Current frontier large-language models rely on reasoning to achieve state-of-the-art performance. Many existing interpretability are limited in this area, as standard methods have been designed to study single forward passes of a model rather than the multi-token computational steps that unfold during reasoning. We argue that analyzing reasoning traces at the sentence level is a promising approach to understanding reasoning processes. We introduce a black-box method that measures each sentence's counterfactual importance by repeatedly sampling replacement sentences from the model, filtering for semantically different ones, and continuing the chain of thought from that point onwards to quantify the sentence's impact on the distribution of final answers. We discover that certain sentences can have an outsized impact on the trajectory of the reasoning trace and final answer. We term these sentences \textit{thought anchors}. These are generally planning or uncertainty management sentences, and specialized attention heads consistently attend from subsequent sentences to thought anchors. We further show that examining sentence-sentence causal links within a reasoning trace gives insight into a model's behavior. Such information can be used to predict a problem's difficulty and the extent different question domains involve sequential or diffuse reasoning. As a proof-of-concept, we demonstrate that our techniques together provide a practical toolkit for analyzing reasoning models by conducting a detailed case study of how the model solves a difficult math problem, finding that our techniques yield a consistent picture of the reasoning trace's structure. We provide an open-source tool (thought-anchors.com) for visualizing the outputs of our methods on further problems. The convergence across our methods shows the potential of sentence-level analysis for a deeper understanding of reasoning models.

Autonomous robotic navigation in real-world environments requires exploration to acquire environmental information as well as goal-directed navigation in order to reach specified targets. Active inference (AIF) based on the free-energy principle provides a unified framework for these behaviors by minimizing the expected free energy (EFE), thereby combining epistemic and extrinsic values. To realize this practically, we propose a deep AIF framework that integrates a diffusion policy as the policy model and a multiple timescale recurrent state-space model (MTRSSM) as the world model. The diffusion policy generates diverse candidate actions while the MTRSSM predicts their long-horizon consequences through latent imagination, enabling action selection that minimizes EFE. Real-world navigation experiments demonstrated that our framework achieved higher success rates and fewer collisions compared with the baselines, particularly in exploration-demanding scenarios. These results highlight how AIF based on EFE minimization can unify exploration and goal-directed navigation in real-world robotic settings.

Generalization across Agentic tool-calling environments remains a key unsolved challenge in developing reliable agentic reasoning systems. While large language models (LLMs) demonstrate strong performance on isolated benchmarks, their ability to transfer reasoning strategies and co-ordinate tools across diverse domains is poorly understood. In this work, we conduct a large-scale evaluation of state-of-the-art LLMs on multiple tool-calling benchmarksBFCL v3, TauBench, Tau2Bench, and AceBenchand introduce MAVEN (Math & Physics Adversarial Verification & Evaluation Network), a new out of distribution (OOD) benchmark designed to stress-test multi-step reasoning through explicit verification and adversarial task composition. Our results show that most current models achieve below 50% accuracy on MAVEN, revealing a significant generalization gap across tool-use settings. To address this, we present the CoreThink Agentic Reasoner, a framework that augments LLMs with a lightweight symbolic reasoning layer for structured decomposition and adaptive tool orchestration. Without additional training, it generalizes across all benchmarks, achieving state-of-the-art performance with 530% improvements over existing baselines at roughly one-tenth the computational cost.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models (LLMs). In this context, models explore reasoning trajectories and exploit rollouts with correct answers as positive signals for policy optimization. However, these rollouts might involve flawed patterns such as answer-guessing and jump-in-reasoning. Such flawed-positive rollouts are rewarded identically to fully correct ones, causing policy models to internalize these unreliable reasoning patterns. In this work, we first conduct a systematic study of flawed-positive rollouts in RL and find that they enable rapid capability gains during the early optimization stage, while constraining reasoning capability later by reinforcing unreliable patterns. Building on these insights, we propose Flawed-Aware Policy Optimization (FAPO), which presents a parameter-free reward penalty for flawed-positive rollouts, enabling the policy to leverage them as useful shortcuts in the warm-up stage, securing stable early gains, while gradually shifting optimization toward reliable reasoning in the later refinement stage. To accurately and comprehensively detect flawed-positive rollouts, we introduce a generative reward model (GenRM) with a process-level reward that precisely localizes reasoning errors. Experiments show that FAPO is effective in broad domains, improving outcome correctness, process reliability, and training stability without increasing the token budget.

Large Language Models (LLMs) have demonstrated remarkable reasoning abilities when they generate step-by-step solutions, known as chain-of-thought (CoT) reasoning. When trained to using chain-of-thought reasoning examples, the resulting models (called Large Reasoning Models, or LRMs) appear to learn hierarchical thinking strategies similar to those used by humans. However, understanding LRMs emerging reasoning capabilities remains a difficult open problem, with many potential important applications including improving training and understanding robustness. In this paper, we adopt a memoryless Finite State Machine formulation to approximate LRM's emerging hierarchical reasoning dynamics as a structured, interpretable abstraction. We identify a small set of discrete reasoning states including - initialization, deduction, augmentation-strategy, uncertainty-estimation, backtracking, and final-conclusion that capture the high-level states present in the model's reasoning process. By annotating each step of a model's CoT with these states, we can represent the reasoning trajectory as a transition sequence through the state graph. This FSM formulation provides a systematic way to analyze, interpret and visualize how different models approach problems. We describe the FSM model, provide examples of CoT annotations under this scheme, and discuss how it can shed light on differences between available models in their approach to reasoning. Our results demonstrate that this FSM-based analysis reveals distinct reasoning patterns and potential shortcomings, offering a new lens to evaluate and improve LLM reasoning.

Chain-of-thought (CoT) traces promise transparency for reasoning language models, but prior work shows they are not always faithful reflections of internal computation. This raises challenges for oversight: practitioners may misinterpret decorative reasoning as genuine. We introduce Concept Walk, a general framework for tracing how a model's internal stance evolves with respect to a concept direction during reasoning. Unlike surface text, Concept Walk operates in activation space, projecting each reasoning step onto the concept direction learned from contrastive data. This allows us to observe whether reasoning traces shape outcomes or are discarded. As a case study, we apply Concept Walk to the domain of Safety using Qwen 3-4B. We find that in 'easy' cases, perturbed CoTs are quickly ignored, indicating decorative reasoning, whereas in 'hard' cases, perturbations induce sustained shifts in internal activations, consistent with faithful reasoning. The contribution is methodological: Concept Walk provides a lens to re-examine faithfulness through concept-specific internal dynamics, helping identify when reasoning traces can be trusted and when they risk misleading practitioners.

Autonomous landing in unstructured (cluttered, uneven, and map-poor) environments is a core requirement for Unmanned Aerial Vehicles (UAVs), yet purely vision-based or deep learning models often falter under covariate shift and provide limited interpretability. We propose NeuroSymLand, a neuro-symbolic framework that tightly couples two complementary pipelines: (i) an offline pipeline, where Large Language Models (LLMs) and human-in-the-loop refinement synthesize Scallop code from diverse landing scenarios, distilling generalizable and verifiable symbolic knowledge; and (ii) an online pipeline, where a compact foundation-based semantic segmentation model generates probabilistic Scallop facts that are composed into semantic scene graphs for real-time deductive reasoning. This design combines the perceptual strengths of lightweight foundation models with the interpretability and verifiability of symbolic reasoning. Node attributes (e.g., flatness, area) and edge relations (adjacency, containment, proximity) are computed with geometric routines rather than learned, avoiding the data dependence and latency of train-time graph builders. The resulting Scallop program encodes landing principles (avoid water and obstacles; prefer large, flat, accessible regions) and yields calibrated safety scores with ranked Regions of Interest (ROIs) and human-readable justifications. Extensive evaluations across datasets, diverse simulation maps, and real UAV hardware show that NeuroSymLand achieves higher accuracy, stronger robustness to covariate shift, and superior efficiency compared with state-of-the-art baselines, while advancing UAV safety and reliability in emergency response, surveillance, and delivery missions.

We present a novel approach for controllable mathematical reasoning that leverages self-optimizing thought vectors with entropy minimization. Our method introduces learnable thought vectors that dynamically modulate the internal reasoning process of large language models. Using Gemma-2-9B on GSM8K, we achieve 90.1% accuracy with a controllability score of 0.42, demonstrating that entropy-based rewards effectively guide focused reasoning patterns without requiring external reward annotations. Our analysis reveals distinct thought vector clusters and consistent low-entropy distributions across control conditions, validating our framework for controllable AI reasoning.

The field of artificial intelligence (AI) has taken a tight hold on broad aspects of society, industry, business, and governance in ways that dictate the prosperity and might of the world's economies. The AI market size is projected to grow from 189 billion USD in 2023 to 4.8 trillion USD by 2033. Currently, AI is dominated by large language models that exhibit linguistic and visual intelligence. However, training these models requires a massive amount of data scraped from the web as well as large amounts of energy (50--60 GWh to train GPT-4). Despite these costs, these models often hallucinate, a characteristic that prevents them from being deployed in critical application domains. In contrast, the human brain consumes only 20~W of power. What is needed is the next level of AI evolution in which lightweight domain-specific multimodal models with higher levels of intelligence can reason, plan, and make decisions in dynamic environments with real-time data and prior knowledge, while learning continuously and evolving in ways that enhance future decision-making capability. This will define the next wave of AI, progressing from today's large models, trained with vast amounts of data, to nimble energy-efficient domain-specific agents that can reason and think in a world full of uncertainty. To support such agents, hardware will need to be reimagined to allow energy efficiencies greater than 1000x over the state of the art. Such a vision of future AI systems is developed in this work.

Math word problem (MWP) serves as a fundamental research topic in artificial intelligence (AI) dating back to 1960s. This research aims to advance the reasoning abilities of AI by mirroring the human-like cognitive intelligence. The mainstream technological paradigm has evolved from the early rule-based methods, to deep learning models, and is rapidly advancing towards large language models. However, the field still lacks a systematic taxonomy for the MWP survey along with a discussion of current development trends. Therefore, in this paper, we aim to comprehensively review related research in MWP solving through the lens of human cognition, to demonstrate how recent AI models are advancing in simulating human cognitive abilities. Specifically, we summarize 5 crucial cognitive abilities for MWP solving, including Problem Understanding, Logical Organization, Associative Memory, Critical Thinking, and Knowledge Learning. Focused on these abilities, we review two mainstream MWP models in recent 10 years: neural network solvers, and LLM based solvers, and discuss the core human-like abilities they demonstrated in their intricate problem-solving process. Moreover, we rerun all the representative MWP solvers and supplement their performance on 5 mainstream benchmarks for a unified comparison. To the best of our knowledge, this survey first comprehensively analyzes the influential MWP research of the past decade from the perspective of human reasoning cognition and provides an integrative overall comparison across existing approaches. We hope it can inspire further research in AI reasoning. Our repository is released on https://github.com/Ljyustc/FoI-MWP.