arXiv:2605. 28983v2 Announce Type: replace-cross Abstract: In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights.
By Jose Marie Antonio Mi\~noza, Erika Fille T. Legara, Christopher P. Monterola
arXiv:2602. 18849v2 Announce Type: replace-cross Abstract: We develop a sensitivity analysis for transformer attention in a geometry aligned with tokenwise computation.
By Seyed Morteza Emadi
arXiv:2607. 20171v3 Announce Type: replace-cross Abstract: A second order finite volume scheme rests on two local quantities: a gradient reconstructed in each cell, and a limiter which scales it down where the reconstruction would overshoot.
By Denis Gueyffier (ONERA -- Institut Polytechnique de Paris)
arXiv:2606. 09929v1 Announce Type: cross Abstract: Physical reservoir computing harnesses nonlinear mechanical dynamics but, by convention, freezes the substrate and trains only a linear readout, presuming the substrate is not usefully trainable.
By Caleb Munigety
arXiv:2607. 13380v1 Announce Type: new Abstract: Predictive Coding (PC) offers a biologically motivated alternative to backpropagation via local weight updates, yet routing error between layers still relies on an autograd Jacobian-transpose ($J^\top$) product - the last non-local operation in PC.
By Junlong Shen, Xingyu Li
arXiv:2605. 01928v2 Announce Type: replace Abstract: We optimize losses that jump: spiking thresholds, quantized layers, and discrete routing put jumps in the forward pass, where backpropagation does not apply.
By An T. Le