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This study reveals a fundamental shift in how transformer encoders represent identity prompts during instruction tuning, moving from direction-based to magnitude-based geometric encoding. The finding that multimodal RLHF specifically drives this reorganization while standard SFT and distillation do not offers critical insight into the architectural changes required for robust persona retention.
From Direction to Magnitude: How Multimodal Instruction-Tuning Reorganizes the Geometric Encoding of Identity-Specifying Prompts in Transformer Hidden States
arXiv:2607.09842v2 Announce Type: replace-cross Abstract: We investigate whether identity-specifying system prompts produce statistically distinguishable geometric fingerprints in the hidden-state trajectories of four open-weight transformer language models spanning four post-training regimes: no training (Gemma-4-E4B base), multimodal RLHF (Gemma-4-E4B-it), RL distillation (DeepSeek-R1-Distill-Qwen-7B), and SFT (Qwen2.5-7B-Instruct). Three prompt conditions (an identity-specifying axis prompt, a length-matched generic-assistant prompt, and a 26-token vanilla baseline) are compared via five geometric metrics, principally the 1-Wasserstein distance between edge-wise distributions of Ollivier-Ricci curvature on k-NN trajectory graphs. Claims rest on trajectory-level permutation tests with multiple geometric controls (teacher-forced content controls, temporal-chain vs k-NN topology, ABT-projected k-NN, angular vs Euclidean graph construction, B=5000 permutations on borderline statistics). The central finding is a qualitative reorganization of identity encoding across the instruction-tuning boundary: in the base model the fingerprint is direction-coded (separation 0.034, p=0.002 under angular k-NN); in the multimodal instruction-tuned model it migrates into the magnitude (angular separation collapses to p=0.439 while Euclidean survives at p=0.042, and the mean norm of the first generated state inverts its length-ordering, being lowest for the identity prompt). This direction-to-magnitude reorganization is specific to the multimodal instruction-tuning regime, absent under RL distillation and SFT. A teacher-forced control attributes ~30% of the free-running cosine signal to prompt-driven effects. We position W_1 on edge-wise Ollivier-Ricci distributions on k-NN trajectory graphs as a methodological contribution of independent interest.
Abstract:We investigate whether identity-specifying system prompts produce statistically distinguishable geometric fingerprints in the hidden-state trajectories of four open-weight transformer language models spanning four post-training regimes: no training (Gemma-4-E4B base), multimodal RLHF (Gemma-4-E4B-it), RL distillation (DeepSeek-R1-Distill-Qwen-7B), and SFT (Qwen2.5-7B-Instruct). Three prompt conditions (an identity-specifying axis prompt, a length-matched generic-assistant prompt, and a 26-token vanilla baseline) are compared via five geometric metrics, principally the 1-Wasserstein distance between edge-wise distributions of Ollivier-Ricci curvature on k-NN trajectory graphs. Claims rest on trajectory-level permutation tests with multiple geometric controls (teacher-forced content controls, temporal-chain vs k-NN topology, ABT-projected k-NN, angular vs Euclidean graph construction, B=5000 permutations on borderline statistics). The central finding is a qualitative reorganization of identity encoding across the instruction-tuning boundary: in the base model the fingerprint is direction-coded (separation 0.034, p=0.002 under angular k-NN); in the multimodal instruction-tuned model it migrates into the magnitude (angular separation collapses to p=0.439 while Euclidean survives at p=0.042, and the mean norm of the first generated state inverts its length-ordering, being lowest for the identity prompt). This direction-to-magnitude reorganization is specific to the multimodal instruction-tuning regime, absent under RL distillation and SFT. A teacher-forced control attributes ~30% of the free-running cosine signal to prompt-driven effects. We position W_1 on edge-wise Ollivier-Ricci distributions on k-NN trajectory graphs as a methodological contribution of independent interest.
16 pages, 8 tables. Working draft v0.3. Uses Ollivier-Ricci curvature and edge-wise Wasserstein-1 as primary geometric statistic; four models (Gemma-4-E4B, Gemma-4-E4B-it, DeepSeek-R1-Distill-Qwen-7B, Qwen2.5-7B-Instruct)
Machine Learning (cs.LG); Computation and Language (cs.CL)
arXiv:2607.09842 [cs.LG]
(or arXiv:2607.09842v2 [cs.LG] for this version)
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