Selected work

Representative Papers

Mapping the political landscape from data traces: multidimensional opinions of users, politicians and media outlets on X

Feb 06, 2026

This study addresses the limitations of existing political stance analysis, which predominantly relies on a unidimensional left–right spectrum rooted in the U.S. context and fails to capture the nuanced positions of users, politicians, and media across multiple policy dimensions in diverse democracies. To overcome this constraint, the work introduces the first multidimensional political stance dataset applicable across multiple countries, encompassing key dimensions such as immigration, European Union attitudes, liberal values, views on elites and institutions, nationalism, and environmental concerns. Leveraging behavioral data from the X platform and integrating content analysis with stance inference techniques, the authors develop a multidimensional positioning framework that incorporates activity-based metrics. Empirical validation demonstrates that the dataset and its associated benchmarks effectively support research on polarization and information diversity, substantially expanding the scope of computational political science beyond U.S.-centric paradigms.

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Shallower ReLU Network Representations via Exact Linear Algebra

Jul 22, 2026

This work investigates the minimal-depth ReLU neural network architectures capable of exactly representing the max function and general continuous piecewise linear (CPWL) functions. By reformulating the problem as a linear algebraic one over the rational field and leveraging symmetry reduction together with finite linear system solving, the authors construct networks with improved depth bounds. Their main contributions include the first proof that the max function over $ n \leq 10 $ inputs can be exactly realized by a ReLU network with only two hidden layers; for $ n > 10 $, they establish a depth upper bound of $ \lceil \log_5(n/2) \rceil + 1 $, which improves upon the previously known $ \log_3 $ bound. Furthermore, they extend these results to show that any CPWL function in dimension $ d \leq 9 $ can also be exactly represented by a two-hidden-layer ReLU network.

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ITGPT: A Transformer Based Architecture for the Generation of Dance Dance Revolution and In the Groove Charts

Jul 14, 2026

This work addresses the labor-intensive process of chart authoring in rhythm games such as Dance Dance Revolution and In the Groove by proposing ITGPT, the first end-to-end Transformer-based model for automatic chart generation. ITGPT jointly models audio and rhythmic features to achieve precise alignment between music and dance step sequences. The proposed method significantly outperforms existing approaches in both generation quality and computational efficiency: it produces charts that better adhere to rhythmic patterns while substantially reducing inference overhead. This advancement establishes a highly effective and practical paradigm for automated content creation in rhythm games.

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Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse

Jul 03, 2026

This work investigates the implicit bias of noisy stochastic gradient descent in infinitely wide two-layer ReLU networks. By modeling the training dynamics as a Wasserstein gradient flow via mean-field theory, the authors prove convergence to a unique stationary measure and show that the learned predictor exhibits a continuous piecewise affine structure determined by a finite arrangement of hyperplanes. Despite the infinite network width, input weights and biases align only along finitely many directions, leading to an effective collapse of the width; each such direction induces a unique ternary activation pattern over the training data, ensuring a non-redundant representation. Furthermore, the number of affine regions of the predictor is shown to be at most \(2P - 1\), where \(P\) denotes the number of linearly realizable dichotomies on the training set, revealing that model complexity is governed by the combinatorial geometry of the data.

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The Value Function Semi-Algebraic Set in Partially Observable Markov Decision Processes

Jun 01, 2026

This study investigates the set of achievable value functions in infinite-horizon partially observable Markov decision processes (POMDPs) under memoryless stochastic policies. Addressing the long-standing lack of a precise mathematical characterization of this set, the work establishes for the first time that it forms a semialgebraic set. Specifically, it explicitly constructs a system of polynomial inequalities—derived from the system dynamics, observation kernel, and reward structure—that fully describes the feasible value functions, thereby revealing the nonlinear constraints and intricate geometric structure induced by partial observability. This result generalizes the classical finding that the value function set in fully observable MDPs is polyhedral, clarifies the dependence of achievable values on the initial state distribution, and uncovers novel phenomena such as isolated locally optimal policies, thus providing a new theoretical foundation for POMDP policy optimization.

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Recent publications

Latest Papers

Shallower ReLU Network Representations via Exact Linear Algebra

Jul 22, 2026

This work investigates the minimal-depth ReLU neural network architectures capable of exactly representing the max function and general continuous piecewise linear (CPWL) functions. By reformulating the problem as a linear algebraic one over the rational field and leveraging symmetry reduction together with finite linear system solving, the authors construct networks with improved depth bounds. Their main contributions include the first proof that the max function over $ n \leq 10 $ inputs can be exactly realized by a ReLU network with only two hidden layers; for $ n > 10 $, they establish a depth upper bound of $ \lceil \log_5(n/2) \rceil + 1 $, which improves upon the previously known $ \log_3 $ bound. Furthermore, they extend these results to show that any CPWL function in dimension $ d \leq 9 $ can also be exactly represented by a two-hidden-layer ReLU network.

0 citationsRead paper

ITGPT: A Transformer Based Architecture for the Generation of Dance Dance Revolution and In the Groove Charts

Jul 14, 2026

This work addresses the labor-intensive process of chart authoring in rhythm games such as Dance Dance Revolution and In the Groove by proposing ITGPT, the first end-to-end Transformer-based model for automatic chart generation. ITGPT jointly models audio and rhythmic features to achieve precise alignment between music and dance step sequences. The proposed method significantly outperforms existing approaches in both generation quality and computational efficiency: it produces charts that better adhere to rhythmic patterns while substantially reducing inference overhead. This advancement establishes a highly effective and practical paradigm for automated content creation in rhythm games.

0 citationsRead paper

Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse

Jul 03, 2026

This work investigates the implicit bias of noisy stochastic gradient descent in infinitely wide two-layer ReLU networks. By modeling the training dynamics as a Wasserstein gradient flow via mean-field theory, the authors prove convergence to a unique stationary measure and show that the learned predictor exhibits a continuous piecewise affine structure determined by a finite arrangement of hyperplanes. Despite the infinite network width, input weights and biases align only along finitely many directions, leading to an effective collapse of the width; each such direction induces a unique ternary activation pattern over the training data, ensuring a non-redundant representation. Furthermore, the number of affine regions of the predictor is shown to be at most \(2P - 1\), where \(P\) denotes the number of linearly realizable dichotomies on the training set, revealing that model complexity is governed by the combinatorial geometry of the data.

0 citationsRead paper

The Value Function Semi-Algebraic Set in Partially Observable Markov Decision Processes

Jun 01, 2026

This study investigates the set of achievable value functions in infinite-horizon partially observable Markov decision processes (POMDPs) under memoryless stochastic policies. Addressing the long-standing lack of a precise mathematical characterization of this set, the work establishes for the first time that it forms a semialgebraic set. Specifically, it explicitly constructs a system of polynomial inequalities—derived from the system dynamics, observation kernel, and reward structure—that fully describes the feasible value functions, thereby revealing the nonlinear constraints and intricate geometric structure induced by partial observability. This result generalizes the classical finding that the value function set in fully observable MDPs is polyhedral, clarifies the dependence of achievable values on the initial state distribution, and uncovers novel phenomena such as isolated locally optimal policies, thus providing a new theoretical foundation for POMDP policy optimization.

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TriSearch: Learning to Optimize Triangulations via Bistellar Flips

May 28, 2026

This work addresses the challenge of optimizing objective functions over triangulations of polyhedral spaces without explicitly enumerating the exponentially large set of all possible triangulations. To this end, the authors propose TriSearch, a framework that integrates reinforcement learning with bistellar flips and leverages support-circuit-encoded representations of local sub-triangulation moves to enable dimension-agnostic, efficient search. The method demonstrates zero-shot generalization to larger polyhedra and achieves state-of-the-art performance on 3D tasks. Under a fixed computational budget in 4D, TriSearch discovers significantly more Calabi–Yau threefold-associated fine regular star triangulations than existing samplers, highlighting its superior exploration capability in high-dimensional combinatorial spaces.

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