Paper tackles catastrophic forgetting in sequential learning.
problem Catastrophic forgetting in sequential learning.
method Regularizes training with sketches of Jacobian matrix of past data.
result Proves overcoming catastrophic forgetting for linear and wide neural networks.
New algorithm for efficient prediction intervals in neural networks.
problem Challenges in estimating uncertainty in neural network predictions.
method Applies matrix sketching to approximate Jacobian matrix for efficient uncertainty estimation.
result Produces approximate prediction intervals with competitive performance.
New analysis shows SNG's effectiveness in small samples.
problem Limited understanding of SNG in small data settings.
method Sketch-and-project analysis of SNG.
result Global convergence and rate characterization for SNG.
Sketch-BERT learns vector sketches using BERT-like self-supervised learning.
problem Lack of effective vector sketch representation for recognition and retrieval tasks.
method Generalized BERT to sketch domain with novel embedding networks and self-supervised sketch gestalt learning.
result Improved performance on sketch recognition, retrieval, and gestalt tasks.
The Jacobian Conjecture is proven for all Jacobian maps.
problem Proving the Jacobian Conjecture for all Jacobian maps.
method Using the Weyl algebra and holonomic modules, the paper shows that the Jacobian module is 1-generated and has finite length.
result The Jacobian Conjecture is true for all Jacobian maps.
This study connects Jacobian regularization to adversarial robustness and improves generalization.
problem Adversarial attacks make deep neural networks vulnerable.
method Developed a connection between Jacobian regularization and adversarial training, and established robust generalization gaps.
result Jacobian norms are related to both standard and robust generalization.
A new method improves convergence in low-rank approximation.
problem Efficiently solving large-scale numerical linear algebra problems.
method Error-Powered Sketched Inverse Iteration (EPSI) Method.
result Convergence rate improves at least linearly with sketch size.
We address the statistical and optimization impacts of the classical sketch and Hessian sketch used to approximately solve the Matrix Ridge Regression (MRR) problem. Prior research has quantified the effects of classical sketch on the strictly simpler least squares regression (LSR) problem. We establish that classical …
We present a mechanism to compute a sketch (succinct summary) of how a complex modular deep network processes its inputs. The sketch summarizes essential information about the inputs and outputs of the network and can be used to quickly identify key components and summary statistics of the inputs. Furthermore, the sket…
Study shows connections between Jacobian torsors and Fermat curves.
problem Understanding torsors of Jacobian of universal Fermat curves.
method Analyzes torsors of Jacobian of universal family of degree-m Fermat curves. result Every torsor is a connected component of the Picard scheme.
Localized sketching improves matrix multiplication and ridge regression complexity.
problem Efficiently approximate matrix multiplication and ridge regression with limited data availability.
method Localized sketching matrices for block diagonal structure, reducing sample complexity.
result Localized sketching achieves sample complexity matching global sketching methods.
We introduce a new sub-linear space sketch---the Weight-Median Sketch---for learning compressed linear classifiers over data streams while supporting the efficient recovery of large-magnitude weights in the model. This enables memory-limited execution of several statistical analyses over streams, including online featu…
The paper sharpens the analysis of sketch-and-project methods using randomized singular value decomposition.
problem Improving convergence rates of sketch-and-project methods for solving linear systems and non-linear optimization problems.
method Developing a theoretical framework and new spectral bounds for the expected sketched projection matrix.
result The convergence rate improves linearly with sketch size and even faster with certain spectral decays.
New method reduces linear regret in high-dimensional bandit problems.
problem Heavy spectral tails in streaming matrices lead to linear regret in sketch-based linear bandits.
method Dyadic Block Sketching, a multi-scale matrix sketching approach.
result Achieves sublinear regret bounds without prior knowledge of streaming matrix properties.
This work proves the asymptotic freeness of layerwise Jacobians in MLPs with Haar orthogonal matrices.
problem Proving the asymptotic freeness of layerwise Jacobians in multilayer perceptrons (MLPs).
method Replacing each layer's parameter matrix with itself multiplied by a Haar orthogonal matrix, and using the invariance of the MLP.
result Proves the asymptotic freeness of layerwise Jacobians in MLPs with Haar orthogonal matrices.
Efficiently regularizes deep learning models using Jacobian nuclear norm.
problem Regularizing deep learning models to prevent overfitting and improve generalization.
method Proposes a denoising-style approximation to penalize the Jacobian nuclear norm without computing the Jacobian matrix.
result Demonstrates that penalizing the average squared Frobenius norm of Jg and Jh is equivalent to penalizing the Jacobian nuclear norm for function compositions. New guarantees for asymmetric sketching in compressive learning.
problem Statistical guarantees for compressive learning with asymmetric feature maps.
method Proves existing guarantees carry over to asymmetric scheme with LPD property, applies to quantized sketches.
result Existing statistical guarantees for compressive learning extend to asymmetric schemes with controlled error.
New analysis proves sketching operators' RIP guarantees for mixture models without importance sampling.
problem Proving sketching operators' Restricted Isometry Property (RIP) for mixture models without assuming importance sampling.
method Proposed alternative analysis based on new deterministic bounds and concentration inequalities.
result Theoretical guarantees for sketching operators without importance sampling.
A fast sketching algorithm solves regularized least squares problems efficiently.
problem Solving large-scale optimization problems with convex or nonconvex regularization.
method Sketching for Regularized Optimization (SRO) algorithm that generates a sketch of the original data matrix and solves the sketched problem.
result General theoretical results for the approximation error between the original and sketched problems, including minimax rates for sparse signal estimation.
Abstract: Unknown status of Jacobian Conjecture, proof has a gap.
problem Status of Jacobian Conjecture
method Analysis of proof of theorem 2.1
result Proof of theorem 2.1 contains a gap
A new method for estimating large-scale linear models with improved precision.
problem Estimating large-scale linear statistical models efficiently.
method Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), integrating Sketch-and-Solve and Iterative-Sketching methods.
result SLSE-FRS produces high-precision estimators, outperforming state-of-the-art methods.
Private sketches protect linear regression data privacy.
problem Protecting sensitive information in linear regression.
method Release private sketches of datasets, compute approximate solutions.
result Private sketches maintain good approximation guarantees to the original problem.
Sketching is a randomized dimensionality-reduction method that aims to preserve relevant information in large-scale datasets. Count sketch is a simple popular sketch which uses a randomized hash function to achieve compression. In this paper, we propose a novel extension known as Higher-order Count Sketch (HCS). While …
DiPS learns to optimize sketching policies for better recommendation quality.
problem Optimizing sketching policies for long-term user interest prediction in recommender systems.
method Differentiable policy for sketching that learns from training data.
result DiPS requires up to 50% fewer sketch items to achieve the same recommendation quality.
Paper proposes Nyström sketches for better adaptive compressive learning.
problem Improving adaptability of sketching for compressive learning.
method Data-dependent Nyström approximation for mean embedding.
result Excess risk can be controlled with geometric assumption.
Sketching is more fundamental to human cognition than speech. Deep Neural Networks (DNNs) have achieved the state-of-the-art in speech-related tasks but have not made significant development in generating stroke-based sketches a.k.a sketches in vector format. Though there are Variational Auto Encoders (VAEs) for genera…
Density sketches summarize data distributions for accurate sampling and estimation.
problem Accurately estimating and sampling from complex data distributions.
method Online algorithm generating additive density sketches.
result Density sketches provide statistically sound estimators and sampling capabilities.
Improved sketching for logistic and ℓ1 regression with near-linear dimensions.
problem Efficiently approximate ℓ1 and logistic regression problems. method New sketching techniques achieving near-linear dimensions for both problems.
result Achieved near-linear sketching dimensions for ℓ1 and logistic regression. A well-conditioned Jacobian spectrum has a vital role in preventing exploding or vanishing gradients and speeding up learning of deep neural networks. Free probability theory helps us to understand and handle the Jacobian spectrum. We rigorously show almost sure asymptotic freeness of layer-wise Jacobians of deep neura…
Unified bounds for sketched bilinear forms in machine learning and statistics.
problem Uniform bounds on sketched bilinear forms for modern analyses.
method Generic chaining and new techniques for handling suprema over pairs of sets.
result Improved convergence bounds for sketched Federated Learning and bandit algorithms.
We improve prediction risk estimation for large datasets using sketching and ridge regression.
problem Estimating prediction risks for large datasets efficiently and accurately.
method Random matrix theory, generalized cross validation, sketched ridge regression ensembles, and ensemble trick.
result Consistent risk estimation and prediction intervals for large-scale datasets.
Sketching accelerates structured prediction methods for large datasets.
problem Scaling surrogate kernel methods for large datasets.
method Sketching approximations applied to input and output feature maps.
result Achieves close-to-optimal rates with reduced sketch size.
Linear regression is a classic method of data analysis. In recent years, sketching -- a method of dimension reduction using random sampling, random projections, or both -- has gained popularity as an effective computational approximation when the number of observations greatly exceeds the number of variables. In this p…
Paper develops a bootstrap method for estimating sketched SVD errors.
problem Lack of tools for accurately estimating sketched SVD errors.
method Develops a fully data-driven bootstrap method for numerical error estimation.
result Allows users to adaptively predict extra work needed for desired error tolerance.
Sketching techniques have become popular for scaling up machine learning algorithms by reducing the sample size or dimensionality of massive data sets, while still maintaining the statistical power of big data. In this paper, we study sketching from an optimization point of view: we first show that the iterative Hessia…
The Jacobian conjecture is simplified using polynomial mappings.
problem Simplifying the Jacobian conjecture over the real field.
method Using polynomial mappings to restrict transitions on manifolds.
result An equivalent statement of the Jacobian conjecture.
Paper tackles Hessian/Jacobian-free stochastic bilevel optimization with O(ε−1.5) complexity.
problem Nonconvex-strongly-convex bilevel optimization problem.
method FdeHBO optimizer with finite-difference Hessian/Jacobian-vector approximation and momentum.
result FdeHBO achieves O(ε−1.5) iterations for ε-accurate stationary point. We present sketch-rnn, a recurrent neural network (RNN) able to construct stroke-based drawings of common objects. The model is trained on thousands of crude human-drawn images representing hundreds of classes. We outline a framework for conditional and unconditional sketch generation, and describe new robust training …
Sketching reduces data size for accurate spectral estimation.
problem Estimating spectral density from large simulation datasets.
method Sketching for dimensionality reduction and data compression.
result Sketching provides 90% accurate spectral density estimate with 10% data.
Downsampling can improve generalization in ridgeless linear regression, especially with optimal sketching size.
problem Improving generalization in ridgeless linear regression with limited data.
method Investigating the effects of downsampling on the sketched ridgeless least square estimator in the proportional regime.
result Optimal sketching size minimizes out-of-sample prediction risks and stabilizes risk curves.
A new data-oblivious sketch for logistic regression reduces data size while maintaining approximation accuracy.
problem Efficiently solving logistic regression in one pass over a data stream.
method Data-oblivious sketching approach that reduces data size to poly(μdlog n) weighted points.
result Sketching reduces data size significantly and provides approximation guarantees.
Sketch-GNN reduces GNN training time and memory usage to sublinear scales.
problem Training GNNs on large graphs is computationally expensive and memory-intensive.
method Develops a sketch-based algorithm that trains GNNs on compact sketches of graph adjacency and node embeddings.
result Training time and memory usage grow sublinearly with respect to graph size.
This paper speeds up kernel methods using sparsified Gaussian sketches.
problem Kernel methods' computational limitations.
method Sparsified Gaussian sketches for kernel methods.
result Efficient time and space savings for kernel methods.
Newton-LESS sparsifies Gaussian sketching for faster optimization.
problem Computing the Hessian matrix in optimization is computationally expensive.
method Uses a sparsified version of a dense Gaussian sketching matrix.
result Achieves nearly the same convergence rate as dense Gaussian embeddings without the computational cost.
Recent work (Pennington et al, 2017) suggests that controlling the entire distribution of Jacobian singular values is an important design consideration in deep learning. Motivated by this, we study the distribution of singular values of the Jacobian of the generator in Generative Adversarial Networks (GANs). We find th…
Recent work has explored transforming data sets into smaller, approximate summaries in order to scale Bayesian inference. We examine a related problem in which the parameters of a Bayesian model are very large and expensive to store in memory, and propose more compact representations of parameter values that can be use…
Recently, randomly mapping vectorial data to strings of discrete symbols (i.e., sketches) for fast and space-efficient similarity searches has become popular. Such random mapping is called similarity-preserving hashing and approximates a similarity metric by using the Hamming distance. Although many efficient similarit…
FetchSGD reduces communication in federated learning with sketching.
problem Communication bottlenecks and convergence issues in federated learning.
method FetchSGD uses Count Sketch to compress and merge model updates efficiently.
result FetchSGD achieves high compression rates and good convergence without sparse client participation.