Bayesian neural network unit priors and generalized Weibull-tail property

Mariia Vladimirova; Julyan Arbel; Stéphane Girard

Home/Archive/arXiv

arXiv · 2110.02885

Bayesian neural network unit priors and generalized Weibull-tail property

Mariia Vladimirova·Julyan Arbel·Stéphane Girard

View original source ↗Read source document ↗Export metadata ↓

Abstract

The connection between Bayesian neural networks and Gaussian processes gained a lot of attention in the last few years. Hidden units are proven to follow a Gaussian process limit when the layer width tends to infinity. Recent work has suggested that finite Bayesian neural networks may outperform their infinite counterparts because they adapt their internal representations flexibly. To establish solid ground for future research on finite-width neural networks, our goal is to study the prior induced on hidden units. Our main result is an accurate description of hidden units tails which shows that unit priors become heavier-tailed going deeper, thanks to the introduced notion of generalized Weibull-tail. This finding sheds light on the behavior of hidden units of finite Bayesian neural networks.

Explore related subjects

stat.ML cs.LG

Keep this discovery

BibTeX RIS

Mariia Vladimirova, Julyan Arbel, Stéphane Girard. 2021-10-06. Bayesian neural network unit priors and generalized Weibull-tail property. https://arxiv.org/abs/2110.02885

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Hilbert-Valued Functional Decomposition Framework for Explaining Time-Dependent Outputs

Feature-based explanations quantify features' influence on model predictions, but are primarily designed for scalar outputs. In many applications, however, outputs are functional or multivariate, such as time-dependent trajectories in demand forecasting. Consequently, existing approaches typically explain each output location independently, ignoring dependencies across the output components. We address this limitation by developing a unified framework for feature-based explanations of time-dependent outputs. Specifically, we generalize functional decomposition to Hilbert-valued prediction functions and extend an existing feature-based explanation framework to this setting. Our framework introduces kernel-based output representations that enable time-dependency-aware explanations at multiple levels of temporal granularity, including time-specific, time-resolved, and time-aggregated, while providing a unified view in which existing methods arise as special cases. We validate our framework on synthetic and real-world data, including intraday financial market volatility prediction and energy demand forecasting.

stat.ML↗

arXiv2026

Risk-Averse Decision Making with Multi-Level Reliability Guarantees

Many applications in engineering, including wireless broadcasting, require designs that provide performance certificates at different target outage levels. This paper studies the problem of maximizing the weighted average of such certificates in the presence of uncertainty about the true system state. The problem is shown to be equivalent to an optimization over nested prediction sets, connecting to the literature on conformal prediction and extending prior art on single-level risk-averse decision making. Furthermore, we derive a dual formulation that decouples optimization across input values. Numerical experiments on a diversity-based wireless transmission system illustrate the cost of enforcing multi-level certificates with a single shared policy and trace the Pareto trade-off between multiple reliability levels.

stat.ML↗

arXiv2026

A distribution-free certification framework for trustworthy crash-severity prediction

Crash-severity models inform screening, dispatch and site prioritization, yet are deployed without a finite-sample statement of what one prediction means. Off-the-shelf guarantees fail here, because the features that make crash severity distinctive defeat them: the KABCO outcome is ordinal, the recorded label is a field assessment agreeing with medical severity about half the time, erring in a structured way, and deployment crosses jurisdictions and years calibration never saw. We develop a certification layer that wraps any severity model unmodified, with distribution-free guarantees using this structure: contiguous ordinal sets that read as "B or worse"; per-class validity for any pre-declared partition, with an oracle efficiency characterization; transfer of coverage to unobserved true severity through a declared reporting band, with a worst-case sharpness result; a one-sided certificate under deployment shift; and severity-weighted risk control. The guarantees compose with an attributable slack budget. The same analysis bounds what certification can achieve. A certified set's informativeness is governed by a functional of the true law that no base model can evade and that cannot be lower-bounded distribution-free; given a declared misreporting channel identified from record-linkage data, a nonvacuous lower bound on that floor becomes computable. On 5.2 million Texas records across seven base models spanning four decades, the layer attaches identical validity and certifies, on the vulnerable road users, a model-independent floor on set width that no base model beats, separating it from a remainder that stays bounded but distribution-free unidentifiable. The framework is released as an open-source package with theorem-level tests.

stat.ML↗