The Universal Landscape of Human Reasoning

TL;DR

The paper presents Information Flow Tracking (IF-Track), a unified, quantitative framework that models human reasoning as a Hamiltonian flow in an information phase space defined by two conjugate variables: $u_t$ (uncertainty) and $e_t$ (cognitive effort). By using large language models as probabilistic encoders, IF-Track computes stepwise information entropy and its changes to map reasoning trajectories, showing approximate Liouville (volume) conservation and a reduced Hamiltonian structure $H(u,e)=\tfrac{1}{2}e^2+U(u)+C$. Empirically, IF-Track yields a universal landscape across diverse tasks, distinguishes classical reasoning types via trajectory patterns, and reveals how personality and education shape reasoning paths, while also highlighting how single- versus dual-process theories can be reconciled within a single global flow. The framework further explores how the era of LLMs reshapes human reasoning, with post-LLM flows aligning closely with model trajectories, offering a quantitative bridge between theory and measurement and enabling mechanistic insights for cognitive science and AI alignment.

Abstract

Understanding how information is dynamically accumulated and transformed in human reasoning has long challenged cognitive psychology, philosophy, and artificial intelligence. Existing accounts, from classical logic to probabilistic models, illuminate aspects of output or individual modelling, but do not offer a unified, quantitative description of general human reasoning dynamics. To solve this, we introduce Information Flow Tracking (IF-Track), that uses large language models (LLMs) as probabilistic encoder to quantify information entropy and gain at each reasoning step. Through fine-grained analyses across diverse tasks, our method is the first successfully models the universal landscape of human reasoning behaviors within a single metric space. We show that IF-Track captures essential reasoning features, identifies systematic error patterns, and characterizes individual differences. Applied to discussion of advanced psychological theory, we first reconcile single- versus dual-process theories in IF-Track and discover the alignment of artificial and human cognition and how LLMs reshaping human reasoning process. This approach establishes a quantitative bridge between theory and measurement, offering mechanistic insights into the architecture of reasoning.

Figures (8)

• Figure 1: Theoretical Framework and Modelling Applications of IF-Track. a. Computation of reasoning metrics. An LLM-based probability encoder estimates the conditional probability of each reasoning step, yielding two variables: uncertainty (information entropy, $u_t$) and cognitive effort (information gain, $e_t$). b. Theoretical foundation: Information phase space. Reasoning can be modeled as a trajectory within a two-dimensional information phase space $(u_t, e_t)$, formulated as a Hamiltonian system that models the reasoning landscape. This framework depicts the transition from high uncertainty and low effort (Step 2) to low uncertainty and high effort (Step 3). c. Applications under the framework. Built on this framework, IF-Track models reasoning across Reasoning Type (e.g. Deductive and Inductive Reasoning), Individual Feature (e.g., personality, professional background), and Error Type (e.g., intuition collapse, metacognitive conflict, rationale error).
• Figure 2: Comparison of static representations of reasoning trajectories and relevant reasoning paradigms modelling. a. t-SNE projection of step embeddings, showing chaotic representations across different human reasoning processes. b. Visualization of the landscape of thought, showing clustered but temporally unordered patterns across different human reasoning processes. c. Reasoning trajectories in the entropy–gain phase space reveal a globally consistent flow, where arrows represent the direction of information flow, illustrating the dynamic evolution of reasoning states from high uncertainty toward stable cognitive states. d. Empirical validation of the information phase space. The pseudocolor map shows the local divergence $\nabla\cdot\vec{V}$ of the reasoning flow in the $(u,e)$ space. Most regions exhibit near-zero divergence (uniform color), indicating approximate volume preservation and supporting a quasi-Hamiltonian structure of human reasoning dynamics. e. Different reasoning paradigms (deductive vs. inductive reasoning) in phase space. f. Abductive reasoning in phase space, lying between deductive and inductive and showing a hybrid pattern.
• Figure 3: Three categories of reasoning errors identified by IF-Track, positioned in the uncertainty–effort phase space. ($n_{total}$=9,991, $n_{error}=374$). These errors were clustered into three stages by directions: Stage 1: Intuition Collapse (Ratio 87.3%), Stage 2: Metacognition Conflict (Ratio 73.7%), and Stage 3: Rationale Error (Ratio 90.4%)
• Figure 4: Personality-related modulation of reasoning trajectories and cognitive–informational dynamics. a. Extraversion. Individuals with higher extraversion exhibit greater mean and maximal entropy, indicating higher tolerance for uncertainty and broader exploratory reasoning. b. Conscientiousness. The high-conscientiousness group shows lower average entropy but higher maximal effort, consistent with disciplined and goal-oriented reasoning. c. Emotional Stability. Individuals with higher emotional stability maintain a more balanced entropy–effort profile, reflected in higher ratios of high-entropy and high-effort states. d. Openness. Higher openness corresponds to a greater proportion of high-effort reasoning phases, suggesting deeper cognitive engagement and flexible information integration. e. Agreeableness. High-agreeableness participants show higher maximal cognitive effort and lower minimal entropy, suggesting more sustained and focused reasoning. f. Education Level. Across undergraduate, master, and PhD groups, higher educational attainment correlates with slightly higher uncertainty at reasoning origins, indicating broader hypothesis search spaces in early-stage reasoning. Total $n=3{,}215$.
• Figure 5: Application IF-Track for Adavanced Psychological Theory Discussion. a. Comparison between single- and dual-process theories of reasoning ($n=1632$). Dual-process theories posit interacting intuitive and analytic systems, whereas single-process accounts treat reasoning as a graded, continuously integrated computation. b. Pre-LLM human reasoning flow ($n=1667$). Before the LLM era, human reasoning often began with low effort under high uncertainty and, via analytic integration, progressed toward higher effort with lower uncertainty. c. Model reasoning flow ($n=1537$). LLMs exhibit a similar trajectory: uncertainty declines as computational depth increases, mirroring human analytic patterns. d. Post-LLM human reasoning flow ($n=1549$). After interacting with LLMs, human reasoning shows a compressed trajectory, starting at higher effort and lower uncertainty, converging sooner, and often skipping further exploration. e. Comparison of pre- and post-LLM human reasoning. Pre-LLM reasoning featured extended exploration and late convergence, whereas post-LLM reasoning stabilizes earlier and is more efficient, signaling a shift from discovery-oriented to synthesis-oriented cognition. f. Comparison between post-LLM human and LLM reasoning. Both trajectories now begin at similar levels of uncertainty and effort, suggesting an emerging convergence in reasoning structure across humans and models.