Recent progress has pushed AI frontiers from pattern recognition tasks toward problems that require step by step, System2 style reasoning, especially with large language models. Yet, unlike learning, where generalization and out of distribution (OoD) evaluation concepts are well formalized, there is no clear, consistent definition or metric for reasoning ability. We propose Complexity Out of Distribution (Complexity OoD) generalization as a framework and problem setting to define and measure reasoning. A model exhibits Complexity OoD generalization when it maintains performance on test instances whose minimal required solution complexity, either representational (richer solution structure) or computational (more reasoning steps/program length), exceeds that of all training examples. We formalize complexity via solution description Kolmogorov complexity and operational proxies (e.g., object/relation counts; reasoning step counts), clarifying how Complexity OoD differs from length and compositional OoD. This lens unifies learning and reasoning: many cases solvable with System1 like processing at low complexity become System2 like under complexity pressure, while System2 can be viewed as generalization over solution structures. We translate this perspective into practice with recommendations for operationalizing Complexity OoD across the stack: incorporating complexity into benchmark and evaluation metric design, rethinking supervision to target solution traces, seeking and designing inductive biases for Complexity OoD generalization, addressing learning to reason spillovers such as spurious shortcuts, semantic robustness, catastrophic forgetting, and step wise calibration. Because Complexity OoD cannot be solved by scaling data alone, progress toward robust reasoning will require architectures and training regimes that explicitly model and allocate computation with respect to complexity.

Long chain-of-thought (CoT) prompting helps Large Language Models (LLMs) solve difficult problems, but very long traces often slow or even degrade performance on fast, intuitive "System-1" tasks. We introduce Connector-Aware Compact CoT (CAC-CoT) -- a method that deliberately restricts reasoning to a small, fixed set of connector phrases, steering the model toward concise and well -- structured explanations. Despite its simplicity, our synthetic method with general-purpose LLMs yields a high-quality training quality. CAC-CoT achieves approximately 85% on GSM8K and approximately 40% on GPQA (System-2) while also achieving approximately 85% on S1-Bench (System-1), surpassing the baseline by over 20%. Its reasoning traces average approximately 300 tokens(ART), about one-third the length of baseline traces, delivering higher efficiency without loss of accuracy.

Recent studies have shown that making a model spend more time thinking through longer Chain of Thoughts (CoTs) enables it to gain significant improvements in complex reasoning tasks. While current researches continue to explore the benefits of increasing test-time compute by extending the CoT lengths of Large Language Models (LLMs), we are concerned about a potential issue hidden behind the current pursuit of test-time scaling: Would excessively scaling the CoT length actually bring adverse effects to a model's reasoning performance? Our explorations on mathematical reasoning tasks reveal an unexpected finding that scaling with longer CoTs can indeed impair the reasoning performance of LLMs in certain domains. Moreover, we discover that there exists an optimal scaled length distribution that differs across different domains. Based on these insights, we propose a Thinking-Optimal Scaling strategy. Our method first uses a small set of seed data with varying response length distributions to teach the model to adopt different reasoning efforts for deep thinking. Then, the model selects its shortest correct response under different reasoning efforts on additional problems for self-improvement. Our self-improved models built upon Qwen2.5-32B-Instruct outperform other distillation-based 32B o1-like models across various math benchmarks, and achieve performance on par with QwQ-32B-Preview.

Language models can be used to solve long-horizon planning problems in two distinct modes: a fast 'System-1' mode, directly generating plans without any explicit search or backtracking, and a slow 'System-2' mode, planning step-by-step by explicitly searching over possible actions. While System-2 is typically more effective, it is also more computationally expensive, making it infeasible for long plans or large action spaces. Moreover, isolated System-1 or 2 ignores the user's end goals, failing to provide ways to control the model's behavior. To this end, we propose the System-1.x Planner, a controllable planning framework with LLMs that is capable of generating hybrid plans and balancing between the two planning modes based on the difficulty of the problem at hand. System-1.x consists of (i) a controller, (ii) a System-1 Planner, and (iii) a System-2 Planner. Based on a user-specified hybridization factor (x) governing the mixture between System-1 and 2, the controller decomposes a problem into sub-goals, and classifies them as easy or hard to be solved by either System-1 or 2, respectively. We fine-tune all three components on top of a single base LLM, requiring only search traces as supervision. Experiments with two diverse planning tasks -- Maze Navigation and Blocksworld -- show that our System-1.x Planner outperforms a System-1 Planner, a System-2 Planner trained to approximate A* search, and also a symbolic planner (A*). We demonstrate the following key properties of our planner: (1) controllability: increasing the hybridization factor (e.g., System-1.75 vs 1.5) performs more search, improving performance, (2) flexibility: by building a neuro-symbolic variant with a neural System-1 and a symbolic System-2, we can use existing symbolic methods, and (3) generalizability: by being able to learn from different search algorithms, our method is robust to the choice of search algorithm.

Attempts to import dual-system descriptions of System-1 and System-2 into AI have been hindered by a lack of clarity over their distinction. We address this and other issues by situating System-1 and System-2 within the Common Model of Cognition. Results show that what are thought to be distinctive characteristics of System-1 and 2 instead form a spectrum of cognitive properties. The Common Model provides a comprehensive vision of the computational units involved in System-1 and System-2, their underlying mechanisms, and the implications for learning, metacognition, and emotion.

There have been increasing challenges to dual-system descriptions of System-1 and System-2, critiquing them as imprecise and fostering misconceptions. We address these issues here by way of Dennett's appeal to use computational thinking as an analytical tool, specifically we employ the Common Model of Cognition. Results show that the characteristics thought to be distinctive of System-1 and System-2 instead form a spectrum of cognitive properties. By grounding System-1 and System-2 in the Common Model we aim to clarify their underlying mechanisms, persisting misconceptions, and implications for metacognition.

A cognitive architecture aimed at cumulative learning must provide the necessary information and control structures to allow agents to learn incrementally and autonomously from their experience. This involves managing an agent's goals as well as continuously relating sensory information to these in its perception-cognition information stack. The more varied the environment of a learning agent is, the more general and flexible must be these mechanisms to handle a wider variety of relevant patterns, tasks, and goal structures. While many researchers agree that information at different levels of abstraction likely differs in its makeup and structure and processing mechanisms, agreement on the particulars of such differences is not generally shared in the research community. A binary processing architecture (often referred to as System-1 and System-2) has been proposed as a model of cognitive processing for low- and high-level information, respectively. We posit that cognition is not binary in this way and that knowledge at any level of abstraction involves what we refer to as neurosymbolic information, meaning that data at both high and low levels must contain both symbolic and subsymbolic information. Further, we argue that the main differentiating factor between the processing of high and low levels of data abstraction can be largely attributed to the nature of the involved attention mechanisms. We describe the key arguments behind this view and review relevant evidence from the literature.