arXiv:2605. 07914v2 Announce Type: replace Abstract: Sharpness-aware and gradient-alignment methods have been shown to improve generalization, however each family of methods targets a single geometric property of the loss landscape, while ignoring the other.
arXiv:2608. 04382v1 Announce Type: new Abstract: Gradient descent has been of particular interest in modern machine learning beyond sole focus on optimization.
arXiv:2606. 28662v1 Announce Type: cross Abstract: The flatness hypothesis suggests that flatness of the loss landscape, as measured by the eigenvalues of the loss Hessian, correlates with better neural network generalization.
arXiv:2602. 02877v2 Announce Type: replace Abstract: This paper studies optimization for a family of problems termed $\textbf{compositional entropic risk minimization}$, in which each data's loss is formulated as a Log-Expectation-Exponential (Log-E-Exp) function.
arXiv:2606. 31524v1 Announce Type: cross Abstract: The Self-Improving Alignment (SAIL) algorithm addresses distribution shift by reducing a bilevel formulation of the problem to an efficient, single-level method.
arXiv:2606. 20469v1 Announce Type: new Abstract: A widely held intuition in deep learning is that stochastic gradient descent (SGD) implicitly favors flat minima and that flat minima generalize better, but standard Euclidean measures of flatness such as the trace or maximum eigenvalue of the loss Hessian are not invariant under reparametrizations that preserve the network function, which undermines the theoretical foundations of this narrative.
arXiv:2605. 24395v2 Announce Type: replace Abstract: Alignment plays a fundamental role in many machine learning problems, such as multi-network analysis, multimodal learning, and point cloud registration.
arXiv:2607. 22004v1 Announce Type: new Abstract: Energy natural gradient descent (ENGD) aligns parameter updates with the curvature of an underlying function-space energy, but existing formulations assume an unconstrained Euclidean parameter domain.
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
arXiv:2606. 16454v1 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) enables efficient adaptation of large pre-trained models to downstream tasks by parameterizing weight updates with low-rank matrices.
arXiv:2607. 26247v1 Announce Type: new Abstract: Low-rank adaptation (LoRA) fine-tunes large pretrained models at a fraction of the cost of full fine-tuning, but its performance depends strongly on how the adapters are initialized.
arXiv:2606. 30523v1 Announce Type: new Abstract: Covariance matrices serve as compact descriptors of feature distributions in many machine-learning pipelines, including domain adaptation and Gaussian embeddings.
arXiv:2602. 05600v2 Announce Type: replace Abstract: Stochastic Gradient Descent (SGD) introduces anisotropic noise that is correlated with the local curvature of the loss landscape, thereby biasing optimization toward flat minima.