arXiv AI
Oct 26
Implicit Neural Representations for Variational Problems on Graphons
arXiv:2610. 32147v1 Announce Type: cross Abstract: We propose a neural exploratory framework for variational problems over graphons, i.
Is Variational Monte Carlo Robust? Sharp Moment Thresholds and Heavy-tailed Stochastic Optimization
arXiv:2606. 26009v1 Announce Type: new Abstract: Variational Monte Carlo (VMC) is a central algorithm in electronic structure theory and has gained renewed importance through modern neural-network ans\"atze such as FermiNet.
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arXiv Machine Learning
Jun 15
Direct/adaptive-mixture phase-gradient learning for neural-network quantum states with complex phase structure
arXiv:2606. 13912v1 Announce Type: cross Abstract: Neural-network quantum states (NQS) are a leading variational tool for quantum many-body physics, yet their optimization is fragile whenever the ground state carries a non-trivial sign or complex phase structure, a situation generic to gauge fields, broken time-reversal symmetry, and fermionic statistics.
arXiv Machine Learning
Sep 14
Almost Sure Convergence Analysis of Stochastic Gradient Methods with Clipping and Additive Noise
The paper proves that stochastic gradient descent with gradient clipping and additive Gaussian noise (SGD‑CN) converges almost surely under smoothness and bounded noise assumptions, given standard decaying step sizes. The analysis extends to momentum variants such as the stochastic heavy ball and Nesterov's accelerated gradient, showing that careful energy constructions yield similar guarantees. These results provide stronger theoretical foundations for understanding the pathwise behaviour of clipped stochastic gradient methods in both convex and nonconvex regimes.
arXiv Machine Learning
Sep 30
High-Probability Convergence of Clipped SGD under Heavy-Tailed Noise and $(L_0,L_1)$-Smoothness
arXiv:2505.20817v3 Announce Type: replace-cross Abstract: Gradient clipping is widely used in language-model training to control heavy-tailed gradient noise and can improve convergence guarantees ove...
arXiv Statistics ML
Sep 30
A stochastic subgradient method with optimal failure exponent
arXiv:2609.37425v1 Announce Type: cross Abstract: Fix a target accuracy $\varepsilon$, a gradient-noise level $s$, and a horizon $N$. We wish to design algorithms which minimize the probability of ob...
arXiv Machine Learning
Sep 22
Gradient-estimator design overcomes trainability barriers in neural-network-based variational optimization
arXiv:2609.22342v1 Announce Type: cross Abstract: Neural networks provide expressive representations for scientific computing. However, even sufficiently expressive networks can suffer training failu...
arXiv Machine Learning
Oct 12
NucleoNet: A Nuclear-Aware Determinant Ansatz for Multi-Geometry Neural Variational Monte Carlo
NucleoNet is a neural‑network variational Monte Carlo ansatz that treats electrons and nuclei as a unified particle set, allowing a single model to be optimized across multiple geometries. The approach uses a shared electron–nucleus backbone to evolve one‑particle and two‑particle representations, with nuclear streams learning representations that condition orbital construction while antisymmetry is enforced only by electronic determinants. On small‑molecule benchmarks, NucleoNet matches the accuracy of established neural‑wavefunction baselines with far fewer parameters and successfully describes dissociation curves and minimum‑energy paths for several systems, demonstrating that a compact wavefunction can capture molecular geometries with a single set of parameters.
arXiv Machine Learning
Jul 3
One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective
arXiv:2607. 02292v1 Announce Type: new Abstract: Neural quantum states (NQS) provide a flexible and scalable framework for approximating quantum many-body wavefunctions.
arXiv Machine Learning
Oct 5
Can SGD Handle Heavy-Tailed Noise?
arXiv:2508.04860v2 Announce Type: replace-cross Abstract: Stochastic Gradient Descent (SGD) is a cornerstone of large-scale optimization, yet its theoretical behavior under heavy-tailed noise -- comm...
arXiv Machine Learning
Oct 5
Trade-off Functions for DP-SGD with Subsampling based on Random Allocation: Tight Upper and Lower Bounds
arXiv:2605. 06259v3 Announce Type: replace Abstract: Within the $f$-DP framework, we derive a tight analysis of the trade-off function for Differentially Private Stochastic Gradient Descent (DP-SGD) with subsampling based on random allocation in which each sample is independently assigned to exactly one of $M$ minibatches per epoch, each minibatch corresponding to one of the $M$ SGD rounds within a single epoch.
arXiv AI
Oct 22
Graph-Theoretic Formulation of Hamiltonian and Ground-State Sign Structures in Heisenberg Antiferromagnets
The paper presents a graph-theoretic framework for analyzing Heisenberg antiferromagnets, where the Hamiltonian in a fixed-magnetization sector is represented as a constant minus the weighted Laplacian of a Hilbert graph (HG). The ground-state energy is linked to the largest eigenvalue of this Laplacian, equivalent to a spectral relaxation of weighted Max‑Cut on the HG, while the phase-dependent part of the variational energy maps to an antiferromagnetic XY model on the same graph. Restricting to real variational states reduces the problem to an Ising model, and the optimal sign structure of the ground state can be recovered in polynomial time from the HG weights, with the bipartiteness of the HG determining whether a diagonal sign transformation can eliminate all positive off-diagonal elements.
arXiv Machine Learning
Jun 2
Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise
arXiv:2605. 18528v2 Announce Type: replace-cross Abstract: A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized.