Three papers at IJCAI 2024

Hyperparameter optimization (HPO) is indispensable for achieving optimal performance in machine learning tasks. A popular class of methods in this regard is based on Successive Halving (SHA), which casts HPO into a pure-exploration multi-armed bandit problem under finite sampling budget constraints. This is accomplished by considering hyperparameter configurations as arms and rewards as the negative validation losses. While enjoying theoretical guarantees as well as working well in practice, SHA comes, however, with several hyperparameters itself, one of which is the maximum budget that can be allocated to evaluate a single arm (hyperparameter configuration). Although there are already solutions to this meta hyperparameter optimization problem, such as the doubling trick or asynchronous extensions of SHA, these are either practically inefficient or lack theoretical guarantees. In this paper, we propose incremental SHA (iSHA), a synchronous extension of SHA, allowing to increase the maximum budget a posteriori while still enjoying theoretical guarantees. Our empirical analysis of HPO problems corroborates our theoretical findings and shows that iSHA is more resource-efficient than existing SHA-based approaches.

Abstract notions are often comprehended through analogies, wherein there exists correspondence or partial similarity with more concrete concepts. A fundamental aspect of human cognition involves synthesising embodied experiences into spatial schemas, which profoundly influence conceptualisation and underlie language acquisition. Recent studies have demonstrated that Large Language Models (LLMs) exhibit certain spatial intuitions akin to human language. For instance, both humans and LLMs tend to associate ↑ with hope more readily than with warn. However, the nuanced partial similarities between concrete (e.g., ↑) and abstract (e.g., hope) concepts, remain insufficiently explored. Therefore, we propose a novel methodology utilising analogical reasoning to elucidate these associations and examine whether LLMs adjust their associations in response to analogy-prompts. We find that analogy-prompting is slightly increasing agreement with human choices and the answers given by models include valid explanations supported by analogies, even when in disagreement with human results.

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are considered prohibitively expensive for large modern architectures. Local methods, which have emerged as a popular alternative, focus on specific parameter regions that can be approximated by functions with tractable integrals. While these often yield satisfactory empirical results, they fail, by definition, to account for the multi-modality of the parameter posterior. In this work, we argue that the dilemma between exact-but-unaffordable and cheap-but-inexact approaches can be mitigated by exploiting symmetries in the posterior landscape. Such symmetries, induced by neuron interchangeability and certain activation functions, manifest in different parameter values leading to the same functional output value. We show theoretically that the posterior predictive density in Bayesian neural networks can be restricted to a symmetry-free parameter reference set. By further deriving an upper bound on the number of Monte Carlo chains required to capture the functional diversity, we propose a straightforward approach for feasible Bayesian inference. Our experiments suggest that efficient sampling is indeed possible, opening up a promising path to accurate uncertainty quantification in deep learning.