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

arXiv: https://arxiv.org/abs/2601.06238 · HTML: https://mlsanity.com/paper/2601.06238/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 8 of 8)

- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Traditional and Heavy-Tailed Self Regularization in Neural Network Models](https://mlsanity.com/paper/1901.08276/) (2019)
- [What Makes and Breaks Safety Fine-tuning? A Mechanistic Study](https://mlsanity.com/paper/2407.10264/) (2024)
- [The Hidden Dimensions of LLM Alignment: A Multi-Dimensional Analysis of Orthogonal Safety Directions](https://mlsanity.com/paper/2502.09674/) (2025)
- [Alignment Quality Index (AQI) : Beyond Refusals: AQI as an Intrinsic Alignment Diagnostic via Latent Geometry, Cluster Divergence, and Layer wise Pooled Representations](https://mlsanity.com/paper/2506.13901/) (2025)

## Built on by (most cited first, 1 of 1)

- [HeadEdit: Calibrating Language Model Behavior Through the Frozen Unembedding Matrix](https://mlsanity.com/paper/2610.01170/) (2026)

## Abstract (arXiv)

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.