Thinking Large Language Models (LLMs) used as judges for pairwise preferences remain noisy at the single-sample level, and common aggregation rules (majority vote, soft self-consistency, or instruction-based self-aggregation) are inconsistent when ties are allowed. We study inference-time compute (ITC) for evaluators that generate n independent thinking-rating samples per item, and propose a principled, distribution-calibrated aggregation scheme. Our method models three-way preferences with a Bradley-Terry-Davidson formulation on rating counts, leveraging both polarity (margin among non-ties) and decisiveness (non-tie rate) to distinguish narrow margins from strong consensus. Across various evaluation benchmarks, our approach consistently reduces MAE and increases pairwise accuracy versus standard baselines, and when evaluated against human-consensus meta-labels, matches or exceeds individual human raters. These results show that carefully allocating ITC and aggregating with distribution-aware methods turns noisy individual model judgments into reliable ratings for evaluation. Thinking large language models (LLMs) are increasingly being employed as automated judges for evaluating the output of other generative systems, a paradigm known as "Thinking-LLM-as-a-Judge" (Saha et al., 2025). This approach offers a scalable and cost-effective alternative to human evaluation, which is often slow and expensive. To mitigate the inherent stochasticity and noise of single-pass judgments, a common strategy is to leverage inference-time compute (ITC) Snell et al. (2024) by generating multiple independent reasoning and rating samples for each item being evaluated. However, the reliability of the final judgment hinges critically on how these multiple outputs are aggregated. Current aggregation methods, such as majority voting (Self-Consistency (Wang et al., 2023b)) or heuristics based on model confidence scores or LLM generated aggregators, are often brittle and statistically suboptimal.

Self-consistency (SC) is a widely used test-time inference technique for improving performance in chain-of-thought reasoning. It involves generating multiple responses, or samples from a large language model (LLM) and selecting the most frequent answer. This procedure can naturally be viewed as a majority vote or empirical mode estimation. Despite its effectiveness, SC is prohibitively expensive at scale when naively applied to datasets, and it lacks a unified theoretical treatment of sample efficiency and scaling behavior. In this paper, we provide the first comprehensive analysis of SC's scaling behavior and its variants, drawing on mode estimation and voting theory. We derive and empirically validate power law scaling for self-consistency across datasets, and analyze the sample efficiency for fixed-allocation and dynamic-allocation sampling schemes. From these insights, we introduce Blend-ASC, a novel variant of self-consistency that dynamically allocates samples to questions during inference, achieving state-of-the-art sample efficiency. Our approach uses 6.8x fewer samples than vanilla SC on average, outperforming both fixed- and dynamic-allocation SC baselines, thereby demonstrating the superiority of our approach in terms of efficiency. In contrast to existing variants, Blend-ASC is hyperparameter-free and can fit an arbitrary sample budget, ensuring it can be easily applied to any self-consistency application.

Hallucinations pose a critical challenge to the real-world deployment of large language models (LLMs) in high-stakes domains. In this paper, we present a framework for stress testing factual fidelity in LLMs in the presence of adversarial nudge. Our framework consists of three steps. In the first step, we instruct the LLM to produce sets of truths and lies consistent with the closed domain in question. In the next step, we instruct the LLM to verify the same set of assertions as truths and lies consistent with the same closed domain. In the final step, we test the robustness of the LLM against the lies generated (and verified) by itself. Our extensive evaluation, conducted using five widely known proprietary LLMs across two closed domains of popular movies and novels, reveals a wide range of susceptibility to adversarial nudges: \texttt{Claude} exhibits strong resilience, \texttt{GPT} and \texttt{Grok} demonstrate moderate resilience, while \texttt{Gemini} and \texttt{DeepSeek} show weak resilience. Considering that a large population is increasingly using LLMs for information seeking, our findings raise alarm.

Detecting hateful content is a challenging and important problem. Automated tools, like machine-learning models, can help, but they require continuous training to adapt to the ever-changing landscape of social media. In this work, we evaluate eight open-source LLMs' capability to detect antisemitic content, specifically leveraging in-context definition. We also study how LLMs understand and explain their decisions given a moderation policy as a guideline. First, we explore various prompting techniques and design a new CoT-like prompt, Guided-CoT, and find that injecting domain-specific thoughts increases performance and utility. Guided-CoT handles the in-context policy well, improving performance and utility by reducing refusals across all evaluated models, regardless of decoding configuration, model size, or reasoning capability. Notably, Llama 3.1 70B outperforms fine-tuned GPT-3.5. Additionally, we examine LLM errors and introduce metrics to quantify semantic divergence in model-generated rationales, revealing notable differences and paradoxical behaviors among LLMs. Our experiments highlight the differences observed across LLMs' utility, explainability, and reliability. Code and resources available at: https://github.com/idramalab/quantify-llm-explanations

Chain-of-Thought (CoT) and its variants have markedly advanced the reasoning abilities of Large Language Models (LLMs), yet their monolithic and auto-regressive architecture inherently conflates high-level strategic planning with low-level step-by-step execution, leading to computational inefficiency, limited exploration of reasoning paths, and reduced interpretability. To overcome these issues, we propose the Explore-Execute Chain ($E^2C$), a structured reasoning framework that decouples reasoning into two distinct phases: an exploratory phase that stochastically generates succinct high-level plans, followed by an execution phase that deterministically carries out the chosen plan. Our approach incorporates a two-stage training methodology, which combines Supervised Fine-Tuning (SFT) - augmented by a novel data generation algorithm enforcing strict plan adherence - with a subsequent Reinforcement Learning (RL) stage that capitalizes on the informativeness of exploration and reinforces the determinism of execution. This decomposition enables an efficient test-time scaling strategy: on AIME'2024, $E^2C$ Test Time Scaling reaches 58.1% accuracy using <10% of the decoding tokens required by comparable methods (e.g., Forest-of-Thought), sharply cutting self-consistency overhead. For cross-domain adaptation, our Exploration-Focused SFT (EF-SFT) fine-tunes with only 3.5% of the tokens used by standard SFT yet yields up to 14.5% higher accuracy than standard SFT on medical benchmarks, delivering state-of-the-art performance, strong generalization, and greater interpretability by separating planning from execution. The code and pre-trained models for the project are available at: https://github.com/yks23/Explore-Execute-Chain.git

The performance of Large Language Models (LLMs) depends heavily on the chosen prompting strategy, yet static approaches such as Zero-Shot, Few-Shot, or Chain-of-Thought (CoT) impose a rigid efficiency-accuracy trade-off. Highly accurate strategies like Self-Consistency (SC) incur substantial computational waste on simple tasks, while lightweight methods often fail on complex inputs. This paper introduces the Prompt Policy Network (PPN), a lightweight reinforcement learning framework that formalizes adaptive strategy selection as a single-step Markov Decision Process (MDP). The PPN, trained with Proximal Policy Optimization (PPO) and guided by a resource-explicit reward function, learns to allocate costly reasoning strategies only when necessary. Experiments on arithmetic reasoning benchmarks demonstrate that PPN achieves superior performance on the efficiency-accuracy Pareto front, delivering up to 61.5% token cost reduction compared to Self-Consistency while maintaining competitive accuracy. This work contributes a systematic, adaptive framework for cost-efficient LLM deployment, advancing the design of lightweight optimization techniques for scalable and sustainable language model applications.

Recently, Test-Time Scaling (TTS) has gained increasing attention for improving LLM reasoning performance at test time without retraining the model. A notable TTS technique is Self-Consistency (SC), which generates multiple reasoning chains in parallel and selects the final answer via majority voting. While effective, the order-of-magnitude computational overhead limits its broad deployment. Prior attempts to accelerate SC mainly rely on model-based confidence scores or heuristics with limited empirical support. For the first time, we theoretically and empirically analyze the inefficiencies of SC and reveal actionable opportunities for improvement. Building on these insights, we propose Slim-SC, a step-wise pruning strategy that identifies and removes redundant chains using inter-chain similarity at the thought level. Experiments on three STEM reasoning datasets and two recent LLM architectures show that Slim-SC reduces inference latency and KVC usage by up to 45% and 26%, respectively, with R1-Distill, while maintaining or improving accuracy, thus offering a simple yet efficient TTS alternative for SC.

Video Large Language Models (VideoLLMs) face a critical bottleneck: increasing the number of input frames to capture fine-grained temporal detail leads to prohibitive computational costs and performance degradation from long context lengths. We introduce Video Parallel Scaling (VPS), an inference-time method that expands a model's perceptual bandwidth without increasing its context window. VPS operates by running multiple parallel inference streams, each processing a unique, disjoint subset of the video's frames. By aggregating the output probabilities from these complementary streams, VPS integrates a richer set of visual information than is possible with a single pass. We theoretically show that this approach effectively contracts the Chinchilla scaling law by leveraging uncorrelated visual evidence, thereby improving performance without additional training. Extensive experiments across various model architectures and scales (2B-32B) on benchmarks such as Video-MME and EventHallusion demonstrate that VPS consistently and significantly improves performance. It scales more favorably than other parallel alternatives (e.g. Self-consistency) and is complementary to other decoding strategies, offering a memory-efficient and robust framework for enhancing the temporal reasoning capabilities of VideoLLMs.

Large language models (LLMs) have shown strong performance across natural language reasoning tasks, yet their reasoning processes remain brittle and difficult to interpret. Prompting techniques like Chain-of-Thought (CoT) enhance reliability by eliciting intermediate reasoning steps or aggregating multiple outputs. However, they lack mechanisms for enforcing logical structure and assessing internal coherence. We introduce Theorem-of-Thought (ToTh), a novel framework that models reasoning as collaboration among three parallel agents, each simulating a distinct mode of inference: abductive, deductive, and inductive. Each agent produces a reasoning trace, which is structured into a formal reasoning graph. To evaluate consistency, we apply Bayesian belief propagation guided by natural language inference (NLI), assigning confidence scores to each step. The most coherent graph is selected to derive the final answer. Experiments on symbolic (WebOfLies) and numerical (MultiArith) reasoning benchmarks show that ToTh consistently outperforms CoT, Self-Consistency, and CoT-Decoding across multiple LLMs, while producing interpretable and logically grounded reasoning chains. Our findings suggest a promising direction for building more robust and cognitively inspired LLM reasoning. The implementation is available at https://github.com/KurbanIntelligenceLab/theorem-of-thought.

Large language models (LLMs) have demonstrated strong capabilities in translating natural language questions about relational databases into SQL queries. In particular, test-time scaling techniques such as Self-Consistency and Self-Correction can enhance SQL generation accuracy by increasing computational effort during inference. However, these methods have notable limitations: Self-Consistency may select suboptimal outputs despite majority votes, while Self-Correction typically addresses only syntactic errors. To leverage the strengths of both approaches, we propose CSC-SQL, a novel method that integrates Self-Consistency and Self-Correction. CSC-SQL selects the two most frequently occurring outputs from parallel sampling and feeds them into a merge revision model for correction. Additionally, we employ the Group Relative Policy Optimization (GRPO) algorithm to fine-tune both the SQL generation and revision models via reinforcement learning, significantly enhancing output quality. Experimental results confirm the effectiveness and generalizability of CSC-SQL. On the BIRD private test set, our 7B model achieves 71.72\% execution accuracy, while the 32B model achieves 73.67\%. The code has been open sourced at https://github.com/CycloneBoy/csc_sql.