Reasoning models often exhibit overthinking, characterized by redundant reasoning steps. We identify \emph{internal bias} elicited by the input question as a key trigger of such behavior. Upon encountering a problem, the model immediately forms a preliminary guess about the answer, which we term an internal bias since it may not be explicitly generated, and it arises without systematic reasoning. When this guess conflicts with its subsequent reasoning, the model tends to engage in excessive reflection, resulting in wasted computation. We validate the association between internal bias and overthinking across multiple models and diverse reasoning tasks. To demonstrate the causal relationship more rigorously, we conduct two counterfactual interventions, showing that removing the input question after the model reduces the redundant reasoning across various complex reasoning tasks, and manually injecting bias affects overthinking accordingly. Further interpretability experiments suggest that excessive attention to the input question serves as a key mechanism through which internal bias influences subsequent reasoning trajectories. Finally, we evaluated several methods aimed at mitigating overthinking, yet the influence of internal bias persisted under all conditions.

Invariant representations are core to representation learning, yet a central challenge remains: uncovering invariants that are stable and transferable without suppressing task-relevant signals. This raises fundamental questions, requiring further inquiry, about the appropriate level of abstraction at which such invariants should be defined and which aspects of a system they should characterize. Interpretation of the environment relies on abstract knowledge structures to make sense of the current state, which leads to interactions, essential drivers of learning and knowledge acquisition. Interpretation operates at the level of higher-order relational knowledge; hence, we propose that invariant structures must be where knowledge resides, specifically as partitions defined by the closure of relational paths within an abstract knowledge space. These partitions serve as the core invariant representations, forming the structural substrate where knowledge is stored and learning occurs. On the other hand, inter-partition connectors enable the deployment of these knowledge partitions encoding task-relevant transitions. Thus, invariant partitions provide the foundational primitives of structured representation. We formalize the computational foundations for structured relational representations of the invariant partitions based on closed semiring, a relational algebraic structure.

Chain-of-Thought (CoT) reasoning has advanced the capabilities and transparency of language models (LMs); however, reasoning chains can contain inaccurate statements that reduce performance and trustworthiness. To address this, we propose to augment each reasoning step in a CoT with a latent veracity (or correctness) variable. To efficiently explore this expanded space, we introduce Veracity Search (VS), a discrete search algorithm over veracity assignments. It performs otherwise intractable inference in the posterior distribution over latent veracity values by leveraging the LM's joint likelihood over veracity and the final answer as a proxy reward. This efficient inference-time verification method facilitates supervised fine-tuning of an Amortized Veracity Inference (AVI) machine by providing pseudo-labels for veracity. AVI generalizes VS, enabling accurate zero-shot veracity inference in novel contexts. Empirical results demonstrate that VS reliably identifies errors in logical (ProntoQA), mathematical (GSM8K), and commonsense (CommonsenseQA) reasoning benchmarks, with AVI achieving comparable zero-shot accuracy. Finally, we demonstrate the utility of latent veracity inference for providing feedback during self-correction and self-improvement.

Class-Incremental Learning (CIL) aims to endow models with the ability to continuously adapt to evolving data streams. Recent advances in pre-trained vision-language models (e.g., CLIP) provide a powerful foundation for this task. However, existing approaches often rely on simplistic templates, such as "a photo of a [CLASS]", which overlook the hierarchical nature of visual concepts. For example, recognizing "cat" versus "car" depends on coarse-grained cues, while distinguishing "cat" from "lion" requires fine-grained details. Similarly, the current feature mapping in CLIP relies solely on the representation from the last layer, neglecting the hierarchical information contained in earlier layers. In this work, we introduce HiErarchical Representation MAtchiNg (HERMAN) for CLIP-based CIL. Our approach leverages LLMs to recursively generate discriminative textual descriptors, thereby augmenting the semantic space with explicit hierarchical cues. These descriptors are matched to different levels of the semantic hierarchy and adaptively routed based on task-specific requirements, enabling precise discrimination while alleviating catastrophic forgetting in incremental tasks. Extensive experiments on multiple benchmarks demonstrate that our method consistently achieves state-of-the-art performance.

The capability of predicting environmental dynamics underpins both biological neural systems and general embodied AI in adapting to their surroundings. Yet prevailing approaches rest on static world models that falter when confronted with novel or rare configurations. We investigate in-context environment learning (ICEL), shifting attention from zero-shot performance to the growth and asymptotic limits of the world model. Our contributions are three-fold: (1) we formalize in-context learning of a world model and identify two core mechanisms: environment recognition and environment learning; (2) we derive error upper-bounds for both mechanisms that expose how the mechanisms emerge; and (3) we empirically confirm that distinct ICL mechanisms exist in the world model, and we further investigate how data distribution and model architecture affect ICL in a manner consistent with theory. These findings demonstrate the potential of self-adapting world models and highlight the key factors behind the emergence of ICEL, most notably the necessity of long context and diverse environments.

ABSTRACT An associative memory (AM) enables cue-response recall, and associative memorization has recently been noted to underlie the operation of modern neural architectures such as Transformers. This work addresses a distributed setting where agents maintain a local AM to recall their own associations as well as selective information from others. Specifically, we introduce a distributed online gradient descent method that optimizes local AMs at different agents through communication over routing trees. Our theoretical analysis establishes sublinear regret guarantees, and experiments demonstrate that the proposed protocol consistently outperforms existing online optimization baselines. Index T erms-- Associative Memory, Distributed Optimization, Online Convex Optimization 1. INTRODUCTION An associative memory (AM), a classical concept in cognitive science, stores cue-response associations, recalling the response when the corresponding cue is presented [1]. This principle, fundamental to human cognition, provides a natural abstraction for modeling how information can be efficiently retained, updated, and retrieved.

The "black box" nature of Large Reasoning Models (LRMs) presents critical limitations in reliability and transparency, fueling the debate around the "illusion of thinking" and the challenge of state hallucinations in agentic systems. In response, we introduce The STAR-XAI Protocol (Socratic, Transparent, Agentic, Reasoning - for eXplainable Artificial Intelligence), a novel operational methodology for training and operating verifiably reliable AI agents. Our method reframes the human-AI interaction as a structured Socratic dialogue governed by an explicit, evolving symbolic rulebook (the Consciousness Transfer Package - CTP) and a suite of integrity protocols, including a state-locking Checksum that eradicates internal state corruption. Through an exhaustive case study in the complex strategic game "Caps i Caps," we demonstrate that this "Clear Box" framework transforms an opaque LRM into a disciplined strategist. The agent not only exhibits the emergence of complex tactics, such as long-term planning, but also achieves ante-hoc transparency by justifying its intentions before acting. Crucially, it demonstrates Second-Order Agency by identifying and correcting flaws in its own supervisor-approved plans, leading to empirically-proven, 100% reliable state tracking and achieving "zero hallucinations by design." The STAR-XAI Protocol thus offers a practical pathway toward building AI agents that are not just high-performing but intrinsically auditable, trustworthy, and reliable.

Today's AI systems have human-designed, fixed architectures and cannot autonomously and continuously improve themselves. The advance of AI could itself be automated. If done safely, that would accelerate AI development and allow us to reap its benefits much sooner. Meta-learning can automate the discovery of novel algorithms, but is limited by first-order improvements and the human design of a suitable search space. The Gödel machine proposed a theoretical alternative: a self-improving AI that repeatedly modifies itself in a provably beneficial manner. Unfortunately, proving that most changes are net beneficial is impossible in practice. We introduce the Darwin Gödel Machine (DGM), a self-improving system that iteratively modifies its own code (thereby also improving its ability to modify its own codebase) and empirically validates each change using coding benchmarks. Inspired by Darwinian evolution and open-endedness research, the DGM maintains an archive of generated coding agents. It grows the archive by sampling an agent from it and using a foundation model to create a new, interesting, version of the sampled agent. This open-ended exploration forms a growing tree of diverse, high-quality agents and allows the parallel exploration of many different paths through the search space. Empirically, the DGM automatically improves its coding capabilities (e.g., better code editing tools, long-context window management, peer-review mechanisms), increasing performance on SWE-bench from 20.0% to 50.0%, and on Polyglot from 14.2% to 30.7%. Furthermore, the DGM significantly outperforms baselines without self-improvement or open-ended exploration. All experiments were done with safety precautions (e.g., sandboxing, human oversight). The DGM is a significant step toward self-improving AI, capable of gathering its own stepping stones along paths that unfold into endless innovation.

Large reasoning models improve accuracy by producing long reasoning traces, but this inflates latency and cost, motivating inference-time efficiency. We propose Retrieval-of-Thought (RoT), which reuses prior reasoning as composable "thought" steps to guide new problems. RoT organizes steps into a thought graph with sequential and semantic edges to enable fast retrieval and flexible recombination. At inference, RoT retrieves query-relevant nodes and applies reward-guided traversal to assemble a problem-specific template that guides generation. This dynamic template reuse reduces redundant exploration and, therefore, reduces output tokens while preserving accuracy. We evaluate RoT on reasoning benchmarks with multiple models, measuring accuracy, token usage, latency, and memory overhead. Findings show small prompt growth but substantial efficiency gains, with RoT reducing output tokens by up to 40%, inference latency by 82%, and cost by 59% while maintaining accuracy. RoT establishes a scalable paradigm for efficient LRM reasoning via dynamic template construction through retrieval. Large Reasoning Models (LRMs) have demonstrated impressive capabilities in solving complex tasks by producing outputs accompanied by detailed reasoning trajectories (Xu et al., 2025a). These models adopt an intentionally slower and more deliberative inference process, mimicking human-like reasoning. This approach typically involves generating longer outputs and consuming increased inference-time compute to effectively address reasoning-intensive queries. Recent efforts to improve reasoning in LLMs have primarily focused on generating more output tokens to simulate thoughtful, multi-step reasoning (Snell et al., 2024). A common approach involves guiding generation using external reward models Zhang et al. (2024). These include outcome-based reward models, such as Best-of-N (BoN) sampling.

Large Language Models (LLMs) have achieved impressive performance across a wide range of applications. However, they often suffer from hallucinations in knowledge-intensive domains due to their reliance on static pretraining corpora. To address this limitation, Retrieval-Augmented Generation (RAG) enhances LLMs by incorporating external knowledge sources during inference. Among these sources, textual graphs provide structured and semantically rich information that supports more precise and interpretable reasoning. This has led to growing interest in graph-based RAG systems. Despite their potential, most existing approaches rely on a single retriever to identify relevant subgraphs, which limits their ability to capture the diverse aspects of complex queries. Moreover, these systems often struggle to accurately judge the relevance of retrieved content, making them prone to distraction by irrelevant noise. To address these challenges, in this paper, we propose MIXRAG, a Mixture-of-Experts Graph-RAG framework that introduces multiple specialized graph retrievers and a dynamic routing controller to better handle diverse query intents. Each retriever is trained to focus on a specific aspect of graph semantics, such as entities, relations, or subgraph topology. A Mixture-of-Experts module adaptively selects and fuses relevant retrievers based on the input query. To reduce noise in the retrieved information, we introduce a query-aware GraphEncoder that carefully analyzes relationships within the retrieved subgraphs, highlighting the most relevant parts while down-weighting unnecessary noise. Empirical results demonstrate that our method achieves state-of-the-art performance and consistently outperforms various baselines. MIXRAG is effective across a wide range of graph-based tasks in different domains. The code will be released upon paper acceptance.