arXiv subjects

Dimitri Kanevsky

Publications and source records attributed to Dimitri Kanevsky.

6 recordsLinked to original sources

arXiv2026

AI co-mathematician: Accelerating mathematicians with agentic AI

We introduce the AI co-mathematician, a workbench for mathematicians to interactively leverage AI agents to pursue open-ended research. The AI co-mathematician is optimized to provide holistic support for the exploratory and iterative reality of mathematical workflows, including ideation, literature search, computational exploration, theorem proving and theory building. By providing an asynchronous, stateful workspace that manages uncertainty, refines user intent, tracks failed hypotheses, and outputs native mathematical artifacts, the system mirrors human collaborative workflows. In early tests, the AI co-mathematician helped researchers solve open problems, identify new research directions, and uncover overlooked literature references. Besides demonstrating a highly interactive paradigm for AI-assisted mathematical discovery, the AI co-mathematician also achieves state of the art results on hard problem-solving benchmarks, including scoring 48% on FrontierMath Tier 4, a new high score among all AI systems evaluated.

cs.AI↗

arXiv2026

$R$-equivalence on Cubic Surfaces I: Existing Cases with Non-Trivial Universal Equivalence

Let $V$ be a smooth cubic surface over a $p$-adic field $k$ with good reduction. Swinnerton-Dyer (1981) proved that $R$-equivalence is trivial on $V(k)$ except perhaps if $V$ is one of three special types--those whose $R$-equivalence he could not bound by proving the universal (admissible) equivalence is trivial. We consider all surfaces $V$ currently known to have non-trivial universal equivalence. Beyond being intractable to Swinnerton-Dyer's approach, we observe that if these surfaces also had non-trivial $R$-equivalence, they would contradict Colliot-Th\'el\`ene and Sansuc's conjecture regarding the $k$-rationality of universal torsors for geometrically rational surfaces. By devising new methods to study $R$-equivalence, we prove that for 2-adic surfaces with all-Eckardt reductions (the third special type, which contains every existing case of non-trivial universal equivalence), $R$-equivalence is trivial or of exponent 2. For the explicit cases, we confirm triviality: the diagonal cubic $X^3+Y^3+Z^3+\zeta_3 T^3=0$ over $\mathbb{Q}_2(\zeta_3)$--answering a long-standing question of Manin's (Cubic Forms, 1972)--and the cubic with universal equivalence of exponent 2 (Kanevsky, 1982). This is the first in a series of works derived from a year of interactions with generative AI models such as AlphaEvolve and Gemini 3 Deep Think, with the latter proving many of our lemmas. We disclose the timeline and nature of their use towards this paper, and describe our broader AI-assisted research program in a companion report (in preparation).

math.AG↗

arXiv2025

SpeechCompass: Enhancing Mobile Captioning with Diarization and Directional Guidance via Multi-Microphone Localization

Speech-to-text capabilities on mobile devices have proven helpful for hearing and speech accessibility, language translation, note-taking, and meeting transcripts. However, our foundational large-scale survey (n=263) shows that the inability to distinguish and indicate speaker direction makes them challenging in group conversations. SpeechCompass addresses this limitation through real-time, multi-microphone speech localization, where the direction of speech allows visual separation and guidance (e.g., arrows) in the user interface. We introduce efficient real-time audio localization algorithms and custom sound perception hardware running on a low-power microcontroller and four integrated microphones, which we characterize in technical evaluations. Informed by a large-scale survey (n=494), we conducted an in-person study of group conversations with eight frequent users of mobile speech-to-text, who provided feedback on five visualization styles. The value of diarization and visualizing localization was consistent across participants, with everyone agreeing on the value and potential of directional guidance for group conversations.

cs.HC↗

arXiv2021

An example of a non-associative Moufang loop of point classes on a cubic surface

Let $V$ be a cubic surface defined by the equation $T_0^3+T_1^3+T_2^3+\theta T_3^3=0$ over a quadratic extension of 3-adic numbers $k=\mathbb{Q}_3(\theta)$, where $\theta^3=1$. We show that a relation on a set of geometric k-points on $V$ modulo $(1-\theta)^3$ (in a ring of integers of $k$) defines an admissible relation and a commutative Moufang loop associated with classes of this admissible equivalence is non-associative. This answers a problem that was formulated by Yu. I. Manin more than 50 years ago about existence of a cubic surface with a non-associative Moufang loop of point classes.

math.NT↗

arXiv2019

Parrotron: An End-to-End Speech-to-Speech Conversion Model and its Applications to Hearing-Impaired Speech and Speech Separation

We describe Parrotron, an end-to-end-trained speech-to-speech conversion model that maps an input spectrogram directly to another spectrogram, without utilizing any intermediate discrete representation. The network is composed of an encoder, spectrogram and phoneme decoders, followed by a vocoder to synthesize a time-domain waveform. We demonstrate that this model can be trained to normalize speech from any speaker regardless of accent, prosody, and background noise, into the voice of a single canonical target speaker with a fixed accent and consistent articulation and prosody. We further show that this normalization model can be adapted to normalize highly atypical speech from a deaf speaker, resulting in significant improvements in intelligibility and naturalness, measured via a speech recognizer and listening tests. Finally, demonstrating the utility of this model on other speech tasks, we show that the same model architecture can be trained to perform a speech separation task

eess.AS↗

arXiv2013

Semistochastic Quadratic Bound Methods

Partition functions arise in a variety of settings, including conditional random fields, logistic regression, and latent gaussian models. In this paper, we consider semistochastic quadratic bound (SQB) methods for maximum likelihood inference based on partition function optimization. Batch methods based on the quadratic bound were recently proposed for this class of problems, and performed favorably in comparison to state-of-the-art techniques. Semistochastic methods fall in between batch algorithms, which use all the data, and stochastic gradient type methods, which use small random selections at each iteration. We build semistochastic quadratic bound-based methods, and prove both global convergence (to a stationary point) under very weak assumptions, and linear convergence rate under stronger assumptions on the objective. To make the proposed methods faster and more stable, we consider inexact subproblem minimization and batch-size selection schemes. The efficacy of SQB methods is demonstrated via comparison with several state-of-the-art techniques on commonly used datasets.

stat.ML↗