A Quantum Tensor Network-Based Viewpoint for Modeling and Analysis of Time Series Data

Accurate uncertainty quantification is a critical challenge in machine learning. While neural networks are highly versatile and capable of learning complex patterns, they often lack interpretability due to their ``black box'' nature. On the other hand, probabilistic ``white box'' models, though interpretable, often suffer from a significant performance gap when compared to neural networks. To address this, we propose a novel quantum physics-based ``white box'' method that offers both accurate uncertainty quantification and enhanced interpretability. By mapping the kernel mean embedding (KME) of a time series data vector to a reproducing kernel Hilbert space (RKHS), we construct a tensor network-inspired 1D spin chain Hamiltonian, with the KME as one of its eigen-functions or eigen-modes. We then solve the associated Schr{ö}dinger equation and apply perturbation theory to quantify uncertainty, thereby improving the interpretability of tasks performed with the quantum tensor network-based model. We demonstrate the effectiveness of this methodology, compared to state-of-the-art ``white box" models, in change point detection and time series clustering, providing insights into the uncertainties associated with decision-making throughout the process.

Novel Deep Neural Network Classifier Characterization Metrics with Applications to Dataless Evaluation

The mainstream AI community has seen a rise in large-scale open-source classifiers, often pre-trained on vast datasets and tested on standard benchmarks; however, users facing diverse needs and limited, expensive test data may be overwhelmed by available choices. Deep Neural Network (DNN) classifiers undergo training, validation, and testing phases using example dataset, with the testing phase focused on determining the classification accuracy of test examples without delving into the inner working of the classifier. In this work, we evaluate a DNN classifier's training quality without any example dataset. It is assumed that a DNN is a composition of a feature extractor and a classifier which is the penultimate completely connected layer. The quality of a classifier is estimated using its weight vectors. The feature extractor is characterized using two metrics that utilize feature vectors it produces when synthetic data is fed as input. These synthetic input vectors are produced by backpropagating desired outputs of the classifier. Our empirical study of the proposed method for ResNet18, trained with CAFIR10 and CAFIR100 datasets, confirms that data-less evaluation of DNN classifiers is indeed possible.

Minimizing Chebyshev Prototype Risk Magically Mitigates the Perils of Overfitting

Overparameterized deep neural networks (DNNs), if not sufficiently regularized, are susceptible to overfitting their training examples and not generalizing well to test data. To discourage overfitting, researchers have developed multicomponent loss functions that reduce intra-class feature correlation and maximize inter-class feature distance in one or more layers of the network. By analyzing the penultimate feature layer activations output by a DNN's feature extraction section prior to the linear classifier, we find that modified forms of the intra-class feature covariance and inter-class prototype separation are key components of a fundamental Chebyshev upper bound on the probability of misclassification, which we designate the Chebyshev Prototype Risk (CPR). While previous approaches' covariance loss terms scale quadratically with the number of network features, our CPR bound indicates that an approximate covariance loss in log-linear time is sufficient to reduce the bound and is scalable to large architectures. We implement the terms of the CPR bound into our Explicit CPR (exCPR) loss function and observe from empirical results on multiple datasets and network architectures that our training algorithm reduces overfitting and improves upon previous approaches in many settings. Our code is available at https://github.com/Deano1718/Regularization_exCPR .

Fantastic DNN Classifiers and How to Identify them without Data

Current algorithms and architecture can create excellent DNN classifier models from example data. In general, larger training datasets result in better model estimations, which improve test performance. Existing methods for predicting generalization performance are based on hold-out test examples. To the best of our knowledge, at present no method exists that can estimate the quality of a trained DNN classifier without test data. In this paper, we show that the quality of a trained DNN classifier can be assessed without any example data. We consider DNNs to be composed of a feature extractor and a feature classifier; the feature extractor's output is fed to the classifier. The proposed method iteratively creates class prototypes in the input space for each class by minimizing a cross-entropy loss function at the output of the network. We use these prototypes and their feature relationships to reveal the quality of the classifier. We have developed two metrics: one using the features of the prototypes and the other using adversarial examples corresponding to each prototype. Empirical evaluations show that accuracy obtained from test examples is directly proportional to quality measures obtained from the proposed metrics. We report our observations for ResNet18 with Tiny ImageNet, CIFAR100, and CIFAR10 datasets. The proposed metrics can be used to compare performances of two or more classifiers without test examples.

A Perturbation Resistant Transformation and Classification System for Deep Neural Networks

Deep convolutional neural networks accurately classify a diverse range of natural images, but may be easily deceived when designed, imperceptible perturbations are embedded in the images. In this paper, we design a multi-pronged training, input transformation, and image ensemble system that is attack agnostic and not easily estimated. Our system incorporates two novel features. The first is a transformation layer that computes feature level polynomial kernels from class-level training data samples and iteratively updates input image copies at inference time based on their feature kernel differences to create an ensemble of transformed inputs. The second is a classification system that incorporates the prediction of the undefended network with a hard vote on the ensemble of filtered images. Our evaluations on the CIFAR10 dataset show our system improves the robustness of an undefended network against a variety of bounded and unbounded white-box attacks under different distance metrics, while sacrificing little accuracy on clean images. Against adaptive full-knowledge attackers creating end-to-end attacks, our system successfully augments the existing robustness of adversarially trained networks, for which our methods are most effectively applied.