S-GMM-QFs). The framework reconciles streaming, non-stationary data with the Riemannian structure of the parameter space while handling distributional mismatch through experience replay. S-GMM-QFs are introduced via Hadamard overparametrization, enabling interpretable sparsification through smooth regularization that facilitates Riemannian-based optimization. Overparametrization allows the framework to adaptively identify meaningful components from a large initial pool, yielding sparse models where interpretability emerges naturally from geometry: each component's parameters (means and covariances) explicitly encode its geometric role in the ambient state-action space. These geometric roles are learned through online gradient descent on a smooth objective over a (Cartesian-product) Riemannian manifold. Numerical tests demonstrate that S-GMM-QFs match or exceed deep RL methods while using substantially fewer parameters and achieving faster improvement per observed transition. Notably, parameter efficiency and interpretability combine to maintain strong generalization in low-parameter regimes where sparsified deep RL approaches degrade.
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 paper tackles the problem of stock ranking and portfolio construction under realistic investment settings by jointly modeling temporal dynamics and cross-sectional dependencies. We propose the Soft-Threshold NMI-prior Transformer Graph Attention Network (STN-TGAT), which integrates a temporal Transformer with a Graph Attention Network to capture long-horizon sequential patterns and dynamic inter-stock relationships. An NMI-based prior graph combined with a soft-threshold sparsification mechanism enhances structural robustness by mitigating noisy correlations while preserving informative connections. The portfolio formation process incorporates practical considerations, including Top-5 selection within the Top-50 $S\&P$ 500 constituents, explicit weight allocation, and transaction cost adjustment, thereby aligning the evaluation with real-world trading conditions. Empirical results on real-world data demonstrate that STN-TGAT consistently outperforms benchmark models from predictive accuracy and investment profitability measured by portfolio returns. These findings suggest that combining decision-aligned training with adaptive relational modeling provides a coherent and practically effective framework for data-driven portfolio construction.
Ignacio Echave-Sustaeta Rodríguez, Aida Abiad, Frank Röttgerstat.ME stat.ML
Graph Laplacians encode graph structures in matrix form, and thus facilitate the application of linear algebra to graph theory. In statistics, two related families of probabilistic graphical models can be parameterized by graph Laplacians. The first one is the Laplacian-constrained Gaussian graphical model (LCGGM), which imposes that the (pseudo-)inverse covariance matrix of a Gaussian random vector is a Laplacian matrix. Applications include graph signal processing and network topology learning. The second one is the Hüsler-Reiss graphical model, which is considered as an extremal analog of the Gaussian graphical model, and can be used in extremal dependence modeling of floods, heatwaves, and financial losses. For both models, the restriction to positive edge weights in the graph Laplacian gives rise to an approach for graph structure learning that does not require tuning parameters. While these approaches yield a strong model fit in many settings, the resulting graph estimates are typically much denser than the underlying ground truth, limiting interpretability and scalability. In order to improve the accuracy of Laplacian-constrained graph learning, we propose to use spectral graph sparsification as a post-estimation operation. To do so, we replace the original Laplacian estimate by a sparser Laplacian that is spectrally close, and re-fit the model on the resulting graph. We refer to the two resulting methods as Spectral-LCGGM and Spectral-HR. We investigate the properties of the proposed estimators and show several theoretical results on their performance. Furthermore, we demonstrate that the newly proposed methods perform well by running simulations on Erdős-Rényi and stochastic block model graphs, and we also showcase their applications to real data.
Xinge Wu, Huaxin Wang, Jiajun Liu +4quant-ph cs.AI cs.LG
Machine-learning approaches to quantum state tomography can achieve high reconstruction fidelity, but the physical structure used by the trained model often remains implicit. Here we ask whether a sparsified Kolmogorov-Arnold Network (KAN) can be used not only as a regressor, but also as an inspectable reconstruction rule whose internal organization can be checked against known Pauli structure. We study a controlled three-qubit GHZ-family benchmark in which all 63 non-identity Pauli expectation values are used to reconstruct three GHZ-subspace variables: the population imbalance $z$, the real off-diagonal component $c$, and the imaginary off-diagonal component $s$. Under finite-shot sampling and depolarizing noise, external ablation identifies the extended 12-channel GHZ-relevant Pauli set from the 63 measurements, with exact top-12 recovery across the tested shot counts and depolarizing-noise strengths. These support patterns remain stable across multi-seed random-initialization and noise-level analyses, and collapse under random-label controls. The dominant pruned input-hidden-output pathways organize Z-type population observables and X/Y off-diagonal observables in a pattern consistent with the analytic GHZ Pauli grouping, and sparse formula recovery recovers the canonical signed Pauli relations. The contribution of the KAN is therefore pathway-level structural interpretability within a neural reconstruction model, rather than superior sparse regression. Together with negative controls, these probes provide a consistency chain for auditing learned reconstruction rules against known physical structure.