Deyuan Liu
Publications
Gradients Must Earn Their Influence: Unifying SFT with Generalized Entropic Objectives
Standard negative log-likelihood (NLL) for Supervised Fine-Tuning (SFT) applies uniform token-level weighting. This rigidity creates a two-fold failure mode: (i) overemphasizing low-probability targets can amplify gradients on noisy supervision and disrupt robust priors, and (ii) uniform weighting provides weak sharpening when the model is already confident. Existing methods fail to resolve the resulting plasticity--stability dilemma, often suppressing necessary learning signals alongside harmful ones. To address this issue, we unify token-level SFT objectives within a generalized deformed-log family and expose a universal gate $\times$ error gradient structure, where the gate controls how much the model trusts its current prediction. By employing the Cayley transform, we map the model's continuously evolving uncertainty onto a continuous focus trajectory, which enables seamless interpolation between scenarios involving uncertain novel concepts and those involving well-established knowledge. We then introduce Dynamic Entropy Fine-Tuning (DEFT), a parameter-free objective that modulates the trust gate using distribution concentration (Rényi-2 entropy) as a practical proxy for the model's predictive state. Extensive experiments and analyses demonstrate that DEFT achieves a better balance between exploration and exploitation, leading to improved overall performance.
Beyond Confidence: The Rhythms of Reasoning in Generative Models
Large Language Models (LLMs) exhibit impressive capabilities yet suffer from sensitivity to slight input context variations, hampering reliability. Conventional metrics like accuracy and perplexity fail to assess local prediction robustness, as normalized output probabilities can obscure the underlying resilience of an LLM's internal state to perturbations. We introduce the Token Constraint Bound ($δ_{\mathrm{TCB}}$), a novel metric that quantifies the maximum internal state perturbation an LLM can withstand before its dominant next-token prediction significantly changes. Intrinsically linked to output embedding space geometry, $δ_{\mathrm{TCB}}$ provides insights into the stability of the model's internal predictive commitment. Our experiments show $δ_{\mathrm{TCB}}$ correlates with effective prompt engineering and uncovers critical prediction instabilities missed by perplexity during in-context learning and text generation. $δ_{\mathrm{TCB}}$ offers a principled, complementary approach to analyze and potentially improve the contextual stability of LLM predictions.