Fast BATLLNN speeds up verification of TLL NNs by 400x.
problem Verifying output constraints for TLL NNs.
method Uses TLL architecture and decoupled box constraints to improve verification performance.
result 400x faster than state-of-the-art verifiers.
New NN design for nonlinear systems control with guarantees.
problem Designing NN architectures for nonlinear system control with guarantees.
method Exploits system model to design NN architecture, uses TLL NN for approximation.
result Guaranteed NN architecture sufficient for implementing a controller.
Polynomial-time reachability for LTI systems with TLL NN controllers is achieved.
problem Bounding the reachable set of LTI systems controlled by TLL NN controllers.
method Polynomial-time computation of exact one-step reachable set and tight bounding box via two methods.
result Exact reachability computation in polynomial time for TLL NN controllers.
The paper designs neural networks with assurance for controlling nonlinear systems.
problem Designing neural networks with assurance for nonlinear system control.
method Bounding the number of affine functions needed for a CPWA function, connecting it to a TLL NN architecture.
result The TLL NN architecture is parameterized by the number of affine functions in the CPWA function it realizes.
We present NN-grams, a novel, hybrid language model integrating n-grams and neural networks (NN) for speech recognition. The model takes as input both word histories as well as n-gram counts. Thus, it combines the memorization capacity and scalability of an n-gram model with the generalization ability of neural network…
This paper shows how path spaces on two-level manifolds can be Hilbert manifold structures.
problem Addressing the structure of path spaces on two-level manifolds.
method Introducing the notion of tameness and constructing charts on path spaces of two-level manifolds.
result Path spaces on tame two-level manifolds have the structure of a Hilbert manifold.
Spiking neural networks (SNNs) with a lattice architecture are introduced in this work, combining several desirable properties of SNNs and self-organized maps (SOMs). Networks are trained with biologically motivated, unsupervised learning rules to obtain a self-organized grid of filters via cooperative and competitive …
New framework explains why over-parameterized neural networks work well.
problem Why over-parameterized neural networks perform well in practice.
method Neural feature repopulation framework using gradient descent.
result Over-parameterized two-level neural networks learn near optimal feature distributions.
This work analyzes generalization in federated learning using information theory.
problem Generalization performance in federated learning is less explored compared to centralized learning.
method The work applies an information-theoretic analysis via the conditional mutual information (CMI) framework to study federated learning's two-level generalization.
result The work derives multiple CMI-based bounds, including hypothesis-based CMI bounds and fast-rate evaluated CMI bounds, which improve convergence rates for specific model aggregation strategies and structured loss functions.
We propose a simple approach which, given distributed computing resources, can nearly achieve the accuracy of k-NN prediction, while matching (or improving) the faster prediction time of 1-NN. The approach consists of aggregating denoised 1-NN predictors over a small number of distributed subsamples. We show, bot…
Randomly trained neural networks can generalize well if there's a simpler underlying teacher model.
problem Why randomly trained neural networks generalize well despite interpolating training data.
method Examined a random neural network that interpolates training data and showed it generalizes well if there's a simpler underlying teacher model.
result Randomly trained neural networks can generalize well if there's a simpler underlying teacher model.
As a contribution to interpretable machine learning research, we develop a novel optimization framework for learning accurate and sparse two-level Boolean rules. We consider rules in both conjunctive normal form (AND-of-ORs) and disjunctive normal form (OR-of-ANDs). A principled objective function is proposed to trade …
This paper analyzes deep Stable neural networks, showing convergence rates under different growth settings.
problem Analyzing the behavior of deep Stable neural networks as width increases.
method Large-width asymptotic analysis and convergence rates for fully connected feed-forward deep Stable NNs.
result The rescaled deep Stable NN converges weakly to a Stable SP under joint growth, with sup-norm convergence rates established.
Study bridges GARCH and NN models for volatility forecasting.
problem Lack of interaction between GARCH and NN approaches for volatility forecasting.
method Established equivalence between GARCH and NN models, introduced GARCH-NN approach.
result GARCH-NN approach enhances volatility forecasting compared to standalone models.
Paper proposes MS-k-NN for improved convergence rate in k-NN classification.
problem Improving convergence rate of k-NN classification methods.
method Proposes MS-k-NN that extrapolates unweighted k-NN estimators to k=0.
result MS-k-NN achieves improved convergence rate under certain conditions.
Develops a two-level monotonic multistage recommender system for better user-specific prediction.
problem Leveraging user-item-stage dependencies in a monotonic chain of events for enhanced prediction accuracy.
method A multistage recommender system with a two-level monotonic property, using a large-margin classifier based on a nonnegative additive latent factor model.
result The proposed method outperforms existing methods in simulations and an article sharing dataset.
A fast method for LOOCV in k-NN regression reduces computation time.
problem Efficient computation of LOOCV for k-NN regression.
method Identical LOOCV estimate to (k+1)-NN MSE on training data.
result LOOCV computation can be done with (k+1)-NN regression once.
Adds layers to NNs to protect them from reverse engineering.
problem Extracting the underlying model of a Neural Network.
method Introducing parasitic layers that approximate a noisy identity mapping with a Convolutional NN.
result The protected NN's predictions remain mostly unchanged while making reverse-engineering more complex.
Artificial neural networks (NN) are instrumental in realizing highly-automated driving functionality. An overarching challenge is to identify best safety engineering practices for NN and other learning-enabled components. In particular, there is an urgent need for an adequate set of metrics for measuring all-important …
Prototype rules simplify multiclass classification in metric spaces, achieving consistency and reduced complexity.
problem Multiclass classification in metric spaces, focusing on universal consistency and convergence rates.
method Novel Proto-NN and hybrid rules for multiclass classification in metric spaces, analyzing convergence rates.
result Proto-NN is universally consistent and simpler to implement, with similar computational advantages.
Neural Networks (NN) have recently emerged as backbone of several sensitive applications like automobile, medical image, security, etc. NNs inherently offer Partial Fault Tolerance (PFT) in their architecture; however, the biased PFT of NNs can lead to severe consequences in applications like cryptography and security …
This work improves interpretability in deep learning models by introducing a two-level concept discovery framework.
problem High complexity and lack of interpretability in deep learning models, especially for safety-critical tasks.
method Concept Bottleneck Models (CBMs) framework combining vision-language models and data-driven coarse-to-fine concept selection.
result The proposed framework outperforms recent CBM approaches and provides a principled interpretability.
This work establishes the equivalence between neural networks and support vector machines.
problem Establishing the equivalence between neural networks and support vector machines.
method Proposed a method to establish the equivalence between infinitely wide neural networks trained by soft margin loss and standard soft margin SVMs with NTK trained by subgradient descent.
result The equivalence between NN and SVM is established, enabling practical applications such as non-vacuous generalization bounds and robustness certificates.
In the k-nearest neighborhood model (k-NN), we are given a set of points P, and we shall answer queries q by returning the k nearest neighbors of q in P according to some metric. This concept is crucial in many areas of data analysis and data processing, e.g., computer vision, document retrieval and machi…
Estimates generalization error for two-layer ReLU NNs through minimum norm solutions.
problem Estimating generalization error for two-layer ReLU NNs trained by mean squared error.
method Uses minimum norm solutions and Neural Tangent Kernel (NTK) regime to derive generalization error bounds.
result Derives an a priori generalization error bound for two-layer ReLU NNs without requiring exponentially large number of neurons.
Machine Learning (ML) is making a strong resurgence in tune with the massive generation of unstructured data which in turn requires massive computational resources. Due to the inherently compute- and power-intensive structure of Neural Networks (NNs), hardware accelerators emerge as a promising solution. However, with …
This paper studies large-width asymptotics for ReLU neural networks with α-Stable initializations.
problem Characterizing the large-width behavior of ReLU neural networks with α-Stable initializations.
method Analysis of the large-width distributions and training dynamics of ReLU neural networks initialized with α-Stable distributions.
result For ReLU neural networks with α-Stable initializations, the large-width training dynamics achieve zero training error at a linear rate, characterized by a random kernel.
Qualitative analysis of MC dropout for NN model uncertainty.
problem Measuring uncertainty in neural network models.
method Mathematical formulation of Monte Carlo dropout and its benefits/costs in NN models.
result Potential benefits and associated costs of using MC dropout in NN models.
Training a Neural Network (NN) with lots of parameters or intricate architectures creates undesired phenomena that complicate the optimization process. To address this issue we propose a first modular approach to NN design, wherein the NN is decomposed into a control module and several functional modules, implementing …
The paper optimizes k-NN for distributed learning with minimax optimal performance.
problem Minimizing error rates in classification, regression, and density estimation.
method Optimal aggregation of fixed-k nearest neighbors from multiple subsets of data.
result Achieves minimax optimal error rates up to a logarithmic factor.
Despite the success of neural networks (NNs), there is still a concern among many over their "black box" nature. Why do they work? Here we present a simple analytic argument that NNs are in fact essentially polynomial regression models. This view will have various implications for NNs, e.g. providing an explanation for…
Neural Networks (NNs) have been extensively used for a wide spectrum of real-world regression tasks, where the goal is to predict a numerical outcome such as revenue, effectiveness, or a quantitative result. In many such tasks, the point prediction is not enough: the uncertainty (i.e. risk or confidence) of that predic…
Study on dropout in neural networks using percolation theory.
problem Understanding dropout's effect on neural network training.
method Investigates percolation models mimicking dropout in neural networks.
result Dropout can cause a breakdown in neural networks.
We derive high-probability finite-sample uniform rates of consistency for k-NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that k-NN regression adapts to an unknown lower intrinsic dimension automatically. We then apply the k-NN regression rates to establish new …
LARF improves random forests with attention mechanisms and contamination models.
problem Improving accuracy in classification tasks with random forests.
method Introduces a two-level attention mechanism and uses a mixture of contamination models.
result Significantly improved classification performance on various datasets.
Ensembles of neural networks (NNs) have long been used to estimate predictive uncertainty; a small number of NNs are trained from different initialisations and sometimes on differing versions of the dataset. The variance of the ensemble's predictions is interpreted as its epistemic uncertainty. The appeal of ensembling…
A garland based on a manifold P is a finite set of manifolds homeomorphic to P with some of them glued together at marked points. Fix a manifold M and consider a space $\NN$ of all smooth mappings of garlands based on P into M. We construct operations ∙ and [−,−] on the bordism groups $\bor_*(\NN)$ …
Exact bounds derived for neural network outputs with noisy inputs.
problem Bounding the output distribution of neural networks with random inputs.
method Applying ReLU NNs to derive bounds for general NNs, then using these to find exact error guarantees.
result Exact upper and lower bounds for the output distribution of neural networks with random inputs.
The k-nearest neighbor classification method (k-NNC) is one of the simplest nonparametric classification methods. The mutual k-NN classification method (MkNNC) is a variant of k-NNC based on mutual neighborship. We propose another variant of k-NNC, the symmetric k-NN classification method (SkNNC) based …
A new method for learning distance metrics for K-NN classification.
problem Improving the performance of K-NN classifier by learning an appropriate distance metric.
method Designing a continuous decision function for K-NN and minimizing its continuous empirical risk function.
result The proposed ANN algorithm outperforms existing methods like LMNN, NCA, and pairwise constraints.
Implementing k-NN classification using Gromov--Wasserstein distances
problem Comparing metric measure spaces
method Gromov--Wasserstein and fused Gromov--Wasserstein distances
result Universal consistency of k-NN classifiers The paper certifies neural network-based control barrier functions efficiently.
problem Certifying neural network-based barrier functions for safety in autonomous systems.
method Combines NN reachability and hyperplane arrangement enumeration for efficient certification.
result Soundly finds regions where neural networks are certified as barrier functions.
NNs accurately predict energy eigenvalues and other physical phenomena in 1D quantum mechanics.
problem Understanding how neural networks interpret physics.
method Training NNs to predict energy eigenvalues from potentials and testing their ability to generalize.
result NNs can predict physical phenomena not learned during training, indicating a new way of understanding physics.
We present a formal measure-theoretical theory of neural networks (NN) built on probability coupling theory. Our main contributions are summarized as follows. * Built on the formalism of probability coupling theory, we derive an algorithm framework, named Hierarchical Measure Group and Approximate System (HMGAS), nickn…
This paper uses second-order Poincaré inequalities to establish quantitative central limit theorems for Gaussian neural networks.
problem Establishing quantitative central limit theorems for Gaussian neural networks.
method Using second-order Poincaré inequalities to reduce the problem to computing the gradient and Hessian of the NN's output.
result Suboptimal rates of convergence for the NN's output due to the use of second-order Poincaré inequalities.
The k-Nearest Neighbor Search (k-NNS) is the backbone of several cloud-based services such as recommender systems, face recognition, and database search on text and images. In these services, the client sends the query to the cloud server and receives the response in which case the query and response are revealed t…
Paper develops efficient algorithms for robust optimization across multiple groups.
problem Minimizing maximal empirical risk across distinct groups in robust optimization.
method Develops ALEG and ALEM algorithms for two-level finite-sum convex-concave minimax optimization.
result Achieves ε-accuracy with complexity O(m√(nlnm/ε)) and outperforms state-of-the-art methods.
The k-nearest neighbour (k-NN) classifier is one of the oldest and most important supervised learning algorithms for classifying datasets. Traditionally the Euclidean norm is used as the distance for the k-NN classifier. In this thesis we investigate the use of alternative distances for the k-NN classifier. We …