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Found 24 papers, 1 papers with code
Dual VC Dimension Obstructs Sample Compression by Embeddings
In particular, we prove that for every $d$ there is a class with VC dimension $d$ that cannot be embedded in any extremal class of VC dimension smaller than exponential in $d$.
The Sample Complexity Of ERMs In Stochastic Convex Optimization
In this work we show that in fact $\tilde{O}(\frac{d}{\epsilon}+\frac{1}{\epsilon^2})$ data points are also sufficient.
Local Borsuk-Ulam, Stability, and Replicability
To offer a broader and more comprehensive view of our topological approach, we prove a local variant of the Borsuk-Ulam theorem in topology and a result in combinatorics concerning Kneser colorings.
A Unified Characterization of Private Learnability via Graph Theory
Learning $\mathcal{H}$ under pure DP is captured by the fractional clique number of $G$.
Replicability and stability in learning
Impagliazzo et al. showed how to boost any replicable algorithm so that it produces the same output with probability arbitrarily close to 1.
A Characterization of Multiclass Learnability
This work resolves this problem: we characterize multiclass PAC learnability through the DS dimension, a combinatorial dimension defined by Daniely and Shalev-Shwartz (2014).
Regularization by Misclassification in ReLU Neural Networks
We study the implicit bias of ReLU neural networks trained by a variant of SGD where at each step, the label is changed with probability $p$ to a random label (label smoothing being a close variant of this procedure).
Slicing the hypercube is not easy
We prove that at least $\Omega(n^{0. 51})$ hyperplanes are needed to slice all edges of the $n$-dimensional hypercube.
On Symmetry and Initialization for Neural Networks
This work provides an additional step in the theoretical understanding of neural networks.
Learnability can be undecidable
We show that, in some cases, a solution to the ‘estimating the maximum’ problem is equivalent to the continuum hypothesis.
Average-Case Information Complexity of Learning
Can it be that all concepts in the class require leaking a large amount of information?
On the Perceptron's Compression
We study and provide exposition to several phenomena that are related to the perceptron's compression.
On the Covariance-Hessian Relation in Evolution Strategies
We consider Evolution Strategies operating only with isotropic Gaussian mutations on positive quadratic objective functions, and investigate the covariance matrix when constructed out of selected individuals by truncation.
A Direct Sum Result for the Information Complexity of Learning
We introduce a class of functions of VC dimension $d$ over the domain $\mathcal{X}$ with information complexity at least $\Omega\left(d\log \log \frac{|\mathcal{X}|}{d}\right)$ bits for any consistent and proper algorithm (deterministic or random).
On Communication Complexity of Classification Problems
To naturally fit into the framework of learning theory, the players can send each other examples (as well as bits) where each example/bit costs one unit of communication.
A learning problem that is independent of the set theory ZFC axioms
We consider the following statistical estimation problem: given a family F of real valued functions over some domain X and an i. i. d.
Learners that Use Little Information
We discuss an approach that allows us to prove upper bounds on the amount of information that algorithms reveal about their inputs, and also provide a lower bound by showing a simple concept class for which every (possibly randomized) empirical risk minimizer must reveal a lot of information.
Submultiplicative Glivenko-Cantelli and Uniform Convergence of Revenues
In this work we derive a variant of the classic Glivenko-Cantelli Theorem, which asserts uniform convergence of the empirical Cumulative Distribution Function (CDF) to the CDF of the underlying distribution.
Supervised learning through the lens of compression
This work continues the study of the relationship between sample compression schemes and statistical learning, which has been mostly investigated within the framework of binary classification.
On statistical learning via the lens of compression
(iv) A dichotomy for sample compression in multiclass categorization problems: If a non-trivial compression exists then a compression of logarithmic size exists.
On the Theoretical Capacity of Evolution Strategies to Statistically Learn the Landscape Hessian
We study the theoretical capacity to statistically learn local landscape information by Evolution Strategies (ESs).
Sample compression schemes for VC classes
Sample compression schemes were defined by Littlestone and Warmuth (1986) as an abstraction of the structure underlying many learning algorithms.
Teaching and compressing for low VC-dimension
We further construct sample compression schemes of size $k$ for $C$, with additional information of $k \log(k)$ bits.
