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Found 35 papers, 5 papers with code
An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization
In this paper, we review emerging applications of diffusion models, understanding their sample generation under various controls.
Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning
LLM unlearning aims to eliminate the influence of undesirable data from the pre-trained model while preserving the model's utilities on other tasks.
Mean-field variational inference with the TAP free energy: Geometric and statistical properties in linear models
In settings where it is conjectured that no efficient algorithm can find this local neighborhood, we prove analogous geometric properties for a local minimizer of the TAP free energy reachable by AMP, and show that posterior inference based on this minimizer remains correctly calibrated.
How Do Transformers Learn In-Context Beyond Simple Functions? A Case Study on Learning with Representations
Through extensive probing and a new pasting experiment, we further reveal several mechanisms within the trained transformers, such as concrete copying behaviors on both the inputs and the representations, linear ICL capability of the upper layers alone, and a post-ICL representation selection mechanism in a harder mixture setting.
Transformers as Decision Makers: Provable In-Context Reinforcement Learning via Supervised Pretraining
This provides the first quantitative analysis of the ICRL capabilities of transformers pretrained from offline trajectories.
Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Models
We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling.
Lower Bounds for Learning in Revealing POMDPs
However, the fundamental limits for learning in revealing POMDPs are much less understood, with existing lower bounds being rather preliminary and having substantial gaps from the current best upper bounds.
Near-optimal multiple testing in Bayesian linear models with finite-sample FDR control
In this paper, we develop near-optimal multiple testing procedures for high dimensional Bayesian linear models with isotropic covariates.
Partially Observable RL with B-Stability: Unified Structural Condition and Sharp Sample-Efficient Algorithms
Recent work has identified several tractable subclasses that are learnable with polynomial samples, such as Partially Observable Markov Decision Processes (POMDPs) with certain revealing or decodability conditions.
Unified Algorithms for RL with Decision-Estimation Coefficients: No-Regret, PAC, and Reward-Free Learning
Finding unified complexity measures and algorithms for sample-efficient learning is a central topic of research in reinforcement learning (RL).
Efficient Phi-Regret Minimization in Extensive-Form Games via Online Mirror Descent
A conceptually appealing approach for learning Extensive-Form Games (EFGs) is to convert them to Normal-Form Games (NFGs).
Sample-Efficient Learning of Correlated Equilibria in Extensive-Form Games
We then design an uncoupled no-regret algorithm that finds an $\varepsilon$-approximate $K$-EFCE within $\widetilde{\mathcal{O}}(\max_{i}X_iA_i^{K}/\varepsilon^2)$ iterations in the full feedback setting, where $X_i$ and $A_i$ are the number of information sets and actions for the $i$-th player.
Efficient and Differentiable Conformal Prediction with General Function Classes
Experiments show that our algorithm is able to learn valid prediction sets and improve the efficiency significantly over existing approaches in several applications such as prediction intervals with improved length, minimum-volume prediction sets for multi-output regression, and label prediction sets for image classification.
Near-Optimal Learning of Extensive-Form Games with Imperfect Information
This improves upon the best known sample complexity of $\widetilde{\mathcal{O}}((X^2A+Y^2B)/\varepsilon^2)$ by a factor of $\widetilde{\mathcal{O}}(\max\{X, Y\})$, and matches the information-theoretic lower bound up to logarithmic factors.
Learning with convolution and pooling operations in kernel methods
Recent empirical work has shown that hierarchical convolutional kernels inspired by convolutional neural networks (CNNs) significantly improve the performance of kernel methods in image classification tasks.
The Three Stages of Learning Dynamics in High-Dimensional Kernel Methods
To understand how deep learning works, it is crucial to understand the training dynamics of neural networks.
When Can We Learn General-Sum Markov Games with a Large Number of Players Sample-Efficiently?
First, we design algorithms for learning an $\epsilon$-Coarse Correlated Equilibrium (CCE) in $\widetilde{\mathcal{O}}(H^5S\max_{i\le m} A_i / \epsilon^2)$ episodes, and an $\epsilon$-Correlated Equilibrium (CE) in $\widetilde{\mathcal{O}}(H^6S\max_{i\le m} A_i^2 / \epsilon^2)$ episodes.
Spectral Multiplicity Entails Sample-wise Multiple Descent
Moreover, we theoretically show that the ridge estimator with optimal regularization can result in a monotone generalization risk curve and thereby eliminate multiple descent under some assumptions.
Local convexity of the TAP free energy and AMP convergence for Z2-synchronization
This provides a rigorous foundation for variational inference in high dimensions via minimization of the TAP free energy.
Understanding the Under-Coverage Bias in Uncertainty Estimation
Estimating the data uncertainty in regression tasks is often done by learning a quantile function or a prediction interval of the true label conditioned on the input.
Exact Gap between Generalization Error and Uniform Convergence in Random Feature Models
We show that, in the setting where the classical uniform convergence bound is vacuous (diverges to $\infty$), uniform convergence over the interpolators still gives a non-trivial bound of the test error of interpolating solutions.
Learning with invariances in random features and kernel models
Certain neural network architectures -- for instance, convolutional networks -- are believed to owe their success to the fact that they exploit such invariance properties.
Don't Just Blame Over-parametrization for Over-confidence: Theoretical Analysis of Calibration in Binary Classification
Modern machine learning models with high accuracy are often miscalibrated -- the predicted top probability does not reflect the actual accuracy, and tends to be over-confident.
Generalization error of random features and kernel methods: hypercontractivity and kernel matrix concentration
We show that the test error of random features ridge regression is dominated by its approximation error and is larger than the error of KRR as long as $N\le n^{1-\delta}$ for some $\delta>0$.
When Do Neural Networks Outperform Kernel Methods?
Recent empirical work showed that, for some classification tasks, RKHS methods can replace NNs without a large loss in performance.
Limitations of Lazy Training of Two-layers Neural Network
We study the supervised learning problem under either of the following two models: (1) Feature vectors x_i are d-dimensional Gaussian and responses are y_i = f_*(x_i) for f_* an unknown quadratic function; (2) Feature vectors x_i are distributed as a mixture of two d-dimensional centered Gaussians, and y_i's are the corresponding class labels.
The generalization error of random features regression: Precise asymptotics and double descent curve
We compute the precise asymptotics of the test error, in the limit $N, n, d\to \infty$ with $N/d$ and $n/d$ fixed.
Limitations of Lazy Training of Two-layers Neural Networks
We study the supervised learning problem under either of the following two models: (1) Feature vectors ${\boldsymbol x}_i$ are $d$-dimensional Gaussians and responses are $y_i = f_*({\boldsymbol x}_i)$ for $f_*$ an unknown quadratic function; (2) Feature vectors ${\boldsymbol x}_i$ are distributed as a mixture of two $d$-dimensional centered Gaussians, and $y_i$'s are the corresponding class labels.
Linearized two-layers neural networks in high dimension
Both these approaches can also be regarded as randomized approximations of kernel ridge regression (with respect to different kernels), and enjoy universal approximation properties when the number of neurons $N$ diverges, for a fixed dimension $d$.
Proximal algorithms for constrained composite optimization, with applications to solving low-rank SDPs
We study a family of (potentially non-convex) constrained optimization problems with convex composite structure.
Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit
Earlier work shows that (under some regularity assumptions), the mean field description is accurate as soon as the number of hidden units is much larger than the dimension $D$.
A Mean Field View of the Landscape of Two-Layers Neural Networks
Does SGD converge to a global optimum of the risk or only to a local optimum?
The landscape of the spiked tensor model
We compute the expected number of critical points and local maxima of this objective function and show that it is exponential in the dimensions $n$, and give exact formulas for the exponential growth rate.
Solving SDPs for synchronization and MaxCut problems via the Grothendieck inequality
In this paper we study the rank-constrained version of SDPs arising in MaxCut and in synchronization problems.
The Landscape of Empirical Risk for Non-convex Losses
We establish uniform convergence of the gradient and Hessian of the empirical risk to their population counterparts, as soon as the number of samples becomes larger than the number of unknown parameters (modulo logarithmic factors).
