arXiv:2609.12439v1 Announce Type: cross Abstract: LLM-as-a-judge protocols are commonly debiased by instructing judges to ignore presentation cues such as citation formatting, source labels, and evidence-display style. We show that this intervention can suppress bias while damaging the resolution of the measurement instrument. We introduce TraceJudgeBench, a diagnostic benchmark for auditing citation-like artifacts in RAG and agent-workflow evaluation, covering content-equivalent pairs, citation ablations, correctness conflicts, human-validated soft and moderate quality gaps, prompt-strength ladders, decoupled judging, and a controlled workflow-ranking probe. Across GPT-5.5, Claude Sonnet 4.6, and DeepSeek V4-Flash, stronger anti-citation prompts reduce worse-cited wins from up to 50.5% to 0%; yet some operating points already convert validated moderate-gap decisions into Tie before the strict stress-test endpoint, while correctness-conflict accuracy remains at or above 93.0%. A second, 50-pair FinQA moderate-gap construction reproduces the qualitative frontier, and open-weight Qwen2.5-14B-Instruct-AWQ and Gemma-3-12B-IT runs reproduce the central HotpotQA frontier. TRACE-style decoupling recovers 96.5-100.0% better-plain resolution across the reported settings. Human validation separates three meanings of Tie: correct equivalence Tie, calibrated soft-boundary Tie, and resolution-destroying Tie on validated quality gaps. We frame debiasing as a measurement intervention whose bias suppression, resolution retention, Tie cost, and protocol cost must be reported jointly. The supplementary artifact contains benchmark splits, prompts, raw judge outputs, validation summaries, and analysis.

arXiv:2603.06651v1 Announce Type: cross Abstract: Euclidean gradient descent algorithms barely capture the geometry of objective function-induced hypersurfaces and risk driving update trajectories off the hypersurfaces. Riemannian gradient descent algorithms address these issues but fail to represent complex hypersurfaces via a single classic manifold. We propose geodesic gradient descent (GGD), a generic and learning-rate-free Riemannian gradient descent algorithm. At each iteration, GGD uses an n-dimensional sphere to approximate a local neighborhood on the objective function-induced hypersurface, adapting to arbitrarily complex geometries. A tangent vector derived from the Euclidean gradient is projected onto the sphere to form a geodesic, ensuring the update trajectory stays on the hypersurface. Parameter updates are performed using the endpoint of the geodesic. The maximum step size of the gradient in GGD is equal to a quarter of the arc length on the n-dimensional sphere, thus eliminating the need for a learning rate. Experimental results show that compared with the classic Adam algorithm, GGD achieves test MSE reductions ranging from 35.79% to 48.76% for fully connected networks on the Burgers' dataset, and cross-entropy loss reductions ranging from 3.14% to 11.59% for convolutional neural networks on the MNIST dataset.

arXiv:2507.00790v4 Announce Type: replace-cross Abstract: Unified image restoration is a significantly challenging task in low-level vision. Existing methods either make tailored designs for specific tasks, limiting their generalizability across various types of degradation, or rely on training with paired datasets, thereby suffering from closed-set constraints. To address these issues, we propose a novel, dataset-free, and unified approach through recurrent posterior sampling utilizing a pretrained latent diffusion model. Our method incorporates the multimodal understanding model to provide sematic priors for the generative model under a task-blind condition. Furthermore, it utilizes a lightweight module to align the degraded input with the generated preference of the diffusion model, and employs recurrent refinement for posterior sampling. Extensive experiments demonstrate that our method outperforms state-of-the-art methods, validating its effectiveness and robustness. Our code and data are available at https://github.com/AMAP-ML/LD-RPS.

Nature, Published online: 10 March 2026; doi:10.1038/s41586-026-10351-8

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