arXiv subjects

Benjamin Friedman

Publications and source records attributed to Benjamin Friedman.

5 recordsLinked to original sources

arXiv2026

Annotation-Free Furniture Codes: What They Encode, and How Far They Transfer

Layout-based 3D scene synthesizers place each object using two human-annotated channels: a categorical class label and a canonical-pose convention. We ask whether a single self-supervised token derived from object geometry can replace both, and study such tokens directly as a representation, decoupled from any synthesizer. A Finite Scalar Quantization (FSQ) point-cloud autoencoder is chamfer-trained on placed 3D-FUTURE furniture with no labels or pose annotations. Diagnostic probes recover fine-category (62.6 +/- 0.5%), super-category (85.6 +/- 1.3%), and yaw (52.7 +/- 0.5 deg) from the codes alone. Swapping the chamfer target from the rotated to the un-rotated point cloud collapses the yaw signal while raising class recovery, showing the codes' rotation content can be set by the training objective. Scaling across asset libraries needs codes that transfer; on an unseen dataset (ShapeNet), alignment is category-dependent: box-like furniture transfers, organically-shaped furniture does not, and a target-blind augmentation partly closes the gap.

cs.CV↗

arXiv2026

When and How to Canonize: A Generalization Perspective

While invariant architectures are standard for processing symmetric data, there is growing interest in achieving invariance by applying group averaging or canonization to non-invariant backbones. However, the theoretical generalization properties of these alternative strategies remain poorly understood. We introduce a theoretical framework to analyze the generalization error of these methods by bounding their covering numbers. We establish a rigorous generalization hierarchy: the error bounds of canonized models are at best equal to the error bounds of structurally invariant and group-averaged models, and at worst equal to the bounds of non-invariant baselines. Furthermore, we show that there exist optimal canonizations which attain the optimal error bounds, and poor canonizations which attain the non-invariant error bounds, and that this depends on the regularity of the canonization. Finally, applying this framework to permutation groups in point cloud processing, we rigorously prove that the covering number of lexicographical sorting grows exponentially with point cloud dimension, whereas Hilbert curve canonization guarantees polynomial growth. This provides the first formal theoretical justification for the empirical success of Hilbert curve serialization in state-of-the-art point cloud architectures. We conclude with experiments that support our theoretical claims. Code is available at https://github.com/yonatansverdlov/Canonization

cs.LG↗

arXiv2025

Generic special Lagrangian moduli spaces of a non-K\"ahler Calabi--Yau threefold

Given a (possibly non-K\"ahler) Calabi--Yau threefold $(X,\Omega)$, we introduce the notion of a (perturbed) special Lagrangian (SL) submanifold of $(X,\omega,\Omega)$, where $\omega$ is a Hermitian metric on $X$. The equations defining this class of submanifolds reduce to the usual SL equations when $\omega$ is a K\"ahler metric. Using the Sard--Smale technique, we prove the existence of a comeagre set of Hermitian metrics $\omega$ on $X$ such that the moduli space of perturbed SL submanifolds in $(X,\omega,\Omega)$ consists of isolated points.

math.DG↗

arXiv2024

Gromov-Hausdorff continuity of non-K\"ahler Calabi-Yau conifold transitions

We study the geometry of Calabi-Yau conifold transitions. This deformation process is known to possibly connect a K\"ahler threefold to a non-K\"ahler threefold. We use balanced and Hermitian-Yang-Mills metrics to geometrize the conifold transition and show that the whole operation is continuous in the Gromov-Hausdorff topology.

math.DG↗

arXiv2019

Girth conditions and Rota's basis conjecture

Rota's basis conjecture (RBC) states that given a collection $\mathcal{B}$ of $n$ bases in a matroid $M$ of rank $n$, one can always find $n$ disjoint rainbow bases with respect to $\mathcal{B}$. In this paper, we show that if $M$ has girth at least $n-o(\sqrt{n})$, and no element of $M$ belongs to more than $o(\sqrt{n})$ bases in $\mathcal{B}$, then one can find at least $n - o(n)$ disjoint rainbow bases with respect to $\mathcal{B}$. This result can be seen as an extension of the work of Geelen and Humphries, who proved RBC in the case where $M$ is paving, and $\mathcal{B}$ is a pairwise disjoint collection. We make extensive use of the cascade idea introduced by Buci\'c et al.

math.CO↗