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.
Idris Karel Seunda Ekwe, Patrick Tenga Shako, Ernest Parfait Fokouécs.LG
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.
Bryce A. Christopherson, Jack Baretz, Darian Colgrove +1cs.LG math.OC
The lottery ticket hypothesis proposes that large random neural networks contain sparse subnetworks that can match the performance of dense models after comparable training. A stronger version asserts that sufficiently overparameterized random networks contain subnetworks that are already accurate before any weight training. Existing theory establishes that such strong lottery tickets exist, but reliable extraction remains difficult. We revisit edge-popup, a frozen-weight score-training method for extracting strong tickets, and identify layerwise sparsity selection as a central bottleneck. We introduce double-scoring, an augmented score-space parameterization that replaces a layerwise sparsity search with optimization over enlarged score tensors. We prove that fixed-density masking in an augmented score space preserves access to all original-coordinate masks, and we show that the resulting method can be interpreted as edge-popup on a zero-augmented network. In controlled experiments, double-scoring substantially improves strong-ticket extraction over fixed-density edge-popup and pruning-at-initialization baselines, improves on the performance of rewound sparse-training topologies, and exhibits markedly lower sensitivity to sparsity hyperparameters. Ablations show that the gain is not merely due to additional trainable score parameters, but is tied to the augmented score-space competition that induces the effective original sparsity.
Compositionality is believed to be the foundation for generalization, enabling models to reuse meaningful primitives in novel combinations. Yet, models trained with standard gradient-based optimization rarely, and often only weakly, exhibit compositional internal structure, and it remains unclear how or why such compositionality forms. In this work, we show that compositionality emerges in a narrow connectivity-depth sweet spot. Along the connectivity axis, compositionality only appears in some specifically sparse networks, heavily depends on which connections remain rather than on weights' sparsity alone. Along the depth axis, compositionality emerges within a narrow, target-dependent regime, peaking at specific depths, while both shallower and deeper networks fail. When either the depth or connectivity condition is violated, gradient descent silently converges to fractured solutions rather than compositional ones. To discover and exploit this emergence, we introduce (i) similarity-based pruning (SP) to recover compositional connectivity and (ii) a heuristic depth predictor to estimate where compositionality is most likely to appear. Finally, we support these empirical findings with a theoretical framework based on compositional sparsity, volume-ratio arguments, and feature-interference bounds, explaining why compositional solutions are reachable only in a narrow depth-connectivity regime.