About

Jacob Abernethy is an Associate Professor at the College of Computing at Georgia Tech. His research focuses on the mathematics behind Machine Learning and Game Theory, with particular interest in discovering connections to Optimization, Statistics, and Economics. He is affiliated with the School of Computer Science and is involved in the Machine Learning (ML@GT) resources. His work emphasizes understanding the theoretical foundations of machine learning algorithms and their applications.

Research topics

• Artificial Intelligence
• Computer Science
• Mathematics
• Data Mining
• Machine Learning
• Applied mathematics
• Economics
• Mathematical optimization
• Geometry
• Statistics
• Statistical physics
• Engineering
• Physics

Selected publications

• Agentic Multimodal Reasoning: A Comprehensive Survey of Recent Advances, Taxonomies, Limitations, and Future Directions

  2026-01-01

  articleOpen access
  PublisherDOI

• Faster margin maximization rates for generic and adversarially robust optimization methods

  Mathematical Programming · 2025-10-09

  articleOpen accessSenior author

  Abstract First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias , plays a critical role in understanding the generalization capabilities of optimization algorithms. Recent research has revealed that in separable binary classification tasks gradient-descent-based methods exhibit an implicit bias for the $$\ell _2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -maximal margin classifier. Similarly, generic optimization methods, such as mirror descent and steepest descent, have been shown to converge to maximal margin classifiers defined by alternative geometries. While gradient-descent-based algorithms provably achieve fast implicit bias rates, corresponding rates in the literature for generic optimization methods are relatively slow. To address this limitation, we present a series of state-of-the-art implicit bias rates for mirror descent and steepest descent algorithms. Our primary technique involves transforming a generic optimization algorithm into an online optimization dynamic that solves a regularized bilinear game, providing a unified framework for analyzing the implicit bias of various optimization methods. Our accelerated rates are derived by leveraging the regret bounds of online learning algorithms within this game framework. We then show the flexibility of this framework by analyzing the implicit bias in adversarial training , and again obtain significantly improved convergence rates.

  PublisherDOI

• CapuchinAI 1.0: Development of a machine learning-based touchscreen paradigm to test cognition in wild capuchins

  bioRxiv (Cold Spring Harbor Laboratory) · 2025-11-10

  preprintOpen access

  ABSTRACT Advancing the study of primate cognition requires methods that preserve ecological validity while enabling the experimental control typical of laboratory research. We introduce CapuchinAI , a field-deployable touchscreen system that integrates real-time facial recognition with automated cognitive testing, providing a novel methodological framework for studying cognition in wild primates. Our approach combines a high-performing (&gt;97% accuracy) YOLOv7-based facial recognition model ( Multiple Capuchins v1.0 ) with a portable Raspberry Pi–driven touchscreen–reward apparatus designed for automated operation in natural habitats. The system detects approaching capuchins, initiates video recording, presents touchscreen stimuli, and dispenses food rewards contingent on task performance. During a two-week presentation to two habituated groups of wild white-faced capuchins ( Cebus imitator ) at the Taboga Forest Reserve, 16 individuals voluntarily interacted with the apparatus, 10 learned to trigger rewards , and 8 formed and retained robust screen–reward associations . The rapid habituation and learning rates demonstrate the feasibility of deploying AI-mediated cognitive experiments in the wild. CapuchinAI addresses several long-standing challenges in field cognition research by enabling: (1) autonomous, individualized task administration without researcher intervention; (2) standardized, repeatable trials across individuals and sessions; (3) scalable deployment across groups and sites; and (4) parallel data collection on behavior, identity, and performance. This methodology provides a blueprint for integrating machine learning, touchscreen testing, and automated reward delivery to study within- and between-individual cognitive variation under natural conditions. CapuchinAI represents a significant step toward long-term comparative research on primate cognition by making laboratory experimental paradigms accessible in the wild, bridging the gap between lab and field. Research Highlights We present CapuchinAI, a field-ready touchscreen testing station that uses real-time facial recognition to study cognition in wild capuchin monkeys We developed a YOLOv7-based facial recognition model (Multiple Capuchins v1.0) that identifies individual capuchins with &gt;97% precision and recall from static images, video, and live footage, enabling fully automated, individualized testing in the wild. We integrated a version of this model into a closed-loop touchscreen–reward pipeline that detects an approaching monkey, presents a basic learning task, and automatically delivers food rewards based on the monkey’s responses. Wild capuchins rapidly habituated and learned touchscreen–reward associations, showing that AI-enabled touchscreens provide a scalable field method for deploying lab-style cognitive tests and mapping individual differences across tasks, species, and sites.

  PublisherOA PDFDOI

• SPARQ: Synthetic Problem Generation for Reasoning via Quality-Diversity Algorithms

  ArXiv.org · 2025-06-06

  preprintOpen accessSenior author

  Large language model (LLM) driven synthetic data generation has emerged as a powerful method for improving model reasoning capabilities. However, most methods either distill large state-of-the-art models into small students or use natural ground-truth problem statements to guarantee problem statement quality. This limits the scalability of these approaches to more complex and diverse problem domains. To address this, we present SPARQ: Synthetic Problem Generation for Reasoning via Quality-Diversity Algorithms, a novel approach for generating high-quality and diverse synthetic math problem and solution pairs using only a single model by measuring a problem's solve-rate: a proxy for problem difficulty. Starting from a seed dataset of 7.5K samples, we generate over 20 million new problem-solution pairs. We show that filtering the generated data by difficulty and then fine-tuning the same model on the resulting data improves relative model performance by up to 24\%. Additionally, we conduct ablations studying the impact of synthetic data quantity, quality and diversity on model generalization. We find that higher quality, as measured by problem difficulty, facilitates better in-distribution performance. Further, while generating diverse synthetic data does not as strongly benefit in-distribution performance, filtering for more diverse data facilitates more robust OOD generalization. We also confirm the existence of model and data scaling laws for synthetically generated problems, which positively benefit downstream model generalization.

  PublisherOA PDFDOI

• Can Transformers Reason Logically? A Study in SAT Solving

  arXiv (Cornell University) · 2024-10-09

  preprintOpen access

  We formally study the logical reasoning capabilities of decoder-only Transformers in the context of the boolean satisfiability (SAT) problem. First, we prove by construction that decoder-only Transformers can decide 3-SAT, in a non-uniform model of computation, using backtracking and deduction via Chain-of-Thought (CoT). %We prove its correctness by showing trace equivalence to the well-known DPLL SAT-solving algorithm. Second, we implement our construction as a PyTorch model with a tool (PARAT) that we designed to empirically demonstrate its correctness and investigate its properties. Third, rather than \textit{programming} a transformer to reason, we evaluate empirically whether it can be \textit{trained} to do so by learning directly from algorithmic traces (``reasoning paths'') from our theoretical construction. The trained models demonstrate strong out-of-distribution generalization on problem sizes seen during training but has limited length generalization, which is consistent with the implications of our theoretical result

  PublisherOA PDFDOI

• Lexicographic Optimization: Algorithms and Stability

  arXiv (Cornell University) · 2024-05-02 · 1 citations

  preprintOpen access1st authorCorresponding

  A lexicographic maximum of a set $X \subseteq \mathbb{R}^n$ is a vector in $X$ whose smallest component is as large as possible, and subject to that requirement, whose second smallest component is as large as possible, and so on for the third smallest component, etc. Lexicographic maximization has numerous practical and theoretical applications, including fair resource allocation, analyzing the implicit regularization of learning algorithms, and characterizing refinements of game-theoretic equilibria. We prove that a minimizer in $X$ of the exponential loss function $L_c(\mathbf{x}) = \sum_i \exp(-c x_i)$ converges to a lexicographic maximum of $X$ as $c \rightarrow \infty$, provided that $X$ is stable in the sense that a well-known iterative method for finding a lexicographic maximum of $X$ cannot be made to fail simply by reducing the required quality of each iterate by an arbitrarily tiny degree. Our result holds for both near and exact minimizers of the exponential loss, while earlier convergence results made much stronger assumptions about the set $X$ and only held for the exact minimizer. We are aware of no previous results showing a connection between the iterative method for computing a lexicographic maximum and exponential loss minimization. We show that every convex polytope is stable, but that there exist compact, convex sets that are not stable. We also provide the first analysis of the convergence rate of an exponential loss minimizer (near or exact) and discover a curious dichotomy: While the two smallest components of the vector converge to the lexicographically maximum values very quickly (at roughly the rate $\frac{\log n}{c}$), all other components can converge arbitrarily slowly.

  PublisherOA PDFDOI

• Minimizing Dynamic Regret on Geodesic Metric Spaces

  arXiv (Cornell University) · 2023-02-17

  preprintOpen accessSenior author

  In this paper, we consider the sequential decision problem where the goal is to minimize the general dynamic regret on a complete Riemannian manifold. The task of offline optimization on such a domain, also known as a geodesic metric space, has recently received significant attention. The online setting has received significantly less attention, and it has remained an open question whether the body of results that hold in the Euclidean setting can be transplanted into the land of Riemannian manifolds where new challenges (e.g., curvature) come into play. In this paper, we show how to get optimistic regret bound on manifolds with non-positive curvature whenever improper learning is allowed and propose an array of adaptive no-regret algorithms. To the best of our knowledge, this is the first work that considers general dynamic regret and develops "optimistic" online learning algorithms which can be employed on geodesic metric spaces.

  PublisherOA PDFDOI

• Artificial Intelligence for Climate Smart Forestry: A Forward Looking Vision

  2023-11-01 · 4 citations

  article

  Forests and forest ecosystems are vital to our social, economic, and environmental well-being. However, climate change and climate-driven disturbances (CDDs) are undermining the health and resilience of forests worldwide and pose significant uncertainty to sustainable forest management. Climate-smart forestry (CSF) remains a grand challenge in practice due to our limited knowledge of how forests respond to climate change and our abilities to collect related information to empower decision making. Rapid advances in artificial intelligence (AI) can offer a timely opportunity to address the challenges in CSF. We argue that the AI-enabled, next-generation CSF can be achievable through synergistically coordinated and transdisciplinary efforts that develop and advance foundational and use-inspired AI technologies that can lead to building next-generation forest decision support systems.

  PublisherDOI

• Faster Margin Maximization Rates for Generic and Adversarially Robust Optimization Methods

  arXiv (Cornell University) · 2023-05-27

  preprintOpen accessSenior author

  First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias, plays a critical role in understanding the generalization capabilities of optimization algorithms. Recent research has revealed that in separable binary classification tasks gradient-descent-based methods exhibit an implicit bias for the $\ell_2$-maximal margin classifier. Similarly, generic optimization methods, such as mirror descent and steepest descent, have been shown to converge to maximal margin classifiers defined by alternative geometries. While gradient-descent-based algorithms provably achieve fast implicit bias rates, corresponding rates in the literature for generic optimization methods are relatively slow. To address this limitation, we present a series of state-of-the-art implicit bias rates for mirror descent and steepest descent algorithms. Our primary technique involves transforming a generic optimization algorithm into an online optimization dynamic that solves a regularized bilinear game, providing a unified framework for analyzing the implicit bias of various optimization methods. Our accelerated rates are derived by leveraging the regret bounds of online learning algorithms within this game framework. We then show the flexibility of this framework by analyzing the implicit bias in adversarial training, and again obtain significantly improved convergence rates.

  PublisherOA PDFDOI

• Faster Margin Maximization Rates for Generic Optimization Methods

  2023-01-01

  article1st authorCorresponding
  PublisherDOI

Recent grants

• CAREER: Machine Learning through the Lens of Economics (And Vice Versa)

  NSF · $403k · 2015–2018

• CAREER: Machine Learning through the Lens of Economics (And Vice Versa)

  NSF · $310k · 2017–2020

• RI: Small: Training Modularized Learning Systems

  NSF · $466k · 2019–2022

Frequent coauthors

• Ambuj Tewari

  18 shared

• Peter L. Bartlett

  15 shared

• Jun-Kun Wang

  Yale University

  14 shared

• Alexander Rakhlin

  14 shared

• Rafael Frongillo

  13 shared

• Chansoo Lee

  13 shared

• Eric M. Schwartz

  13 shared

• Andre Wibisono

  12 shared

Education

• Ph.D., Electrical Engineering and Computer Science

  Massachusetts Institute of Technology

  2004

• M.S., Electrical Engineering and Computer Science

  Massachusetts Institute of Technology

  2000

• B.S., Computer Science and Engineering

  University of California, San Diego

  1998