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Sharpness-aware minimization (SAM) encourages flat minima by perturbing parameters along directions of high loss curvature, but treats all p… (see more)arameter directions uniformly, ignoring the underlying loss geometry. We introduce LLQR+SAM, which combines SAM with a learned preconditioner obtained from the recently proposed LLQR framework, a second-order method that recasts steepest descent as a layerwise linear-quadratic regulator problem. The preconditioner is updated sparsely and maintained as a slow exponential moving average, so it captures a smoothed, low-resolution picture of the loss landscape geometry. The SAM perturbation then operates on top of this learned geometry, probing curvature at a faster timescale. We show that this two-timescale structure is not merely a computational convenience: theoretically, the preconditioner amplifies the SAM escape signal in directions that are flat under the average geometry but locally sharp (potholes). Wide, flat basins, by contrast, remain stable. Empirically, LLQR+SAM gives consistent gains over both SAM and LLQR alone across standard vision and sequence modeling benchmarks, supporting the view that slow learned geometry and fast sharpness correction are genuinely complementary.
When training neural networks, dying neurons -- units becoming inactive or saturated -- are traditionally seen as harmful. This paper sheds … (see more)new light on this phenomenon. By exploring the impact of various hyperparameter configurations on dying neurons during training, we gather insights on how to improve upon sparse training approaches to pruning. We introduce Demon Pruning (DemP), a method that controls the proliferation of dead neurons through a combination of noise injection on active units and a one-cycle schedule regularization strategy, dynamically leading to network sparsity. Experiments on CIFAR-10 and ImageNet datasets demonstrate that DemP outperforms existing dense-to-sparse structured pruning methods, achieving better accuracy-sparsity tradeoffs and accelerating training by up to 3.56