Circuit Claims Depend on What Is Extracted and How It Is Compared

Circuit extraction identifies a small set of model components whose presence preserves a target behavior under ablation, and the resulting circuit is often read as the mechanism behind that behavior. We argue that this reading is under-determined: preserving behavior does not single out one circuit, because the claim it supports depends on which circuit is reported and how two circuits are compared. We make this concrete in a synthetic Lean tactic-prediction benchmark -- predicting the next step of a proof -- where fixed proof rules with randomized surface form let differences between extracted circuits be attributed to these choices rather than to the task. Across dense and weight-sparse checkpoints (most weights constrained to zero) of the same transformer, evaluated on atomic (single-rule) and compositional (multi-rule) proofs, we vary which extracted object is reported (a compact prediction-preserving circuit, a broader graph that also keeps surrounding read, write, and routing structure, or the smallest subgraph meeting a post-ablation loss threshold), and whether each attention head's query and key are represented jointly or separately. Exact component-to-component edge overlap is low and sensitive to these choices, at times dropping to a random baseline, while two coarser summaries stay stable: the set of selected attention heads, and the circuit-size ranking of conditions that differ in which supervised checkpoint initializes reinforcement learning (RL). The largest accuracy gains from RL on compositional proofs come with the most structure beyond the atomic circuits. A circuit-level claim is therefore well defined only once one states which circuit is reported, the pruning threshold used to extract it, and the level at which circuits are compared. We distill these requirements into a reporting practice for circuit-extraction studies.

FormalJudge: A Neuro-Symbolic Paradigm for Agentic Oversight

As LLM-based agents increasingly operate in high-stakes domains with real-world consequences, ensuring their behavioral safety becomes paramount. The dominant oversight paradigm, LLM-as-a-Judge, faces a fundamental dilemma: how can probabilistic systems reliably supervise other probabilistic systems without inheriting their failure modes? We argue that formal verification offers a principled escape from this dilemma, yet its adoption has been hindered by a critical bottleneck: the translation from natural language requirements to formal specifications. This paper bridges this gap by proposing , a neuro-symbolic framework that employs a bidirectional Formal-of-Thought architecture: LLMs serve as specification compilers that top-down decompose high-level human intent into atomic, verifiable constraints, then bottom-up prove compliance using Dafny specifications and Z3 Satisfiability modulo theories solving, which produces mathematical guarantees rather than probabilistic scores. We validate across three benchmarks spanning behavioral safety, multi-domain constraint adherence, and agentic upward deception detection. Experiments on 7 agent models demonstrate that achieves an average improvement of 16.6% over LLM-as-a-Judge baselines, enables weak-to-strong generalization where a 7B judge achieves over 90% accuracy detecting deception from 72B agents, and provides near-linear safety improvement through iterative refinement.

Counter-intuitive: Large Language Models Can Better Understand Knowledge Graphs Than We Thought

Although the method of enhancing large language models' (LLMs') reasoning ability and reducing their hallucinations through the use of knowledge graphs (KGs) has received widespread attention, the exploration of how to enable LLMs to integrate the structured knowledge in KGs on-the-fly remains inadequate. Researchers often co-train KG embeddings and LLM parameters to equip LLMs with the ability of comprehending KG knowledge. However, this resource-hungry training paradigm significantly increases the model learning cost and is also unsuitable for non-open-source, black-box LLMs. In this paper, we employ complex question answering (CQA) as a task to assess the LLM's ability of comprehending KG knowledge. We conducted a comprehensive comparison of KG knowledge injection methods (from triples to natural language text), aiming to explore the optimal prompting method for supplying KG knowledge to LLMs, thereby enhancing their comprehension of KG. Contrary to our initial expectations, our analysis revealed that LLMs effectively handle messy, noisy, and linearized KG knowledge, outperforming methods that employ well-designed natural language (NL) textual prompts. This counter-intuitive finding provides substantial insights for future research on LLMs' comprehension of structured knowledge.

A Radiomics-Incorporated Deep Ensemble Learning Model for Multi-Parametric MRI-based Glioma Segmentation

We developed a deep ensemble learning model with a radiomics spatial encoding execution for improved glioma segmentation accuracy using multi-parametric MRI (mp-MRI). This model was developed using 369 glioma patients with a 4-modality mp-MRI protocol: T1, contrast-enhanced T1 (T1-Ce), T2, and FLAIR. In each modality volume, a 3D sliding kernel was implemented across the brain to capture image heterogeneity: fifty-six radiomic features were extracted within the kernel, resulting in a 4th order tensor. Each radiomic feature can then be encoded as a 3D image volume, namely a radiomic feature map (RFM). PCA was employed for data dimension reduction and the first 4 PCs were selected. Four deep neural networks as sub-models following the U-Net architecture were trained for the segmenting of a region-of-interest (ROI): each sub-model utilizes the mp-MRI and 1 of the 4 PCs as a 5-channel input for a 2D execution. The 4 softmax probability results given by the U-net ensemble were superimposed and binarized by Otsu method as the segmentation result. Three ensemble models were trained to segment enhancing tumor (ET), tumor core (TC), and whole tumor (WT). The adopted radiomics spatial encoding execution enriches the image heterogeneity information that leads to the successful demonstration of the proposed deep ensemble model, which offers a new tool for mp-MRI based medical image segmentation.