SPINAL -- Scaling-law and Preference Integration in Neural Alignment Layers

TL;DR

SPINAL is a diagnostic tool that analyzes how neural language model alignment reshapes internal representations across layers, revealing that alignment effects are concentrated in the final layers and providing a way to audit and understand model behavior.

Contribution

The paper introduces SPINAL, a novel method for measuring and visualizing the layerwise geometric effects of alignment in large language models, enhancing interpretability and auditability.

Findings

Alignment effects are concentrated in the final decoder layers.

Aligned models show increased contraction and smoother representation transitions.

Unaligned models exhibit higher curvature and more incoherent depth paths.

Abstract

Direct Preference Optimization (DPO) is a principled, scalable alternative to RLHF for aligning large language models from pairwise preferences, but its internal geometric footprint remains undercharacterized, limiting audits, checkpoint comparisons, and failure prediction. We introduce SPINAL (Scaling-law and Preference Integration in Neural Alignment Layers), a diagnostic that measures how alignment reshapes representations across depth by tracing localized structural change layer by layer. Across model families, DPO produces a layerwise calibration effect concentrated in the final decoder blocks (often layers 21-30), where preference gradients most directly affect the next-token distribution. SPINAL encodes each checkpoint as a depth trace over (layer index, contraction score, transport score). The contraction score summarizes how quickly the tail of a layer's spectrum decays (how fast small modes vanish); higher values indicate stronger contraction into fewer effective directions. The transport score summarizes how much the token distribution shifts between adjacent layers using a bounded overlap measure; lower values indicate shorter, smoother steps through representation space. Aligned checkpoints show a late-layer ramp-up in contraction and a smooth reduction in transport, consistent with tightened and stabilized policy mass, while unaligned models trace higher-curvature, more entropic, and geometrically incoherent depth paths. Overall, alignment is geometrically localized: the final layers encode the dominant preference-induced corrections. SPINAL turns this localization into a practical audit signal, quantifying where alignment concentrates, how strongly it manifests, and when it begins to destabilize during training.