arXiv subjects

Jinho Kang

Publications and source records attributed to Jinho Kang.

4 recordsLinked to original sources

arXiv2026

Machine Learning Beyond Statistical Consistency for Hybrid AI

We propose a new definition of machine learning, according to which a machine learns a function when it computes the function successfully, that is, when the value it returns for each input has a proper derivation in a formal system. We extend Gödel's Representability Theorem, which equates computation with derivation, to empirical targets in two ways: the theorem is extended to the computable reals, and the data are admitted into the system as empirical definitions that record what has been observed. We prove that a machine learns a true probability if and only if two conditions are met. The Truth Condition is that its estimate converges to the true probability, which is statistical consistency. The Assurance Condition is that the machine properly derives its own convergence inside the system. Learning thus lies beyond statistical consistency, for it requires a derivation of the convergence from the record. A global assumption about the data, such as the i.i.d. assumption, does not supply such a derivation, because it leads only to a circular one, as we show for PAC learning. On the other hand, the two conditions are met for the probability of a sentence over a finite ideal corpus. A real machine can approximate a true probability only if an ideal machine can learn it precisely, that is, only in a domain that meets the two conditions. Modern AI works in such a domain, and we offer this as a clue to its success. Modern AI is hybrid as well, in two senses: First, it performs two kinds of tasks, namely probabilistic ones such as predicting the next word and deductive ones such as proving and coding. Second, it combines two parts of different kinds, a statistical proposer and a deductive verifier, for proving and coding. Our framework explains both senses of hybridity in one formal system.

cs.LG↗

arXiv2025

Flat Posterior Does Matter For Bayesian Model Averaging

Bayesian neural networks (BNNs) estimate the posterior distribution of model parameters and utilize posterior samples for Bayesian Model Averaging (BMA) in prediction. However, despite the crucial role of flatness in the loss landscape in improving the generalization of neural networks, its impact on BMA has been largely overlooked. In this work, we explore how posterior flatness influences BMA generalization and empirically demonstrate that (1) most approximate Bayesian inference methods fail to yield a flat posterior and (2) BMA predictions, without considering posterior flatness, are less effective at improving generalization. To address this, we propose Flat Posterior-aware Bayesian Model Averaging (FP-BMA), a novel training objective that explicitly encourages flat posteriors in a principled Bayesian manner. We also introduce a Flat Posterior-aware Bayesian Transfer Learning scheme that enhances generalization in downstream tasks. Empirically, we show that FP-BMA successfully captures flat posteriors, improving generalization performance.

stat.ML↗

arXiv2024

A Theory of Machine Learning

We critically review three major theories of machine learning and provide a new theory according to which machines learn a function when the machines successfully compute it. We show that this theory challenges common assumptions in the statistical and the computational learning theories, for it implies that learning true probabilities is equivalent neither to obtaining a correct calculation of the true probabilities nor to obtaining an almost-sure convergence to them. We also briefly discuss some case studies from natural language processing and macroeconomics from the perspective of the new theory.

cs.LG↗

arXiv2013

Frequency comb-based microwave transfer over fiber with $7 \times 10^{-19}$ instability using fiber-loop optical-microwave phase detectors

We demonstrate a remote microwave/radio-frequency (RF) transfer technique based on the stabilization of a fiber link using a fiber-loop optical-microwave phase detector (FLOM-PD). This method compensates for the excess phase fluctuations introduced in fiber transfer by direct phase comparison between the optical pulse train reflected from the remote site and the local microwave/RF signal using the FLOM-PD. This enables sub-fs resolution and long-term stable link stabilization while having wide timing detection range and less demand in fiber dispersion compensation. The demonstrated relative frequency instability between 2.856-GHz RF oscillators separated by a 2.3-km fiber link is $7.6 \times 10^{-18}$ and $6.5 \times 10^{-19}$ at 1000 s and 82500 s averaging time, respectively.

physics.optics↗