SNLP: Layer-Parallel Inference via Structured Newton Corrections

2026-05-18

AI Summary

This work addresses the inference latency in autoregressive language models caused by the sequential execution of Transformer layers, which is difficult to mitigate with conventional parallelization techniques. The authors propose Structured Newton Layer Parallelism (SNLP), a framework that models cross-layer hidden states as a system of nonlinear residual equations and leverages structured Newton iterations to enable inter-layer parallel inference. By exploiting architecture-induced surrogate dynamics, SNLP avoids costly exact Jacobian computations, while introducing SNLP-aware regularization to enhance approximation accuracy. Evaluated on a 0.5B-parameter NanoChat model, the method achieves a 2.3× speedup in inference with a 6.1% reduction in perplexity; further regularization yields an additional 4.7%–23.4% improvement in standard sequence perplexity, demonstrating the effectiveness of layer-parallel inference as a solver-induced inductive bias.

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.

Problem

• layer-parallel inference
• autoregressive language models
• Transformer latency
• nonlinear residual equation
• sequential dependency

Innovation

• layer-parallel inference
• structured Newton methods
• Transformer acceleration
• SNLP regularization
• nonlinear residual equation