Study robust regression learning under adversarial attacks.
problem Understanding which function classes are learnable in the presence of adversarial attacks.
method Introduced a novel agnostic sample compression scheme and used fat-shattering dimension to construct adversarially robust sample compression schemes.
result Finite fat-shattering dimension classes are learnable in both realizable and agnostic settings.
While machine learning has proven to be a powerful data-driven solution to many real-life problems, its use in sensitive domains has been limited due to privacy concerns. A popular approach known as **differential privacy** offers provable privacy guarantees, but it is often observed in practice that it could substanti…
Study shows multi-source learning is more resilient to adversarial corruption than single-source learning.
problem Learning from multiple untrusted data sources, especially when some are adversarially corrupted.
method Analyzed the scenario where an adversary can corrupt a fixed fraction of data sources, derived a generalization bound for this setting.
result PAC-learnability is possible in the multi-source setting even when some data sources are adversarially corrupted.
New method optimizes complex models with minimal data, proving global optimality.
problem Optimizing complex models with unknown cost functions and prior distributions.
method Introduces 'coarse learnability' and an iterative MBO algorithm with sample correction.
result Achieves global optimality with polynomial sample complexity.
Paper analyzes distributional reinforcement learning with value function approximation, introducing Bellman unbiasedness and a new algorithm.
problem Improving reinforcement learning by capturing environmental stochasticity and addressing infinite dimensionality.
method Introduces Bellman unbiasedness and proposes SF-LSVI algorithm for provably efficient distributional reinforcement learning.
result Achieves a tight regret bound of O(d_E H^3/2 √K) for distributional reinforcement learning.
Study shows realizable learnability doesn't imply agnostic learnability for distributions.
problem Learnability and robustness of distribution classes.
method Analyzes the relationship between learnability and robustness for distribution learning.
result Realizable learnability does not imply agnostic learnability for distributions.
Sparse activations in neural networks are hard to exploit but lead to advantages in learning.
problem Sparse activations in neural networks are hard to exploit but lead to advantages in learning.
method Formal study of PAC learnability of MLP layers with activation sparsity.
result Classes of functions with activation sparsity lead to provable computational and statistical advantages over their non-sparse counterparts.
New method uses low logit rank to simplify complex language models.
problem Understanding and learning from modern language models.
method Exploiting the low logit rank structure of language models for efficient learning.
result An efficient algorithm for learning low logit rank models from queries.
This paper improves RNN generalization without normalization conditions.
problem Generalization of over-parameterized RNNs without normalization constraints.
method Detailed analysis of neural tangent kernel matrix for improved generalization bounds.
result RNNs can learn functions without normalization conditions and with almost-polynomial scaling in input length.
Paper generalizes strategic classification framework and introduces SVC for PAC-learning.
problem Strategic manipulation of testing data to fool classifiers.
method Unified framework for strategic classification, strategic VC-dimension (SVC).
result Characterizes the learnability and computational tractability of linear classifiers.
Study extends learnability equivalence to multi-class and regression, overcoming binary classification limits.
problem Equivalence of online and private learnability in multi-class and regression settings.
method Introduced a novel Littlestone dimension variant and threshold functions for multi-class classification.
result Online learnability implies private learnability in multi-class classification but not in regression.
Efficiently learns private models using public data.
problem Improving private learning performance with public data.
method Proves computationally efficient algorithms for private learning with public data.
result First computationally efficient algorithms for private learning with public data.
Lazy neural networks are vulnerable to adversarial attacks.
problem Adversarial robustness issues in lazy training models.
method Extending recent work on adversarial examples to lazy training models.
result Over-parametrized neural networks that generalize well remain vulnerable to single-step gradient ascent attacks.
Extends PAC learning theory to handle partial concepts with special properties.
problem Traditional PAC learning theory cannot handle tasks with special data properties.
method Introduces partial concepts and new PAC learning framework.
result Partial concept classes cannot be captured by traditional PAC theory.
Example shows learnable distributions not privately learnable.
problem Learnable distributions under non-private conditions not transferable to differential privacy.
method Example of a distribution class learnable up to constant error in total variation distance but not under differential privacy.
result Contradicts conjecture of Ashtiani on learnability under differential privacy.
Characterizes learnability of multioutput functions in various settings.
problem Learning multioutput function classes in batch and online settings.
method Characterizes learnability based on single-output restrictions.
result Complete characterization of learnability in multioutput classification and regression.
Research characterizes learnability of multilabel ranking problems.
problem Learnability of multilabel ranking problems with relevance-score feedback.
method Characterizes learnability in batch and online settings for a large family of ranking losses.
result Characterizes two equivalence classes of ranking losses based on learnability.
We consider the fundamental question of learnability of a hypotheses class in the supervised learning setting and in the general learning setting introduced by Vladimir Vapnik. We survey classic results characterizing learnability in term of suitable notions of complexity, as well as more recent results that establish …
No single parameter characterizes the learnability of probability distributions.
problem Finding a parameter to characterize the learnability of probability distributions.
method Analyzing various notions of learnability and showing impossibility results.
result No such parameter exists for characterizing learnability of probability distributions.
New insights into Valiant's learnability model reveal classes learnable with membership queries.
problem Which classes are learnable in Valiant's original model?
method Characterization using poly-size adaptive query-compression schemes and techniques for arbitrary domains.
result Learnability in Valiant's model is sandwiched between PAC and query-less variants, with halfspaces learnable with queries.
New graph convolution captures local features on non-Euclidean grids.
problem Capturing local features on irregular, coarse non-Euclidean grids.
method Low-rank learnable local filters in graph convolutions.
result Proves more expressive than previous spectral graph convolution methods.
New sample complexity bounds for linear predictors and neural networks, focusing on initialization.
problem Understanding sample complexity for vector-valued linear predictors and neural networks, especially under initialization-dependent conditions.
method Size-independent bounds on Frobenius norm distance from a fixed reference matrix, applying to vector-valued predictors and neural networks.
result Established new sample complexity bounds for feed-forward neural networks, resolving open questions and introducing a new learnable problem.
New learnability criteria for non-iid processes equivalent to online learning.
problem Statistical learning under non-iid stochastic processes is underdeveloped.
method Defined two learnability notions and showed their equivalence to online learning.
result Learnability criteria for non-iid processes are equivalent to online learning.
New approach to nonuniform learnability using measure theory.
problem Nonuniform learnability of hypotheses with varying sample sizes.
method Measure theoretic approach to redefine nonuniform learnability, introducing a new algorithm (Generalize Measure Learnability).
result Achieved statistical consistency in learning countable hypothesis classes.
In this paper we study the learnability of deep random networks from both theoretical and practical points of view. On the theoretical front, we show that the learnability of random deep networks with sign activation drops exponentially with its depth. On the practical front, we find that the learnability drops sharply…
New algorithm learns regression models privately under growth condition.
problem Private learning of nonparametric regression models.
method Novel filtering procedure to output stable hypotheses for nonparametric function classes.
result Established first nonparametric private learnability guarantee for diverging fat shattering dimensions.
This paper studies systematic exploration for reinforcement learning with rich observations and function approximation. We introduce a new model called contextual decision processes, that unifies and generalizes most prior settings. Our first contribution is a complexity measure, the Bellman rank, that we show enables …
In Ben-David et al.'s "Learnability Can Be Undecidable," they prove an independence result in theoretical machine learning. In particular, they define a new type of learnability, called Estimating The Maximum (EMX) learnability. They argue that this type of learnability fits in with other notions such as PAC learnabili…
This work characterizes when a hypothesis class can be k-list learned.
problem Characterizing when a hypothesis class can be k-list learned.
method Introducing the k-DS dimension and proving the equivalence of k-list learnability and the finiteness of the k-DS dimension.
result A hypothesis class is k-list learnable if and only if the k-DS dimension is finite.
This work studies learning a multi-head attention layer from random examples.
problem Learning a multi-head attention layer from random examples.
method The work initiates the study of provably learning a multi-head attention layer from random examples, providing upper and lower bounds.
result The first nontrivial upper and lower bounds for learning a multi-head attention layer from random examples are given.
Three-layer networks learn more complex features than two-layer networks.
problem Understanding feature learning in deep neural networks.
method Analysis of three-layer neural networks trained with gradient descent.
result Three-layer networks can learn functions that two-layer networks cannot.
Characterizes learnability of forgiving 0-1 loss functions in multiclass settings.
problem Understanding when multiclass learning with forgiving 0-1 loss functions is possible.
method Introduces a new combinatorial dimension based on Natarajan Dimension to determine learnability.
result A hypothesis class is learnable if and only if the Generalized Natarajan Dimension is finite.
New findings on depth vs. width in neural networks, showing depth can improve learnability.
problem Understanding the role of depth in neural networks, especially when width is unbounded.
method Analyzing sample complexity for learnability in norm-controlled depth-2 and depth-3 ReLU networks.
result Depth can improve learnability of functions that are otherwise unlearnable with depth-2 networks.
The paper solves open questions in computable PAC learning, providing a complete landscape.
problem Understanding the boundaries and capabilities of computable PAC learning.
method Analyzing and constructing decidable hypothesis classes with different sample complexities and Littlestone dimensions.
result A complete understanding of CPAC learnability, answering open questions and confirming conjectures.
Estimating the relative importance of each sample in a training set has important practical and theoretical value, such as in importance sampling or curriculum learning. This kind of focus on individual samples invokes the concept of sample-wise learnability: How easy is it to correctly learn each sample (cf. PAC learn…
This work proves DP learnability implies online learnability for general classification tasks.
problem Link between differential privacy and online learning for general classification tasks.
method Establishes Ramsey-type theorems for trees to prove DP learnability implies online learnability.
result DP learnability implies online learnability for general classification tasks.
Two-layer NN with channel attention learns low-degree spherical polynomials efficiently.
problem Learning low-degree spherical polynomials with over-parameterized neural networks.
method Two-layer neural network with channel attention, vanilla gradient descent, learnable channel selection.
result Minimally improved sample complexity of $n \asymp Θ(d^{\ell_0}/\eps)$ for learning low-degree polynomials.
Proposes a new loss function for learning with noisy labels.
problem Improving model learnability with noisy labels.
method Uses generalized Jensen-Shannon divergence as a noise-robust loss function.
result Shows state-of-the-art results on noisy data.
Study reveals how spectral bias affects learnability on real-world data.
problem Understanding how well complex datasets can be learned using kernel methods.
method Use eigenvalues and eigenfunctions from idealized data to reveal spectral bias on real-world data.
result Bound learnability on real-world data using symmetries of realistic kernels.
We study the question of learning an adversarially robust predictor. We show that any hypothesis class H with finite VC dimension is robustly PAC learnable with an improper learning rule. The requirement of being improper is necessary as we exhibit examples of hypothesis classes H with finite VC…
Stability is a general notion that quantifies the sensitivity of a learning algorithm's output to small change in the training dataset (e.g. deletion or replacement of a single training sample). Such conditions have recently been shown to be more powerful to characterize learnability in the general learning setting und…
Characterizes concept classes for optimistic online learning.
problem Understanding minimal assumptions for online learnability.
method Investigates two questions about concept classes' learnability.
result Characterizes all concept classes for optimistically universal online learnability.
Online learning of linear operators between infinite-dimensional spaces is possible but with limitations.
problem Learning linear operators between infinite-dimensional Hilbert spaces in an online setting.
method Online learning approach for linear operators with bounded p-Schatten norm, proving impossibility for operator norm. result Separation between online learnability and uniform convergence for bounded linear operators.
New findings show learnable distributions remain learnable even with noisy or adversarial perturbations.
problem Learning from perturbed samples in high-dimensional spaces.
method Developed a perturbation-quantization framework to analyze additive noise and adversarial corruption models.
result Sample compressible families remain learnable even under noisy or adversarial perturbations.
Two-parameter models can learn high-dimensional targets via gradient flow.
problem Learning high-dimensional targets with limited parameters.
method Gradient flow approach for W<d models. result Two-parameter models can learn targets with arbitrarily high success probability.
We characterize learnability for stochastic noisy bandits, identifying optimal query complexities.
problem Learnability of stochastic noisy bandit models.
method Complete characterization through model class analysis and proof of optimal query complexities.
result Characterization of learnability for stochastic noisy bandit models.
Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of two-layer neural networks. We provide risk bounds for our proposed method, with…
Study online multiclass classification under bandit feedback, extending previous results.
problem Online multiclass classification with bandit feedback, focusing on label space unboundedness.
method Extend Daniely and Helbertal's results, show necessity and sufficiency of Bandit Littlestone dimension for learnability.
result Sequential uniform convergence is necessary but not sufficient for bandit online learnability.