Discretizing input space improves DLN robustness against adversarial attacks.
problem Improving machine learning models' resistance to adversarial attacks.
method Input discretization and Binary Neural Networks (BNNs).
result 2-bit input discretization significantly enhances adversarial robustness with minimal accuracy loss.
Adversaries reprogram text classification models without changing the original network.
problem Reprogramming neural networks trained on discrete input spaces like text classification.
method Context-based vocabulary remapping model for white-box and black-box settings.
result Successfully repurposed various text-classification models for new tasks.
D2D-SPL uses discrete states and a classifier to train RL faster.
problem Training neural networks in RL due to correlated samples.
method Discretizes state space, uses actor-critic, selects input/target pairs, trains classifier.
result Trains faster than state-of-the-art methods.
Physics-informed neural operator learns from coarse to fine discretized data.
problem Lack of high-fidelity training data and uneven grid resolution.
method Physics-informed multi-resolution neural operator framework.
result Learn from arbitrarily discretized input functions using latent embedding and finite difference solver.
Framework estimates multiple plausible solutions with uncertainty measures.
problem Machine learning models need to propose multiple plausible solutions with meaningful uncertainty.
method Discrete latent variables model one-to-many mappings, allowing effective conditional probability estimation.
result Framework outperforms state-of-the-art in uncertainty estimation and is practical.
We find a normal form for two-input flat discrete-time systems.
problem No comparable normal form exists for flat continuous-time systems.
method State- and input transformations to achieve a triangular structure.
result A systematic parameterization of system variables by the flat output and its shifts.
Efficient algorithm for reinforcement learning in large state-action spaces with adaptive discretization.
problem Efficient reinforcement learning in large, potentially continuous state-action spaces.
method Adaptive Q-learning policy with data-driven adaptive discretization. result Demonstrates improved performance compared to existing methods, especially in adapting to the problem's structure.
Following great success in the image processing field, the idea of adversarial training has been applied to tasks in the natural language processing (NLP) field. One promising approach directly applies adversarial training developed in the image processing field to the input word embedding space instead of the discrete…
The paper tackles exact linearization and control of flat discrete-time systems.
problem Exact linearization and control of flat nonlinear discrete-time systems.
method Investigates conditions for choosing new inputs and feedbacks that may depend on forward-shifts of the new input.
result Easily verifiable conditions for choosing a feasible input and a new input that minimizes forward-shifts of the flat output.
1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with a certain number of critical cells. Our measure will depend on the topology of the space, but also on how nicely the spa…
Proposes a VAE with a discrete bottleneck for better text generation.
problem VAEs struggle with latent variable auto-regressive decoding in text generation.
method Introduces a discretized bottleneck to enforce latent feature matching in a compact space.
result Demonstrates improved text generation capabilities across various tasks.
Neural networks learn discrete tasks on continuous data via emergent geometry.
problem Understanding how neural networks perform discrete computations on continuous data.
method Analysis of Riemannian pullback metric across neural network layers.
result Neural networks learn to discretize continuous inputs and perform logical operations on these discretized variables.
RI-DeepONet learns neural operators from arbitrary sensor data.
problem Discretization of input functions limits practical applications of DeepONet.
method Introduces RI-DeepONet and two dictionary learning algorithms for INRs.
result RINO handles arbitrary sensor data robustly and applies to various problems.
RAD approach models both continuous and discrete data.
problem Flow models struggle with discrete structures in data.
method Domain partitioning with locally invertible functions for real and discrete latent variables.
result RAD approach models both continuous and discrete structures.
Proposes a method to quantify uncertainty in DNN models for discrete inputs.
problem Uncertainty quantification for DNN models with categorical and discrete feature variables.
method Develops a mathematical framework to quantify prediction uncertainty from discrete input noise and model parameters.
result Identifies risk-sensitive cases prone to misclassification due to discrete predictor errors.
Decomposes flat nonlinear discrete-time systems into simpler components.
problem Flatness of nonlinear discrete-time systems.
method Coordinate transformations and feedback, using flow-box and Frobenius theorems.
result Flatness of a discrete-time system can be checked algorithmically.
State-space systems generate probabilistic dependencies between inputs and outputs.
problem Understanding probabilistic dependencies in state-space systems.
method Introducing a probabilistic framework and proving sufficient conditions for output existence and uniqueness.
result State-space systems can generate probabilistic dependencies, even without functional relations.
RIPE predicts and explains continuous/discrete data with sparse rule sets.
problem Predicting and explaining continuous/discrete data.
method RIPE infers a model from a sample, extracting a sparse set of hyperrectangles (rules) to partition the feature space.
result RIPE efficiently predicts and explains data, superior to other algorithms.
LOL-BO improves latent space Bayesian optimization over structured inputs.
problem Optimizing complex functions over high-dimensional, structured search spaces.
method Adapting trust regions from high-dimensional to structured settings, using a DAE to map inputs into a latent space.
result Achieves up to 20x improvement over state-of-the-art methods.
HyBO optimizes hybrid structures using diffusion kernels.
problem Optimizing complex interactions between discrete and continuous variables.
method HyBO uses diffusion kernels over hybrid spaces with additive kernel formulation.
result HyBO significantly outperforms state-of-the-art methods on real-world benchmarks.
DDEQs extend DEQs to discrete measure inputs using Wasserstein gradient flows.
problem Applying DEQs to discrete measure inputs like sets or point clouds.
method Wasserstein gradient flows for finding fixed points of discrete measures under permutation-invariance.
result DDEQs can compete with state-of-the-art models in tasks like point cloud classification and completion.
VAIOM models financial returns using continuous input and categorical output.
problem Modeling continuous, noisy, and heterogeneous financial data.
method VAIOM is a decoder-only Transformer that separates input representation from output likelihood.
result VAIOM models outperform fixed single-bar LightGBM baseline in both Test halves.
Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These differences can be inherent to the inference task or present for other reasons: sensors in a sensor network may be placed far apart, affecting their individual meas…
Paper explores neural network approximations on sphere domains.
problem Approximating functionals on sphere domains using neural networks.
method Encoder-decoder framework with spherical harmonics for infinite-dimensional domain.
result Approximation rates of neural networks with different encoder structures.
Develops neural network approximations for infinite-dimensional input-output maps.
problem Approximating input-output maps between infinite-dimensional spaces.
method Combines neural networks and model reduction techniques.
result Proves convergence of the proposed approximation methodology.
Ricci-Filtration enhances retrieval-augmented generation rerankers for query-answer tasks by using discrete Ricci flow on graphs.
problem Improving retrieval-augmented generation rerankers for query-answer tasks.
method Discrete Ricci flow on graphs to evaluate structural importance of chunks.
result Ricci-Filtration outperforms baseline methods in accuracy, precision, recall, and F1 scores.
HiPPO-Prophecy models can learn dynamical systems without fine-tuning.
problem Learning dynamical systems in context without fine-tuning parameters.
method Introduced a novel weight construction for SSMs that approximates derivatives of input signals.
result Discrete SSMs can predict the next state of any dynamical system after observing previous states.
Our work proves robustness of embedding schemes to discrete changes in text.
problem Discrete changes in text, like replacing a word, affect model robustness.
method Formal proofs and quantitative bounds for embedding schemes (concatenation, TF-IDF, Paragraph Vector).
result Embedding schemes are robust to discrete changes in text with Hölder or Lipschitz properties.
Bayesian optimization adapted for discrete spaces using random mappings.
problem Global optimization of expensive black-box functions with discrete variables.
method Embeds discrete space into a convex polytope, performs optimization in continuous space.
result Method outperforms existing methods in large combinatorial spaces.
Random feature model approximates PDE solutions efficiently.
problem Approximating solutions to PDEs with high-dimensional inputs and outputs.
method Random feature model applied to infinite-dimensional operators.
result Efficient and accurate approximation of PDE solutions.
DreamerV2 learns Atari game behaviors from a world model, achieving human-level performance.
problem Learning complex behaviors in Atari games from limited data.
method DreamerV2 uses a world model with discrete representations to predict behaviors in a compact latent space.
result Achieves human-level performance on 55 Atari tasks.
Method generates counterfactual explanations for graph classifiers.
problem Generating high-quality explanations for graph predictions.
method Permutation equivariant graph variational autoencoder to traverse latent space.
result Empirically validated model is high-performing and robust.
Multilayer bootstrap network builds a gradually narrowed multilayer nonlinear network from bottom up for unsupervised nonlinear dimensionality reduction. Each layer of the network is a nonparametric density estimator. It consists of a group of k-centroids clusterings. Each clustering randomly selects data points with r…
Quantum algorithm finds extremal values without direct function access.
problem Finding extremal values of hidden functions without direct access.
method Parametric quantum circuit trained with a trainable quantum feature map.
result Algorithm successfully finds extremal values even with sparse training data.
Efficient method certifies robustness of discrete data models, especially graphs.
problem Certifying robustness of discrete data models, especially graphs, is difficult.
method Randomized smoothing framework, sparsity-aware, model-agnostic, tight and efficient.
result Proposes a scalable method for certifying robustness of discrete data models, especially graphs.
We develop a method for quantile-based sensitivity analysis in models with discontinuities.
problem Uncertainty in interpreting discontinuous models using traditional derivatives.
method Quantile-based derivatives for discontinuous models with discrete inputs.
result Derivatives of quantile-based outputs are well-defined and provide meaningful insights.
Study the geometry of signal spaces in deep neural networks.
problem Contradiction between theoretical predictions and finite-size effects in deep neural networks.
method Analyze the manifold and curvature of embedded signal spaces in deep networks.
result The scalar curvature of the embedded manifold converges to a constant or diverges to infinity slowly, leading to a stable fixed value in the limit of infinite layers and neurons.
We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance δ from a given input function. The result is achieved by establishing a connection between discrete Morse theory and persistent homology. Our method completely removes homological noise with pe…
New algorithm learns halfspaces over hypercube with random bit flips.
problem Agnostic learning of Boolean halfspaces over discrete domains is computationally hard.
method Smoothed analysis with random bit flips for discrete inputs.
result First efficient algorithm for smoothed agnostic learning of halfspaces over Boolean hypercube.
Gradient-based framework for optimizing text prompts in diffusion models.
problem Efficiently optimizing prompts in text-to-image diffusion models with large domain space and non-differentiable embeddings.
method Formulated as discrete optimization over language space, designed compact subspaces, and introduced shortcut text gradient.
result Empirically discovered prompts that enhance or destroy image faithfulness.
Neural networks' feature geometry evolves like discrete Ricci flow.
problem Understanding neural feature representations and their geometric transformations.
method Approximating input manifold with geometric graphs and analyzing their evolution during training.
result Neural feature geometry evolves like discrete Ricci flow, with nonlinear activations playing a crucial role.
We solve the ANOVA decomposition for categorical inputs.
problem Lack of a closed-form expression for ANOVA decomposition with categorical dependent variables.
method Bridge functional analysis with discrete Fourier analysis to derive a closed-form decomposition.
result Closed-form decomposition for categorical inputs without assumptions.
BEACON optimizes discovery by efficiently finding novel behaviors.
problem Discovering diverse system behaviors without a scalar objective.
method Bayesian optimization inspired strategy using multi-output Gaussian processes.
result BEACON discovers broader sets of distinct behaviors than competing methods.
This paper addresses Gaussian Process regression over probability measures, revealing a non-stationarity issue between Euclidean and Wasserstein kernels.
problem Non-stationarity issue between Euclidean and Wasserstein kernels in Gaussian Process regression over probability measures.
method Assuming Euclidean input space, applying algebraic transformation based on uncovered non-stationarity relationship to create a non-stationary and Wasserstein-based Gaussian Process model.
result An algebraic transformation simplifies learning a non-stationary Gaussian Process model over probability measures.
Paper introduces scalable neural architecture for solving NP-hard problems.
problem Solving NP-hard reasoning problems from natural inputs.
method Scalable neural architecture and loss function for discrete Graphical Models.
result Empirically shows efficient learning of NP-hard problems.
Paper develops a method to generate discrete adversarial attacks on text classification models using submodular optimization.
problem Generating adversarial examples for discrete structures like text is challenging.
method Formulated adversarial attacks as an optimization task on submodular set functions, guided by gradient information.
result Achieved a 1-1/e approximation factor for attacks using the greedy algorithm.
New method selects data points for better model performance.
problem Balancing input coverage and model utility in selective prediction.
method Study training dynamics to reject inputs with unstable predictions.
result State-of-the-art selective prediction performance achieved without model modifications.
We propose and analyze sequential design methods for the problem of ranking several response surfaces. Namely, given L≥2 response surfaces over a continuous input space X, the aim is to efficiently find the index of the minimal response across the entire X. The response surfaces are not known and ha…