Mahdi Soltanolkotabi

Emmanuel Candes, Xiaodong Li, Mahdi Soltanolkotabi

We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge of the phase of these samples would yield a linear system). This paper develops a non-convex formulation of the phase retrieval problem as well as a concrete solution algorithm. In a nutshell, this algorithm starts with a careful initialization obtained by means of a spectral method, and then refines this initial estimate by iteratively applying novel update rules, which have low computational complexity, much like in a gradient descent scheme. The main contribution is that this algorithm is shown to rigorously allow the exact retrieval of phase information from a nearly minimal number of random measurements. Indeed, the sequence of successive iterates provably converges to the solution at a geometric rate so that the proposed scheme is efficient both in terms of computational and data resources. In theory, a variation on this scheme leads to a near-linear time algorithm for a physically realizable model based on coded diffraction patterns. We illustrate the effectiveness of our methods with various experiments on image data. Underlying our analysis are insights for the analysis of non-convex optimization schemes that may have implications for computational problems beyond phase retrieval.

Berk Tinaz, Changzhi Xie, Mahdi Soltanolkotabi

In this paper, we study the gradient descent dynamics for jointly training both layers of a one-hidden-layer ReLU network to fit a linear target function. Concretely, we consider a realizable setting where inputs are drawn i.i.d. from a Gaussian distribution and labels follow a planted linear model. This stylized framework captures salient features of end-to-end training in inverse problems and certain auto-encoder models. Despite its apparent simplicity, the dynamics remain poorly understood, in part because the loss landscape contains multiple non-strict saddle points, making it unclear why gradient descent from random initialization reliably escapes bad stationary regions. We provide a detailed characterization of the optimization landscape and prove that gradient descent from a moderately small random initialization-simultaneously training both layers-converges to a global minimizer at a linear rate with order-wise optimal sample complexity. Our analysis tracks the trajectory through three phases: an alignment phase in which hidden weights progressively align with the planted direction while the output weights maintain the correct sign pattern; a growth phase in which the norms of both layers increase while preserving alignment; and a local refinement phase in which the aligned neurons rapidly converge to the planted direction, yielding fast local convergence. To rigorously show that GD avoids non-strict saddles, we develop trajectory-level control arguments for the end-to-end dynamics. In addition, we establish novel uniform concentration results that hold along the entire trajectory, and are essential for obtaining order-wise optimal sample complexity. We corroborate our theory with extensive experiments across a range of configurations.

Rui Xu, Mahdi Soltanolkotabi, Justin P. Haldar et al.

This paper presents a new algorithm, Accelerated Wirtinger Flow (AWF), for ptychographic image reconstruction from phaseless diffraction pattern measurements. AWF is based on combining Nesterov's acceleration approach with Wirtinger gradient descent. Theoretical results enable prespecification of all AWF algorithm parameters, with no need for computationally-expensive line searches and no need for manual parameter tuning. AWF is evaluated in the context of simulated X-ray ptychography, where we demonstrate fast convergence and low per-iteration computational complexity. We also show examples where AWF reaches higher image quality with less computation than classical algorithms. AWF is also shown to have robustness to noise and probe misalignment.

Alex Damian, Jason D. Lee, Mahdi Soltanolkotabi

Significant theoretical work has established that in specific regimes, neural networks trained by gradient descent behave like kernel methods. However, in practice, it is known that neural networks strongly outperform their associated kernels. In this work, we explain this gap by demonstrating that there is a large class of functions which cannot be efficiently learned by kernel methods but can be easily learned with gradient descent on a two layer neural network outside the kernel regime by learning representations that are relevant to the target task. We also demonstrate that these representations allow for efficient transfer learning, which is impossible in the kernel regime. Specifically, we consider the problem of learning polynomials which depend on only a few relevant directions, i.e. of the form $f^\star(x) = g(Ux)$ where $U: \R^d \to \R^r$ with $d \gg r$. When the degree of $f^\star$ is $p$, it is known that $n \asymp d^p$ samples are necessary to learn $f^\star$ in the kernel regime. Our primary result is that gradient descent learns a representation of the data which depends only on the directions relevant to $f^\star$. This results in an improved sample complexity of $n\asymp d^2 r + dr^p$. Furthermore, in a transfer learning setup where the data distributions in the source and target domain share the same representation $U$ but have different polynomial heads we show that a popular heuristic for transfer learning has a target sample complexity independent of $d$.

Sara Babakniya, Zalan Fabian, Chaoyang He et al.

Deep learning models often suffer from forgetting previously learned information when trained on new data. This problem is exacerbated in federated learning (FL), where the data is distributed and can change independently for each user. Many solutions are proposed to resolve this catastrophic forgetting in a centralized setting. However, they do not apply directly to FL because of its unique complexities, such as privacy concerns and resource limitations. To overcome these challenges, this paper presents a framework for $\textbf{federated class incremental learning}$ that utilizes a generative model to synthesize samples from past distributions. This data can be later exploited alongside the training data to mitigate catastrophic forgetting. To preserve privacy, the generative model is trained on the server using data-free methods at the end of each task without requesting data from clients. Moreover, our solution does not demand the users to store old data or models, which gives them the freedom to join/leave the training at any time. Additionally, we introduce SuperImageNet, a new regrouping of the ImageNet dataset specifically tailored for federated continual learning. We demonstrate significant improvements compared to existing baselines through extensive experiments on multiple datasets.

Zalan Fabian, Berk Tinaz, Mahdi Soltanolkotabi

In accelerated MRI reconstruction, the anatomy of a patient is recovered from a set of under-sampled and noisy measurements. Deep learning approaches have been proven to be successful in solving this ill-posed inverse problem and are capable of producing very high quality reconstructions. However, current architectures heavily rely on convolutions, that are content-independent and have difficulties modeling long-range dependencies in images. Recently, Transformers, the workhorse of contemporary natural language processing, have emerged as powerful building blocks for a multitude of vision tasks. These models split input images into non-overlapping patches, embed the patches into lower-dimensional tokens and utilize a self-attention mechanism that does not suffer from the aforementioned weaknesses of convolutional architectures. However, Transformers incur extremely high compute and memory cost when 1) the input image resolution is high and 2) when the image needs to be split into a large number of patches to preserve fine detail information, both of which are typical in low-level vision problems such as MRI reconstruction, having a compounding effect. To tackle these challenges, we propose HUMUS-Net, a hybrid architecture that combines the beneficial implicit bias and efficiency of convolutions with the power of Transformer blocks in an unrolled and multi-scale network. HUMUS-Net extracts high-resolution features via convolutional blocks and refines low-resolution features via a novel Transformer-based multi-scale feature extractor. Features from both levels are then synthesized into a high-resolution output reconstruction. Our network establishes new state of the art on the largest publicly available MRI dataset, the fastMRI dataset. We further demonstrate the performance of HUMUS-Net on two other popular MRI datasets and perform fine-grained ablation studies to validate our design.

Samet Oymak, Ankit Singh Rawat, Mahdi Soltanolkotabi et al.

Prompt-tuning is an emerging strategy to adapt large language models (LLM) to downstream tasks by learning a (soft-)prompt parameter from data. Despite its success in LLMs, there is limited theoretical understanding of the power of prompt-tuning and the role of the attention mechanism in prompting. In this work, we explore prompt-tuning for one-layer attention architectures and study contextual mixture-models where each input token belongs to a context-relevant or -irrelevant set. We isolate the role of prompt-tuning through a self-contained prompt-attention model. Our contributions are as follows: (1) We show that softmax-prompt-attention is provably more expressive than softmax-self-attention and linear-prompt-attention under our contextual data model. (2) We analyze the initial trajectory of gradient descent and show that it learns the prompt and prediction head with near-optimal sample complexity and demonstrate how prompt can provably attend to sparse context-relevant tokens. (3) Assuming a known prompt but an unknown prediction head, we characterize the exact finite sample performance of prompt-attention which reveals the fundamental performance limits and the precise benefit of the context information. We also provide experiments that verify our theoretical insights on real datasets and demonstrate how prompt-tuning enables the model to attend to context-relevant information.

Vinu Sankar Sadasivan, Mahdi Soltanolkotabi, Soheil Feizi

Large-scale training of modern deep learning models heavily relies on publicly available data on the web. This potentially unauthorized usage of online data leads to concerns regarding data privacy. Recent works aim to make unlearnable data for deep learning models by adding small, specially designed noises to tackle this issue. However, these methods are vulnerable to adversarial training (AT) and/or are computationally heavy. In this work, we propose a novel, model-free, Convolution-based Unlearnable DAtaset (CUDA) generation technique. CUDA is generated using controlled class-wise convolutions with filters that are randomly generated via a private key. CUDA encourages the network to learn the relation between filters and labels rather than informative features for classifying the clean data. We develop some theoretical analysis demonstrating that CUDA can successfully poison Gaussian mixture data by reducing the clean data performance of the optimal Bayes classifier. We also empirically demonstrate the effectiveness of CUDA with various datasets (CIFAR-10, CIFAR-100, ImageNet-100, and Tiny-ImageNet), and architectures (ResNet-18, VGG-16, Wide ResNet-34-10, DenseNet-121, DeIT, EfficientNetV2-S, and MobileNetV2). Our experiments show that CUDA is robust to various data augmentations and training approaches such as smoothing, AT with different budgets, transfer learning, and fine-tuning. For instance, training a ResNet-18 on ImageNet-100 CUDA achieves only 8.96$\%$, 40.08$\%$, and 20.58$\%$ clean test accuracies with empirical risk minimization (ERM), $L_{\infty}$ AT, and $L_{2}$ AT, respectively. Here, ERM on the clean training data achieves a clean test accuracy of 80.66$\%$. CUDA exhibits unlearnability effect with ERM even when only a fraction of the training dataset is perturbed. Furthermore, we also show that CUDA is robust to adaptive defenses designed specifically to break it.

Mohammad Shahab Sepehri, Zalan Fabian, Maryam Soltanolkotabi et al.

Multimodal Large Language Models (MLLMs) have tremendous potential to improve the accuracy, availability, and cost-effectiveness of healthcare by providing automated solutions or serving as aids to medical professionals. Despite promising first steps in developing medical MLLMs in the past few years, their capabilities and limitations are not well-understood. Recently, many benchmark datasets have been proposed that test the general medical knowledge of such models across a variety of medical areas. However, the systematic failure modes and vulnerabilities of such models are severely underexplored with most medical benchmarks failing to expose the shortcomings of existing models in this safety-critical domain. In this paper, we introduce MediConfusion, a challenging medical Visual Question Answering (VQA) benchmark dataset, that probes the failure modes of medical MLLMs from a vision perspective. We reveal that state-of-the-art models are easily confused by image pairs that are otherwise visually dissimilar and clearly distinct for medical experts. Strikingly, all available models (open-source or proprietary) achieve performance below random guessing on MediConfusion, raising serious concerns about the reliability of existing medical MLLMs for healthcare deployment. We also extract common patterns of model failure that may help the design of a new generation of more trustworthy and reliable MLLMs in healthcare.

Chaoyang He, Shuai Zheng, Aston Zhang et al.

The mixture of Expert (MoE) parallelism is a recent advancement that scales up the model size with constant computational cost. MoE selects different sets of parameters (i.e., experts) for each incoming token, resulting in a sparsely-activated model. Despite several successful applications of MoE, its training efficiency degrades significantly as the number of experts increases. The routing stage in MoE relies on the efficiency of the All2All communication collective, which suffers from network congestion and has poor scalability. To mitigate these issues, we introduce SMILE, which exploits heterogeneous network bandwidth and splits a single-step routing into bi-level routing. Our experimental results show that the proposed method obtains a 2.5x speedup over Switch Transformer in terms of pretraining throughput on the Colossal Clean Crawled Corpus without losing any convergence speed.

Romain Cosentino, Sarath Shekkizhar, Mahdi Soltanolkotabi et al.

Self-supervised learning (SSL) has emerged as a desirable paradigm in computer vision due to the inability of supervised models to learn representations that can generalize in domains with limited labels. The recent popularity of SSL has led to the development of several models that make use of diverse training strategies, architectures, and data augmentation policies with no existing unified framework to study or assess their effectiveness in transfer learning. We propose a data-driven geometric strategy to analyze different SSL models using local neighborhoods in the feature space induced by each. Unlike existing approaches that consider mathematical approximations of the parameters, individual components, or optimization landscape, our work aims to explore the geometric properties of the representation manifolds learned by SSL models. Our proposed manifold graph metrics (MGMs) provide insights into the geometric similarities and differences between available SSL models, their invariances with respect to specific augmentations, and their performances on transfer learning tasks. Our key findings are two fold: (i) contrary to popular belief, the geometry of SSL models is not tied to its training paradigm (contrastive, non-contrastive, and cluster-based); (ii) we can predict the transfer learning capability for a specific model based on the geometric properties of its semantic and augmentation manifolds.

Liam Collins, Hamed Hassani, Mahdi Soltanolkotabi et al.

An increasingly popular machine learning paradigm is to pretrain a neural network (NN) on many tasks offline, then adapt it to downstream tasks, often by re-training only the last linear layer of the network. This approach yields strong downstream performance in a variety of contexts, demonstrating that multitask pretraining leads to effective feature learning. Although several recent theoretical studies have shown that shallow NNs learn meaningful features when either (i) they are trained on a {\em single} task or (ii) they are {\em linear}, very little is known about the closer-to-practice case of {\em nonlinear} NNs trained on {\em multiple} tasks. In this work, we present the first results proving that feature learning occurs during training with a nonlinear model on multiple tasks. Our key insight is that multi-task pretraining induces a pseudo-contrastive loss that favors representations that align points that typically have the same label across tasks. Using this observation, we show that when the tasks are binary classification tasks with labels depending on the projection of the data onto an $r$-dimensional subspace within the $d\gg r$-dimensional input space, a simple gradient-based multitask learning algorithm on a two-layer ReLU NN recovers this projection, allowing for generalization to downstream tasks with sample and neuron complexity independent of $d$. In contrast, we show that with high probability over the draw of a single task, training on this single task cannot guarantee to learn all $r$ ground-truth features.

Romain Cosentino, Anirvan Sengupta, Salman Avestimehr et al.

Self-supervised learning (SSL) is currently one of the premier techniques to create data representations that are actionable for transfer learning in the absence of human annotations. Despite their success, the underlying geometry of these representations remains elusive, which obfuscates the quest for more robust, trustworthy, and interpretable models. In particular, mainstream SSL techniques rely on a specific deep neural network architecture with two cascaded neural networks: the encoder and the projector. When used for transfer learning, the projector is discarded since empirical results show that its representation generalizes more poorly than the encoder's. In this paper, we investigate this curious phenomenon and analyze how the strength of the data augmentation policies affects the data embedding. We discover a non-trivial relation between the encoder, the projector, and the data augmentation strength: with increasingly larger augmentation policies, the projector, rather than the encoder, is more strongly driven to become invariant to the augmentations. It does so by eliminating crucial information about the data by learning to project it into a low-dimensional space, a noisy estimate of the data manifold tangent plane in the encoder representation. This analysis is substantiated through a geometrical perspective with theoretical and empirical results.

Nuri Mert Vural, Alberto Bietti, Mahdi Soltanolkotabi et al. · utoronto

Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training and retrieve it at inference. Existing theoretical analyses typically study transformers under idealized assumptions such as infinite data or orthogonal embeddings. In realistic settings, however, models are trained on finite datasets with non-orthogonal (random) embeddings. We address this gap by analyzing a single-layer transformer with random embeddings trained with (empirical) gradient descent on a simple token-retrieval task, where the model must identify an informative token within a length-$L$ sequence and learn a one-to-one mapping from tokens to labels. Our analysis tracks the ``early phase'' of gradient descent and yields explicit formulas for the model's storage capacity -- revealing a multiplicative dependence between sample size $N$, embedding dimension $d$, and sequence length $L$. We validate these scalings numerically and further complement them with a lower bound for the underlying statistical problem, demonstrating that this multiplicative scaling is intrinsic under non-orthogonal embeddings.

Zalan Fabian, Berk Tinaz, Mahdi Soltanolkotabi

Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily corrupted measurements. However, in what is widely known as the perception-distortion trade-off, the price of perceptually appealing reconstructions is often paid in declined distortion metrics, such as PSNR. Distortion metrics measure faithfulness to the observation, a crucial requirement in inverse problems. In this work, we propose a novel framework for inverse problem solving, namely we assume that the observation comes from a stochastic degradation process that gradually degrades and noises the original clean image. We learn to reverse the degradation process in order to recover the clean image. Our technique maintains consistency with the original measurement throughout the reverse process, and allows for great flexibility in trading off perceptual quality for improved distortion metrics and sampling speedup via early-stopping. We demonstrate the efficiency of our method on different high-resolution datasets and inverse problems, achieving great improvements over other state-of-the-art diffusion-based methods with respect to both perceptual and distortion metrics.

Anselm Krainovic, Mahdi Soltanolkotabi, Reinhard Heckel

Deep neural networks provide excellent performance for inverse problems such as denoising. However, neural networks can be sensitive to adversarial or worst-case perturbations. This raises the question of whether such networks can be trained efficiently to be worst-case robust. In this paper, we investigate whether jittering, a simple regularization technique that adds isotropic Gaussian noise during training, is effective for learning worst-case robust estimators for inverse problems. While well studied for prediction in classification tasks, the effectiveness of jittering for inverse problems has not been systematically investigated. In this paper, we present a novel analytical characterization of the optimal $\ell_2$-worst-case robust estimator for linear denoising and show that jittering yields optimal robust denoisers. Furthermore, we examine jittering empirically via training deep neural networks (U-nets) for natural image denoising, deconvolution, and accelerated magnetic resonance imaging (MRI). The results show that jittering significantly enhances the worst-case robustness, but can be suboptimal for inverse problems beyond denoising. Moreover, our results imply that training on real data which often contains slight noise is somewhat robustness enhancing.

Zalan Fabian, Berk Tinaz, Mahdi Soltanolkotabi

Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground truth signal structure, the severity of the degradation and the complex interactions between the above. This results in natural sample-by-sample variation in the difficulty of a reconstruction problem. Our key observation is that most existing inverse problem solvers lack the ability to adapt their compute power to the difficulty of the reconstruction task, resulting in subpar performance and wasteful resource allocation. We propose a novel method, $\textit{severity encoding}$, to estimate the degradation severity of corrupted signals in the latent space of an autoencoder. We show that the estimated severity has strong correlation with the true corruption level and can provide useful hints on the difficulty of reconstruction problems on a sample-by-sample basis. Furthermore, we propose a reconstruction method based on latent diffusion models that leverages the predicted degradation severities to fine-tune the reverse diffusion sampling trajectory and thus achieve sample-adaptive inference times. Our framework, Flash-Diffusion, acts as a wrapper that can be combined with any latent diffusion-based baseline solver, imbuing it with sample-adaptivity and acceleration. We perform experiments on both linear and nonlinear inverse problems and demonstrate that our technique greatly improves the performance of the baseline solver and achieves up to $10\times$ acceleration in mean sampling speed.

Sara Babakniya, Zalan Fabian, Chaoyang He et al.

Deep learning models are prone to forgetting information learned in the past when trained on new data. This problem becomes even more pronounced in the context of federated learning (FL), where data is decentralized and subject to independent changes for each user. Continual Learning (CL) studies this so-called \textit{catastrophic forgetting} phenomenon primarily in centralized settings, where the learner has direct access to the complete training dataset. However, applying CL techniques to FL is not straightforward due to privacy concerns and resource limitations. This paper presents a framework for federated class incremental learning that utilizes a generative model to synthesize samples from past distributions instead of storing part of past data. Then, clients can leverage the generative model to mitigate catastrophic forgetting locally. The generative model is trained on the server using data-free methods at the end of each task without requesting data from clients. Therefore, it reduces the risk of data leakage as opposed to training it on the client's private data. We demonstrate significant improvements for the CIFAR-100 dataset compared to existing baselines.

Yue Niu, Zalan Fabian, Sunwoo Lee et al.

Quasi-Newton methods still face significant challenges in training large-scale neural networks due to additional compute costs in the Hessian related computations and instability issues in stochastic training. A well-known method, L-BFGS that efficiently approximates the Hessian using history parameter and gradient changes, suffers convergence instability in stochastic training. So far, attempts that adapt L-BFGS to large-scale stochastic training incur considerable extra overhead, which offsets its convergence benefits in wall-clock time. In this paper, we propose mL-BFGS, a lightweight momentum-based L-BFGS algorithm that paves the way for quasi-Newton (QN) methods in large-scale distributed deep neural network (DNN) optimization. mL-BFGS introduces a nearly cost-free momentum scheme into L-BFGS update and greatly reduces stochastic noise in the Hessian, therefore stabilizing convergence during stochastic optimization. For model training at a large scale, mL-BFGS approximates a block-wise Hessian, thus enabling distributing compute and memory costs across all computing nodes. We provide a supporting convergence analysis for mL-BFGS in stochastic settings. To investigate mL-BFGS potential in large-scale DNN training, we train benchmark neural models using mL-BFGS and compare performance with baselines (SGD, Adam, and other quasi-Newton methods). Results show that mL-BFGS achieves both noticeable iteration-wise and wall-clock speedup.

Paula Arguello, Berk Tinaz, Mohammad Shahab Sepehri et al.

Deep learning underpins a wide range of applications in MRI, including reconstruction, artifact removal, and segmentation. However, progress has been driven largely by public datasets focused on brain and knee imaging, shaping how models are trained and evaluated. As a result, careful studies of the reliability of these models across diverse anatomical settings remain limited. In this work, we introduce MosaicMRI, a large and diverse collection of fully sampled raw musculoskeletal (MSK) MR measurements designed for training and evaluating machine-learning-based methods. MosaicMRI is the largest open-source raw MSK MRI dataset to date, comprising 2,671 volumes and 80,156 slices. The dataset offers substantial diversity in volume orientation (e.g., axial, sagittal), imaging contrasts (e.g., PD, T1, T2), anatomies (e.g., spine, knee, hip, ankle, and others), and numbers of acquisition coils. Using VarNet as a baseline for accelerated reconstruction task, we perform a comprehensive set of experiments to study scaling behavior with respect to both model capacity and dataset size. Interestingly, models trained on the combined anatomies significantly outperform anatomy-specific models in low-sample regimes, highlighting the benefits of anatomical diversity and the presence of exploitable cross-anatomical correlations. We further evaluate robustness and cross-anatomy generalization by training models on one anatomy (e.g., spine) and testing them on another (e.g., knee). Notably, we identify groups of body parts (e.g., foot and elbow) that generalize well with each other, and highlight that performance under domain shifts depends on both training set size, anatomy, and protocol-specific factors.

Sara Fridovich-Keil, Fabrizio Valdivia, Gordon Wetzstein et al.

In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves inverting this nonlinearity as a preprocessing step and then solving a convex inverse problem. However, this nonlinear measurement preprocessing required to use the Radon transform is poorly conditioned in the vicinity of high-density materials, such as metal. This preprocessing makes CT reconstruction methods numerically sensitive and susceptible to artifacts near high-density regions. In this paper, we study a technique where the signal is directly reconstructed from raw measurements through the nonlinear forward model. Though this optimization is nonconvex, we show that gradient descent provably converges to the global optimum at a geometric rate, perfectly reconstructing the underlying signal with a near minimal number of random measurements. We also prove similar results in the under-determined setting where the number of measurements is significantly smaller than the dimension of the signal. This is achieved by enforcing prior structural information about the signal through constraints on the optimization variables. We illustrate the benefits of direct nonlinear CT reconstruction with cone-beam CT experiments on synthetic and real 3D volumes. We show that this approach reduces metal artifacts compared to a commercial reconstruction of a human skull with metal dental crowns.

Mohammad Shahab Sepehri, Asal Mehradfar, Berk Tinaz et al.

Text-to-image diffusion models achieve high visual fidelity but surprisingly exhibit systematic failures in numerical control when prompts specify explicit object counts. To address this limitation, we introduce ATHENA, a model-agnostic, test-time adaptive steering framework that improves object count fidelity without modifying model architectures or requiring retraining. ATHENA leverages intermediate representations during sampling to estimate object counts and applies count-aware noise corrections early in the denoising process, steering the generation trajectory before structural errors become difficult to revise. We present three progressively more advanced variants of ATHENA that trade additional computation for improved numerical accuracy, ranging from static prompt-based steering to dynamically adjusted count-aware control. Experiments on established benchmarks and a new visually and semantically complex dataset show that ATHENA consistently improves count fidelity, particularly at higher target counts, while maintaining favorable accuracy-runtime trade-offs across multiple diffusion backbones.

Gautam Goel, Mahdi Soltanolkotabi, Peter Bartlett

We study the training dynamics of gradient descent in a softmax self-attention layer trained to perform linear regression and show that a simple first-order optimization algorithm can converge to the globally optimal self-attention parameters at a geometric rate. Our analysis proceeds in two steps. First, we show that in the infinite-data limit the regression problem solved by the self-attention layer is equivalent to a nonconvex matrix factorization problem. Second, we exploit this connection to design a novel "structure-aware" variant of gradient descent which efficiently optimizes the original finite-data regression objective. Our optimization algorithm features several innovations over standard gradient descent, including a preconditioner and regularizer which help avoid spurious stationary points, and a data-dependent spectral initialization of parameters which lie near the manifold of global minima with high probability.

Amin Banayeeanzade, Mahdi Soltanolkotabi, Mohammad Rostami

Multi-task learning (MTL) is a machine learning paradigm that aims to improve the generalization performance of a model on multiple related tasks by training it simultaneously on those tasks. Unlike MTL, where the model has instant access to the training data of all tasks, continual learning (CL) involves adapting to new sequentially arriving tasks over time without forgetting the previously acquired knowledge. Despite the wide practical adoption of CL and MTL and extensive literature on both areas, there remains a gap in the theoretical understanding of these methods when used with overparameterized models such as deep neural networks. This paper studies the overparameterized linear models as a proxy for more complex models. We develop theoretical results describing the effect of various system parameters on the model's performance in an MTL setup. Specifically, we study the impact of model size, dataset size, and task similarity on the generalization error and knowledge transfer. Additionally, we present theoretical results to characterize the performance of replay-based CL models. Our results reveal the impact of buffer size and model capacity on the forgetting rate in a CL setup and help shed light on some of the state-of-the-art CL methods. Finally, through extensive empirical evaluations, we demonstrate that our theoretical findings are also applicable to deep neural networks, offering valuable guidance for designing MTL and CL models in practice.

Zarif Ikram, Arad Firouzkouhi, Stephen Tu et al.

A central challenge in large language model (LLM) editing is capability preservation: methods that successfully change targeted behavior can quietly game the editing proxy and corrupt general capabilities, producing degenerate behaviors reminiscent of proxy/reward hacking. We present CrispEdit, a scalable and principled second-order editing algorithm that treats capability preservation as an explicit constraint, unifying and generalizing several existing editing approaches. CrispEdit formulates editing as constrained optimization and enforces the constraint by projecting edit updates onto the low-curvature subspace of the capability-loss landscape. At the crux of CrispEdit is expressing capability constraint via Bregman divergence, whose quadratic form yields the Gauss-Newton Hessian exactly and even when the base model is not trained to convergence. We make this second-order procedure efficient at the LLM scale using Kronecker-factored approximate curvature (K-FAC) and a novel matrix-free projector that exploits Kronecker structure to avoid constructing massive projection matrices. Across standard model-editing benchmarks, CrispEdit achieves high edit success while keeping capability degradation below 1% on average across datasets, significantly improving over prior editors.

Omar Zamzam, Haleh Akrami, Mahdi Soltanolkotabi et al.

In this paper, we address the problem of learning a binary (positive vs. negative) classifier given Positive and Unlabeled data commonly referred to as PU learning. Although rudimentary techniques like clustering, out-of-distribution detection, or positive density estimation can be used to solve the problem in low-dimensional settings, their efficacy progressively deteriorates with higher dimensions due to the increasing complexities in the data distribution. In this paper we propose to learn a neural network-based data representation using a loss function that can be used to project the unlabeled data into two (positive and negative) clusters that can be easily identified using simple clustering techniques, effectively emulating the phenomenon observed in low-dimensional settings. We adopt a vector quantization technique for the learned representations to amplify the separation between the learned unlabeled data clusters. We conduct experiments on simulated PU data that demonstrate the improved performance of our proposed method compared to the current state-of-the-art approaches. We also provide some theoretical justification for our two cluster-based approach and our algorithmic choices.

Filip Kovačević, Hong Chang Ji, Denny Wu et al.

It is folklore that reusing training data more than once can improve the statistical efficiency of gradient-based learning. However, beyond linear regression, the theoretical advantage of full-batch gradient descent (GD, which always reuses all the data) over one-pass stochastic gradient descent (online SGD, which uses each data point only once) remains unclear. In this work, we consider learning a $d$-dimensional single-index model with a quadratic activation, for which it is known that one-pass SGD requires $n\gtrsim d\log d$ samples to achieve weak recovery. We first show that this $\log d$ factor in the sample complexity persists for full-batch spherical GD on the correlation loss; however, by simply truncating the activation, full-batch GD exhibits a favorable optimization landscape at $n \simeq d$ samples, thereby outperforming one-pass SGD (with the same activation) in statistical efficiency. We complement this result with a trajectory analysis of full-batch GD on the squared loss from small initialization, showing that $n \gtrsim d$ samples and $T \gtrsim\log d$ gradient steps suffice to achieve strong (exact) recovery.

Chaoyang He, Alay Dilipbhai Shah, Zhenheng Tang et al.

Federated Learning (FL) is a distributed learning paradigm that can learn a global or personalized model from decentralized datasets on edge devices. However, in the computer vision domain, model performance in FL is far behind centralized training due to the lack of exploration in diverse tasks with a unified FL framework. FL has rarely been demonstrated effectively in advanced computer vision tasks such as object detection and image segmentation. To bridge the gap and facilitate the development of FL for computer vision tasks, in this work, we propose a federated learning library and benchmarking framework, named FedCV, to evaluate FL on the three most representative computer vision tasks: image classification, image segmentation, and object detection. We provide non-I.I.D. benchmarking datasets, models, and various reference FL algorithms. Our benchmark study suggests that there are multiple challenges that deserve future exploration: centralized training tricks may not be directly applied to FL; the non-I.I.D. dataset actually downgrades the model accuracy to some degree in different tasks; improving the system efficiency of federated training is challenging given the huge number of parameters and the per-client memory cost. We believe that such a library and benchmark, along with comparable evaluation settings, is necessary to make meaningful progress in FL on computer vision tasks. FedCV is publicly available: https://github.com/FedML-AI/FedCV.

Chaoyang He, Shen Li, Mahdi Soltanolkotabi et al.

The size of Transformer models is growing at an unprecedented pace. It has only taken less than one year to reach trillion-level parameters after the release of GPT-3 (175B). Training such models requires both substantial engineering efforts and enormous computing resources, which are luxuries most research teams cannot afford. In this paper, we propose PipeTransformer, which leverages automated and elastic pipelining and data parallelism for efficient distributed training of Transformer models. PipeTransformer automatically adjusts the pipelining and data parallelism by identifying and freezing some layers during the training, and instead allocates resources for training of the remaining active layers. More specifically, PipeTransformer dynamically excludes converged layers from the pipeline, packs active layers into fewer GPUs, and forks more replicas to increase data-parallel width. We evaluate PipeTransformer using Vision Transformer (ViT) on ImageNet and BERT on GLUE and SQuAD datasets. Our results show that PipeTransformer attains a 2.4 fold speedup compared to the state-of-the-art baseline. We also provide various performance analyses for a more comprehensive understanding of our algorithmic and system-wise design. We also develop open-sourced flexible APIs for PipeTransformer, which offer a clean separation among the freeze algorithm, model definitions, and training accelerations, hence allowing it to be applied to other algorithms that require similar freezing strategies.

Mahdi Soltanolkotabi, Dominik Stöger, Changzhi Xie

Recently, there has been significant progress in understanding the convergence and generalization properties of gradient-based methods for training overparameterized learning models. However, many aspects including the role of small random initialization and how the various parameters of the model are coupled during gradient-based updates to facilitate good generalization remain largely mysterious. A series of recent papers have begun to study this role for non-convex formulations of symmetric Positive Semi-Definite (PSD) matrix sensing problems which involve reconstructing a low-rank PSD matrix from a few linear measurements. The underlying symmetry/PSDness is crucial to existing convergence and generalization guarantees for this problem. In this paper, we study a general overparameterized low-rank matrix sensing problem where one wishes to reconstruct an asymmetric rectangular low-rank matrix from a few linear measurements. We prove that an overparameterized model trained via factorized gradient descent converges to the low-rank matrix generating the measurements. We show that in this setting, factorized gradient descent enjoys two implicit properties: (1) coupling of the trajectory of gradient descent where the factors are coupled in various ways throughout the gradient update trajectory and (2) an algorithmic regularization property where the iterates show a propensity towards low-rank models despite the overparameterized nature of the factorized model. These two implicit properties in turn allow us to show that the gradient descent trajectory from small random initialization moves towards solutions that are both globally optimal and generalize well.

Halil Alperen Gozeten, M. Emrullah Ildiz, Xuechen Zhang et al.

Test-time training (TTT) methods explicitly update the weights of a model to adapt to the specific test instance, and they have found success in a variety of settings, including most recently language modeling and reasoning. To demystify this success, we investigate a gradient-based TTT algorithm for in-context learning, where we train a transformer model on the in-context demonstrations provided in the test prompt. Specifically, we provide a comprehensive theoretical characterization of linear transformers when the update rule is a single gradient step. Our theory (i) delineates the role of alignment between pretraining distribution and target task, (ii) demystifies how TTT can alleviate distribution shift, and (iii) quantifies the sample complexity of TTT including how it can significantly reduce the eventual sample size required for in-context learning. As our empirical contribution, we study the benefits of TTT for TabPFN, a tabular foundation model. In line with our theory, we demonstrate that TTT significantly reduces the required sample size for tabular classification (3 to 5 times fewer) unlocking substantial inference efficiency with a negligible training cost.

Mohammad Shahab Sepehri, Zalan Fabian, Mahdi Soltanolkotabi

The landscape of computational building blocks of efficient image restoration architectures is dominated by a combination of convolutional processing and various attention mechanisms. However, convolutional filters, while efficient, are inherently local and therefore struggle with modeling long-range dependencies in images. In contrast, attention excels at capturing global interactions between arbitrary image regions, but suffers from a quadratic cost in image dimension. In this work, we propose Serpent, an efficient architecture for high-resolution image restoration that combines recent advances in state space models (SSMs) with multi-scale signal processing in its core computational block. SSMs, originally introduced for sequence modeling, can maintain a global receptive field with a favorable linear scaling in input size. We propose a novel hierarchical architecture inspired by traditional signal processing principles, that converts the input image into a collection of sequences and processes them in a multi-scale fashion. Our experimental results demonstrate that Serpent can achieve reconstruction quality on par with state-of-the-art techniques, while requiring orders of magnitude less compute (up to $150$ fold reduction in FLOPS) and a factor of up to $5\times$ less GPU memory while maintaining a compact model size. The efficiency gains achieved by Serpent are especially notable at high image resolutions.

Bhavya Vasudeva, Jung Whan Lee, Vatsal Sharan et al.

Adam is the de facto optimization algorithm for several deep learning applications, but an understanding of its implicit bias and how it differs from other algorithms, particularly standard first-order methods such as (stochastic) gradient descent (GD), remains limited. In practice, neural networks (NNs) trained with SGD are known to exhibit simplicity bias -- a tendency to find simple solutions. In contrast, we show that Adam is more resistant to such simplicity bias. First, we investigate the differences in the implicit biases of Adam and GD when training two-layer ReLU NNs on a binary classification task with Gaussian data. We find that GD exhibits a simplicity bias, resulting in a linear decision boundary with a suboptimal margin, whereas Adam leads to much richer and more diverse features, producing a nonlinear boundary that is closer to the Bayes' optimal predictor. This richer decision boundary also allows Adam to achieve higher test accuracy both in-distribution and under certain distribution shifts. We theoretically prove these results by analyzing the population gradients. Next, to corroborate our theoretical findings, we present extensive empirical results showing that this property of Adam leads to superior generalization across various datasets with spurious correlations where NNs trained with SGD are known to show simplicity bias and do not generalize well under certain distributional shifts.

Berk Tinaz, Zalan Fabian, Mahdi Soltanolkotabi

Diffusion models have become the go-to method for text-to-image generation, producing high-quality images from noise through a process called reverse diffusion. Understanding the dynamics of the reverse diffusion process is crucial in steering the generation and achieving high sample quality. However, the inner workings of diffusion models is still largely a mystery due to their black-box nature and complex, multi-step generation process. Mechanistic Interpretability (MI) techniques, such as Sparse Autoencoders (SAEs), aim at uncovering the operating principles of models through granular analysis of their internal representations. These MI techniques have been successful in understanding and steering the behavior of large language models at scale. However, the great potential of SAEs has not yet been applied toward gaining insight into the intricate generative process of diffusion models. In this work, we leverage the SAE framework to probe the inner workings of a popular text-to-image diffusion model, and uncover a variety of human-interpretable concepts in its activations. Interestingly, we find that even before the first reverse diffusion step is completed, the final composition of the scene can be predicted surprisingly well by looking at the spatial distribution of activated concepts. Moreover, going beyond correlational analysis, we show that the discovered concepts have a causal effect on the model output and can be leveraged to steer the generative process. We design intervention techniques aimed at manipulating image composition and style, and demonstrate that (1) in early stages of diffusion image composition can be effectively controlled, (2) in the middle stages of diffusion image composition is finalized, however stylistic interventions are effective, and (3) in the final stages of diffusion only minor textural details are subject to change.

Tianyi Zhou, Deqing Fu, Mahdi Soltanolkotabi et al.

Large Language Models (LLMs) typically represent numbers using multiple tokens, which requires the model to aggregate these tokens to interpret numerical values. This fragmentation makes both training and inference less efficient and adversely affects the model's performance on number-related tasks. Inspired by the observation that pre-trained LLMs internally learn Fourier-like features for number tokens, we propose Fourier Number Embedding (FoNE), a novel method that directly maps numbers into the embedding space with their Fourier features. FoNE encodes each number as a single token with only two embedding dimensions per digit, effectively capturing numerical values without fragmentation. This compact representation accelerates both training and inference. Compared to traditional subword and digit-wise embeddings, FoNE not only reduces computational overhead but also achieves higher accuracy across various numerical tasks including addition, subtraction and multiplication. On 6-digit decimal addition, FoNE requires 64$\times$ less data to achieve 99% accuracy than subword and digit-wise embeddings while using 3$\times$ and 6$\times$ fewer tokens per number, respectively. Furthermore, FoNE is the only method that yields 100% accuracy on over 100,000 test examples for addition, subtraction, and multiplication. The codes and visualization are available at https://fouriernumber.github.io/.

Erum Mushtaq, Zalan Fabian, Yavuz Faruk Bakman et al.

The growing deployment of Vision-Language Models (VLMs) in high-stakes applications such as autonomous driving and assistive technologies for visually impaired individuals necessitates reliable mechanisms to assess the trustworthiness of their generation. Uncertainty Estimation (UE) plays a central role in quantifying the reliability of model outputs and reducing unsafe generations via selective prediction. In this regard, most existing probability-based UE approaches rely on output probability distributions, aggregating token probabilities into a single uncertainty score using predefined functions such as length-normalization. Another line of research leverages model hidden representations and trains MLP-based models to predict uncertainty. However, these methods often fail to capture the complex multimodal relationships between semantic and textual tokens and struggle to identify biased probabilities often influenced by language priors. Motivated by these observations, we propose a novel UE framework, HARMONY, that jointly leverages fused multimodal information in model activations and the output distribution of the VLM to determine the reliability of responses. The key hypothesis of our work is that both the model's internal belief in its visual understanding, captured by its hidden representations, and the produced token probabilities carry valuable reliability signals that can be jointly leveraged to improve UE performance, surpassing approaches that rely on only one of these components. Experimental results on three open-ended VQA benchmarks, A-OKVQA, VizWiz, and PathVQA, and three state-of-the-art VLMs, LLaVa-7b, LLaVA-13b and InstructBLIP demonstrate that our method consistently performs on par with or better than existing approaches, achieving up to 4\% improvement in AUROC, and 6\% in PRR, establishing new state of the art in uncertainty estimation for VLMs.

Mohammad Shahab Sepehri, Asal Mehradfar, Mahdi Soltanolkotabi et al.

Predicting Bitcoin price remains a challenging problem due to the high volatility and complex non-linear dynamics of cryptocurrency markets. Traditional time-series models, such as ARIMA and GARCH, and recurrent neural networks, like LSTMs, have been widely applied to this task but struggle to capture the regime shifts and long-range dependencies inherent in the data. In this work, we propose CryptoMamba, a novel Mamba-based State Space Model (SSM) architecture designed to effectively capture long-range dependencies in financial time-series data. Our experiments show that CryptoMamba not only provides more accurate predictions but also offers enhanced generalizability across different market conditions, surpassing the limitations of previous models. Coupled with trading algorithms for real-world scenarios, CryptoMamba demonstrates its practical utility by translating accurate forecasts into financial outcomes. Our findings signal a huge advantage for SSMs in stock and cryptocurrency price forecasting tasks.

Hesameddin Mohammadi, Mohammad Tinati, Stephen Tu et al.

The symmetric low-rank matrix factorization serves as a building block in many learning tasks, including matrix recovery and training of neural networks. However, despite a flurry of recent research, the dynamics of its training via non-convex factorized gradient-descent-type methods is not fully understood especially in the over-parameterized regime where the fitted rank is higher than the true rank of the target matrix. To overcome this challenge, we characterize equilibrium points of the gradient flow dynamics and examine their local and global stability properties. To facilitate a precise global analysis, we introduce a nonlinear change of variables that brings the dynamics into a cascade connection of three subsystems whose structure is simpler than the structure of the original system. We demonstrate that the Schur complement to a principal eigenspace of the target matrix is governed by an autonomous system that is decoupled from the rest of the dynamics. In the over-parameterized regime, we show that this Schur complement vanishes at an $O(1/t)$ rate, thereby capturing the slow dynamics that arises from excess parameters. We utilize a Lyapunov-based approach to establish exponential convergence of the other two subsystems. By decoupling the fast and slow parts of the dynamics, we offer new insight into the shape of the trajectories associated with local search algorithms and provide a complete characterization of the equilibrium points and their global stability properties. Such an analysis via nonlinear control techniques may prove useful in several related over-parameterized problems.

Reinhard Heckel, Mahdi Soltanolkotabi, Christos Thramboulidis

Reinforcement learning with verifiable rewards has driven recent advances in LLM post-training, in particular for reasoning. Policy optimization algorithms generate a number of responses for a given prompt and then effectively weight the corresponding gradients depending on the rewards. The most popular algorithms including GRPO, DAPO, and RLOO focus on ambiguous prompts, i.e., prompts with intermediate success probability, while downgrading gradients with very easy and very hard prompts. In this paper, we consider asymmetric prompt weightings that assign higher weights to prompts with low, or even zero, empirical success probability. We find that asymmetric weighting particularly benefits from-scratch RL (as in R1-Zero), where training traverses a wide accuracy range, and less so in post-SFT RL where the model already starts at high accuracy. We also provide theory that characterizes prompt weights which minimize the time needed to raise success probability from an initial level to a target accuracy under a fixed update budget. In low-success regimes, where informative responses are rare and response cost dominates, these optimal weights become asymmetric, upweighting low success probabilities and thereby accelerating effective-time convergence.

Mohammad Shahab Sepehri, Berk Tinaz, Zalan Fabian et al.

Mental visualization, the ability to construct and manipulate visual representations internally, is a core component of human cognition and plays a vital role in tasks involving reasoning, prediction, and abstraction. Despite the rapid progress of Multimodal Large Language Models (MLLMs), current benchmarks primarily assess passive visual perception, offering limited insight into the more active capability of internally constructing visual patterns to support problem solving. Yet mental visualization is a critical cognitive skill in humans, supporting abilities such as spatial navigation, predicting physical trajectories, and solving complex visual problems through imaginative simulation. To bridge this gap, we introduce Hyperphantasia, a synthetic benchmark designed to evaluate the mental visualization abilities of MLLMs through four carefully constructed puzzles. Each task is procedurally generated and presented at three difficulty levels, enabling controlled analysis of model performance across increasing complexity. Our comprehensive evaluation of state-of-the-art models reveals a substantial gap between the performance of humans and MLLMs. Additionally, we explore the potential of reinforcement learning to improve visual simulation capabilities. Our findings suggest that while some models exhibit partial competence in recognizing visual patterns, robust mental visualization remains an open challenge for current MLLMs.

Haosheng Gan, Berk Tinaz, Mohammad Shahab Sepehri et al.

Current text-to-image (T2I) benchmarks evaluate models on rigid prompts, potentially underestimating true generative capabilities due to prompt sensitivity and creating biases that favor certain models while disadvantaging others. We introduce ConceptMix++, a framework that disentangles prompt phrasing from visual generation capabilities by applying iterative prompt optimization. Building on ConceptMix, our approach incorporates a multimodal optimization pipeline that leverages vision-language model feedback to refine prompts systematically. Through extensive experiments across multiple diffusion models, we show that optimized prompts significantly improve compositional generation performance, revealing previously hidden model capabilities and enabling fairer comparisons across T2I models. Our analysis reveals that certain visual concepts -- such as spatial relationships and shapes -- benefit more from optimization than others, suggesting that existing benchmarks systematically underestimate model performance in these categories. Additionally, we find strong cross-model transferability of optimized prompts, indicating shared preferences for effective prompt phrasing across models. These findings demonstrate that rigid benchmarking approaches may significantly underrepresent true model capabilities, while our framework provides more accurate assessment and insights for future development.

Asal Mehradfar, Mohammad Shahab Sepehri, Jose Miguel Hernandez-Lobato et al.

The discovery of new ionizable lipids for efficient lipid nanoparticle (LNP)-mediated RNA delivery remains a critical bottleneck for RNA-based therapeutics development. Recent advances have highlighted the potential of machine learning (ML) to predict transfection efficiency from molecular structure, enabling high-throughput virtual screening and accelerating lead identification. However, existing approaches are hindered by inadequate data quality, ineffective feature representations, low predictive accuracy, and poor generalizability. Here, we present LANTERN (Lipid nANoparticle Transfection Efficiency pRedictioN), a robust ML framework for predicting transfection efficiency based on ionizable lipid representation. We benchmarked a diverse set of ML models against AGILE, a previously published model developed for transfection prediction. Our results show that combining simpler models with chemically informative features, particularly count-based Morgan fingerprints, outperforms more complex models that rely on internally learned embeddings, such as AGILE. We also show that a multi-layer perceptron trained on a combination of Morgan fingerprints and Expert descriptors achieved the highest performance ($\text{R}^2$ = 0.8161, r = 0.9053), significantly exceeding AGILE ($\text{R}^2$ = 0.2655, r = 0.5488). We show that the models in LANTERN consistently have strong performance across multiple evaluation metrics. Thus, LANTERN offers a robust benchmarking framework for LNP transfection prediction and serves as a valuable tool for accelerating lipid-based RNA delivery systems design.

Stephen Tu, Roy Frostig, Mahdi Soltanolkotabi

We initiate a study of supervised learning from many independent sequences ("trajectories") of non-independent covariates, reflecting tasks in sequence modeling, control, and reinforcement learning. Conceptually, our multi-trajectory setup sits between two traditional settings in statistical learning theory: learning from independent examples and learning from a single auto-correlated sequence. Our conditions for efficient learning generalize the former setting--trajectories must be non-degenerate in ways that extend standard requirements for independent examples. Notably, we do not require that trajectories be ergodic, long, nor strictly stable. For linear least-squares regression, given $n$-dimensional examples produced by $m$ trajectories, each of length $T$, we observe a notable change in statistical efficiency as the number of trajectories increases from a few (namely $m \lesssim n$) to many (namely $m \gtrsim n$). Specifically, we establish that the worst-case error rate of this problem is $Θ(n / m T)$ whenever $m \gtrsim n$. Meanwhile, when $m \lesssim n$, we establish a (sharp) lower bound of $Ω(n^2 / m^2 T)$ on the worst-case error rate, realized by a simple, marginally unstable linear dynamical system. A key upshot is that, in domains where trajectories regularly reset, the error rate eventually behaves as if all of the examples were independent, drawn from their marginals. As a corollary of our analysis, we also improve guarantees for the linear system identification problem.

Chaoyang He, Zhengyu Yang, Erum Mushtaq et al.

Federated Learning (FL) is transforming the ML training ecosystem from a centralized over-the-cloud setting to distributed training over edge devices in order to strengthen data privacy. An essential but rarely studied challenge in FL is label deficiency at the edge. This problem is even more pronounced in FL compared to centralized training due to the fact that FL users are often reluctant to label their private data. Furthermore, due to the heterogeneous nature of the data at edge devices, it is crucial to develop personalized models. In this paper we propose self-supervised federated learning (SSFL), a unified self-supervised and personalized federated learning framework, and a series of algorithms under this framework which work towards addressing these challenges. First, under the SSFL framework, we demonstrate that the standard FedAvg algorithm is compatible with recent breakthroughs in centralized self-supervised learning such as SimSiam networks. Moreover, to deal with data heterogeneity at the edge devices in this framework, we have innovated a series of algorithms that broaden existing supervised personalization algorithms into the setting of self-supervised learning. We further propose a novel personalized federated self-supervised learning algorithm, Per-SSFL, which balances personalization and consensus by carefully regulating the distance between the local and global representations of data. To provide a comprehensive comparative analysis of all proposed algorithms, we also develop a distributed training system and related evaluation protocol for SSFL. Our findings show that the gap of evaluation accuracy between supervised learning and unsupervised learning in FL is both small and reasonable. The performance comparison indicates the representation regularization-based personalization method is able to outperform other variants.

Yu Cheng, Ilias Diakonikolas, Rong Ge et al.

We explore the connection between outlier-robust high-dimensional statistics and non-convex optimization in the presence of sparsity constraints, with a focus on the fundamental tasks of robust sparse mean estimation and robust sparse PCA. We develop novel and simple optimization formulations for these problems such that any approximate stationary point of the associated optimization problem yields a near-optimal solution for the underlying robust estimation task. As a corollary, we obtain that any first-order method that efficiently converges to stationarity yields an efficient algorithm for these tasks. The obtained algorithms are simple, practical, and succeed under broader distributional assumptions compared to prior work.

Jianyu Wang, Zachary Charles, Zheng Xu et al.

Federated learning and analytics are a distributed approach for collaboratively learning models (or statistics) from decentralized data, motivated by and designed for privacy protection. The distributed learning process can be formulated as solving federated optimization problems, which emphasize communication efficiency, data heterogeneity, compatibility with privacy and system requirements, and other constraints that are not primary considerations in other problem settings. This paper provides recommendations and guidelines on formulating, designing, evaluating and analyzing federated optimization algorithms through concrete examples and practical implementation, with a focus on conducting effective simulations to infer real-world performance. The goal of this work is not to survey the current literature, but to inspire researchers and practitioners to design federated learning algorithms that can be used in various practical applications.

Dominik Stöger, Mahdi Soltanolkotabi

Recently there has been significant theoretical progress on understanding the convergence and generalization of gradient-based methods on nonconvex losses with overparameterized models. Nevertheless, many aspects of optimization and generalization and in particular the critical role of small random initialization are not fully understood. In this paper, we take a step towards demystifying this role by proving that small random initialization followed by a few iterations of gradient descent behaves akin to popular spectral methods. We also show that this implicit spectral bias from small random initialization, which is provably more prominent for overparameterized models, also puts the gradient descent iterations on a particular trajectory towards solutions that are not only globally optimal but also generalize well. Concretely, we focus on the problem of reconstructing a low-rank matrix from a few measurements via a natural nonconvex formulation. In this setting, we show that the trajectory of the gradient descent iterations from small random initialization can be approximately decomposed into three phases: (I) a spectral or alignment phase where we show that that the iterates have an implicit spectral bias akin to spectral initialization allowing us to show that at the end of this phase the column space of the iterates and the underlying low-rank matrix are sufficiently aligned, (II) a saddle avoidance/refinement phase where we show that the trajectory of the gradient iterates moves away from certain degenerate saddle points, and (III) a local refinement phase where we show that after avoiding the saddles the iterates converge quickly to the underlying low-rank matrix. Underlying our analysis are insights for the analysis of overparameterized nonconvex optimization schemes that may have implications for computational problems beyond low-rank reconstruction.

Zalan Fabian, Reinhard Heckel, Mahdi Soltanolkotabi

Deep neural networks have emerged as very successful tools for image restoration and reconstruction tasks. These networks are often trained end-to-end to directly reconstruct an image from a noisy or corrupted measurement of that image. To achieve state-of-the-art performance, training on large and diverse sets of images is considered critical. However, it is often difficult and/or expensive to collect large amounts of training images. Inspired by the success of Data Augmentation (DA) for classification problems, in this paper, we propose a pipeline for data augmentation for accelerated MRI reconstruction and study its effectiveness at reducing the required training data in a variety of settings. Our DA pipeline, MRAugment, is specifically designed to utilize the invariances present in medical imaging measurements as naive DA strategies that neglect the physics of the problem fail. Through extensive studies on multiple datasets we demonstrate that in the low-data regime DA prevents overfitting and can match or even surpass the state of the art while using significantly fewer training data, whereas in the high-data regime it has diminishing returns. Furthermore, our findings show that DA can improve the robustness of the model against various shifts in the test distribution.

Samet Oymak, Mingchen Li, Mahdi Soltanolkotabi

Neural Architecture Search (NAS) is a popular method for automatically designing optimized architectures for high-performance deep learning. In this approach, it is common to use bilevel optimization where one optimizes the model weights over the training data (inner problem) and various hyperparameters such as the configuration of the architecture over the validation data (outer problem). This paper explores the statistical aspects of such problems with train-validation splits. In practice, the inner problem is often overparameterized and can easily achieve zero loss. Thus, a-priori it seems impossible to distinguish the right hyperparameters based on training loss alone which motivates a better understanding of the role of train-validation split. To this aim this work establishes the following results. (1) We show that refined properties of the validation loss such as risk and hyper-gradients are indicative of those of the true test loss. This reveals that the outer problem helps select the most generalizable model and prevent overfitting with a near-minimal validation sample size. This is established for continuous search spaces which are relevant for differentiable schemes. Extensions to transfer learning are developed in terms of the mismatch between training & validation distributions. (2) We establish generalization bounds for NAS problems with an emphasis on an activation search problem. When optimized with gradient-descent, we show that the train-validation procedure returns the best (model, architecture) pair even if all architectures can perfectly fit the training data to achieve zero error. (3) Finally, we highlight connections between NAS, multiple kernel learning, and low-rank matrix learning. The latter leads to novel insights where the solution of the outer problem can be accurately learned via efficient spectral methods to achieve near-minimal risk.

Bill Yuchen Lin, Chaoyang He, Zihang Zeng et al.

Increasing concerns and regulations about data privacy and sparsity necessitate the study of privacy-preserving, decentralized learning methods for natural language processing (NLP) tasks. Federated learning (FL) provides promising approaches for a large number of clients (e.g., personal devices or organizations) to collaboratively learn a shared global model to benefit all clients while allowing users to keep their data locally. Despite interest in studying FL methods for NLP tasks, a systematic comparison and analysis is lacking in the literature. Herein, we present the FedNLP, a benchmarking framework for evaluating federated learning methods on four different task formulations: text classification, sequence tagging, question answering, and seq2seq. We propose a universal interface between Transformer-based language models (e.g., BERT, BART) and FL methods (e.g., FedAvg, FedOPT, etc.) under various non-IID partitioning strategies. Our extensive experiments with FedNLP provide empirical comparisons between FL methods and helps us better understand the inherent challenges of this direction. The comprehensive analysis points to intriguing and exciting future research aimed at developing FL methods for NLP tasks.