Ansh Tiwari

Tatsuhiro Nakamori, Laura Gomezjurado Gonzalez, Ganesh Talluri et al.

Low-rank gradient compression reduces communication in distributed training by representing updates with rank-$r$ factors. Dion is a recent method that approximates Muon, a spectral optimizer that orthogonalizes momentum, using one step of power iteration followed by column normalization (rescaling each column of the right factor to unit length). This makes it compatible with fully sharded data parallel training, but it converges more slowly than full-rank spectral methods. We show that this gap is geometric: column normalization does not yield the rank-$r$ polar factor that Muon implicitly targets, so the resulting direction violates the dual-norm constraint of the low-rank spectral geometry, and the rate picks up an extra factor of $\sqrt{r}$ even though the low-rank approximation of the gradient itself is accurate. The same mismatch enters the smoothness term and the error-feedback recursion in the analysis, which has a knock-on effect on empirical performance. We propose Orth-Dion, which replaces column normalization with QR orthogonalization of the right factor. Under non-Euclidean smoothness, with $L_r$ the curvature constant along rank-$r$ directions, Orth-Dion attains rate $O(\sqrt{L_r/T})$, matching exact spectral methods at the same per-step communication cost as Dion. The proof removes the bounded-drift assumption common in prior error-feedback analyses via a self-consistent fixed-point argument, and uses a time-averaged contraction that only requires the error sequence to contract on average rather than at every step. Experiments on large-scale language model pre-training validate the predicted $\sqrt{r}$ scaling and show that Orth-Dion closes the convergence gap to Muon at Dion's communication cost.

Ansh Tiwari, Ayush Chauhan

Spiking neural networks (SNNs) promise energy-efficient artificial intelligence on neuromorphic hardware but struggle with tasks requiring both fast adaptation and long-term memory, especially in continual learning. We propose Local Timescale Gating (LT-Gate), a neuron model that combines dual time-constant dynamics with an adaptive gating mechanism. Each spiking neuron tracks information on a fast and a slow timescale in parallel, and a learned gate locally adjusts their influence. This design enables individual neurons to preserve slow contextual information while responding to fast signals, addressing the stability-plasticity dilemma. We further introduce a variance-tracking regularization that stabilizes firing activity, inspired by biological homeostasis. Empirically, LT-Gate yields significantly improved accuracy and retention in sequential learning tasks: on a challenging temporal classification benchmark it achieves about 51 percent final accuracy, compared to about 46 percent for a recent Hebbian continual-learning baseline and lower for prior SNN methods. Unlike approaches that require external replay or expensive orthogonalizations, LT-Gate operates with local updates and is fully compatible with neuromorphic hardware. In particular, it leverages features of Intel's Loihi chip (multiple synaptic traces with different decay rates) for on-chip learning. Our results demonstrate that multi-timescale gating can substantially enhance continual learning in SNNs, narrowing the gap between spiking and conventional deep networks on lifelong-learning tasks.