Thomas Y. Chen

Thomas Y. Chen, Biprateep Dey, Aishik Ghosh et al.

Estimating uncertainty is at the core of performing scientific measurements in HEP: a measurement is not useful without an estimate of its uncertainty. The goal of uncertainty quantification (UQ) is inextricably linked to the question, "how do we physically and statistically interpret these uncertainties?" The answer to this question depends not only on the computational task we aim to undertake, but also on the methods we use for that task. For artificial intelligence (AI) applications in HEP, there are several areas where interpretable methods for UQ are essential, including inference, simulation, and control/decision-making. There exist some methods for each of these areas, but they have not yet been demonstrated to be as trustworthy as more traditional approaches currently employed in physics (e.g., non-AI frequentist and Bayesian methods). Shedding light on the questions above requires additional understanding of the interplay of AI systems and uncertainty quantification. We briefly discuss the existing methods in each area and relate them to tasks across HEP. We then discuss recommendations for avenues to pursue to develop the necessary techniques for reliable widespread usage of AI with UQ over the next decade.

Gabriele Benelli, Thomas Y. Chen, Javier Duarte et al.

The growing role of data science (DS) and machine learning (ML) in high-energy physics (HEP) is well established and pertinent given the complex detectors, large data, sets and sophisticated analyses at the heart of HEP research. Moreover, exploiting symmetries inherent in physics data have inspired physics-informed ML as a vibrant sub-field of computer science research. HEP researchers benefit greatly from materials widely available materials for use in education, training and workforce development. They are also contributing to these materials and providing software to DS/ML-related fields. Increasingly, physics departments are offering courses at the intersection of DS, ML and physics, often using curricula developed by HEP researchers and involving open software and data used in HEP. In this white paper, we explore synergies between HEP research and DS/ML education, discuss opportunities and challenges at this intersection, and propose community activities that will be mutually beneficial.

John C. Dorelli, Chris Bard, Thomas Y. Chen et al.

Traditionally, data analysis and theory have been viewed as separate disciplines, each feeding into fundamentally different types of models. Modern deep learning technology is beginning to unify these two disciplines and will produce a new class of predictively powerful space weather models that combine the physical insights gained by data and theory. We call on NASA to invest in the research and infrastructure necessary for the heliophysics' community to take advantage of these advances.

M. I. Sitnov, G. K. Stephens, V. G. Merkin et al.

In the Earth's magnetosphere, there are fewer than a dozen dedicated probes beyond low-Earth orbit making in-situ observations at any given time. As a result, we poorly understand its global structure and evolution, the mechanisms of its main activity processes, magnetic storms, and substorms. New Artificial Intelligence (AI) methods, including machine learning, data mining, and data assimilation, as well as new AI-enabled missions will need to be developed to meet this Sparse Data challenge.

Thomas Chen, Patricia Muñoz Ewald

In this paper, we explicitly determine local and global minimizers of the $\mathcal{L}^2$ cost function in underparametrized Deep Learning (DL) networks; our main goal is to shed light on their geometric structure and properties. We accomplish this by a direct construction, without invoking the gradient descent flow at any point of this work. We specifically consider $L$ hidden layers, a ReLU ramp activation function, an $\mathcal{L}^2$ Schatten class (or Hilbert-Schmidt) cost function, input and output spaces $\mathbb{R}^Q$ with equal dimension $Q\geq1$, and hidden layers also defined on $\mathbb{R}^{Q}$; the training inputs are assumed to be sufficiently clustered. The training input size $N$ can be arbitrarily large - thus, we are considering the underparametrized regime. More general settings are left to future work. We construct an explicit family of minimizers for the global minimum of the cost function in the case $L\geq Q$, which we show to be degenerate. Moreover, we determine a set of $2^Q-1$ distinct degenerate local minima of the cost function. In the context presented here, the concatenation of hidden layers of the DL network is reinterpreted as a recursive application of a {\em truncation map} which "curates" the training inputs by minimizing their noise to signal ratio.

Thomas Chen, Patrícia Muñoz Ewald

In this paper, we approach the problem of cost (loss) minimization in underparametrized shallow ReLU networks through the explicit construction of upper bounds which appeal to the structure of classification data, without use of gradient descent. A key focus is on elucidating the geometric structure of approximate and precise minimizers. We consider an $L^2$ cost function, input space $\mathbb{R}^M$, output space ${\mathbb R}^Q$ with $Q\leq M$, and training input sample size that can be arbitrarily large. We prove an upper bound on the minimum of the cost function of order $O(δ_P)$ where $δ_P$ measures the signal-to-noise ratio of training data. In the special case $M=Q$, we explicitly determine an exact degenerate local minimum of the cost function, and show that the sharp value differs from the upper bound obtained for $Q\leq M$ by a relative error $O(δ_P^2)$. The proof of the upper bound yields a constructively trained network; we show that it metrizes a particular $Q$-dimensional subspace in the input space ${\mathbb R}^M$. We comment on the characterization of the global minimum of the cost function in the given context.

Thomas Chen, Patrícia Muñoz Ewald

We prove that the standard gradient flow in parameter space that underlies many training algorithms in deep learning can be continuously deformed into an adapted gradient flow which yields (constrained) Euclidean gradient flow in output space. Moreover, for the $L^{2}$ loss, if the Jacobian of the outputs with respect to the parameters is full rank (for fixed training data), then the time variable can be reparametrized so that the resulting flow is simply linear interpolation, and a global minimum can be achieved. For the cross-entropy loss, under the same rank condition and assuming the labels have positive components, we derive an explicit formula for the unique global minimum.

Thomas Y. Chen

We establish the first information-theoretic limits for multimodal retrieval. Casting ranking as lossy source coding, we derive a single-letter rate-distortion function $R(D)$ for reciprocal-rank distortion and prove a converse bound that splits into a modality-balanced term plus a skew penalty $κ\,ΔH$ capturing entropy imbalance and cross-modal redundancy. We then construct an explicit entropy-weighted stochastic quantizer with an adaptive, per-modality temperature decoder; a Blahut-Arimoto argument shows this scheme achieves distortion within $O(n^{-1})$ of $R(D)$ using $n$ training triples. A VC-type analysis yields the first finite-sample excess-risk bound whose complexity scales sub-linearly in both the number of modalities and the entropy gap. Experiments on controlled Gaussian mixtures and Flickr30k confirm that our adaptive codes sit within two percentage points of the theoretical frontier, while fixed-temperature and naive CLIP baselines lag significantly. Taken together, our results give a principled answer to "how many bits per query are necessary" for high-quality multimodal retrieval and provide design guidance for entropy-aware contrastive objectives, continual-learning retrievers, and retrieval-augmented generators.

Thomas Y. Chen

In recent years, the monarch butterfly's iconic migration patterns have come under threat from a number of factors, from climate change to pesticide use. To track trends in their populations, scientists as well as citizen scientists must identify individuals accurately. This is uniquely key for the study of monarch butterflies because there exist other species of butterfly, such as viceroy butterflies, that are "look-alikes" (coined by the Convention on International Trade in Endangered Species of Wild Fauna and Flora), having similar phenotypes. To tackle this problem and to aid in more efficient identification, we present MonarchNet, the first comprehensive dataset consisting of butterfly imagery for monarchs and five look-alike species. We train a baseline deep-learning classification model to serve as a tool for differentiating monarch butterflies and its various look-alikes. We seek to contribute to the study of biodiversity and butterfly ecology by providing a novel method for computational classification of these particular butterfly species. The ultimate aim is to help scientists track monarch butterfly population and migration trends in the most precise and efficient manner possible.

Thomas Y. Chen

Natural disasters ravage the world's cities, valleys, and shores on a regular basis. Deploying precise and efficient computational mechanisms for assessing infrastructure damage is essential to channel resources and minimize the loss of life. Using a dataset that includes labeled pre- and post- disaster satellite imagery, we take a machine learning-based remote sensing approach and train multiple convolutional neural networks (CNNs) to assess building damage on a per-building basis. We present a novel methodology of interpretable deep learning that seeks to explicitly investigate the most useful modalities of information in the training data to create an accurate classification model. We also investigate which loss functions best optimize these models. Our findings include that ordinal-cross entropy loss is the most optimal criterion for optimization to use and that including the type of disaster that caused the damage in combination with pre- and post-disaster training data most accurately predicts the level of damage caused. Further, we make progress in the qualitative representation of which parts of the images that the model is using to predict damage levels, through gradient-weighted class activation mapping (Grad-CAM). Our research seeks to computationally contribute to aiding in this ongoing and growing humanitarian crisis, heightened by anthropogenic climate change.