SNLP: Layer-Parallel Inference via Structured Newton Corrections

TL;DR

SNLP introduces a layer-parallel inference framework for Transformers that reduces latency and improves perplexity by using structured Newton corrections and regularization, enabling practical speedups.

Contribution

The paper proposes Structured Newton Layer Parallelism (SNLP), a novel method replacing exact Jacobians with surrogate dynamics to enable layer-parallel inference in Transformers.

Findings

SNLP improves layer-parallel compatibility and reduces perplexity by up to 23.4%.

On a 0.5B Nanochat model, SNLP achieves 2.3x speedup during inference.

SNLP regularization enhances the accuracy of structured Newton iterations, benefiting both training and inference.

Abstract

Autoregressive language models execute Transformer layers sequentially, creating a latency bottleneck that is not removed by conventional tensor or pipeline parallelism. We study whether this layerwise dependency can be relaxed by treating the hidden-state trace across layers as the solution of a nonlinear residual equation and solving it with parallel Newton-style updates. While this view is principled, exact Newton corrections require expensive Jacobian-vector products and naive fixed-point iterations are unstable on trained Transformers. We introduce Structured Newton Layer Parallelism (SNLP), a training and inference framework that replaces exact layer Jacobians with cheap architecture-induced surrogate dynamics. In residual Transformers, this yields Identity Newton (IDN), where the correction reduces to a prefix-sum-like update; in mHC-style architectures, HC Newton (HCN) uses the model's residual mixing matrix. We further introduce SNLP-aware regularization, which trains models to make one or a few structured Newton iterations accurately approximate the sequential forward. Experiments on nanochat-scale Transformers show that SNLP regularization improves layer-parallel compatibility and can also improve standard sequential perplexity, reducing baseline PPL by 4.7%-23.4%. At inference time, SNLP combined with layer fusion and chunkwise decomposition achieves practical wall-clock speedups: on a 0.5B Nanochat model, it reaches 2.3x speedup while still improving PPL by 6.1%. These results suggest that layer-parallel inference is not merely a numerical approximation to sequential execution, but can act as a useful solver-induced inference bias. We also characterize limitations: off-the-shelf pretrained models are less amenable to this procedure, and exact convergence recovers the sequential computation rather than providing monotonic inference-time scaling.