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Found 81 papers, 11 papers with code
Why Clean Generalization and Robust Overfitting Both Happen in Adversarial Training
However, in constrast with clean generalization, while adversarial training method is able to achieve low $\textit{robust training error}$, there still exists a significant $\textit{robust generalization gap}$, which promotes us exploring what mechanism leads to both $\textit{clean generalization and robust overfitting (CGRO)}$ during learning process.
Toward Understanding Why Adam Converges Faster Than SGD for Transformers
We further observe that only a small fraction of the coordinates causes the bad sharpness and slow convergence of SGD, and propose to use coordinate-wise clipping as a solution to SGD and other optimization algorithms.
SPRING: GPT-4 Out-performs RL Algorithms by Studying Papers and Reasoning
Finally, we show the potential of games as a test bed for LLMs.
Physics of Language Models: Part 1, Context-Free Grammar
We design experiments to study $\textit{how}$ generative language models, like GPT, learn context-free grammars (CFGs) -- diverse language systems with a tree-like structure capturing many aspects of natural languages, programs, and human logics.
The probability flow ODE is provably fast
We provide the first polynomial-time convergence guarantees for the probability flow ODE implementation (together with a corrector step) of score-based generative modeling.
TinyStories: How Small Can Language Models Be and Still Speak Coherent English?
In this work, we introduce TinyStories, a synthetic dataset of short stories that only contain words that a typical 3 to 4-year-olds usually understand, generated by GPT-3. 5 and GPT-4.
Weighted Tallying Bandits: Overcoming Intractability via Repeated Exposure Optimality
Motivated by this, a significant line of work has formalized settings where an action's loss is a function of the number of times that action was recently played in the prior $m$ timesteps, where $m$ corresponds to a bound on human memory capacity.
Plan, Eliminate, and Track -- Language Models are Good Teachers for Embodied Agents
We propose the Plan, Eliminate, and Track (PET) framework.
On the Importance of Contrastive Loss in Multimodal Learning
Recently, contrastive learning approaches (e. g., CLIP (Radford et al., 2021)) have received huge success in multimodal learning, where the model tries to minimize the distance between the representations of different views (e. g., image and its caption) of the same data point while keeping the representations of different data points away from each other.
Sparks of Artificial General Intelligence: Early experiments with GPT-4
We contend that (this early version of) GPT-4 is part of a new cohort of LLMs (along with ChatGPT and Google's PaLM for example) that exhibit more general intelligence than previous AI models.
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The Benefits of Mixup for Feature Learning
We consider a feature-noise data model and show that Mixup training can effectively learn the rare features (appearing in a small fraction of data) from its mixture with the common features (appearing in a large fraction of data).
How Do Transformers Learn Topic Structure: Towards a Mechanistic Understanding
While the successes of transformers across many domains are indisputable, accurate understanding of the learning mechanics is still largely lacking.
Read and Reap the Rewards: Learning to Play Atari with the Help of Instruction Manuals
Read and Reward speeds up RL algorithms on Atari games by reading manuals released by the Atari game developers.
What Matters In The Structured Pruning of Generative Language Models?
Auto-regressive large language models such as GPT-3 require enormous computational resources to use.
How Does Adaptive Optimization Impact Local Neural Network Geometry?
The traditional viewpoint in optimization, particularly in convex optimization, explains this improved performance by arguing that, unlike vanilla gradient schemes, adaptive algorithms mimic the behavior of a second-order method by adapting to the global geometry of the loss function.
Vision Transformers provably learn spatial structure
On the theoretical side, we consider a binary classification task and show that while the learning problem admits multiple solutions that generalize, our model implicitly learns the spatial structure of the dataset while generalizing: we call this phenomenon patch association.
Dissecting adaptive methods in GANs
By considering an update rule with the magnitude of the Adam update and the normalized direction of SGD, we empirically show that the adaptive magnitude of Adam is key for GAN training.
Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
We provide theoretical convergence guarantees for score-based generative models (SGMs) such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of large-scale real-world generative models such as DALL$\cdot$E 2.
Towards Understanding Mixture of Experts in Deep Learning
To our knowledge, this is the first result towards formally understanding the mechanism of the MoE layer for deep learning.
Towards understanding how momentum improves generalization in deep learning
Stochastic gradient descent (SGD) with momentum is widely used for training modern deep learning architectures.
Learning (Very) Simple Generative Models Is Hard
Motivated by the recent empirical successes of deep generative models, we study the computational complexity of the following unsupervised learning problem.
The Mechanism of Prediction Head in Non-contrastive Self-supervised Learning
The substitution effect happens when learning the stronger features in some neurons can substitute for learning these features in other neurons through updating the prediction head.
Complete Policy Regret Bounds for Tallying Bandits
Policy regret is a well established notion of measuring the performance of an online learning algorithm against an adaptive adversary.
Learning Polynomial Transformations
Our first main result is a polynomial-time algorithm for learning quadratic transformations of Gaussians in a smoothed setting.
Minimax Optimality (Probably) Doesn't Imply Distribution Learning for GANs
Arguably the most fundamental question in the theory of generative adversarial networks (GANs) is to understand to what extent GANs can actually learn the underlying distribution.
Local Signal Adaptivity: Provable Feature Learning in Neural Networks Beyond Kernels
We therefore propose the "local signal adaptivity" (LSA) phenomenon as one explanation for the superiority of neural networks over kernel methods.
Settling the Horizon-Dependence of Sample Complexity in Reinforcement Learning
Notably, for an RL environment with horizon length $H$, previous work have shown that there is a probably approximately correct (PAC) algorithm that learns an $O(1)$-optimal policy using $\mathrm{polylog}(H)$ episodes of environment interactions when the number of states and actions is fixed.
On the One-sided Convergence of Adam-type Algorithms in Non-convex Non-concave Min-max Optimization
To the best of our knowledge, this is the very first result which provides an empirical observation and a strict theoretical guarantee on the one-sided convergence of Adam-type algorithms in min-max optimization.
Adam is no better than normalized SGD: Dissecting how adaptivity improves GAN performance
We empirically show that SGDA with the same vector norm as Adam reaches similar or even better performance than the latter.
Understanding the Generalization of Adam in Learning Neural Networks with Proper Regularization
In this paper, we provide a theoretical explanation for this phenomenon: we show that in the nonconvex setting of learning over-parameterized two-layer convolutional neural networks starting from the same random initialization, for a class of data distributions (inspired from image data), Adam and gradient descent (GD) can converge to different global solutions of the training objective with provably different generalization errors, even with weight decay regularization.
LoRA: Low-Rank Adaptation of Large Language Models
We propose Low-Rank Adaptation, or LoRA, which freezes the pre-trained model weights and injects trainable rank decomposition matrices into each layer of the Transformer architecture, greatly reducing the number of trainable parameters for downstream tasks.
Sample Efficient Reinforcement Learning In Continuous State Spaces: A Perspective Beyond Linearity
Reinforcement learning (RL) is empirically successful in complex nonlinear Markov decision processes (MDPs) with continuous state spaces.
Forward Super-Resolution: How Can GANs Learn Hierarchical Generative Models for Real-World Distributions
Generative adversarial networks (GANs) are among the most successful models for learning high-complexity, real-world distributions.
Toward Understanding the Feature Learning Process of Self-supervised Contrastive Learning
We present an underlying principle called $\textbf{feature decoupling}$ to explain the effects of augmentations, where we theoretically characterize how augmentations can reduce the correlations of dense features between positive samples while keeping the correlations of sparse features intact, thereby forcing the neural networks to learn from the self-supervision of sparse features.
Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability
We empirically demonstrate that full-batch gradient descent on neural network training objectives typically operates in a regime we call the Edge of Stability.
When Is Generalizable Reinforcement Learning Tractable?
Agents trained by reinforcement learning (RL) often fail to generalize beyond the environment they were trained in, even when presented with new scenarios that seem similar to the training environment.
Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning
Our result sheds light on how ensemble works in deep learning in a way that is completely different from traditional theorems, and how the ``dark knowledge'' is hidden in the outputs of the ensemble and can be used in distillation.
A law of robustness for two-layers neural networks
We make a precise conjecture that, for any Lipschitz activation function and for most datasets, any two-layers neural network with $k$ neurons that perfectly fit the data must have its Lipschitz constant larger (up to a constant) than $\sqrt{n/k}$ where $n$ is the number of datapoints.
Learning Over-Parametrized Two-Layer ReLU Neural Networks beyond NTK
We consider the dynamic of gradient descent for learning a two-layer neural network.
Feature Purification: How Adversarial Training Performs Robust Deep Learning
Finally, we also prove a complexity lower bound, showing that low complexity models such as linear classifiers, low-degree polynomials, or even the neural tangent kernel for this network, CANNOT defend against perturbations of this same radius, no matter what algorithms are used to train them.
Making Method of Moments Great Again? -- How can GANs learn distributions
In GANs, the training of the generator usually stops when the discriminator can no longer distinguish the generator's output from the set of training examples.
Backward Feature Correction: How Deep Learning Performs Deep Learning
On the technical side, we show for regression and even binary classification, for every input dimension $d>0$, there is a concept class of degree $\omega(1)$ polynomials so that, using $\omega(1)$-layer neural networks as learners, SGD can learn any function from this class in $\mathsf{poly}(d)$ time and sample complexity to any $\frac{1}{\mathsf{poly}(d)}$ error, through learning to represent it as a composition of $\omega(1)$ layers of quadratic functions.
Towards Explaining the Regularization Effect of Initial Large Learning Rate in Training Neural Networks
This concept translates to a larger-scale setting: we demonstrate that one can add a small patch to CIFAR-10 images that is immediately memorizable by a model with small initial learning rate, but ignored by the model with large learning rate until after annealing.
Complexity of Highly Parallel Non-Smooth Convex Optimization
Namely we consider optimization algorithms interacting with a highly parallel gradient oracle, that is one that can answer $\mathrm{poly}(d)$ gradient queries in parallel.
What Can ResNet Learn Efficiently, Going Beyond Kernels?
Recently, there is an influential line of work relating neural networks to kernels in the over-parameterized regime, proving they can learn certain concept class that is also learnable by kernels with similar test error.
Non-Stochastic Multi-Player Multi-Armed Bandits: Optimal Rate With Collision Information, Sublinear Without
We consider the non-stochastic version of the (cooperative) multi-player multi-armed bandit problem.
Can SGD Learn Recurrent Neural Networks with Provable Generalization?
Recurrent Neural Networks (RNNs) are among the most popular models in sequential data analysis.
Improved Path-length Regret Bounds for Bandits
We study adaptive regret bounds in terms of the variation of the losses (the so-called path-length bounds) for both multi-armed bandit and more generally linear bandit.
Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers
In this work, we prove that overparameterized neural networks can learn some notable concept classes, including two and three-layer networks with fewer parameters and smooth activations.
A Convergence Theory for Deep Learning via Over-Parameterization
In terms of network architectures, our theory at least applies to fully-connected neural networks, convolutional neural networks (CNN), and residual neural networks (ResNet).
On the Convergence Rate of Training Recurrent Neural Networks
In this paper, we focus on recurrent neural networks (RNNs) which are multi-layer networks widely used in natural language processing.
Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Data
Neural networks have many successful applications, while much less theoretical understanding has been gained.
Algorithmic Framework for Model-based Deep Reinforcement Learning with Theoretical Guarantees
Model-based reinforcement learning (RL) is considered to be a promising approach to reduce the sample complexity that hinders model-free RL.
The Well-Tempered Lasso
Every regression parameter in the Lasso changes linearly as a function of the regularization value.
The Well Tempered Lasso
Every regression parameter in the Lasso changes linearly as a function of the regularization value.
Online Improper Learning with an Approximation Oracle
We revisit the question of reducing online learning to approximate optimization of the offline problem.
Learning Mixtures of Linear Regressions with Nearly Optimal Complexity
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications.
An Alternative View: When Does SGD Escape Local Minima?
Stochastic gradient descent (SGD) is widely used in machine learning.
Make the Minority Great Again: First-Order Regret Bound for Contextual Bandits
Regret bounds in online learning compare the player's performance to $L^*$, the optimal performance in hindsight with a fixed strategy.
Algorithmic Regularization in Over-parameterized Matrix Sensing and Neural Networks with Quadratic Activations
We show that the gradient descent algorithm provides an implicit regularization effect in the learning of over-parameterized matrix factorization models and one-hidden-layer neural networks with quadratic activations.
Neon2: Finding Local Minima via First-Order Oracles
We propose a reduction for non-convex optimization that can (1) turn an stationary-point finding algorithm into an local-minimum finding one, and (2) replace the Hessian-vector product computations with only gradient computations.
Near-Optimal Discrete Optimization for Experimental Design: A Regret Minimization Approach
The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points.
Sparsity, variance and curvature in multi-armed bandits
In (online) learning theory the concepts of sparsity, variance and curvature are well-understood and are routinely used to obtain refined regret and generalization bounds.
Linear Convergence of a Frank-Wolfe Type Algorithm over Trace-Norm Balls
We propose a rank-$k$ variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball.
Near-Optimal Design of Experiments via Regret Minimization
We consider computationally tractable methods for the experimental design problem, where k out of n design points of dimension p are selected so that certain optimality criteria are approximately satisfied.
A Nearly Instance Optimal Algorithm for Top-k Ranking under the Multinomial Logit Model
We study the active learning problem of top-$k$ ranking from multi-wise comparisons under the popular multinomial logit model.
Provable Alternating Gradient Descent for Non-negative Matrix Factorization with Strong Correlations
Non-negative matrix factorization is a basic tool for decomposing data into the feature and weight matrices under non-negativity constraints, and in practice is often solved in the alternating minimization framework.
Convergence Analysis of Two-layer Neural Networks with ReLU Activation
We also show that the identity mapping is necessary for convergence, as it moves the initial point to a better place for optimization.
Follow the Compressed Leader: Faster Online Learning of Eigenvectors and Faster MMWU
The online problem of computing the top eigenvector is fundamental to machine learning.
Algorithms and matching lower bounds for approximately-convex optimization
In recent years, a rapidly increasing number of applications in practice requires solving non-convex objectives, like training neural networks, learning graphical models, maximum likelihood estimation etc.
Recovery Guarantee of Non-negative Matrix Factorization via Alternating Updates
Non-negative matrix factorization is a popular tool for decomposing data into feature and weight matrices under non-negativity constraints.
Faster Principal Component Regression and Stable Matrix Chebyshev Approximation
We solve principal component regression (PCR), up to a multiplicative accuracy $1+\gamma$, by reducing the problem to $\tilde{O}(\gamma^{-1})$ black-box calls of ridge regression.
First Efficient Convergence for Streaming k-PCA: a Global, Gap-Free, and Near-Optimal Rate
We provide $\textit{global}$ convergence for Oja's algorithm which is popularly used in practice but lacks theoretical understanding for $k>1$.
Doubly Accelerated Methods for Faster CCA and Generalized Eigendecomposition
We study $k$-GenEV, the problem of finding the top $k$ generalized eigenvectors, and $k$-CCA, the problem of finding the top $k$ vectors in canonical-correlation analysis.
LazySVD: Even Faster SVD Decomposition Yet Without Agonizing Pain
In the $O(\mathsf{nnz}(A) + \mathsf{poly}(1/\varepsilon))$ running-time regime, LazySVD outperforms [3] in certain parameter regimes without even using alternating minimization.
Approximate maximum entropy principles via Goemans-Williamson with applications to provable variational methods
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's razor" interpretation.
An optimal algorithm for bandit convex optimization
We consider the problem of online convex optimization against an arbitrary adversary with bandit feedback, known as bandit convex optimization.
Recovery guarantee of weighted low-rank approximation via alternating minimization
We show that the properties only need to hold in an average sense and can be achieved by the clipping step.
Linear Algebraic Structure of Word Senses, with Applications to Polysemy
A novel aspect of our technique is that each extracted word sense is accompanied by one of about 2000 "discourse atoms" that gives a succinct description of which other words co-occur with that word sense.
A Latent Variable Model Approach to PMI-based Word Embeddings
Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods.
A Theoretical Analysis of NDCG Type Ranking Measures
We show that NDCG with logarithmic discount has consistent distinguishability although it converges to the same limit for all ranking functions.
