SPINAL -- Scaling-law and Preference Integration in Neural Alignment Layers
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.
6966aa0ec5e371f6b235cf66
Arion Das
6966aa0ec5e371f6b235cf67
Partha Pratim Saha
6966aa0ec5e371f6b235cf68
Amit Dhanda
6966aa0ec5e371f6b235cf69
Vinija Jain
6966aa0ec5e371f6b235cf6a
Aman Chadha
claimed_verified
2026-01-14T09:52:40.360Z
63a4754927f1f64ed7238dac
https://cdn-avatars.huggingface.co/v1/production/uploads/63a4754927f1f64ed7238dac/aH-eJF-31g4vof9jv2gmI.jpeg
Aman Chadha
amanchadha
user
amanchadha
6966aa0ec5e371f6b235cf6b
Amitava Das
SPINAL -- Scaling-law and Preference Integration in Neural Alignment Layers
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.
SPINAL diagnoses how DPO alignment reshapes representations layer by layer, revealing geometric localization of preference gradients in final decoder blocks and enabling practical auditing of alignment progress.
Direct Preference Optimization RLHF pairwise preferences neural alignment layers depth trace contraction score transport score spectral decay token distribution representation space geometric localization alignment auditing