Researcher profile

Martin Wattenberg

Martin Wattenberg contributes to research discovery and scholarly infrastructure.

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Artificial Intelligence Machine Learning astro-ph.HE Computation and Language gr-qc Human-Computer Interaction

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preprint2026arXiv

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.

preprint2026arXiv

Intentmaking and Sensemaking: Human Interaction with AI-Guided Mathematical Discovery

Artificial intelligence offers powerful new tools for scientific discovery, but the interaction paradigms required to effectively harness these systems remain underexplored. In this paper, we present findings from a formative user study with 11 expert mathematicians who used AlphaEvolve, an evolutionary coding agent, to tackle advanced problems in their fields of expertise. We identify and characterize a distinct workflow we term intentmaking, the iterative process of discovering, defining, and refining one's experimental goals through active system interaction. We frame this as a natural extension to sensemaking, the cognitive process of building an understanding of complex or novel data. We suggest that users enter a cycle of intentmaking (defining and updating their experiment) and sensemaking (interpreting the results) which repeats many times during the course of an investigation. Our documentation of these themes suggests an approach to designing AI tools for scientific discovery that goes beyond the existing question/answer model of many current systems, treating them as collaborative instruments rather than opaque black-box assistants.

preprint2026arXiv

Tensor Product Representation Probes Reveal Shared Structure Across Linear Directions

While researchers are finding concepts represented as linear directions in language models, a bag of linear directions fails to capture relational structure. To better understand this dichotomy, we study a model with known linear representations, but trained in a highly structured domain -- the board game Othello. While the model's internal board-state representation is linearly decodable, we find additional structure in the form of tensor product representations (TPRs). We train TPR probes to recover shared structure amongst the linear probes, yielding a factorization into square-embeddings, color-embeddings, and a binding matrix that composes them to construct the model's board-state representation. We find geometric signatures within the weights of our TPR probe that align with the structure of the board, but perhaps more importantly, that the linear probes can be recovered directly from the parameters of our TPR probe. Our findings suggest that directional representations may be projections of more structured underlying representations.

preprint2024arXiv

A Mechanistic Understanding of Alignment Algorithms: A Case Study on DPO and Toxicity

While alignment algorithms are now commonly used to tune pre-trained language models towards a user's preferences, we lack explanations for the underlying mechanisms in which models become ``aligned'', thus making it difficult to explain phenomena like jailbreaks. In this work we study a popular algorithm, direct preference optimization (DPO), and the mechanisms by which it reduces toxicity. Namely, we first study how toxicity is represented and elicited in a pre-trained language model, GPT2-medium. We then apply DPO with a carefully crafted pairwise dataset to reduce toxicity. We examine how the resulting model averts toxic outputs, and find that capabilities learned from pre-training are not removed, but rather bypassed. We use this insight to demonstrate a simple method to un-align the model, reverting it back to its toxic behavior.

preprint2022arXiv

Interpreting a Machine Learning Model for Detecting Gravitational Waves

We describe a case study of translational research, applying interpretability techniques developed for computer vision to machine learning models used to search for and find gravitational waves. The models we study are trained to detect black hole merger events in non-Gaussian and non-stationary advanced Laser Interferometer Gravitational-wave Observatory (LIGO) data. We produced visualizations of the response of machine learning models when they process advanced LIGO data that contains real gravitational wave signals, noise anomalies, and pure advanced LIGO noise. Our findings shed light on the responses of individual neurons in these machine learning models. Further analysis suggests that different parts of the network appear to specialize in local versus global features, and that this difference appears to be rooted in the branched architecture of the network as well as noise characteristics of the LIGO detectors. We believe efforts to whiten these "black box" models can suggest future avenues for research and help inform the design of interpretable machine learning models for gravitational wave astrophysics.

preprint2020arXiv

Neural Networks Trained on Natural Scenes Exhibit Gestalt Closure

The Gestalt laws of perceptual organization, which describe how visual elements in an image are grouped and interpreted, have traditionally been thought of as innate despite their ecological validity. We use deep-learning methods to investigate whether natural scene statistics might be sufficient to derive the Gestalt laws. We examine the law of closure, which asserts that human visual perception tends to "close the gap" by assembling elements that can jointly be interpreted as a complete figure or object. We demonstrate that a state-of-the-art convolutional neural network, trained to classify natural images, exhibits closure on synthetic displays of edge fragments, as assessed by similarity of internal representations. This finding provides support for the hypothesis that the human perceptual system is even more elegant than the Gestaltists imagined: a single law---adaptation to the statistical structure of the environment---might suffice as fundamental.

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