Study reveals resilience of Chinese guarantee network during financial crisis and stimulus.
problem Limited knowledge about guarantee network dynamics during financial downturn.
method Analyzed comprehensive bank loan dataset covering 80% of total loans in China.
result Guarantee network became smaller, less connected, and more stable during financial crisis.
Develops statistical guarantees for neural networks with regularization.
problem Lack of comprehensive mathematical theories for neural networks.
method General statistical guarantee for least-squares with regularizers.
result Prediction error increases sub-linearly in layers, logarithmically in parameters.
Study finds key subgraphs in Chinese guarantee networks.
problem Understanding the structure of Chinese guarantee networks.
method Analysis of 2- and 3-node subgraphs considering financial heterogeneity.
result Mutual, 2-out-stars, and triangle sub-patterns are common motifs.
The paper provides statistical guarantees for sparse deep learning.
problem Understanding the potential and limitations of sparse deep learning.
method Develops statistical guarantees for different types of sparsity in sparse deep learning.
result Statistical guarantees for sparse deep learning with mild dependence on network widths and depths.
Efficient RNN algorithm guarantees convergence in online learning.
problem Online nonlinear regression with RNNs.
method First-order training algorithm with convergence guarantee.
result The algorithm converges to optimum network parameters.
Networked-guarantee loans may cause the systemic risk related concern of the government and banks in China. The prediction of default of enterprise loans is a typical extremely imbalanced prediction problem, and the networked-guarantee make this problem more difficult to solve. Since the guaranteed loan is a debt oblig…
Paper provides statistical guarantees for GNNs in link prediction.
problem Link prediction accuracy in graph neural networks.
method Proposes a linear GNN architecture (LG-GNN) and derives statistical guarantees.
result LG-GNN produces consistent estimators for edge probabilities and has better detection of high-probability edges.
Fine-tuning neural networks to guarantee performance on specific examples can also introduce incorrect inputs.
problem Ensuring reliable performance of neural networks on specific examples.
method Using SMT solvers to fine-tune ReLU neural networks to guarantee outcomes on a finite set of particular examples.
result Fine-tuning can introduce incorrect inputs that trigger unexpected performance.
Guarantees recovery of compressible signals from adversarial noise.
problem Recovering compressible signals from noise and adversarial attacks.
method Extends adversarial defense framework to ℓ0, ℓ2, and ℓ∞ norms. result Recovery guarantees for various signal recovery methods under different noise types.
Paper provides statistical guarantees for GANs estimating Hölder space densities.
problem Statistical properties and theoretical guarantees for GANs.
method Approximation and statistical guarantees for GANs using Hölder space densities.
result GANs are consistent estimators of data distributions under strong discrepancy metrics.
New model outperforms Neural ODEs while being more efficient.
problem Stable convergence and existence guarantees for implicit-depth models.
method Developed Monotone Operator Equilibrium Network (monDEQ) based on monotone operator theory.
result MonDEQ models outperform Neural ODEs and are more computationally efficient.
Proposes a new backpropagation algorithm for deep learning with guaranteed convergence.
problem Backward locking in backpropagation limits parallel updates in deep neural networks.
method Decouples gradients and splits the network into modules for parallel updates, proving convergence for non-convex problems.
result The proposed algorithm achieves significant speedup without accuracy loss in training deep convolutional neural networks.
New DP algorithms with margin guarantees for various hypothesis sets.
problem Differential privacy in machine learning with margin guarantees.
method Developed pure and efficient DP learning algorithms for linear, kernel-based, and neural network hypotheses.
result Margin guarantees are independent of input dimension and hypothesis type.
Algorithm constructs confidence sets for deep neural networks with PAC guarantees.
problem Ensuring reliable predictions for deep neural networks with high confidence.
method Combines calibrated prediction and learning theory bounds.
result Constructs PAC confidence sets for various deep models.
New research shows deep ReLU networks can be learned with polylogarithmic width.
problem Learning deep ReLU networks with limited over-parameterization.
method Using gradient descent, the study establishes learning guarantees for networks with polylogarithmic width.
result Deep ReLU networks can be learned with a polylogarithmic width condition, not just a high degree polynomial.
Scalable verification for deep neural networks with formal guarantees.
problem Lack of trustworthiness in deep neural networks.
method Test-driven approach that combines scalability and formal guarantees.
result Certifies properties of both deterministic and randomized DNNs with provable guarantees.
Efficient PI for neural networks without distributional assumptions.
problem No distributional assumptions for efficient predictive inference.
method Differential privacy and linear approximation for leave-one-out models.
result Rigorous coverage guarantees with reduced computation.
MPNN improves on UniFL approximation with provable guarantees.
problem Uniform Facility Location (UniFL) optimization problem.
method Graph Neural Network (MPNN) incorporating approximation-algorithmic principles.
result Empirically outperforms standard approximation algorithms.
Guarantees sparse recovery for neural networks with iterative hard thresholding.
problem Recovering sparse network weights in neural networks.
method Structural properties of sparse network weights and iterative hard thresholding algorithm.
result Simple iterative hard thresholding algorithm recovers sparse network weights exactly using linear memory.
New method improves training stochastic neural networks with tighter guarantees.
problem Training stochastic neural networks with provable guarantees.
method Developed partially-aggregated estimators and reformulated PAC-Bayesian bounds.
result Derives a differentiable objective leading to tighter generalisation guarantees.
We show that the standard stochastic gradient decent (SGD) algorithm is guaranteed to learn, in polynomial time, a function that is competitive with the best function in the conjugate kernel space of the network, as defined in Daniely, Frostig and Singer. The result holds for log-depth networks from a rich family of ar…
New method for neural networks provides valid prediction intervals with provable guarantees.
problem Developing reliable prediction intervals for deep neural networks without strong assumptions.
method Proposes a neural network that outputs three values, optimizing a quantile regression loss function.
result Guaranteed finite sample coverage of prediction intervals under minimal assumptions.
AUASE embeds dynamic networks with stability guarantees for node comparison.
problem Stability in dynamic network embeddings for comparing nodes across time.
method Attributed unfolded adjacency spectral embedding (AUASE) for stable unsupervised learning.
result AUASE provides significant improvements in link prediction and node classification.
New framework verifies neural networks with scalable guarantees.
problem Formal verification of neural networks with provable guarantees.
method Formulated as an optimization problem, solved with Lagrangian relaxation.
result Developed algorithms with tightness guarantees under special assumptions.
This paper selects features in deep neural networks with theoretical guarantees.
problem Feature selection in deep neural networks with unknown nonlinear functions.
method Reformulate neural networks as index models, estimate feature sets using Stein's formula, and apply screening-and-selection mechanism.
result Consistent feature selection with theoretical guarantees, even in high-dimensional settings.
Method learns neural network to overestimate reference function with guarantees.
problem Learning a neural network to overestimate a reference function on a given domain.
method Two-step process: constructing Majoring Points and optimizing a neural network.
result The learned neural network overestimates the reference function on the domain.
Neural network method estimates covariate-dependent graphical models with statistical guarantees.
problem Estimating graph structure from covariate-dependent data.
method Neural network approach that allows flexible functional dependency on covariates.
result Theoretical PAC guarantees for the method's performance.
Study on Adam-family methods for nonsmooth optimization with convergence guarantees.
problem Training nonsmooth neural networks with convergence guarantees.
method Two-timescale updating scheme and stochastic subgradient methods with gradient clipping.
result Convergence guarantees for various Adam-family methods in training nonsmooth neural networks.
Paper proposes a method to predict deep neural network confidences with guarantees.
problem Quantifying uncertainty in deep neural networks for safety-critical applications.
method Uses Clopper-Pearson confidence intervals and histogram binning for calibrated prediction.
result Demonstrates the effectiveness of predicted confidences in improving DNN performance and safety.
This research provides theoretical guarantees for hyperparameter estimation in complex network dynamical systems.
problem Theoretical guarantees for hyperparameter estimation in large, inhomogeneous complex network dynamical systems.
method Formulating the system's evolution in a measure transport perspective, proposing a theoretical framework for estimating hyperparameters with mean-type observations.
result A nonasymptotic bound for the deviation of hyperparameter estimates in inhomogeneous complex network dynamical systems with respect to network population size.
Paper develops robust neural network sensors for fuel injection quantities.
problem Adversarial noise increases error in standard neural network models for fuel injection measurements.
method Apply provable robust network learning and verification methods to fuel injection measurements.
result Provable robust model reduces mean relative error to 16.5% under sensor noise.
New algorithm uses untrained neural networks for image recovery, offering better compression.
problem Using untrained neural networks for image recovery and theoretical guarantees.
method Projected gradient descent scheme for solving linear and non-linear inverse problems.
result The method achieves better compression rates for the same image quality compared to hand-crafted priors.
Optimal probing framework for scalable network monitoring.
problem Efficiently monitor growing cloud networks with limited budgets.
method A- and E-optimal experimental designs, Frank-Wolfe algorithm approximations.
result Significant reduction in probing budget with low estimation errors.
BCD algorithm finds global minima in neural networks.
problem Training deep neural networks to find global minima.
method Block coordinate descent with skip connections and non-negative projection.
result Proves convergence to global minima for strictly monotonic and ReLU activations.
Neural network learns fast PDE solvers with proven guarantees.
problem Designing fast iterative solvers for specific PDE problems.
method Learn to modify an existing solver using a deep neural network.
result Achieves 2-3 times speedup compared to state-of-the-art solvers.
This work improves robustness guarantees for neural networks using low rank representations.
problem Certified robustness to adversarial perturbations in neural networks.
method Low rank representations to provide improved robustness guarantees.
result Improved robustness guarantees for ℓ∞ perturbations using natural low rank representations. Estimates robustness of BNNs with statistical guarantees.
problem Measuring robustness of BNNs against adversarial examples.
method Statistical verification techniques for probabilistic models.
result Quantifies uncertainty of BNN predictions in adversarial settings.
Efficiently certifies global robustness of large neural networks with probabilistic guarantees.
problem Certifying robustness of large neural networks in a scalable and efficient manner.
method Sampling an ε-net and invoking a local robustness oracle.
result Certifies a probabilistic relaxation of robustness efficiently and globally.
The paper provides approximation guarantees for neural networks trained with gradient flow.
problem Approximating neural networks trained with gradient flow in continuous L2(Sd−1)-norm. method NTK argument for non-convex second but last layer, under-parametrized regime.
result Gradient flow convergence guarantees for neural networks under Sobolev smoothness assumptions.
Global convergence of multilayer neural networks proven for any depth.
problem Global convergence of multilayer neural networks in the mean field regime.
method Mean field limit framework, neuronal embedding, bidirectional diversity condition.
result Global convergence for multilayer networks of any depths, including correlated initializations.
This paper tackles non-vacuous generalization bounds in ReLU networks by resolving rescaling invariances.
problem Non-vacuous generalization guarantees for ReLU networks with rescaling invariances.
method Proposes a lifted representation to resolve rescaling invariances and studies KL-based rescaling-invariant PAC-Bayes bounds.
result KL-based rescaling-invariant PAC-Bayes bounds provide tighter guarantees and resolve discrepancies in network complexity.
HardNet adds hard constraints to neural networks without sacrificing performance.
problem Ensuring adherence to input-dependent constraints in neural networks.
method Appends a differentiable enforcement layer to neural networks for end-to-end training with hard constraint guarantees.
result HardNet retains neural networks' universal approximation capabilities and enables efficient optimization.
RedEx improves neural network optimization with convex optimization guarantees.
problem Difficult optimization of neural networks.
method RedEx architecture using convex optimization with semi-definite constraints.
result RedEx can efficiently learn functions fixed methods cannot.
Deep residual networks trained with gradient descent have small generalization gap.
problem Limited theoretical understanding of why residual networks generalize well.
method Analyzing overparameterized deep residual networks trained by gradient descent.
result Demonstrates that residual networks have a small generalization gap between training and test error.
Study of infinitely deep but narrow neural networks using NTK theory.
problem Analyzing the role of depth in deep learning with overparameterized networks.
method Infinite-depth limit analysis of MLP and CNN using Neural Tangent Kernel (NTK) theory.
result Established trainability guarantee for infinitely deep but narrow neural networks.
Extends neural net safety guarantees by proving structural properties.
problem Proving formal guarantees for complex DNN architectures.
method Proves structural properties related to neural net structure to infer safety properties.
result Identifies a larger region of input space for safety properties.
Reveals the first layer of deep networks with high activation thresholds.
problem Learning guarantees for deep neural networks with multiple layers.
method Strengthening parameter recovery guarantees for deep networks with a high threshold assumption.
result Reveals the first layer of a deep neural network under specific activation conditions.
New approach ensures neural networks know when they don't know.
problem Neural networks over-confident far from training data in safety-critical applications.
method Proposes a new approach to out-of-distribution detection (OOD) with provable guarantees.
result First certificates for low confidence predictions in a neighborhood of an out-distribution point.