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Benjamin Hoffman

Benjamin Hoffman contributes to research discovery and scholarly infrastructure.

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Published work

6 published item(s)

preprint2026arXiv

Multi-layer attentive probing improves transfer of audio representations for bioacoustics

Probing heads map the representations learned from audio by a machine learning model to downstream task labels and are a key component in evaluating representation learning. Most bioacoustic benchmarks use a fixed, low-capacity probe, such as a linear layer on the final encoder layer. While this standardization enables model comparisons, it may bias results by overlooking the interaction between encoder features and probe design. In this work, we systematically study different probing strategies across two bioacoustic benchmarks, BEANs and BirdSet. We evaluate last- and multi-layer probing, across linear and attention probes. We show that larger probe heads that leverage time information have superior performance. Our results suggest that current benchmarks may misrepresent encoder quality when relying on a last-layer probing setup. Multi-layer probing improves downstream task performance across all tested models, while attention probing has superior performance to linear probing for transformer models.

preprint2020arXiv

Action-angle coordinates on coadjoint orbits and multiplicity free spaces from partial tropicalization

Coadjoint orbits and multiplicity free spaces of compact Lie groups are important examples of symplectic manifolds with Hamiltonian groups actions. Constructing action-angle variables on these spaces is a challenging task. A fundamental result in the field is the Guillemin-Sternberg construction of Gelfand-Zeitlin integrable systems for the groups $K=U(n), SO(n)$. Extending these results to groups of other types is one of the goals of this paper. Partial tropicalizations are Poisson spaces with constant Poisson bracket built using techniques of Poisson-Lie theory and the geometric crystals of Berenstein-Kazhdan. They provide a bridge between dual spaces of Lie algebras ${\rm Lie}(K)^*$ with linear Poisson brackets and polyhedral cones which parametrize the canonical bases of irreducible modules of $G=K^\mathbb{C}$. We generalize the construction of partial tropicalizations to allow for arbitrary cluster charts, and apply it to questions in symplectic geometry. For each regular coadjoint orbit of a compact group $K$, we construct an exhaustion by symplectic embeddings of toric domains. As a by product we arrive at a conjectured formula for Gromov width of regular coadjoint orbits. We prove similar results for multiplicity free $K$-spaces.

preprint2013arXiv

A logical treatment of special relativity, with and without faster-than-light observers

There are three goals of this thesis. First: to present a concise yet accessible description of basic mathematical logic and model theory. Second: to develop an axiomatization of special relativity using only two undefined predicates. Ideally, these axioms should be empirically verifiable and supported by a large body of evidence. Finally: to weaken this axiomatization so as to allow for the existence of faster-than-light observers, which are normally excluded from the theory of special relativity. The modifications to the axiom system should be as slight as possible, and should be motivated by the question: what features of the original axiom system preclude the existence of faster-than-light observers?

preprint2013arXiv

A note on triangulations of sum sets

For finite sets A and B in the plane, we write A+B to denote the set of sums of the elements of A and B. In addition, we write tr(A) to denote the common number of triangles in any triangulation of the convex hull of A using the points of A as vertices. We consider the conjecture that tr(A+B)^{1/2}\geq tr(A)^{1/2}+tr(B)^{1/2}. If true, this conjecture would be a discrete, two-dimensional analogue to the Brunn-Minkowski inequality. We prove the conjecture in three special cases.

preprint2013arXiv

Iterated functions and the Cantor set in one dimension

In this paper we consider the long-term behavior of points in ${\mathbb R}$ under iterations of continuous functions. We show that, given any Cantor set $Λ^*$ embedded in ${\mathbb R}$, there exists a continuous function $F^*:{\mathbb R}\to{\mathbb R}$ such that the points that are bounded under iterations of $F^*$ are just those points in $Λ^*$. In the course of this, we find a striking similarity between the way in which we construct the Cantor middle-thirds set, and the way in which we find the points bounded under iterations of certain continuous functions.