arXiv subjects

Kai Lion

Publications and source records attributed to Kai Lion.

6 recordsLinked to original sources

arXiv2026

Muown Implicitly Performs Angular Step-size Decay

Matrix-aware optimizers such as Muon and Muown have recently shown strong empirical performance for pre-training Transformers. In particular, Muown separates each weight matrix into row magnitudes and an un-normalized direction variable, updating the former with Adam and the latter with Muon. We show that the directional update of Muown is equivalent to a Riemannian step on the normalized directions, while the magnitude of the un-normalized parameterization only modulates the angular step size. This explains the step-size stability of Muown and suggests making the angular step size explicit. The resulting method, AngularMuown, optimizes directly over the normalized directions and uses a schedulable angular multiplier decoupled from the radial magnitude update. AngularMuown improves over Muown and, at the time of writing, a preliminary version is leading the per-optimizer category of the modded nanoGPT speedrunning competition. Further experiments on Qwen2-0.5B, and 1.1B parameter mixture-of-experts models confirm the algorithm scales beyond small models. An implementation of the algorithm is available at https://github.com/fhueb/angular-muown

cs.LG↗

arXiv2026

Muown: Row-Norm Control for Muon Optimization

Muon has emerged as a strong competitor to AdamW for language model pre-training, yet its behavior at scale is sensitive to weight decay. Recent work has observed that, for Muon without decoupled weight decay, the spectral norm of weight matrices drifts upward over training. Through a decomposition of the spectral norm into a row-magnitude factor and a row-coherence factor, we identify the former as the empirical driver of this drift under Muon, while the latter remains well-behaved along the trajectory. Motivated by this diagnosis, we introduce Muown, a drop-in replacement for Muon that treats the row-magnitude vector as an explicit optimizer variable, updating it under the $\ell_\infty$ geometry induced by the decomposition, while applying Muon unchanged to the remaining direction component. We prove that Muown attains the optimal non-convex rates in both deterministic and stochastic regimes under a dual norm aligned with the underlying geometries and with a stochastic noise coefficient that empirically remains below that of Muon throughout training. Across GPT-style pre-training on FineWeb-Edu with model sizes from 124M up to 2.7B parameters, Muown improves perplexity over Muon, SOAP, AdamW, and Lion. It also widens the plateau of near-optimal learning rates across model scales, reduces sensitivity to weight decay, and avoids the spectral norm drift at negligible step-time overhead when appropriately sharded.

cs.LG↗

arXiv2026

Integrated electro-optic attention nonlinearities for transformers

Transformers have emerged as the dominant neural-network architecture, achieving state-of-the-art performance in language processing and computer vision. At the core of these models lies the attention mechanism, which requires a nonlinear, non-negative mapping using the Softmax function. However, although Softmax operations account for less than 1% of the total operation count, they can disproportionately bottleneck overall inference latency. Here, we use thin-film lithium niobate (TFLN) Mach-Zehnder modulators (MZMs) as analog nonlinear computational elements to drastically reduce the latency of nonlinear computations. We implement electro-optic alternatives to digital Softmax and Sigmoid, and evaluate their performance in Vision Transformers and Large Language Models. Our system maintains highly competitive accuracy, even under aggressive 4-bit input-output quantization of the analog units. We further characterize system noise at encoding speeds up to 10 GBaud and assess model robustness under various noise conditions. Our findings suggest that TFLN modulators can serve as nonlinear function units within hybrid co-packaged hardware, enabling high-speed and energy-efficient nonlinear computation.

cs.LG↗

arXiv2025

Optical Computing with Spectrally Multiplexed Features in Complex Media

Artificial intelligence (AI) has rapidly evolved into a critical technology; however, electrical hardware struggles to keep pace with the exponential growth of AI models. Free space optical hardware provides alternative approaches for large-scale optical processing, and in-memory computing, with applications across diverse machine learning tasks. Here, we explore the use of broadband light scattering in free-space optical components, specifically complex media, which generate uncorrelated optical features at each wavelength. By treating individual wavelengths as independent predictors, we demonstrate improved classification accuracy through in-silico majority voting, along with the ability to estimate uncertainty without requiring access to the model's probability outputs. We further demonstrate that linearly combining multiwavelength features, akin to spectral shaping, enables us to tune output features with improved performance on classification tasks, potentially eliminating the need for multiple digital post-processing steps. These findings illustrate the spectral multiplexing or broadband advantage for free-space optical computing.

physics.optics↗

arXiv2025

PoLAR: Polar-Decomposed Low-Rank Adapter Representation

We show that low-rank adaptation of large-scale models suffers from a low stable rank that is well below the linear algebraic rank of the subspace, degrading fine-tuning performance. To mitigate the underutilization of the allocated subspace, we propose PoLAR, a parameterization inspired by the polar decomposition that factorizes the low-rank update into two direction matrices constrained to Stiefel manifolds and an unconstrained scale matrix. Our theory shows that PoLAR yields an exponentially faster convergence rate on a canonical low-rank adaptation problem. Pairing the parameterization with Riemannian optimization leads to consistent gains on three different benchmarks testing general language understanding, commonsense reasoning, and mathematical problem solving with base model sizes ranging from 350M to 27B.

cs.LG↗

arXiv2024

How Good is a Single Basin?

The multi-modal nature of neural loss landscapes is often considered to be the main driver behind the empirical success of deep ensembles. In this work, we probe this belief by constructing various "connected" ensembles which are restricted to lie in the same basin. Through our experiments, we demonstrate that increased connectivity indeed negatively impacts performance. However, when incorporating the knowledge from other basins implicitly through distillation, we show that the gap in performance can be mitigated by re-discovering (multi-basin) deep ensembles within a single basin. Thus, we conjecture that while the extra-basin knowledge is at least partially present in any given basin, it cannot be easily harnessed without learning it from other basins.

cs.LG↗