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Nonrational varieties with unirational parametrizations of coprime degrees
Song Yang, Xun Yu, Zigang Zhu
https://arxiv.org/abs/2508.03623 https://arxiv.org…

Nonrational varieties with unirational parametrizations of coprime degrees
We show that there exists a $2$-dimensional family of smooth cubic threefolds admitting unirational parametrizations of coprime degrees. This together with Clemens--Griffiths' work solves the long standing open problem whether there exists a nonrational variety with unirational parametrizations of coprime degrees. Our proof uses a new approach, called the Noether--Cremona method, for determining the rationality of quotients of hypersurfaces.

Rationality fields of CM modular forms
Kimball Martin
https://arxiv.org/abs/2509.24119 https://arxiv.org/pdf/2509.24119

Rationality fields of CM modular forms
We formulate a conjecture on the finitude of rationality fields (i.e., Fourier coefficient fields) of newforms of bounded degree, and prove this for CM forms assuming a generalized Riemann hypothesis. Then we explicitly determine what quadratic and cubic rationality fields occur for weight 2 CM forms, which is related to classifications of CM abelian varieties of GL(2) type. Several of these fields do not appear in the existing tables of newforms in the LMFDB.

Replaced article(s) found for cs.MA. https://arxiv.org/list/cs.MA/new
[1/1]:
- (Ir)rationality in AI: State of the Art, Research Challenges and Open Questions
Olivia Macmillan-Scott, Mirco Musolesi

Rationality Check! Benchmarking the Rationality of Large Language Models
Zhilun Zhou, Jing Yi Wang, Nicholas Sukiennik, Chen Gao, Fengli Xu, Yong Li, James Evans
https://arxiv.org/abs/2509.14546

Rationality Check! Benchmarking the Rationality of Large Language Models
Large language models (LLMs), a recent advance in deep learning and machine intelligence, have manifested astonishing capacities, now considered among the most promising for artificial general intelligence. With human-like capabilities, LLMs have been used to simulate humans and serve as AI assistants across many applications. As a result, great concern has arisen about whether and under what circumstances LLMs think and behave like real human agents. Rationality is among the most important con…

Beyond Suboptimality: Resource-Rationality and Task Demands Shape the Complexity of Perceptual Representations
Andrew Jun Lee, Daniel Turek, Omer Daglar Tanrikulu
https://arxiv.org/abs/2509.26606

Beyond Suboptimality: Resource-Rationality and Task Demands Shape the Complexity of Perceptual Representations
Early theories of perception as probabilistic inference propose that uncertainty about the interpretation of sensory input is represented as a probability distribution over many interpretations -- a relatively complex representation. However, critics argue that persistent demonstrations of suboptimal perceptual decision-making indicate limits in representational complexity. We contend that suboptimality arises not from genuine limits, but participants' resource-rational adaptations to task dema…

Irrationality as a mean of regularization in Bayesian Persuasion
Romain Duboscq (IMT, INSA Toulouse), Fr\'ed\'eric de Gournay (IMT, INSA Toulouse)
https://arxiv.org/abs/2510.01759

Irrationality as a mean of regularization in Bayesian Persuasion
We study a regularized variant of the Bayesian Persuasion problem, where the receiver's decision process includes a divergence-based penalty that accounts for deviations from perfect rationality. This modification smooths the underlying optimization landscape and mitigates key theoretical issues, such as measurability and ill-posedness, commonly encountered in the classical formulation. It also enables the use of scalable second-order optimization methods to compute numerically the optimal sign…

Replaced article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Intermediate Jacobians and rationality over arbitrary fields
Olivier Benoist, Olivier Wittenberg

Secondary Bounded Rationality: A Theory of How Algorithms Reproduce Structural Inequality in AI Hiring
Jia Xiao
https://arxiv.org/abs/2507.09233 https://…

Secondary Bounded Rationality: A Theory of How Algorithms Reproduce Structural Inequality in AI Hiring
AI-driven recruitment systems, while promising efficiency and objectivity, often perpetuate systemic inequalities by encoding cultural and social capital disparities into algorithmic decision making. This article develops and defends a novel theory of secondary bounded rationality, arguing that AI systems, despite their computational power, inherit and amplify human cognitive and structural biases through technical and sociopolitical constraints. Analyzing multimodal recruitment frameworks, we …

Bianchi Modular Forms and the Rationality of Periods
Gradin Anderson, Peter Harrigan, Louisa Hoback, McKayah Pugh, Tian An Wong
https://arxiv.org/abs/2509.17256 https://

Bianchi Modular Forms and the Rationality of Periods
Using an explicit Eichler-Shimura-Harder isomorphism, we establish the analogue of Manin's rationality theorem for Bianchi periods and hence special values of $L$-functions of Bianchi cusp forms. This gives a new short proof of a result of Hida in the case of Euclidean imaginary quadratic fields. In particular, we give an explicit proof using the space of Bianchi period polynomials constructed by Karabulut and describe the action of Hecke operators.

The Alignment Bottleneck
Wenjun Cao
https://arxiv.org/abs/2509.15932 https://arxiv.org/pdf/2509.15932

The Alignment Bottleneck
Large language models improve with scale, yet feedback-based alignment still exhibits systematic deviations from intended behavior. Motivated by bounded rationality in economics and cognitive science, we view judgment as resource-limited and feedback as a constrained channel. On this basis, we model the loop as a two-stage cascade $U \to H \to Y$ given $S$, with cognitive capacity $C_{\text{cog}|S}$ and average total capacity $\bar{C}_{\text{tot}|S}$. Our main result is a capacity-cou…

Game-Theoretic Modeling of Vehicle Unprotected Left Turns Considering Drivers' Bounded Rationality
Yuansheng Lian, Ke Zhang, Meng Li, Shen Li
https://arxiv.org/abs/2507.03002 …

Game-Theoretic Modeling of Vehicle Unprotected Left Turns Considering Drivers' Bounded Rationality
Modeling the decision-making behavior of vehicles presents unique challenges, particularly during unprotected left turns at intersections, where the uncertainty of human drivers is especially pronounced. In this context, connected autonomous vehicle (CAV) technology emerges as a promising avenue for effectively managing such interactions while ensuring safety and efficiency. Traditional approaches, often grounded in game theory assumptions of perfect rationality, may inadequately capture the co…

RationAnomaly: Log Anomaly Detection with Rationality via Chain-of-Thought and Reinforcement Learning
Song Xu, Yilun Liu, Minggui He, Mingchen Dai, Ziang Chen, Chunguang Zhao, Jingzhou Du, Shimin Tao, Weibin Meng, Shenglin Zhang, Yongqian Sun, Boxing Chen, Daimeng Wei
https://arxiv.org/abs/2509.14693…

RationAnomaly: Log Anomaly Detection with Rationality via Chain-of-Thought and Reinforcement Learning
Logs constitute a form of evidence signaling the operational status of software systems. Automated log anomaly detection is crucial for ensuring the reliability of modern software systems. However, existing approaches face significant limitations: traditional deep learning models lack interpretability and generalization, while methods leveraging Large Language Models are often hindered by unreliability and factual inaccuracies. To address these issues, we propose RationAnomaly, a novel framewor…

Equivariant rationality of Fano threefolds in the family \textnumero 2.12
Oliver Li, Joseph Malbon, Antoine Pinardin
https://arxiv.org/abs/2508.19471 https://

Equivariant rationality of Fano threefolds in the family \textnumero 2.12
We prove that a faithful group action on the smooth complete intersection $X$ of three divisors of bidegree $(1,1)$ in $\p^3\times\p^3$ is linearisable if and only if $\rk(\pic^G(X))\ne1$.

A game played by tandem-running ants: Hint of procedural rationality
Joy Das Bairagya, Udipta Chakraborti, Sumana Annagiri, Sagar Chakraborty
https://arxiv.org/abs/2509.17147 ht…

A game played by tandem-running ants: Hint of procedural rationality
Navigation through narrow passages during colony relocation by the tandem-running ants, $\textit{Diacamma}$ $\textit{indicum}$, is a tour de force of biological traffic coordination. Even on one-lane paths, the ants tactfully manage a bidirectional flow: Informed individuals (termed leaders) guide nest-mates (termed followers) from a suboptimal nest to a new optimal nest, and then return to recruit additional followers. We propose that encounters between the ants moving in opposite directions c…

Coordinating cooperation in stag-hunt game: Emergence of evolutionarily stable procedural rationality
Joy Das Bairagya, Sagar Chakraborty
https://arxiv.org/abs/2508.08301 https:…

Coordinating cooperation in stag-hunt game: Emergence of evolutionarily stable procedural rationality
Humans are bounded rational at best and this, we argue, has worked in their favour in the hunter-gatherer society where emergence of a coordinated action, leading to cooperation, is otherwise the standard stag-hunt dilemma (when individuals are rational). In line with the fact the humans strive for developing self-reputation by having less propensity to cheat than to be cheated, we observe that the payoff structure of the stag-hunt game appropriately modifies to that of coordination-II game. Su…

Quantifying Bounded Rationality: Formal Verification of Simon's Satisficing Through Flexible Stochastic Dominance
Jingyuan Li, Zhou Lin
https://arxiv.org/abs/2507.07052

Quantifying Bounded Rationality: Formal Verification of Simon's Satisficing Through Flexible Stochastic Dominance
This paper introduces Flexible First-Order Stochastic Dominance (FFSD), a mathematically rigorous framework that formalizes Herbert Simon's concept of bounded rationality using the Lean 4 theorem prover. We develop machine-verified proofs demonstrating that FFSD bridges classical expected utility theory with Simon's satisficing behavior through parameterized tolerance thresholds. Our approach yields several key results: (1) a critical threshold $\varepsilon < 1/2$ that guarantees uniqueness of …

Strategically Robust Game Theory via Optimal Transport
Nicolas Lanzetti, Sylvain Fricker, Saverio Bolognani, Florian D\"orfler, Dario Paccagnan
https://arxiv.org/abs/2507.15325

Strategically Robust Game Theory via Optimal Transport
In many game-theoretic settings, agents are challenged with taking decisions against the uncertain behavior exhibited by others. Often, this uncertainty arises from multiple sources, e.g., incomplete information, limited computation, bounded rationality. While it may be possible to guide the agents' decisions by modeling each source, their joint presence makes this task particularly daunting. Toward this goal, it is natural for agents to seek protection against deviations around the emergent be…

Symmetry-Guided Multi-Agent Inverse Reinforcement Learnin
Yongkai Tian, Yirong Qi, Xin Yu, Wenjun Wu, Jie Luo
https://arxiv.org/abs/2509.08257 https://arxi…

Symmetry-Guided Multi-Agent Inverse Reinforcement Learnin
In robotic systems, the performance of reinforcement learning depends on the rationality of predefined reward functions. However, manually designed reward functions often lead to policy failures due to inaccuracies. Inverse Reinforcement Learning (IRL) addresses this problem by inferring implicit reward functions from expert demonstrations. Nevertheless, existing methods rely heavily on large amounts of expert demonstrations to accurately recover the reward function. The high cost of collecting…

Evolution favours positively biased reasoning in sequential interactions with high future gains
Marco Saponara, Elias Fernandez Domingos, Jorge M. Pacheco, Tom Lenaerts
https://arxiv.org/abs/2508.20799

Evolution favours positively biased reasoning in sequential interactions with high future gains
Empirical evidence shows that human behaviour often deviates from game-theoretical rationality. For instance, humans may hold unrealistic expectations about future outcomes. As the evolutionary roots of such biases remain unclear, we investigate here how reasoning abilities and cognitive biases co-evolve using Evolutionary Game Theory. In our model, individuals in a population deploy a variety of unbiased and biased level-k reasoning strategies to anticipate others' behaviour in sequential inte…

On the Chow group of Moduli of parabolic connections
Pradeep Das, Snehajit Misra, Anoop Singh
https://arxiv.org/abs/2509.24504 https://arxiv.org/pdf/2509.2…

On the Chow group of Moduli of parabolic connections
We consider the moduli space of parabolic connections with rational generic weights over a compact Riemann surface of genus $g \geq 3$. We determine the Chow group of the moduli space of parabolic connections such that the underlying parabolic bundle is stable. We also discuss the rationality and rationally connectedness of the moduli space of parabolic connections.

Crosslisted article(s) found for q-bio.PE. https://arxiv.org/list/q-bio.PE/new
[1/1]:
- A game played by tandem-running ants: Hint of procedural rationality
Joy Das Bairagya, Udipta Chakraborti, Sumana Annagiri, Sagar Chakraborty

Partially rational preferences under ambiguity
Kensei Nakamura, Shohei Yanagita
https://arxiv.org/abs/2509.11660 https://arxiv.org/pdf/2509.11660

Partially rational preferences under ambiguity
Completeness and transitivity are standard rationality conditions in economics. However, under ambiguity, decision makers sometimes violate these requirements because of the difficulty of forming accurate predictions about ambiguous events. Motivated by this, we study various ambiguity preferences that partially satisfy completeness and transitivity. Our characterization results show that completeness and a novel yet natural weakening of transitivity correspond to two opposite ways of using mul…

Grationality, With a Spoon
L. Jeneva Clark
https://arxiv.org/abs/2508.08267 https://arxiv.org/pdf/2508.08267

Grationality, With a Spoon
The introduction of Grationality at a 2025 sectional meeting of the Mathematical Association of America installed a handle on a concept akin to rationality of numbers, but in a geometric context. A nice $n$-gon was defined to be a regular $n$-gon with side lengths that are natural numbers, and a number $n$ was defined to be grational if and only if there exists a nice $n$-gon such that its area equals the sum of areas of $n$ congruent nice $n$-gons. This paper shows several examples of grationa…

Enhancing Serendipity Recommendation System by Constructing Dynamic User Knowledge Graphs with Large Language Models
Qian Yong, Yanhui Li, Jialiang Shi, Yaguang Dou, Tian Qi
https://arxiv.org/abs/2508.04032

Enhancing Serendipity Recommendation System by Constructing Dynamic User Knowledge Graphs with Large Language Models
The feedback loop in industrial recommendation systems reinforces homogeneous content, creates filter bubble effects, and diminishes user satisfaction. Recently, large language models(LLMs) have demonstrated potential in serendipity recommendation, thanks to their extensive world knowledge and superior reasoning capabilities. However, these models still face challenges in ensuring the rationality of the reasoning process, the usefulness of the reasoning results, and meeting the latency requirem…

Replaced article(s) found for math.AC. https://arxiv.org/list/math.AC/new
[1/1]:
- $F$-rationality of two-dimensional graded rings with a rational singularity
Kohsuke Shibata

A rationality criterion for real Fano threefolds
Andrea Fanelli, Fr\'ed\'eric Mangolte
https://arxiv.org/abs/2507.04012 https://

A rationality criterion for real Fano threefolds
We study the connectedness of the real locus of smooth geometrically rational Fano threefolds and prove a sufficient criterion of $\mathbb{R}$-rationality.

Convergent Q-Learning for Infinite-Horizon General-Sum Markov Games through Behavioral Economics
Yizhou Zhang, Eric Mazumdar
https://arxiv.org/abs/2508.08669 https://

Convergent Q-Learning for Infinite-Horizon General-Sum Markov Games through Behavioral Economics
Risk-aversion and bounded rationality are two key characteristics of human decision-making. Risk-averse quantal-response equilibrium (RQE) is a solution concept that incorporates these features, providing a more realistic depiction of human decision making in various strategic environments compared to a Nash equilibrium. Furthermore a class of RQE has recently been shown in arXiv:2406.14156 to be universally computationally tractable in all finite-horizon Markov games, allowing for the developm…

Decomposing the Diagonals of Invariant Fields
David J Saltman
https://arxiv.org/abs/2508.18471 https://arxiv.org/pdf/2508.18471

Decomposing the Diagonals of Invariant Fields
This work begins the process of using the decomposition of the diagonal as a tool for studying the rationality of invariant fields of finite groups $G$. Our ground field must be characteristic 0 because of the use we make of Bertini theorems. The steps we take are, first, defining and studying an "open" version of Chow zero. Second, we use this to translate our study to that of a Chow group of $G$ Galois extensions. We prove a "Sylow" property and thereby yield a connection between the invarian…

Information Bulletin Strategy in Impatient Queuing
Anthony Kiggundu, Bin Han, Hans D. Schotten
https://arxiv.org/abs/2508.04241 https://arxiv.org/pdf/2508.…

Information Bulletin Strategy in Impatient Queuing
In Sixth Generation (6G) networks, decentralized control in multi-tenant systems is a suggested enabler for autonomous network operations. However, autonomy requires independent rationale decisions be taken by tenants. This rationality can only be underpinned by timely and continuous access to status information. Despite its importance, the questions of what information should be shared, how much should be communicated, and how frequently updates should be dispatched remain open research challe…

Uniform rationality of products with the plane
Juliusz Banecki
https://arxiv.org/abs/2508.07729 https://arxiv.org/pdf/2508.07729

Uniform rationality of products with the plane
Let $X$ be a nonsingular rational variety. We prove that $X\times \mathbb{C}^2$ is uniformly rational. It follows that nonsingular stably rational varieties are stably uniformly rational.

Replaced article(s) found for cs.GT. https://arxiv.org/list/cs.GT/new
[1/1]:
- Collaborative Mean Estimation Among Heterogeneous Strategic Agents: Individual Rationality, Fairn...
Alex Clinton, Yiding Chen, Xiaojin Zhu, Kirthevasan Kandasamy