analiza aiqbench
This research introduces PolyStep, a forward-only optimizer designed to handle non-differentiable networks containing hard thresholds and discrete operations where standard gradients fail. By leveraging optimal transport theory to derive update directions from polytope probes, the method achieves significant accuracy gains on tasks involving spiking neurons and policy search without requiring backpropagation through discontinuities. The study provides a rigorous theoretical foundation for training discrete models, offering a viable alternative to gradient-free baselines in scenarios with non-smooth loss landscapes.
Training Non-Differentiable Networks via Optimal Transport
arXiv:2605.01928v3 Announce Type: replace Abstract: Hard thresholds, quantization, and discrete routing can produce training losses with flat regions and jumps, where ordinary gradients vanish or are undefined. We introduce PolyStep, a forward-only optimizer that evaluates rotated polytope probes and moves parameter blocks along weighted averages of the probe directions. We derive the weights from one-sided entropic transport and use its uncoupled softmax solution in our primary experiments. Our analysis explains when variation among probe costs produces motion and when that motion decreases the loss. On a regular simplex, nonconstant costs always give a nonzero direction. For monotone ridge losses, the softmax update cannot increase the loss at any positive temperature; a perturbation bound gives sufficient conditions for descent near curved jumps. For bounded measurable losses, we randomize the probe radii and identify an exact smoothing whose gradient equals the expected linear cost-weighted direction up to scale. This identity yields a stationarity bound for an idealized fixed-temperature variant: under regularity and sampling assumptions stronger than those met by our trained configurations, the bound has an $O(T^{-1/2})$ term and a persistent bias floor. We evaluate the practical method on networks with hard operations, discrete optimization, and policy search. On MNIST with hard-threshold spiking neurons, PolyStep reaches $93.0 \pm 0.2\%$, compared with $79.6 \pm 5.2\%$ for the best-tuned gradient-free baseline at matched evaluations. These gains come with a query cost proportional to the search dimension per fresh step, which limits the number of updates available at a fixed budget.
Abstract:Hard thresholds, quantization, and discrete routing can produce training losses with flat regions and jumps, where ordinary gradients vanish or are undefined. We introduce PolyStep, a forward-only optimizer that evaluates rotated polytope probes and moves parameter blocks along weighted averages of the probe directions. We derive the weights from one-sided entropic transport and use its uncoupled softmax solution in our primary experiments. Our analysis explains when variation among probe costs produces motion and when that motion decreases the loss. On a regular simplex, nonconstant costs always give a nonzero direction. For monotone ridge losses, the softmax update cannot increase the loss at any positive temperature; a perturbation bound gives sufficient conditions for descent near curved jumps. For bounded measurable losses, we randomize the probe radii and identify an exact smoothing whose gradient equals the expected linear cost-weighted direction up to scale. This identity yields a stationarity bound for an idealized fixed-temperature variant: under regularity and sampling assumptions stronger than those met by our trained configurations, the bound has an $O(T^{-1/2})$ term and a persistent bias floor. We evaluate the practical method on networks with hard operations, discrete optimization, and policy search. On MNIST with hard-threshold spiking neurons, PolyStep reaches $93.0 \pm 0.2\%$, compared with $79.6 \pm 5.2\%$ for the best-tuned gradient-free baseline at matched evaluations. These gains come with a query cost proportional to the search dimension per fresh step, which limits the number of updates available at a fixed budget.
95 pages, 29 tables, 8 figures. Accepted at Transactions on Machine Learning Research. Code: this https URL
Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE); Robotics (cs.RO); Optimization and Control (math.OC)
arXiv:2605.01928 [cs.LG]
(or arXiv:2605.01928v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.01928 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 361 cuvinte
Subiecte conexe
Implicit Neural Optimal Transport via Fixed-Point Optimization
arXiv · 8 iun. 2026
News
Quantum Computing Report · 7 iun. 2026
J++ Lens: Jacobian Filtering Enables More Faithful Workspace Lenses
LessWrong · 8 oct. 2026
Optimal Transport Dropout for Structured Predictive Uncertainty
arXiv · 30 sept. 2026