EDIS: Diagnosing LLM Reasoning via Entropy Dynamics

Entropy-based confidence signals are increasingly leveraged to improve reasoning in large language models (LLMs), yet existing approaches treat confidence as a static quantity -- typically aggregated over tokens. We show that the \emph{temporal evolution} of confidence during generation carries richer information than aggregate statistics alone. Analyzing token-level entropy trajectories, we identify characteristic patterns distinguishing correct from incorrect reasoning: erroneous solutions exhibit unstable dynamics, including burst spikes (sustained uncertainty growth) and peak-valley spikes (sharp rebounds following transient confidence). These patterns persist across models and training stages, suggesting they reflect intrinsic properties of reasoning failure rather than superficial noise. To formalize this observation, we introduce the Entropy Dynamics Instability Score (\textbf{EDIS}), a trajectory-level metric quantifying instability in entropy evolution. EDIS serves as an effective diagnostic signal for inference-time selection, substantially improving reasoning accuracy, and offers a promising direction for training-time sample curation. Our findings establish entropy dynamics as an underexplored yet informative lens for understanding and improving LLM reasoning.

Improving 3D Finger Traits Recognition via Generalizable Neural Rendering

3D biometric techniques on finger traits have become a new trend and have demonstrated a powerful ability for recognition and anti-counterfeiting. Existing methods follow an explicit 3D pipeline that reconstructs the models first and then extracts features from 3D models. However, these explicit 3D methods suffer from the following problems: 1) Inevitable information dropping during 3D reconstruction; 2) Tight coupling between specific hardware and algorithm for 3D reconstruction. It leads us to a question: Is it indispensable to reconstruct 3D information explicitly in recognition tasks? Hence, we consider this problem in an implicit manner, leaving the nerve-wracking 3D reconstruction problem for learnable neural networks with the help of neural radiance fields (NeRFs). We propose FingerNeRF, a novel generalizable NeRF for 3D finger biometrics. To handle the shape-radiance ambiguity problem that may result in incorrect 3D geometry, we aim to involve extra geometric priors based on the correspondence of binary finger traits like fingerprints or finger veins. First, we propose a novel Trait Guided Transformer (TGT) module to enhance the feature correspondence with the guidance of finger traits. Second, we involve extra geometric constraints on the volume rendering loss with the proposed Depth Distillation Loss and Trait Guided Rendering Loss. To evaluate the performance of the proposed method on different modalities, we collect two new datasets: SCUT-Finger-3D with finger images and SCUT-FingerVein-3D with finger vein images. Moreover, we also utilize the UNSW-3D dataset with fingerprint images for evaluation. In experiments, our FingerNeRF can achieve 4.37% EER on SCUT-Finger-3D dataset, 8.12% EER on SCUT-FingerVein-3D dataset, and 2.90% EER on UNSW-3D dataset, showing the superiority of the proposed implicit method in 3D finger biometrics.