arXiv subjects

Suhyun Bae

Publications and source records attributed to Suhyun Bae.

3 recordsLinked to original sources

arXiv2026

Prime Fourier Embeddings: A Principled Basis for Modular Arithmetic

Numbers have algebraic structure that standard neural embeddings often fail to expose. We introduce Prime Fourier Embeddings (PFE), which encode integers as prime-indexed (cos, sin) pairs derived from the harmonic analysis of Q, providing a pre-structured representation in which modular arithmetic reduces to selecting the relevant prime channel rather than discovering algebraic structure from scratch. We prove that any linear map equivariant with respect to the product group action on PFE must be block-diagonal with one independent block per prime -- a consequence of Schur's lemma applied to the resulting character decomposition. For square-free composite moduli, the Chinese Remainder Theorem predicts which prime channels are task-relevant. Both predictions are confirmed empirically: ablation studies show specialization ratios exceeding 500x between task-relevant and task-irrelevant channels, with perfect in-distribution test accuracy across all square-free composite moduli tested.

cs.LG↗

arXiv2026

Numbers Already Carry Their Own Embeddings

We introduce Adelic operation-preserved embeddings (AOE), a training-free representation that captures both a number's real value and its modular (p-adic) signatures. This construction preserves additive and multiplicative structure by design, turning numerical input into embeddings that "speak in the language of mathematics." Unlike prior approaches that rely on task-specific retraining, AOE is plug-and-play and drops seamlessly into existing architectures. On algebraic combinatorics benchmarks, it delivers consistent gains including the first-ever perfect accuracy on the Weaving Pattern task-while suggesting a principled path forward for overcoming the long-standing "number problem" in AI.

cs.LG↗

arXiv2025

One-Point Contraction: Erasing Representational Separability toward Irreversible Deep Forgetting

Machine unlearning is usually evaluated by what the classifier outputs: forget-set accuracy, confidence, membership-inference scores. We show that this is not enough. Across 14 representative unlearning methods on CIFAR-10 and SVHN, a single linear map fitted on a held-out calibration set, with no access to the forgotten data, reverses the unlearning in seconds and recovers forget-set accuracy to within a few percent of the original model. Recovered features even support pixel-level reconstruction through a generic decoder. We call this diagnostic Feature Mapping Recovery (FM-recovery). The pattern it exposes is uniform: current unlearning methods do not erase information from the representation, they apply an invertible linear distortion that hides it from one particular prediction head. We propose One-Point Contraction (OPC), an unlearning objective that collapses forget-set features to the origin while leaving the retain-set geometry intact. We prove that this contraction is equivalent to driving the predictive distribution to maximum entropy, so the same mechanism delivers behavioral forgetting and representation-level erasure at once. Forgotten queries land in a region the network treats as out-of-distribution, and the gradient signal on those queries collapses along with their features. OPC is the only method in our benchmark that survives FM-recovery, resists relearning and gradient-inversion attacks, and decouples forget from retain features in entangled settings, all without sacrificing retain or test accuracy.

cs.LG↗