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Researcher profile

Andrew Lee

Andrew Lee contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningArtificial IntelligenceComputationComputation and LanguageComputer Visionhep-latmath.COMethodology

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Published work

6 published item(s)

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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Hypergraph Fuss-Catalan Numbers

The Catalan numbers $C_n$ are an extremely well-studied sequence of numbers that appear as the answer to many combinatorial problems. Two generalizations of these numbers that have been studied are the Fuss-Catalan numbers and the Hypergraph Catalan numbers. In this paper, we study the combination of these, the Hypergraph Fuss-Catalan numbers. We provide some combinatorial interpretations of these numbers, as well as describe their generating function.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Analyzing and Improving Neural Networks by Generating Semantic Counterexamples through Differentiable Rendering

Even as deep neural networks (DNNs) have achieved remarkable success on vision-related tasks, their performance is brittle to transformations in the input. Of particular interest are semantic transformations that model changes that have a basis in the physical world, such as rotations, translations, changes in lighting or camera pose. In this paper, we show how differentiable rendering can be utilized to generate images that are informative, yet realistic, and which can be used to analyze DNN performance and improve its robustness through data augmentation. Given a differentiable renderer and a DNN, we show how to use off-the-shelf attacks from adversarial machine learning to generate semantic counterexamples -- images where semantic features are changed as to produce misclassifications or misdetections. We validate our approach on DNNs for image classification and object detection. For classification, we show that semantic counterexamples, when used to augment the dataset, (i) improve generalization performance (ii) enhance robustness to semantic transformations, and (iii) transfer between models. Additionally, in comparison to sampling-based semantic augmentation, our technique generates more informative data in a sample efficient manner.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Exactly computing the tail of the Poisson-Binomial Distribution

We offer ShiftConvolvePoibin, a fast exact method to compute the tail of a Poisson-Binomial distribution (PBD). Our method employs an exponential shift to retain its accuracy when computing a tail probability, and in practice we find that it is immune to the significant relative errors that other methods, exact or approximate, can suffer from when computing very small tail probabilities of the PBD. The accompanying R package is also competitive with the fastest implementations for computing the entire PBD.

0 citations0 reviewsNo code linkedOpen access
preprint2009arXiv

Radiative corrections to the m(oving)NRQCD action and heavy-light operators

Rare decays of B mesons, such as B \to K^*γand B\to K^{(*)}\ell^+\ell^- are loop suppressed in the Standard Model and sensitive to new physics. The final state meson in heavy-light decays at large recoil has sizeable momentum in the rest frame of the decaying meson. To reduce the resulting discretization errors we formulate the nonrelativistic heavy quark action in a moving frame. We discuss the perturbative renormalization of the leading order heavy-light operators in the resulting theory which is known as m(oving)NRQCD. We also present radiative corrections to the NRQCD action computed using automated lattice perturbation theory. By combining this technique with high-beta simulations in the weak coupling regime of the theory higher order loop corrections can be calculated very efficiently.

0 citations0 reviewsNo code linkedOpen access