Related papers: Local Inconsistency Resolution: The Interplay betw…
Inconsistent values are commonly encountered in real-world applications, which can negatively impact data analysis and decision-making. While existing research primarily focuses on identifying the smallest removal set to resolve…
In machine learning and statistical modeling, the mean square or absolute error is commonly used as an error metric, also called a "loss function." While effective in reducing the average error, this approach may fail to address localized…
We present a unified convergence theory for gradient-based training of neural network methods for partial differential equations (PDEs), covering both physics-informed neural networks (PINNs) and the Deep Ritz method. For linear PDEs, we…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
We build on abduction-based explanations for ma-chine learning and develop a method for computing local explanations for neural network models in natural language processing (NLP). Our explanations comprise a subset of the words of the…
Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…
An evaluation criterion for safe and trustworthy deep learning is how well the invariances captured by representations of deep neural networks (DNNs) are shared with humans. We identify challenges in measuring these invariances. Prior works…
Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
Miscalibration in deep learning refers to there is a discrepancy between the predicted confidence and performance. This problem usually arises due to the overfitting problem, which is characterized by learning everything presented in the…
Subjective Logic (SL) is one of well-known belief models that can explicitly deal with uncertain opinions and infer unknown opinions based on a rich set of operators of fusing multiple opinions. Due to high simplicity and applicability, SL…
In this paper, we consider the problem of empirical risk minimization (ERM) of smooth, strongly convex loss functions using iterative gradient-based methods. A major goal of this literature has been to compare different algorithms, such as…
The main question is: why and how can we ever predict based on a finite sample? The question is not answered by statistical learning theory. Here, I suggest that prediction requires belief in "predictability" of the underlying dependence,…
Traditional deep network training methods optimize a monolithic objective function jointly for all the components. This can lead to various inefficiencies in terms of potential parallelization. Local learning is an approach to…
Understanding black-box machine learning models is crucial for their widespread adoption. Learning globally interpretable models is one approach, but achieving high performance with them is challenging. An alternative approach is to explain…
Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a…
This paper establishes an approximation theorem for randomized neural networks (RaNNs) whose hidden-layer parameters are uniformly sampled from a prescribed bounded domain. Our analysis shows that, for RaNNs of the form $\mathop{\sum}_i W_i…
Self-paced learning (SPL) mimics the cognitive mechanism of humans and animals that gradually learns from easy to hard samples. One key issue in SPL is to obtain better weighting strategy that is determined by minimizer function. Existing…
Large language models are increasingly deployed in settings where reliability matters, yet output-level uncertainty signals such as token probabilities, entropy, and self-consistency can become brittle under calibration--deployment…
Inspired by the remarkable success of large neural networks, there has been significant interest in understanding the generalization performance of over-parameterized models. Substantial efforts have been invested in characterizing how…