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Found 40 papers, 20 papers with code
Sim2Real in Reconstructive Spectroscopy: Deep Learning with Augmented Device-Informed Data Simulation
This work proposes a deep learning (DL)-based framework, namely Sim2Real, for spectral signal reconstruction in reconstructive spectroscopy, focusing on efficient data sampling and fast inference time.
Decoupled Data Consistency with Diffusion Purification for Image Restoration
To solve image restoration problems, many existing techniques achieve data consistency by incorporating additional likelihood gradient steps into the reverse sampling process of diffusion models.
Analysis of Deep Image Prior and Exploiting Self-Guidance for Image Reconstruction
In this work, we first provide an analysis of how DIP recovers information from undersampled imaging measurements by analyzing the training dynamics of the underlying networks in the kernel regime for different architectures.
Improving Efficiency of Diffusion Models via Multi-Stage Framework and Tailored Multi-Decoder Architectures
This is due to the necessity of tracking extensive forward and reverse diffusion trajectories, and employing a large model with numerous parameters across multiple timesteps (i. e., noise levels).
Efficient Compression of Overparameterized Deep Models through Low-Dimensional Learning Dynamics
We empirically evaluate the effectiveness of our compression technique on matrix recovery problems.
Understanding Deep Representation Learning via Layerwise Feature Compression and Discrimination
To the best of our knowledge, this is the first quantitative characterization of feature evolution in hierarchical representations of deep linear networks.
Neural Collapse in Multi-label Learning with Pick-all-label Loss
We study deep neural networks for the multi-label classification (MLab) task through the lens of neural collapse (NC).
Generalized Neural Collapse for a Large Number of Classes
However, most of the existing empirical and theoretical studies in neural collapse focus on the case that the number of classes is small relative to the dimension of the feature space.
The Emergence of Reproducibility and Consistency in Diffusion Models
In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often yield remarkably similar outputs.
Investigating the Catastrophic Forgetting in Multimodal Large Language Models
However, catastrophic forgetting, a notorious phenomenon where the fine-tuned model fails to retain similar performance compared to the pre-trained model, still remains an inherent problem in multimodal LLMs (MLLM).
Robust Physics-based Deep MRI Reconstruction Via Diffusion Purification
In particular, we present a robustification strategy that improves the resilience of DL-based MRI reconstruction methods by utilizing pretrained diffusion models as noise purifiers.
Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency
However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their applicability as priors for high-dimensional real-world data such as medical images.
The Law of Parsimony in Gradient Descent for Learning Deep Linear Networks
Second, it allows us to better understand deep representation learning by elucidating the linear progressive separation and concentration of representations from shallow to deep layers.
Principled and Efficient Transfer Learning of Deep Models via Neural Collapse
As model size continues to grow and access to labeled training data remains limited, transfer learning has become a popular approach in many scientific and engineering fields.
Hidden State Variability of Pretrained Language Models Can Guide Computation Reduction for Transfer Learning
We propose to select layers based on the variability of their hidden states given a task-specific corpus.
Are All Losses Created Equal: A Neural Collapse Perspective
We extend such results and show through global solution and landscape analyses that a broad family of loss functions including commonly used label smoothing (LS) and focal loss (FL) exhibits Neural Collapse.
Neural Collapse with Normalized Features: A Geometric Analysis over the Riemannian Manifold
When training overparameterized deep networks for classification tasks, it has been widely observed that the learned features exhibit a so-called "neural collapse" phenomenon.
On the Optimization Landscape of Neural Collapse under MSE Loss: Global Optimality with Unconstrained Features
When training deep neural networks for classification tasks, an intriguing empirical phenomenon has been widely observed in the last-layer classifiers and features, where (i) the class means and the last-layer classifiers all collapse to the vertices of a Simplex Equiangular Tight Frame (ETF) up to scaling, and (ii) cross-example within-class variability of last-layer activations collapses to zero.
Robust Training under Label Noise by Over-parameterization
In this work, we propose a principled approach for robust training of over-parameterized deep networks in classification tasks where a proportion of training labels are corrupted.
Ranked #1 on
Learning with noisy labels
on CIFAR-10N-Random3
Rank Overspecified Robust Matrix Recovery: Subgradient Method and Exact Recovery
We study the robust recovery of a low-rank matrix from sparsely and grossly corrupted Gaussian measurements, with no prior knowledge on the intrinsic rank.
A Geometric Analysis of Neural Collapse with Unconstrained Features
In contrast to existing landscape analysis for deep neural networks which is often disconnected from practice, our analysis of the simplified model not only does it explain what kind of features are learned in the last layer, but it also shows why they can be efficiently optimized in the simplified settings, matching the empirical observations in practical deep network architectures.
Convolutional Normalization: Improving Deep Convolutional Network Robustness and Training
Furthermore, we show that our ConvNorm can reduce the layerwise spectral norm of the weight matrices and hence improve the Lipschitzness of the network, leading to easier training and improved robustness for deep ConvNets.
From Symmetry to Geometry: Tractable Nonconvex Problems
We highlight the key role of symmetry in shaping the objective landscape and discuss the different roles of rotational and discrete symmetries.
Robust Recovery via Implicit Bias of Discrepant Learning Rates for Double Over-parameterization
This paper shows that with a double over-parameterization for both the low-rank matrix and sparse corruption, gradient descent with discrepant learning rates provably recovers the underlying matrix even without prior knowledge on neither rank of the matrix nor sparsity of the corruption.
Short and Sparse Deconvolution --- A Geometric Approach
Short-and-sparse deconvolution (SaSD) is the problem of extracting localized, recurring motifs in signals with spatial or temporal structure.
Geometric Analysis of Nonconvex Optimization Landscapes for Overcomplete Learning
Learning overcomplete representations finds many applications in machine learning and data analytics.
Finding the Sparsest Vectors in a Subspace: Theory, Algorithms, and Applications
The problem of finding the sparsest vector (direction) in a low dimensional subspace can be considered as a homogeneous variant of the sparse recovery problem, which finds applications in robust subspace recovery, dictionary learning, sparse blind deconvolution, and many other problems in signal processing and machine learning.
Analysis of the Optimization Landscapes for Overcomplete Representation Learning
In this work, we show these problems can be formulated as $\ell^4$-norm optimization problems with spherical constraint, and study the geometric properties of their nonconvex optimization landscapes.
Weakly Convex Optimization over Stiefel Manifold Using Riemannian Subgradient-Type Methods
To the best of our knowledge, these are the first convergence guarantees for using Riemannian subgradient-type methods to optimize a class of nonconvex nonsmooth functions over the Stiefel manifold.
Short-and-Sparse Deconvolution -- A Geometric Approach
This paper is motivated by recent theoretical advances, which characterize the optimization landscape of a particular nonconvex formulation of SaSD.
A Nonconvex Approach for Exact and Efficient Multichannel Sparse Blind Deconvolution
We study the multi-channel sparse blind deconvolution (MCS-BD) problem, whose task is to simultaneously recover a kernel $\mathbf a$ and multiple sparse inputs $\{\mathbf x_i\}_{i=1}^p$ from their circulant convolution $\mathbf y_i = \mathbf a \circledast \mathbf x_i $ ($i=1,\cdots, p$).
Convolutional Phase Retrieval via Gradient Descent
We study the convolutional phase retrieval problem, of recovering an unknown signal $\mathbf x \in \mathbb C^n $ from $m$ measurements consisting of the magnitude of its cyclic convolution with a given kernel $\mathbf a \in \mathbb C^m $.
Convolutional Phase Retrieval
We study the convolutional phase retrieval problem, which asks us to recover an unknown signal ${\mathbf x} $ of length $n$ from $m$ measurements consisting of the magnitude of its cyclic convolution with a known kernel $\mathbf a$ of length $m$.
A Geometric Analysis of Phase Retrieval
complex Gaussian) and the number of measurements is large enough ($m \ge C n \log^3 n$), with high probability, a natural least-squares formulation for GPR has the following benign geometric structure: (1) there are no spurious local minimizers, and all global minimizers are equal to the target signal $\mathbf x$, up to a global phase; and (2) the objective function has a negative curvature around each saddle point.
Complete Dictionary Recovery over the Sphere II: Recovery by Riemannian Trust-region Method
We consider the problem of recovering a complete (i. e., square and invertible) matrix $\mathbf A_0$, from $\mathbf Y \in \mathbb{R}^{n \times p}$ with $\mathbf Y = \mathbf A_0 \mathbf X_0$, provided $\mathbf X_0$ is sufficiently sparse.
Complete Dictionary Recovery over the Sphere I: Overview and the Geometric Picture
We give the first efficient algorithm that provably recovers $\mathbf A_0$ when $\mathbf X_0$ has $O(n)$ nonzeros per column, under suitable probability model for $\mathbf X_0$.
When Are Nonconvex Problems Not Scary?
In this note, we focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) around any saddle point or local maximizer, the objective has a negative directional curvature.
Complete Dictionary Recovery over the Sphere
We consider the problem of recovering a complete (i. e., square and invertible) matrix $\mathbf A_0$, from $\mathbf Y \in \mathbb R^{n \times p}$ with $\mathbf Y = \mathbf A_0 \mathbf X_0$, provided $\mathbf X_0$ is sufficiently sparse.
Finding a sparse vector in a subspace: Linear sparsity using alternating directions
In this paper, we focus on a **planted sparse model** for the subspace: the target sparse vector is embedded in an otherwise random subspace.
Structured Priors for Sparse-Representation-Based Hyperspectral Image Classification
Pixel-wise classification, where each pixel is assigned to a predefined class, is one of the most important procedures in hyperspectral image (HSI) analysis.
