We study the problem of learning a structured approximation (low-rank, sparse, banded, etc.) to an unknown matrix $\boldsymbol{\mathbf{A}}$ given access to matrix-vector product (matvec) queries of the form $\boldsymbol{\mathbf{x}} \mapsto \boldsymbol{\mathbf{A}}\boldsymbol{\mathbf{x}}$ and $\boldsymbol{\mathbf{x}} \mapsto \boldsymbol{\mathbf{A}}^\transpose \boldsymbol{\mathbf{x}}$. This problem is of central importance in scientific computing and machine learning, with applications to structured matrix compression, preconditioning, and as a theoretical model for operator learning. Prior work focuses on obtaining query complexity upper and lower bounds for learning specific structured matrix families that commonly arise in applications. We initiate the study of the problem in greater generality, aiming to understand the query complexity of learning approximations from general matrix families. Our main result focuses on finding a near-optimal approximation to $\boldsymbol{\mathbf{A}}$ from any \emph{finite-sized} family of matrices, $\mathcal{F}$. Standard results from matrix sketching show that $O(\log|\mathcal{F}|)$ matvec queries suffice in this setting. This bound can also be achieved, and is optimal, for vector-matrix-vector queries of the form $\boldsymbol{\mathbf{x}},\boldsymbol{\mathbf{y}}\mapsto \boldsymbol{\mathbf{x}}^\transpose\boldsymbol{\mathbf{A}}\boldsymbol{\mathbf{y}}$, which have been widely studied in work on rank-$1$ matrix sensing. Surprisingly, we show that it is possible to obtain a nearly quadratic improvement in matvec complexity, to $\tilde{O}(\sqrt{\log|\mathcal{F}|})$ and we prove that this bound is tight up to log-log factors. Via covering number arguments, our result extends to well-studied infinite families. For example, we show that a near-optimal approximation from any \emph{linear matrix family} of dimension $q$ can be learned with $\tilde{O}(\sqrt{q})$ matvec queries, improving on an $O(q)$ bound achievable via sketching techniques.

Parameter-efficient fine-tuning (PEFT) is a critical approach for adapting large models to downstream tasks with reduced computational cost. LoRA, a popular PEFT method, fine-tunes low-rank matrices and has shown strong empirical results. Recently, ReFT emerged as a more effective alternative by updating hidden representations instead of parameters. However, the convergence behavior of both methods remains poorly understood. In this work, we bridge LoRA and ReFT under a unified meta-framework called Model Efficient Fine-Tuning (MeFT). MeFT offers provable convergence guarantees with stochastic gradient descent and reveals how low-rank structures impact convergence error. We extend MeFT to federated learning as FedMeFT, with theoretical analysis and validation across foundation models and benchmarks in centralized and federated settings.

Generative models can reconstruct face images from encoded representations (templates) bearing remarkable likeness to the original face, raising security and privacy concerns. We present FACECLOAK, a neural network framework that protects face templates by generating smart, renewable binary cloaks. Our method proactively thwarts inversion attacks by cloaking face templates with unique disruptors synthesized from a single face template on the fly while provably retaining biometric utility and unlinkability. Our cloaked templates can suppress sensitive attributes while generalizing to novel feature extraction schemes and outperform leading baselines in terms of biometric matching and resiliency to reconstruction attacks. FACECLOAK-based matching is extremely fast (inference time =0.28 ms) and light (0.57 MB). We have released our code for reproducible research.

Generative models have rapidly evolved to generate realistic outputs. However, their synthetic outputs increasingly challenge the clear distinction between natural and AI-generated content, necessitating robust watermarking techniques. Watermarks are typically expected to preserve the integrity of the target image, withstand removal attempts, and prevent unauthorized replication onto unrelated images. To address this need, recent methods embed persistent watermarks into images produced by diffusion models using the initial noise. Yet, to do so, they either distort the distribution of generated images or rely on searching through a long dictionary of used keys for detection. In this paper, we propose a novel watermarking method that embeds semantic information about the generated image directly into the watermark, enabling a distortion-free watermark that can be verified without requiring a database of key patterns. Instead, the key pattern can be inferred from the semantic embedding of the image using locality-sensitive hashing. Furthermore, conditioning the watermark detection on the original image content improves robustness against forgery attacks. To demonstrate that, we consider two largely overlooked attack strategies: (i) an attacker extracting the initial noise and generating a novel image with the same pattern; (ii) an attacker inserting an unrelated (potentially harmful) object into a watermarked image, possibly while preserving the watermark. We empirically validate our method's increased robustness to these attacks. Taken together, our results suggest that content-aware watermarks can mitigate risks arising from image-generative models.

As the quality of image generators continues to improve, deepfakes become a topic of considerable societal debate. Image watermarking allows responsible model owners to detect and label their AI-generated content, which can mitigate the harm. Yet, current state-of-the-art methods in image watermarking remain vulnerable to forgery and removal attacks. This vulnerability occurs in part because watermarks distort the distribution of generated images, unintentionally revealing information about the watermarking techniques. In this work, we first demonstrate a distortion-free watermarking method for images, based on a diffusion model's initial noise. However, detecting the watermark requires comparing the initial noise reconstructed for an image to all previously used initial noises. To mitigate these issues, we propose a two-stage watermarking framework for efficient detection. During generation, we augment the initial noise with generated Fourier patterns to embed information about the group of initial noises we used. For detection, we (i) retrieve the relevant group of noises, and (ii) search within the given group for an initial noise that might match our image. This watermarking approach achieves state-of-the-art robustness to forgery and removal against a large battery of attacks. The project code is available at https://github.com/Kasraarabi/Hidden-in-the-Noise.

Test set contamination, wherein test data from a benchmark ends up in a newer model's training set, is a well-documented obstacle for fair LLM evaluation and can quickly render benchmarks obsolete. To mitigate this, many recent benchmarks crowdsource new prompts and evaluations from human or LLM judges; however, these can introduce significant biases, and break down when scoring hard questions. In this work, we introduce a new benchmark for LLMs designed to be resistant to both test set contamination and the pitfalls of LLM judging and human crowdsourcing. We release LiveBench, the first benchmark that (1) contains frequently-updated questions from recent information sources, (2) scores answers automatically according to objective ground-truth values, and (3) contains a wide variety of challenging tasks, spanning math, coding, reasoning, language, instruction following, and data analysis. To achieve this, LiveBench contains questions that are based on recently-released math competitions, arXiv papers, news articles, and datasets, and it contains harder, contamination-limited versions of tasks from previous benchmarks such as Big-Bench Hard, AMPS, and IFEval. We evaluate many prominent closed-source models, as well as dozens of open-source models ranging from 0.5B to 405B in size. LiveBench is difficult, with top models achieving below 70% accuracy. We release all questions, code, and model answers. Questions are added and updated on a monthly basis, and we release new tasks and harder versions of tasks over time so that LiveBench can distinguish between the capabilities of LLMs as they improve in the future. We welcome community engagement and collaboration for expanding the benchmark tasks and models.

Language model (LLM) post-training can refine behaviors and unlock new skills, but the open science supporting these post-training techniques is still in its infancy. One limiting factor has been the difficulty of conducting large-scale comparative analyses of synthetic data generating models and LLM judges. To close this gap, we introduce WildChat-50M, the largest public chat dataset to date. We extend the existing WildChat dataset to include responses not only from GPT, but from over 50 different open-weight models, ranging in size from 0.5B to 104B parameters. We conduct an extensive comparative analysis and demonstrate the potential of this dataset by creating Re-Wild, our own public SFT mix, which outperforms the recent Tulu-3 SFT mixture from Allen AI with only 40% as many samples.

In concept erasure, a model is modified to selectively prevent it from generating a target concept. Despite the rapid development of new methods, it remains unclear how thoroughly these approaches remove the target concept from the model. We begin by proposing two conceptual models for the erasure mechanism in diffusion models: (i) interfering with the model’s internal guidance processes, and (ii) reducing the unconditional likelihood of generating the target concept, potentially removing it entirely. To assess whether a concept has been truly erased from the model, we introduce a comprehensive suite of independent probing techniques: supplying visual context, modifying the diffusion trajectory, applying classifier guidance, and analyzing the model's alternative generations that emerge in place of the erased concept. Our results shed light on the value of exploring concept erasure robustness outside of adversarial text inputs, and emphasize the importance of comprehensive evaluations for erasure in diffusion models.

This paper introduces VeriThoughts, a novel dataset designed for reasoning-based Verilog code generation. We establish a new benchmark framework grounded in formal verification methods to evaluate the quality and correctness of generated hardware descriptions. Additionally, we present a suite of specialized small-scale models optimized specifically for Verilog generation. Our work addresses the growing need for automated hardware design tools that can produce verifiably correct implementations from high-level specifications, potentially accelerating the hardware development process while maintaining rigorous correctness guarantees.

As Vision Language Models (VLMs) become increasingly accessible to farmers and agricultural experts, there is a growing need to evaluate their potential in specialized tasks. We present AgEval, a comprehensive benchmark for assessing VLMs' capabilities in plant stress phenotyping, offering a solution to the challenge of limited annotated data in agriculture. Our study explores how general-purpose VLMs can be leveraged for domain-specific tasks with only a few annotated examples, providing insights into their behavior and adaptability. AgEval encompasses 12 diverse plant stress phenotyping tasks, evaluating zero-shot and few-shot in-context learning performance of state-of-the-art models including Claude, GPT, Gemini, and LLaVA. Our results demonstrate VLMs' rapid adaptability to specialized tasks, with the best-performing model showing an increase in F1 scores from 46.24% to 73.37% in 8-shot identification. To quantify performance disparities across classes, we introduce metrics such as the coefficient of variation (CV), revealing that VLMs' training impacts classes differently, with CV ranging from 26.02% to 58.03%. We also find that strategic example selection enhances model reliability, with exact category examples improving F1 scores by 15.38% on average. AgEval establishes a framework for assessing VLMs in agricultural applications, offering valuable benchmarks for future evaluations. Our findings suggest that VLMs, with minimal few-shot examples, show promise as a viable alternative to traditional specialized models in plant stress phenotyping, while also highlighting areas for further refinement. Results and benchmark details are available at: https://github.com/arbab-ml/AgEval

Radio remains a pervasive medium for mass information dissemination, with AM/FM stations reaching more Americans than either smartphone-based social networking or live television.Increasingly, radio broadcasts are also streamed online and accessed over the Internet.We present WavePulse, a framework that records, documents, and analyzes radio content in real-time.While our framework is generally applicable, we showcase the efficacy of WavePulse in a collaborative project with a team of political scientists focusing on the 2024 Presidential Election.We use WavePulse to monitor livestreams of 396 news radio stations over a period of three months, processing close to 500,000 hours of audio streams.These streams were converted into time-stamped, diarized transcripts and analyzed to answer key political science questions at both the national and state levels.Our analysis revealed how local issues interacted with national trends, providing insights into information flow.Our results demonstrate WavePulse's efficacy in capturing and analyzing content from radio livestreams sourced from the Web.Code and dataset can be accessed at https://wave-pulse.io

We study active learning methods for single index models of the form $F({\bm x}) = f(⟨{\bm w}, {\bm x}⟩)$, where $f:\mathbb{R} \to \mathbb{R}$ and ${\bx,\bm w} \in \mathbb{R}^d$. In addition to their theoretical interest as simple examples of non-linear neural networks, single index models have received significant recent attention due to applications in scientific machine learning like surrogate modeling for partial differential equations (PDEs). Such applications require sample-efficient active learning methods that are robust to adversarial noise. I.e., that work even in the challenging agnostic learning setting. We provide two main results on agnostic active learning of single index models. First, when $f$ is known and Lipschitz, we show that $\tilde{O}(d)$ samples collected via {statistical leverage score sampling} are sufficient to learn a near-optimal single index model. Leverage score sampling is simple to implement, efficient, and already widely used for actively learning linear models. Our result requires no assumptions on the data distribution, is optimal up to log factors, and improves quadratically on a recent ${O}(d^{2})$ bound of Gajjar et. al 2023. Second, we show that $\tilde{O}(d)$ samples suffice even in the more difficult setting when $f$ is \emph{unknown}. Our results leverage tools from high dimensional probability, including Dudley’s inequality and dual Sudakov minoration, as well as a novel, distribution-aware discretization of the class of Lipschitz functions.

Recent advances in decentralized deep learning algorithms have demonstrated cutting-edge performance on various tasks with large pretrained models. However, a pivotal prerequisite for achieving this level of competitiveness is the significant communication and computation overheads when updating these models, which prohibits the applications of them to real-world scenarios. To address this issue, drawing inspiration from advanced model merging techniques without requiring additional training, we introduce the Decentralized Iterative Merging-And-Training (DIMAT) paradigm-a novel decentralized deep learning framework. Within DIMAT, each agent is trained on their local data and periodically merged with their neighboring agents using advanced model merging techniques like activation matching until convergence is achieved. DIMAT provably converges with the best available rate for non-convex functions with various first-order methods, while yielding tighter error bounds compared to the popular existing approaches. We conduct a comprehensive empirical analysis to validate DIMAT's superiority over baselines across diverse computer vision tasks sourced from multiple datasets. Empirical results validate our theoretical claims by showing that DIMAT attains faster and higher initial gain in accuracy with independent and identically distributed (IID) and non-IID data, incurring lower communication overhead. This DIMAT paradigm presents a new op-portunity for the future decentralized learning, enhancing its adaptability to real-world with sparse and lightweight communication and computation.

With the rise of AI-enabled Real-Time Deepfakes (RTDFs), the integrity of online video interactions has become a growing concern. RTDFs have now made it feasible to replace an imposter's face with their victim in live video interactions. Such advancement in deepfakes also coaxes detection to rise to the same standard. However, existing deepfake detection techniques are asynchronous and hence ill-suited for RTDFs. To bridge this gap, we propose a challenge-response approach that establishes authenticity in live settings. We focus on talking-head style video interaction and present a taxonomy of challenges that specifically target inherent limitations of RTDF generation pipelines. We evaluate representative examples from the taxonomy by collecting a unique dataset comprising eight challenges, which consistently and visibly degrades the quality of state-of-the-art deepfake generators. These results are corroborated both by humans and a new automated scoring function, leading to 88.6% and 80.1% AUC, respectively. The findings under-score the promising potential of challenge-response systems for explainable and scalable real-time deepfake detection in practical scenarios. We provide access to data and code at https://github.com/mittalgovind/GOTCHA-Deepfakes.

Through a large-scale study over diverse face images, we show that facial attribute editing using modern generative AI models can severely degrade automated face recognition systems. This degradation persists even with generative models that include additional identity-based loss function. To mitigate this issue, we propose two novel techniques for local and global attribute editing. We empirically ablate twenty-six facial semantic, demographic and expression-based attributes that have been edited using state-of-the-art generative models, and evaluate them using ArcFace and AdaFace matchers on CelebA, CelebAMaskHQ and LFW datasets. Finally, we use LLaVA, an emerging visual question-answering framework for attribute prediction to validate our editing techniques. Our methods outperform the current state-of-the-art at facial editing (BLIP, InstantID) while retaining identity by a significant extent. Our code is available at https://github.com/sudban3089/MIAFR.git.

Text-to-image generative models can produce photo-realistic images for an extremely broad range of concepts, and their usage has proliferated widely among the general public. On the flip side, these models have numerous drawbacks, including their potential to generate images featuring sexually explicit content, mirror artistic styles without permission, or even hallucinate (or deepfake) the likenesses of celebrities. Consequently, various methods have been proposed in order to "erase" sensitive concepts from text-to-image models. In this work, we examine seven recently proposed concept erasure methods, and show that targeted concepts are not fully excised from any of these methods. Specifically, we leverage the existence of special learned word embeddings that can retrieve "erased" concepts from the sanitized models with no alterations to their weights. Our results highlight the brittleness of post hoc concept erasure methods, and call into question their use in the algorithmic toolkit for AI safety.

While tabular classification has traditionally relied on from-scratch training, a recent breakthrough called prior-data fitted networks (PFNs) challenges this approach. Similar to large language models, PFNs make use of pretraining and in-context learning to achieve strong performance on new tasks in a single forward pass. However, current PFNs have limitations that prohibit their widespread adoption. Notably, TabPFN achieves very strong performance on small tabular datasets but is not designed to make predictions for datasets of size larger than 1000. In this work, we overcome these limitations and substantially improve the performance of PFNs via context optimization. We introduce TuneTables, a parameter-efficient fine-tuning strategy for PFNs that compresses large datasets into a smaller learned context. We conduct extensive experiments on nineteen algorithms over 98 datasets and find that TuneTables achieves the best performance on average, outperforming boosted trees such as CatBoost, while optimizing fewer than 5\% of TabPFN's parameters. Furthermore, we show that TuneTables can be used as an interpretability tool and can even be used to mitigate biases by optimizing a fairness objective.

Data curation is the problem of how to collect and organize samples into a dataset that supports efficient learning. Despite the centrality of the task, little work has been devoted towards a large-scale, systematic comparison of various curation methods. In this work, we take steps towards a formal evaluation of data curation strategies and introduce SELECT, the first large-scale benchmark of curation strategies for image classification.In order to generate baseline methods for the SELECT benchmark, we create a new dataset, ImageNet++, which constitutes the largest superset of ImageNet-1K to date. Our dataset extends ImageNet with 5 new training-data shifts, each approximately the size of ImageNet-1K, and each assembled using a distinct curation strategy. We evaluate our data curation baselines in two ways: (i) using each training-data shift to train identical image classification models from scratch (ii) using it to inspect a fixed pretrained self-supervised representation.Our findings show interesting trends, particularly pertaining to recent methods for data curation such as synthetic data generation and lookup based on CLIP embeddings. We show that although these strategies are highly competitive for certain tasks, the curation strategy used to assemble the original ImageNet-1K dataset remains the gold standard. We anticipate that our benchmark can illuminate the path for new methods to further reduce the gap. We release our checkpoints, code, documentation, and a link to our dataset at https://github.com/jimmyxu123/SELECT.

G-code (Geometric code) or RS-274 is the most widely used computer numerical control (CNC) and 3D printing programming language. G-code provides machine instructions for the movement of the 3D printer, especially for the nozzle, stage, and extrusion of material for extrusion-based additive manufacturing. Currently, there does not exist a large repository of curated CAD models along with their corresponding G-code files for additive manufacturing. To address this issue, we present Slice-100K, a first-of-its-kind dataset of over 100,000 G-code files, along with their tessellated CAD model, LVIS (Large Vocabulary Instance Segmentation) categories, geometric properties, and renderings. We build our dataset from triangulated meshes derived from Objaverse-XL and Thingi10K datasets. We demonstrate the utility of this dataset by finetuning GPT-2 on a subset of the dataset for G-code translation from a legacy G-code format (Sailfish) to a more modern, widely used format (Marlin). Our dataset can be found here. Slice-100K will be the first step in developing a multimodal foundation model for digital manufacturing.

We introduce BioTrove, the largest publicly accessible dataset designed to advance AI applications in biodiversity. Curated from the iNaturalist platform and vetted to include only research-grade data, BioTrove contains 161.9 million images, offering unprecedented scale and diversity from three primary kingdoms: Animalia ("animals"), Fungi ("fungi"), and Plantae ("plants"), spanning approximately 366.6K species. Each image is annotated with scientific names, taxonomic hierarchies, and common names, providing rich metadata to support accurate AI model development across diverse species and ecosystems.We demonstrate the value of BioTrove by releasing a suite of CLIP models trained using a subset of 40 million captioned images, known as BioTrove-Train. This subset focuses on seven categories within the dataset that are underrepresented in standard image recognition models, selected for their critical role in biodiversity and agriculture: Aves ("birds"), Arachnida} ("spiders/ticks/mites"), Insecta ("insects"), Plantae ("plants"), Fungi ("fungi"), Mollusca ("snails"), and Reptilia ("snakes/lizards"). To support rigorous assessment, we introduce several new benchmarks and report model accuracy for zero-shot learning across life stages, rare species, confounding species, and multiple taxonomic levels.We anticipate that BioTrove will spur the development of AI models capable of supporting digital tools for pest control, crop monitoring, biodiversity assessment, and environmental conservation. These advancements are crucial for ensuring food security, preserving ecosystems, and mitigating the impacts of climate change. BioTrove is publicly available, easily accessible, and ready for immediate use.

Existing deep-learning approaches to semantic column type annotation (CTA) have important shortcomings: they rely on semantic types which are fixed at training time; require a large number of training samples per type; incur high run-time inference costs; and their performance can degrade when evaluated on novel datasets, even when types remain constant. Large language models have exhibited strong zero-shot classification performance on a wide range of tasks and in this paper we explore their use for CTA. We introduce ArcheType, a simple, practical method for context sampling, prompt serialization, model querying, and label remapping, which enables large language models to solve CTA problems in a fully zero-shot manner. We ablate each component of our method separately, and establish that improvements to context sampling and label remapping provide the most consistent gains. ArcheType establishes a new state-of-the-art performance on zero-shot CTA benchmarks (including three new domain-specific benchmarks which we release along with this paper), and when used in conjunction with classical CTA techniques, it outperforms a SOTA DoDuo model on the fine-tuned SOTAB benchmark.

Recognizing the activities causing distraction in real-world driving scenarios is critical for ensuring the safety and reliability of both drivers and pedestrians on the roadways. Conventional computer vision techniques are typically data-intensive and require a large volume of annotated training data to detect and classify various distracted driving behaviors, thereby limiting their generalization ability, efficiency and scalability. We aim to develop a generalized framework that showcases robust performance with access to limited or no annotated training data. Recently, vision-language models have offered large-scale visual-textual pretraining that can be adapted to task-specific learning like distracted driving activity recognition. Vision-language pretraining models like CLIP have shown significant promise in learning natural language-guided visual representations. This paper proposes a CLIP-based driver activity recognition approach that identifies driver distraction from naturalistic driving images and videos. CLIP’s vision embedding offers zero-shot transfer and task-based finetuning, which can classify distracted activities from naturalistic driving video. Our results show that this framework offers state-of-the-art performance on zero-shot transfer, finetuning and video-based models for predicting the driver’s state on four public datasets. We propose frame-based and video-based frameworks developed on top of the CLIP’s visual representation for distracted driving detection and classification tasks and report the results. Our code is available at https://github.com/zahid-isu/DriveCLIP

We consider the problem of active learning for single neuron models, also sometimes called “ridge functions”, in the agnostic setting (under adversarial label noise). Such models have been shown to be broadly effective in modeling physical phenomena, and for constructing surrogate data-driven models for partial differential equations. Surprisingly, we show that for a single neuron model with any Lipschitz non-linearity (such as the ReLU, sigmoid, absolute value, low-degree polynomial, among others), strong provable approximation guarantees can be obtained using a well-known active learning strategy for fitting linear functions in the agnostic setting. Namely, we can collect samples via statistical leverage score sampling, which has been shown to be nearoptimal in other active learning scenarios. We support our theoretical results with empirical simulations showing that our proposed active learning strategy based on leverage score sampling outperforms (ordinary) uniform sampling when fitting single neuron models.

Transformer architectures have led to remarkable progress in many state-of-art applications. However, despite their successes, modern transformers rely on the self-attention mechanism, whose time- and space-complexity is quadratic in the length of the input. Several approaches have been proposed to speed up self-attention mechanisms to achieve sub-quadratic running time; however, the large majority of these works are not accompanied by rigorous error guarantees. In this work, we establish lower bounds on the computational complexity of self-attention in a number of scenarios. We prove that the time complexity of self-attention is necessarily quadratic in the input length, unless the Strong Exponential Time Hypothesis (SETH) is false. This argument holds even if the attention computation is performed only approximately, and for a variety of attention mechanisms. As a complement to our lower bounds, we show that it is indeed possible to approximate dot-product self-attention using finite Taylor series in linear-time, at the cost of having an exponential dependence on the polynomial order.

The performance of automated face recognition systems is inevitably impacted by the facial aging process. However, high quality datasets of individuals collected over several years are typically small in scale. In this work, we propose, train, and validate the use of latent text-to-image diffusion models for synthetically aging and de-aging face images. Our models succeed with few-shot training, and have the added benefit of being controllable via intuitive textual prompting. We observe high degrees of visual realism in the generated images while maintaining biometric fidelity measured by commonly used metrics. We evaluate our method on two benchmark datasets (CelebA and AgeDB) and observe significant reduction (~ 44%) in the False Non-Match Rate compared to existing state-of the-art baselines.

We propose a novel policy gradient method for multi-agent reinforcement learning, which leverages two different variance-reduction techniques and does not require large batches over iterations. Specifically, we propose a momentum-based decentralized policy gradient tracking (MDPGT) where a new momentum-based variance reduction technique is used to approximate the local policy gradient surrogate with importance sampling, and an intermediate parameter is adopted to track two consecutive policy gradient surrogates. MDPGT provably achieves the best available sample complexity of O(N -1 e -3) for converging to an e-stationary point of the global average of N local performance functions (possibly nonconcave). This outperforms the state-of-the-art sample complexity in decentralized model-free reinforcement learning and when initialized with a single trajectory, the sample complexity matches those obtained by the existing decentralized policy gradient methods. We further validate the theoretical claim for the Gaussian policy function. When the required error tolerance e is small enough, MDPGT leads to a linear speed up, which has been previously established in decentralized stochastic optimization, but not for reinforcement learning. Lastly, we provide empirical results on a multi-agent reinforcement learning benchmark environment to support our theoretical findings.

Deep generative models have emerged as a powerful class of priors for signals in various inverse problems such as compressed sensing, phase retrieval and super-resolution. Here, we assume an unknown signal to lie in the range of some pre-trained generative model. A popular approach for signal recovery is via gradient descent in the low-dimensional latent space. While gradient descent has achieved good empirical performance, its theoretical behavior is not well understood. In this paper, we introduce the use of stochastic gradient Langevin dynamics (SGLD) for compressed sensing with a generative prior. Under mild assumptions on the generative model, we prove the convergence of SGLD to the true signal. We also demonstrate competitive empirical performance to standard gradient descent.

Private inference (PI) enables inferences directly on cryptographically secure data. While promising to address many privacy issues, it has seen limited use due to extreme runtimes. Unlike plaintext inference, where latency is dominated by FLOPs, in PI non-linear functions (namely ReLU) are the bottleneck. Thus, practical PI demands novel ReLU-aware optimizations. To reduce PI latency we propose a gradient-based algorithm that selectively linearizes ReLUs while maintaining prediction accuracy. We evaluate our algorithm on several standard PI benchmarks. The results demonstrate up to $4.25%$ more accuracy (iso-ReLU count at 50K) or $2.2\times$ less latency (iso-accuracy at 70%) than the current state of the art and advance the Pareto frontier across the latency-accuracy space. To complement empirical results, we present a “no free lunch" theorem that sheds light on how and when network linearization is possible while maintaining prediction accuracy.

Deep generative models have emerged as a powerful class of priors for signals in various inverse problems such as compressed sensing, phase retrieval and super-resolution. In this work, we consider the compressed sensing problem and assume the unknown signal to lie in the range of some pre-trained generative model. A popular approach for signal recovery is via gradient descent in the low-dimensional latent space. While gradient descent has achieved good empirical performance, its theoretical behavior is not well understood. We introduce the use of stochastic gradient Langevin dynamics (SGLD) for compressed sensing with a generative prior. Under mild assumptions on the generative model, we prove the convergence of SGLD to the true signal. We also demonstrate competitive empirical performance to standard gradient descent.

We consider the problem of decentralized deep learning where multiple agents collaborate to learn from a distributed dataset. While several decentralized deep learning approaches exist, the majority consider a central parameter-server topology for aggregating the model parameters from the agents. However, such a topology may be inapplicable in networked systems such as ad-hoc mobile networks, field robotics, and power network systems where direct communication with the central parameter server may be inefficient. In this context, we propose and analyze a novel decentralized deep learning algorithm where the agents interact over a fixed communication topology (without a central server). Our algorithm is based on the heavy-ball acceleration method used in gradient-based optimization. We propose a novel consensus protocol where each agent shares with its neighbors its model parameters and gradient-momentum values during the optimization process. We consider nonconvex objective functions and theoretically analyze our algorithm’s performance. We present several empirical comparisons with competing decentralized learning methods to demonstrate the efficacy of our approach under different communication topologies.

Decentralized learning enables a group of collaborative agents to learn models using a distributed dataset without the need for a central parameter server. Recently, decentralized learning algorithms have demonstrated state-of-the-art results on benchmark data sets, comparable with centralized algorithms. However, the key assumption to achieve competitive performance is that the data is independently and identically distributed (IID) among the agents which, in real-life applications, is often not applicable. Inspired by ideas from continual learning, we propose Cross-Gradient Aggregation (CGA), a novel decentralized learning algorithm where (i) each agent aggregates cross-gradient information, i.e., derivatives of its model with respect to its neighbors’ datasets, and (ii) updates its model using a projected gradient based on quadratic programming (QP). We theoretically analyze the convergence characteristics of CGA and demonstrate its efficiency on non-IID data distributions sampled from the MNIST and CIFAR-10 datasets. Our empirical comparisons show superior learning performance of CGA over existing state-of-the-art decentralized learning algorithms, as well as maintaining the improved performance under information compression to reduce peer-to-peer communication overhead. The code is available here on GitHub.

The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically require that the machine learning models be differentiable, limiting their applicability. Our goal in this paper is to use a new, principled approach to extend gradient-based optimization to functions well modeled by splines, which encompass a large family of piecewise polynomial models. We derive the form of the (weak) Jacobian of such functions and show that it exhibits a block-sparse structure that can be computed implicitly and efficiently. Overall, we show that leveraging this redesigned Jacobian in the form of a differentiable "layer'' in predictive models leads to improved performance in diverse applications such as image segmentation, 3D point cloud reconstruction, and finite element analysis. We also open-source the code at \url{https://github.com/idealab-isu/DSA}.

In this paper, we study the implicit bias of gradient descent for sparse regression. We extend results on regression with quadratic parametrization, which amounts to depth-2 diagonal linear networks, to more general depth-$N$ networks, under more realistic settings of noise and correlated designs. We show that early stopping is crucial for gradient descent to converge to a sparse model, a phenomenon that we call \emph{implicit sparse regularization}. This result is in sharp contrast to known results for noiseless and uncorrelated-design cases. We characterize the impact of depth and early stopping and show that for a general depth parameter $N$, gradient descent with early stopping achieves minimax optimal sparse recovery with sufficiently small initialization $w_0$ and step size $\eta$. In particular, we show that increasing depth enlarges the scale of working initialization and the early-stopping window so that this implicit sparse regularization effect is more likely to take place.

We consider the distributed training of large scale neural networks that serve as PDE (partial differential equation) solvers producing full field outputs. We specifically consider neural solvers for the generalized 3D Poisson equation over megavoxel domains. A scalable framework is presented that integrates two distinct advances. First, we accelerate training a large model via a method analogous to the multigrid technique used in numerical linear algebra. Here, the network is trained using a hierarchy of increasing resolution inputs in sequence, analogous to the `V', `W', `F' and `Half-V' cycles used in multigrid approaches. In conjunction with the multi-grid approach, we implement a distributed deep learning framework which significantly reduces the time to solve. We show scalability of this approach on both GPU (Azure VMs on Cloud) and CPU clusters (PSC Bridges2). This approach is deployed to train a generalized 3D Poisson solver that scales well to predict output full field solutions up to the resolution of 512 X 512 X 512 for a high dimensional family of inputs. This strategy opens up the possibility of fast and scalable training of neural PDE solvers on heterogeneous clusters.

Deep neural networks can achieve impressive performance in the regime where they are massively over-parameterized. Consequently, over the past year, there has been a growing interest in analyzing optimization and generalization properties of over-parameterized networks. However, the majority of existing work only applies to supervised learning. The role of over-parameterization in the unsupervised setting has by contrast gained far less attention. In this paper, we study the inductive bias of gradient descent for two-layer over-parameterized autoencoders with ReLU activation. We first provide theoretical evidence for the memorization phenomena observed in recent work using the property that infinitely wide neural networks under gradient descent evolve as linear models. We also analyze the gradient dynamics of the autoencoders in the finite-width setting. Starting from a randomly initialized autoencoder network, we rigorously prove the linear convergence of gradient descent in two weakly-trained and jointly-trained regimes. Our results indicate the considerable benefits of joint training over weak training in finding global optima, achieving a dramatic decrease in the required level of over-parameterization. Finally, we analyze the case of weight-tied autoencoders and prove that in the over-parameterized setting, training such networks from randomly initialized points leads to certain unexpected degeneracies.

Generative Adversarial Networks (GANs), while widely successful in modeling complex data distributions, have not yet been sufficiently leveraged in scientific computing and design. Reasons for this include the lack of flexibility of GANs to represent discrete-valued image data, as well as the lack of control over physical properties of generated samples. We propose a new conditional generative modeling approach (InvNet) that efficiently enables modeling discrete-valued images, while allowing control over their parameterized geometric and statistical properties. We evaluate our approach on several synthetic and real world problems: navigating manifolds of geometric shapes with desired sizes; generation of binary two-phase materials; and the (challenging) problem of generating multi-orientation polycrystalline microstructures.

Robustness of Deep Reinforcement Learning (DRL) algorithms towards adversarial attacks in real world applications such as those deployed in cyber-physical systems (CPS) are of increasing concern. Numerous studies have investigated the mechanisms of attacks on the RL agent's state space. Nonetheless, attacks on the RL agent's action space (corresponding to actuators in engineering systems) are equally perverse, but such attacks are relatively less studied in the ML literature. In this work, we first frame the problem as an optimization problem of minimizing the cumulative reward of an RL agent with decoupled constraints as the budget of attack. We propose the white-box Myopic Action Space (MAS) attack algorithm that distributes the attacks across the action space dimensions. Next, we reformulate the optimization problem above with the same objective function, but with a temporally coupled constraint on the attack budget to take into account the approximated dynamics of the agent. This leads to the white-box Look-ahead Action Space (LAS) attack algorithm that distributes the attacks across the action and temporal dimensions. Our results showed that using the same amount of resources, the LAS attack deteriorates the agent's performance significantly more than the MAS attack. This reveals the possibility that with limited resource, an adversary can utilize the agent's dynamics to malevolently craft attacks that causes the agent to fail. Additionally, we leverage these attack strategies as a possible tool to gain insights on the potential vulnerabilities of DRL agents.

Traditionally, dynamic range enhancement for images has involved a combination of contrast improvement (via gamma correction or histogram equalization) and a denoising operation to reduce the effects of photon noise. More recently, modulo-imaging methods have been introduced for high dynamic range photography to significantly expand dynamic range at the sensing stage itself. The transformation function for both of these problems is highly non-linear, and the image reconstruction procedure is typically non-convex and ill-posed. A popular recent approach is to regularize the above inverse problem via a neural network prior (such as a trained autoencoder), but this requires extensive training over a dataset with thousands of paired regular/HDR image data samples.In this paper, we introduce a new approach for HDR image reconstruction using neural priors that require no training data. Specifically, we employ deep image priors, which have been successfully used for imaging problems such as denoising, super-resolution, inpainting and compressive sensing with promising performance gains over conventional regularization techniques. In this paper, we consider two different approaches to high dynamic range (HDR) imaging - gamma encoding and modulo encoding - and propose a combination of deep image prior and total variation (TV) regularization for reconstructing low-light images. We demonstrate the significant improvement achieved by both of these approaches as compared to traditional dynamic range enhancement techniques.

We provide a series of results for unsupervised learning with autoencoders. Specifically, we study shallow two-layer autoencoder architectures with shared weights. We focus on three generative models for data that are common in statistical machine learning: (i) the mixture-of-gaussians model, (ii) the sparse coding model, and (iii) the sparsity model with non-negative coefficients. For each of these models, we prove that under suitable choices of hyperparameters, architectures, and initialization, autoencoders learned by gradient descent can successfully recover the parameters of the corresponding model. To our knowledge, this is the first result that rigorously studies the dynamics of gradient descent for weight-sharing autoencoders. Our analysis can be viewed as theoretical evidence that shallow autoencoder modules indeed can be used as feature learning mechanisms for a variety of data models, and may shed insight on how to train larger stacked architectures with autoencoders as basic building blocks.

We propose a new algorithm for hyperparameter selection in machine learning algorithms. The algorithm is a novel modification of Harmonica, a spectral hyperparameter selection approach using sparse recovery methods. In particular, we show that a special encoding of hyperparameter space enables a natural group-sparse recovery formulation, which when coupled with HyperBand (a multi-armed bandit strategy) leads to improvement over existing hyperparameter optimization methods such as Successive Halving and Random Search. Experimental results on image datasets such as CIFAR-10 confirm the benefits of our approach.

The classical problem of phase retrieval arises in various signal acquisition systems. Due to the ill-posed nature of the problem, the solution requires assumptions on the structure of the signal. In the last several years, sparsity and support-based priors have been leveraged successfully to solve this problem. In this work, we propose replacing the sparsity/support priors with generative priors and propose two algorithms to solve the phase retrieval problem. Our proposed algorithms combine the ideas from AltMin approach for non-convex sparse phase retrieval and projected gradient descent approach for solving linear inverse problems using generative priors. We empirically show that the performance of our method with projected gradient descent is superior to the existing approach for solving phase retrieval under generative priors. We support our method with an analysis of sample complexity with Gaussian measurements.

Deep neural networks have been shown to exhibit an intriguing vulnerability to adversarial input images corrupted with imperceptible perturbations. However, the majority of adversarial attacks assume global, fine-grained control over the image pixel space. In this paper, we consider a different setting: what happens if the adversary could only alter specific attributes of the input image? These would generate inputs that might be perceptibly different, but still natural-looking and enough to fool a classifier. We propose a novel approach to generate such ``semantic'' adversarial examples by optimizing a particular adversarial loss over the range-space of a parametric conditional generative model. We demonstrate implementations of our attacks on binary classifiers trained on face images, and show that such natural-looking semantic adversarial examples exist. We evaluate the effectiveness of our attack on synthetic and real data, and present detailed comparisons with existing attack methods. We supplement our empirical results with theoretical bounds that demonstrate the existence of such parametric adversarial examples.

We propose and analyze algorithms for training ReLU networks with skipped connections. Skipped connections are the key feature of residual networks (or ResNets) which have been shown to provide superior performance in deep learning applications. We analyze two approaches for training such networks - gradient descent and alternating minimization - and compare convergence criteria of both methods. We show that under typical (Gaussianity) assumptions on the d-dimensional input data, both gradient descent and alternating minimization provably converge in a linearly convergent fashion, assuming any good enough initialization; moreover, we show that a simple “identity” initialization suffices. Furthermore, we provide statistical upper bounds which indicate that n = O(d3) suffice to achieve this convergence rate. To our knowledge, these constitute the first global parameter recovery guarantees for shallow ResNet-type networks with ReLU activations.

Deep neural networks as image priors have been recently introduced for problems such as denoising, super-resolution and inpainting with promising performance gains over hand-crafted image priors such as sparsity. Unlike learned generative priors they do not require any training over large datasets. However, few theoretical guarantees exist in the scope of using untrained network priors for inverse imaging problems. We explore new applications and theory for untrained neural network priors. Specifically, we consider the problem of solving linear inverse problems, such as compressive sensing, as well as non-linear problems, such as compressive phase retrieval. We model images to lie in the range of an untrained deep generative network with a fixed seed. We further present a projected gradient descent scheme that can be used for both compressive sensing and phase retrieval and provide rigorous theoretical guarantees for its convergence. We also show both theoretically as well as empirically that with deep neural network priors, one can achieve better compression rates for the same image quality as compared to when hand crafted priors are used.

Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input dataset. However, a key challenge is that storage, transmission, and processing of the learned dictionary can be untenably high if the data dimension is high. In this paper, we consider the double-sparsity model introduced by Rubinstein et al. (2010b) where the dictionary itself is the product of a fixed, known basis and a data-adaptive sparse component. First, we introduce a simple algorithm for double-sparse coding that can be amenable to efficient implementation via neural architectures. Second, we theoretically analyze its performance and demonstrate asymptotic sample complexity and running time benefits over existing (provable) approaches for sparse coding. To our knowledge, our work introduces the first computationally efficient algorithm for double-sparse coding that enjoys rigorous statistical guarantees. Finally, we corroborate our theory with several numerical experiments on simulated data, suggesting that our method may be useful for problem sizes encountered in practice.

We consider the problem of recovering a signal x* ∈ Rn, from magnitude-only measurements, yi= |〈ai, x*〉| for i = {1, 2, ... , m}. This is a stylized version of the classical phase retrieval problem, and is a fundamental challenge in nanoand bio-imaging systems, astronomical imaging, and speech processing. It is well-known that the above problem is ill-posed, and therefore some additional assumptions on the signal and/or the measurements are necessary. In this paper, we consider the case where the underlying signal x* is s-sparse. For this case, we develop a novel recovery algorithm that we call Compressive Phase Retrieval with Alternating Minimization, or CoPRAM. Our algorithm is simple and is obtained via a natural combination of the classical alternating minimization approach for phase retrieval with the CoSaMP algorithm for sparse recovery. Despite its simplicity, we prove that our algorithm achieves a sample complexity of O (s2log n) with Gaussian measurements ai, which matches the best known existing results; moreover, it also demonstrates linear convergence in theory and practice. An appealing feature of our algorithm is that it requires no extra tuning parameters other than the signal sparsity level s. Moreover, we show that our algorithm is robust to noise. The quadratic dependence of sample complexity on the sparsity level is suboptimal, and we demonstrate how to alleviate this via additional assumptions beyond sparsity. First, we study the (practically) relevant case where the sorted coefficients of the underlying sparse signal exhibit a power law decay. In this scenario, we show that the CoPRAM algorithm achieves a sample complexity of O (s log n), which is close to the information-theoretic limit. We then consider the case where the underlying signal x* arises from structured sparsity models. We specifically examine the case of block-sparse signals with uniform block size of b and block sparsity k = s/b. For this problem, we design a recovery algorithm that we call Block CoPRAM that further reduces the sample complexity to O (ks logn). For sufficiently large block lengths of b = O(s), this bound equates to O (slogn). To our knowledge, our approach constitutes the first family of linearly convergent algorithms for signal recovery from magnitude-only Gaussian measurements that exhibit a sub-quadratic dependence on the signal sparsity level.

Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given dataset. However, storage, transmission, and processing of the learned dictionary can be untenably high if the data dimension is high. In this paper, we consider the double-sparsity model introduced by Rubinstein, Zibulevsky, and Elad (2010) where the dictionary itself is the product of a fixed, known basis and a data-adaptive sparse component. First, we introduce a simple algorithm for double-sparse coding that can be amenable to efficient implementation via neural architectures. Second, we theoretically analyze its performance and demonstrate asymptotic sample complexity and running time benefits over existing (provable) approaches for sparse coding. To our knowledge, our work introduces the first computationally efficient algorithm for double-sparse coding that enjoys rigorous statistical guarantees. Finally, we support our analysis via several numerical experiments on simulated data, confirming that our method can indeed be useful in problem sizes encountered in practical applications.

We study the problem of (provably) learning the weights of a two-layer neural network with quadratic activations. In particular, we focus on the under-parametrized regime where the number of neurons in the hidden layer is (much) smaller than the dimension of the input. Our approach uses a lifting trick, which enables us to borrow algorithmic ideas from low-rank matrix estimation. In this context, we propose two novel, non-convex training algorithms which do not need any extra tuning parameters other than the number of hidden neurons. We support our algorithms with rigorous theoretical analysis, and show that the proposed algorithms enjoy linear convergence, fast running time per iteration, and near-optimal sample complexity. Finally, we complement our theoretical results with several numerical experiments.

In this paper, we introduce a principled algorithmic approach for Fourier ptychographic imaging of dynamic, time-varying targets. To the best of our knowledge, this setting has not been explicitly addressed in the ptychography literature. We argue that such a setting is very natural, and that our methods provide an important first step towards helping reduce the sample complexity (and hence acquisition time) of imaging dynamic scenes to managaeble levels. With significantly reduced acquisition times per image, it is conceivable that dynamic ptychographic imaging of fast changing scenes indeeed becomes practical in the near future.

We consider the problem of super-resolution for sub-diffraction imaging. We adapt conventional Fourier ptychographic approaches, for the case where the images to be acquired have an underlying structured sparsity. We propose some sub-sampling strategies which can be easily adapted to existing ptychographic setups. We then use a novel technique called CoPRAM with some modifications, to recover sparse (and block sparse) images from sub-sampled pty-chographic measurements. We demonstrate experimentally that this algorithm performs better than existing phase retrieval techniques, in terms of quality of reconstruction, using fewer number of samples.

In recent works, both sparsity-based methods as well as learning-based methods have proven to be successful in solving several challenging linear inverse problems. However, sparsity priors for natural signals and images suffer from poor discriminative capability, while learning-based methods seldom provide concrete theoretical guarantees. In this work, we advocate the idea of replacing hand-crafted priors, such as sparsity, with a Generative Adversarial Network (GAN) to solve linear inverse problems such as compressive sensing. In particular, we propose a projected gradient descent (PGD) algorithm for effective use of GAN priors for linear inverse problems, and also provide theoretical guarantees on the rate of convergence of this algorithm. Moreover, we show empirically that our algorithm demonstrates superior performance over an existing method of leveraging GANs for compressive sensing.

In this paper, we introduce a novel algorithmic framework for sub-diffractive super-resolution imaging of dynamic, time-varying targets. We extend recent works in low rank Fourier ptychographic imaging, to incorporate model-correction schemes, which correct for errors propagated due to inaccuracies in fitting an exact low rank model to the target video acquired. Through our algorithm, we are able to demonstrate superior reconstruction quality of video from phaseless Fourier ptychographic measurements, at low sample complexities, as compared to conventional ptychographic setups.

Existing algorithms for dictionary learning assume that the entries of the (high-dimensional) input data are fully observed. However, in several practical applications, only an incomplete fraction of the data entries may be available. For incomplete settings, no provably correct and polynomial-time algorithm has been reported in the dictionary learning literature. In this paper, we provide provable approaches for learning – from incomplete samples – a family of dictionaries whose atoms have sufficiently “spread-out” mass. First, we propose a descent-style iterative algorithm that linearly converges to the true dictionary when provided a sufficiently coarse initial estimate. Second, we propose an initialization algorithm that utilizes a small number of extra fully observed samples to produce such a coarse initial estimate. Finally, we theoretically analyze their performance and provide asymptotic statistical and computational guarantees.

We consider the problem of estimating a structured high-dimensional parameter vector using random Gaussian quadratic samples. This problem is a generalization of the classical problem of phase retrieval and impacts numerous problems in computational imaging. We provide a generic algorithm based on alternating minimization that, if properly initialized, achieves information-theoretically optimal sample complexity. In essence, we show that solving a system of random quadratic equations with structural constraints is (nearly) as easy as solving the corresponding linear system with the same constraints, if a proper initial guess of the solution is available. As an immediate consequence, our approach improves upon the best known existing sample complexity results for phase retrieval (structured or otherwise). We support our theory via several numerical experiments. A full version of this paper is accessible at: https://gaurijagatap.github.io/assets/ISIT18.pdf.

We study the general problem of optimizing a convex function of a matrix-valued variable subject to low-rank constraints. This problem has attracted significant attention; however, existing first-order methods for solving such problems either are too slow to converge, or require multiple invocations of singular value decompositions. On the other hand, factorization-based non-convex algorithms, while being much faster, require stringent assumptions on the condition number of the optimum. In this paper, we provide a novel algorithmic framework that achieves the best of both worlds: as fast as factorization methods, while requiring no spectral assumptions. We instantiate our framework for the nonlinear affine rank minimization (NLARM) problem. For this problem, we derive explicit bounds on the sample complexity as well as running time of our approach, and show that it achieves the best possible bounds for both cases. We also support our proposed algorithm via several experimental results.

Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a random Gaussian matrix, and then computing an element-wise sinusoid. Theoretical analysis shows that collecting a sufficient number of such features can be reliably used for subsequent inference in kernel classification and regression. In this work, we demonstrate that with a mild increase in the dimension of the embedding, it is also possible to reconstruct the data vector from such random sinusoidal features, provided that the underlying data is sparse enough. In particular, we propose a numerically stable algorithm for reconstructing the data vector given the nonlinear features, and analyze its sample complexity. Our algorithm can be extended to other types of structured inverse problems, such as demixing a pair of sparse (but incoherent) vectors. We support the efficacy of our approach via numerical experiments.

We consider the problem of recovering a signal x in R^n, from magnitude-only measurements, yi = |ai^T x| for i={1,2...m}. Also known as the phase retrieval problem, it is a fundamental challenge in nano-, bio- and astronomical imaging systems, astronomical imaging, and speech processing. The problem is ill-posed, and therefore additional assumptions on the signal and/or the measurements are necessary. In this paper, we first study the case where the underlying signal x is s-sparse. We develop a novel recovery algorithm that we call Compressive Phase Retrieval with Alternating Minimization, or CoPRAM. Our algorithm is simple and can be obtained via a natural combination of the classical alternating minimization approach for phase retrieval, with the CoSaMP algorithm for sparse recovery. Despite its simplicity, we prove that our algorithm achieves a sample complexity of O(s^2 log n) with Gaussian samples, which matches the best known existing results. It also demonstrates linear convergence in theory and practice and requires no extra tuning parameters other than the signal sparsity level s. We then consider the case where the underlying signal x arises from to structured sparsity models. We specifically examine the case of block-sparse signals with uniform block size of b and block sparsity k=s/b. For this problem, we design a recovery algorithm that we call Block CoPRAM that further reduces the sample complexity to O(ks log n). For sufficiently large block lengths of b=Theta(s), this bound equates to O(s log n). To our knowledge, this constitutes the first end-to-end linearly convergent family of algorithms for phase retrieval where the Gaussian sample complexity has a sub-quadratic dependence on the sparsity level of the signal.

There is significant recent interest to parallelize deep learning algorithms in order to handle the enormous growth in data and model sizes. While most advances focus on model parallelization and engaging multiple computing agents via using a central parameter server, aspect of data parallelization along with decentralized computation has not been explored sufficiently. In this context, this paper presents a new consensus-based distributed SGD (CDSGD) (and its momentum variant, CDMSGD) algorithm for collaborative deep learning over fixed topology networks that enables data parallelization as well as decentralized computation. Such a framework can be extremely useful for learning agents with access to only local/private data in a communication constrained environment. We analyze the convergence properties of the proposed algorithm with strongly convex and nonconvex objective functions with fixed and diminishing step sizes using concepts of Lyapunov function construction. We demonstrate the efficacy of our algorithms in comparison with the baseline centralized SGD and the recently proposed federated averaging algorithm (that also enables data parallelism) based on benchmark datasets such as MNIST, CIFAR-10 and CIFAR-100.

We address the problem of recovering a high-dimensional but structured vector from linear observations in a general setting where the vector can come from an arbitrary union of subspaces. This setup includes well-studied problems such as compressive sensing and low-rank matrix recovery. We show how to design more efficient algorithms for the union-of subspace recovery problem by using approximate projections. Instantiating our general framework for the low-rank matrix recovery problem gives the fastest provable running time for an algorithm with optimal sample complexity. Moreover, we give fast approximate projections for 2D histograms, another well-studied low-dimensional model of data. We complement our theoretical results with experiments demonstrating that our framework also leads to improved time and sample complexity empirically.

Identifying “interesting” features, such as faults, unconformities, and other events in subsurface images is a challenging task in seismic data processing. Existing state-of-the-art methods usually involve manual intervention in the form of a visual inspection by an expert, but this is time-consuming, expensive, and error-prone. In this paper, we propose an efficient, automatic approach for seismic feature extraction. The core idea of our approach involves interpreting a given 2D seismic image as a function defined over the vertices of a specially chosen underlying graph. This enables us to formulate the feature extraction task as an instance of the Prize-Collecting Steiner Tree problem encountered in combinatorial optimization. We develop an efficient algorithm to solve this problem, and demonstrate the utility of our method on a number of synthetic and real examples.

We introduce a framework for sparsity structures defined via graphs. Our approach is flexible and generalizes several previously studied sparsity models. Moreover, we provide efficient projection algorithms for our sparsity model that run in nearly-linear time. In the context of sparse recovery, we show that our framework achieves an information-theoretically optimal sample complexity for a wide range of parameters. We complement our theoretical analysis with experiments demonstrating that our algorithms improve on prior work also in practice.

Histograms are among the most popular structures for the succinct summarization of data in a variety of database applications. In this work, we provide fast and near-optimal algorithms for approximating arbitrary one dimensional data distributions by histograms.

Compressive sensing (CS) states that a sparse signal can be recovered from a small number of linear measurements, and that this recovery can be performed efficiently in polynomial time. The framework of model-based CS (model-CS) leverages additional structure in the signal and provides new recovery schemes that can reduce the number of measurements even further. This idea has led to measurement-efficient recovery schemes for a variety of signal models. However, for any given model, model-CS requires an algorithm that solves the model-projection problem: given a query signal, report the signal in the model that is closest to the query signal. Often, this optimization can be computationally very expensive. Moreover, an approximation algorithm is not sufficient for this optimization to provably succeed. As a result, the model-projection problem poses a fundamental obstacle for extending model-CS to many interesting classes of models. In this paper, we introduce a new framework that we call approximation-tolerant model-CS. This framework includes a range of algorithms for sparse recovery that require only approximate solutions for the model-projection problem. In essence, our work removes the aforementioned obstacle to model-CS, thereby extending model-CS to a much wider class of signal models. Interestingly, all our algorithms involve both the minimization and the maximization variants of the model-projection problem. We instantiate this new framework for a new signal model that we call the constrained earth mover distance (CEMD) model. This model is particularly useful for signal ensembles, where the positions of the nonzero coefficients do not change significantly as a function of spatial (or temporal) location. We develop novel approximation algorithms for both the maximization and the minimization versions of the model-projection problem via graph optimization techniques. Leveraging these algorithms and our framework results in a nearly sample-optimal sparse recovery scheme for the CEMD model.

We consider the efficient acquisition, parameter estimation, and recovery of signal ensembles that lie on a low-dimensional manifold in a high-dimensional ambient signal space. Our particular focus is on randomized, compressive acquisition of signals from the manifold generated by the transformation of a base signal by operators from a Lie group. Such manifolds factor prominently in a number of applications, including radar and sonar array processing, camera arrays, and video processing. Leveraging the fact that Lie group manifolds admit a convenient analytical characterization, we develop new theory and algorithms for: (1) estimating the Lie operator parameters from compressive measurements, and (2) recovering the base signal from compressive measurements. We validate our approach with several of numerical simulations, including the reconstruction of an affine-transformed video sequence from compressive measurements.

Localizing fault lines and surfaces in seismic subsurface images is a daunting challenge. Existing state-of-the-art approaches usually involve visual interpretation by an expert, but this is time-consuming, expensive and error-prone. In this paper, we propose some initial steps towards a new algorithmic framework for automatic fault localization. The core of our approach is a deterministic model for 2D images that we call the Constrained Generalized Earth Mover's Distance (CGEMD) model. We propose an algorithm that returns the best approximation in the model for any given input 2D image X; the output of this algorithm is then post-processed to reveal the locations of the faults in the image. We demonstrate the validity of this approach on a number of synthetic and real-world examples.

Sparse signals whose nonzeros obey a tree-like structure occur in a range of applications such as image modeling, genetic data analysis, and compressive sensing. An important problem encountered in recovering signals is that of optimal tree-projection, i.e., finding the closest tree-sparse signal for a given query signal. However, this problem can be computationally very demanding: for optimally projecting a length-n signal onto a tree with sparsity k, the best existing algorithms incur a high runtime of O(nk). This can often be impractical. We suggest an alternative approach to tree-sparse recovery. Our approach is based on a specific approximation algorithm for tree-projection and provably has a near-linear runtime of O(n log(kr)) and a memory cost of O(n), where r is the dynamic range of the signal. We leverage this approach in a fast recovery algorithm for tree-sparse compressive sensing that scales extremely well to high-dimensional datasets. Experimental results on several test cases demonstrate the validity of our approach.

The goal of sparse recovery is to recover a k-sparse signal x ∊ ℝn from (possibly noisy) linear measurements of the form y = Ax, where A ∊ ℝm×n describes the measurement process. Standard results in compressive sensing show that it is possible to recover the signal x from m = O(klog(n/k)) measurements, and that this bound is tight. The framework of model-based compressive sensing [BCDH10] overcomes the lower bound and reduces the number of measurements further to O(k) by limiting the supports of x to a subset ℳ of the possible supports. This has led to many measurement-efficient algorithms for a wide variety of signal models, including block-sparsity and tree-sparsity. Unfortunately, extending the framework to other, more general models has been stymied by the following obstacle: for the framework to apply, one needs an algorithm that, given a signal x, solves the following optimization problem exactly : (here x[n]\Ω denotes the projection of x on coordinates not in Ω). However, an approximation algorithm for this optimization task is not sufficient. Since many problems of this form are not known to have exact polynomial-time algorithms, this requirement poses an obstacle for extending the framework to a richer class of models. In this paper, we remove this obstacle and show how to extend the model-based compressive sensing framework so that it requires only approximate solutions to the aforementioned optimization problems. Interestingly, our extension requires the existence of approximation algorithms for both the maximization and the minimization variants of the optimization problem. Further, we apply our framework to the Constrained Earth Mover's Distance (CEMD) model introduced in [SHI13], obtaining a sparse recovery scheme that uses significantly less than O(klog(n/k)) measurements. This is the first non-trivial theoretical bound for this model, since the validation of the approach presented in [SHI13] was purely empirical. The result is obtained by designing a novel approximation algorithm for the maximization version of the problem and proving approximation guarantees for the minimization algorithm described in [SHI13].

Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear sub-manifold of a high-dimensional ambient space. We introduce Successive Projection onto INcoherent manifolds (SPIN), a first-order projected gradient method to recover the signal components. Despite the nonconvex nature of the recovery problem and the possibility of underdetermined measurements, SPIN provably recovers the signal components, provided that the signal manifolds are incoherent and that the measurement operator satisfies a certain restricted isometry property. SPIN significantly extends the scope of current signal recovery models and algorithms for low-dimensional linear inverse problems, and matches (or exceeds) the current state of the art in terms of performance.

Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear submanifold of a high-dimensional ambient space. We introduce successive projections onto incoherent manifolds (SPIN), a first-order projected gradient method to recover the signal components. Despite the nonconvex nature of the recovery problem and the possibility of underdetermined measurements, SPIN provably recovers the signal components, provided that the signal manifolds are incoherent and that the measurement operator satisfies a certain restricted isometry property. SPIN significantly extends the scope of current recovery models and algorithms for low-dimensional linear inverse problems and matches (or exceeds) the current state of the art in terms of performance.

Compressive Sensing (CS) has emerged as a potentially viable technique for the efficient acquisition of high-resolution signals and images that have a sparse representation in a fixed basis. The number of linear measurements M required for robust polynomial time recovery of S-sparse signals of length N can be shown to be proportional to S log N. However, in many real-life imaging applications, the original S-sparse image may be blurred by an unknown point spread function defined over a domain O; this multiplies the apparent sparsity of the image, as well as the corresponding acquisition cost, by a factor of |Ω|. In this paper, we propose a new CS recovery algorithm for such images that can be modeled as a sparse superposition of pulses. Our method can be used to infer both the shape of the two-dimensional pulse and the locations and amplitudes of the pulses. Our main theoretical result shows that our reconstruction method requires merely M = O(S + |Ω|) linear measurements, so that M is sublinear in the overall image sparsity S|Ω|. Experiments with real world data demonstrate that our method provides considerable gains over standard state-of-the-art compressive sensing techniques in terms of numbers of measurements required for stable recovery.

This paper develops a new class of algorithms for signal recovery in the distributed compressive sensing (DCS) framework. DCS exploits both intra-signal and inter-signal correlations through the concept of joint sparsity to further reduce the number of measurements required for recovery. DCS is well-suited for sensor network applications due to its universality, computational asymmetry, tolerance to quantization and noise, and robustness to measurement loss. In this paper we propose recovery algorithms for the sparse common and innovation joint sparsity model. Our approach leads to a class of efficient algorithms, the Texas Hold 'Em algorithms, which are scalable both in terms of communication bandwidth and computational complexity.

The emergence of low-cost sensing architectures for diverse modalities has made it possible to deploy sensor networks that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these networks acquire large amounts of very high-dimensional data. For example, even a relatively small network of cameras can generate massive amounts of high-dimensional image and video data. One way to cope with this data deluge is to exploit low-dimensional data models. Manifold models provide a particularly powerful theoretical and algorithmic framework for capturing the structure of data governed by a small number of parameters, as is often the case in a sensor network. However, these models do not typically take into account dependencies among multiple sensors. We thus propose a new joint manifold framework for data ensembles that exploits such dependencies. We show that joint manifold structure can lead to improved performance for a variety of signal processing algorithms for applications including classification and manifold learning. Additionally, recent results concerning random projections of manifolds enable us to formulate a scalable and universal dimensionality reduction scheme that efficiently fuses the data from all sensors.

Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for the acquisition of sparse or compressible signals that can be well approximated by just K ¿ N elements from an N -dimensional basis. Instead of taking periodic samples, CS measures inner products with M < N random vectors and then recovers the signal via a sparsity-seeking optimization or greedy algorithm. Standard CS dictates that robust signal recovery is possible from M = O(K log(N/K)) measurements. It is possible to substantially decrease M without sacrificing robustness by leveraging more realistic signal models that go beyond simple sparsity and compressibility by including structural dependencies between the values and locations of the signal coefficients. This paper introduces a model-based CS theory that parallels the conventional theory and provides concrete guidelines on how to create model-based recovery algorithms with provable performance guarantees. A highlight is the introduction of a new class of structured compressible signals along with a new sufficient condition for robust structured compressible signal recovery that we dub the restricted amplification property, which is the natural counterpart to the restricted isometry property of conventional CS. Two examples integrate two relevant signal models-wavelet trees and block sparsity-into two state-of-the-art CS recovery algorithms and prove that they offer robust recovery from just M = O(K) measurements. Extensive numerical simulations demonstrate the validity and applicability of our new theory and algorithms.

Compressive Sensing (CS) combines sampling and compression into a single sub-Nyquist linear measurement process for sparse and compressible signals. In this paper, we extend the theory of CS to include signals that are concisely represented in terms of a graphical model. In particular, we use Markov Random Fields (MRFs) to represent sparse signals whose nonzero coefficients are clustered. Our new model-based reconstruction algorithm, dubbed Lattice Matching Pursuit (LaMP), stably recovers MRF-modeled signals using many fewer measurements and computations than the current state-of-the-art algorithms.

We propose a novel method for {\em linear} dimensionality reduction of manifold modeled data. First, we show that with a small number $M$ of {\em random projections} of sample points in $\reals^N$ belonging to an unknown $K$-dimensional Euclidean manifold, the intrinsic dimension (ID) of the sample set can be estimated to high accuracy. Second, we rigorously prove that using only this set of random projections, we can estimate the structure of the underlying manifold. In both cases, the number random projections required is linear in $K$ and logarithmic in $N$, meaning that $K