Mohammadreza Soltani

Mohammadreza Soltani, Suya Wu, Yuerong Li et al.

We propose a new structured pruning framework for compressing Deep Neural Networks (DNNs) with skip connections, based on measuring the statistical dependency of hidden layers and predicted outputs. The dependence measure defined by the energy statistics of hidden layers serves as a model-free measure of information between the feature maps and the output of the network. The estimated dependence measure is subsequently used to prune a collection of redundant and uninformative layers. Model-freeness of our measure guarantees that no parametric assumptions on the feature map distribution are required, making it computationally appealing for very high dimensional feature space in DNNs. Extensive numerical experiments on various architectures show the efficacy of the proposed pruning approach with competitive performance to state-of-the-art methods.

Shyam Venkatasubramanian, Chayut Wongkamthong, Mohammadreza Soltani et al.

Using an amalgamation of techniques from classical radar, computer vision, and deep learning, we characterize our ongoing data-driven approach to space-time adaptive processing (STAP) radar. We generate a rich example dataset of received radar signals by randomly placing targets of variable strengths in a predetermined region using RFView, a site-specific radio frequency modeling and simulation tool developed by ISL Inc. For each data sample within this region, we generate heatmap tensors in range, azimuth, and elevation of the output power of a minimum variance distortionless response (MVDR) beamformer, which can be replaced with a desired test statistic. These heatmap tensors can be thought of as stacked images, and in an airborne scenario, the moving radar creates a sequence of these time-indexed image stacks, resembling a video. Our goal is to use these images and videos to detect targets and estimate their locations, a procedure reminiscent of computer vision algorithms for object detection$-$namely, the Faster Region-Based Convolutional Neural Network (Faster R-CNN). The Faster R-CNN consists of a proposal generating network for determining regions of interest (ROI), a regression network for positioning anchor boxes around targets, and an object classification algorithm; it is developed and optimized for natural images. Our ongoing research will develop analogous tools for heatmap images of radar data. In this regard, we will generate a large, representative adaptive radar signal processing database for training and testing, analogous in spirit to the COCO dataset for natural images. As a preliminary example, we present a regression network in this paper for estimating target locations to demonstrate the feasibility of and significant improvements provided by our data-driven approach.

Juncheng Dong, Simiao Ren, Yang Deng et al.

Numerous physical systems are described by ordinary or partial differential equations whose solutions are given by holomorphic or meromorphic functions in the complex domain. In many cases, only the magnitude of these functions are observed on various points on the purely imaginary jw-axis since coherent measurement of their phases is often expensive. However, it is desirable to retrieve the lost phases from the magnitudes when possible. To this end, we propose a physics-infused deep neural network based on the Blaschke products for phase retrieval. Inspired by the Helson and Sarason Theorem, we recover coefficients of a rational function of Blaschke products using a Blaschke Product Neural Network (BPNN), based upon the magnitude observations as input. The resulting rational function is then used for phase retrieval. We compare the BPNN to conventional deep neural networks (NNs) on several phase retrieval problems, comprising both synthetic and contemporary real-world problems (e.g., metamaterials for which data collection requires substantial expertise and is time consuming). On each phase retrieval problem, we compare against a population of conventional NNs of varying size and hyperparameter settings. Even without any hyper-parameter search, we find that BPNNs consistently outperform the population of optimized NNs in scarce data scenarios, and do so despite being much smaller models. The results can in turn be applied to calculate the refractive index of metamaterials, which is an important problem in emerging areas of material science.

Cat P. Le, Juncheng Dong, Mohammadreza Soltani et al.

We propose an asymmetric affinity score for representing the complexity of utilizing the knowledge of one task for learning another one. Our method is based on the maximum bipartite matching algorithm and utilizes the Fisher Information matrix. We provide theoretical analyses demonstrating that the proposed score is mathematically well-defined, and subsequently use the affinity score to propose a novel algorithm for the few-shot learning problem. In particular, using this score, we find relevant training data labels to the test data and leverage the discovered relevant data for episodically fine-tuning a few-shot model. Results on various few-shot benchmark datasets demonstrate the efficacy of the proposed approach by improving the classification accuracy over the state-of-the-art methods even when using smaller models.

Anna K. Yanchenko, Mohammadreza Soltani, Robert J. Ravier et al.

Understanding the features learned by deep models is important from a model trust perspective, especially as deep systems are deployed in the real world. Most recent approaches for deep feature understanding or model explanation focus on highlighting input data features that are relevant for classification decisions. In this work, we instead take the perspective of relating deep features to well-studied, hand-crafted features that are meaningful for the application of interest. We propose a methodology and set of systematic experiments for exploring deep features in this setting, where input feature importance approaches for deep feature understanding do not apply. Our experiments focus on understanding which hand-crafted and deep features are useful for the classification task of interest, how robust these features are for related tasks and how similar the deep features are to the meaningful hand-crafted features. Our proposed method is general to many application areas and we demonstrate its utility on orchestral music audio data.

Cat P. Le, Mohammadreza Soltani, Juncheng Dong et al.

We formulate an asymmetric (or non-commutative) distance between tasks based on Fisher Information Matrices, called Fisher task distance. This distance represents the complexity of transferring the knowledge from one task to another. We provide a proof of consistency for our distance through theorems and experiments on various classification tasks from MNIST, CIFAR-10, CIFAR-100, ImageNet, and Taskonomy datasets. Next, we construct an online neural architecture search framework using the Fisher task distance, in which we have access to the past learned tasks. By using the Fisher task distance, we can identify the closest learned tasks to the target task, and utilize the knowledge learned from these related tasks for the target task. Here, we show how the proposed distance between a target task and a set of learned tasks can be used to reduce the neural architecture search space for the target task. The complexity reduction in search space for task-specific architectures is achieved by building on the optimized architectures for similar tasks instead of doing a full search and without using this side information. Experimental results for tasks in MNIST, CIFAR-10, CIFAR-100, ImageNet datasets demonstrate the efficacy of the proposed approach and its improvements, in terms of the performance and the number of parameters, over other gradient-based search methods, such as ENAS, DARTS, PC-DARTS.

Cat P. Le, Mohammadreza Soltani, Robert Ravier et al.

In this paper, we propose a neural architecture search framework based on a similarity measure between some baseline tasks and a target task. We first define the notion of the task similarity based on the log-determinant of the Fisher Information matrix. Next, we compute the task similarity from each of the baseline tasks to the target task. By utilizing the relation between a target and a set of learned baseline tasks, the search space of architectures for the target task can be significantly reduced, making the discovery of the best candidates in the set of possible architectures tractable and efficient, in terms of GPU days. This method eliminates the requirement for training the networks from scratch for a given target task as well as introducing the bias in the initialization of the search space from the human domain.

Cat P. Le, Mohammadreza Soltani, Robert Ravier et al.

The design of handcrafted neural networks requires a lot of time and resources. Recent techniques in Neural Architecture Search (NAS) have proven to be competitive or better than traditional handcrafted design, although they require domain knowledge and have generally used limited search spaces. In this paper, we propose a novel framework for neural architecture search, utilizing a dictionary of models of base tasks and the similarity between the target task and the atoms of the dictionary; hence, generating an adaptive search space based on the base models of the dictionary. By introducing a gradient-based search algorithm, we can evaluate and discover the best architecture in the search space without fully training the networks. The experimental results show the efficacy of our proposed task-aware approach.

Robert J. Ravier, Mohammadreza Soltani, Miguel Simões et al.

Recent advances in time series classification have largely focused on methods that either employ deep learning or utilize other machine learning models for feature extraction. Though successful, their power often comes at the requirement of computational complexity. In this paper, we introduce GeoStat representations for time series. GeoStat representations are based off of a generalization of recent methods for trajectory classification, and summarize the information of a time series in terms of comprehensive statistics of (possibly windowed) distributions of easy to compute differential geometric quantities, requiring no dynamic time warping. The features used are intuitive and require minimal parameter tuning. We perform an exhaustive evaluation of GeoStat on a number of real datasets, showing that simple KNN and SVM classifiers trained on these representations exhibit surprising performance relative to modern single model methods requiring significant computational power, achieving state of the art results in many cases. In particular, we show that this methodology achieves good performance on a challenging dataset involving the classification of fishing vessels, where our methods achieve good performance relative to the state of the art despite only having access to approximately two percent of the dataset used in training and evaluating this state of the art.

Chris Cannella, Mohammadreza Soltani, Vahid Tarokh

We introduce Projected Latent Markov Chain Monte Carlo (PL-MCMC), a technique for sampling from the high-dimensional conditional distributions learned by a normalizing flow. We prove that a Metropolis-Hastings implementation of PL-MCMC asymptotically samples from the exact conditional distributions associated with a normalizing flow. As a conditional sampling method, PL-MCMC enables Monte Carlo Expectation Maximization (MC-EM) training of normalizing flows from incomplete data. Through experimental tests applying normalizing flows to missing data tasks for a variety of data sets, we demonstrate the efficacy of PL-MCMC for conditional sampling from normalizing flows.

Minsu Cho, Mohammadreza Soltani, Chinmay Hegde

In this paper, we study two important problems in the automated design of neural networks -- Hyper-parameter Optimization (HPO), and Neural Architecture Search (NAS) -- through the lens of sparse recovery methods. In the first part of this paper, we establish a novel connection between HPO and structured sparse recovery. In particular, we show that a special encoding of the 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. Experimental results on image datasets such as CIFAR-10 confirm the benefits of our approach. In the second part of this paper, we establish a connection between NAS and structured sparse recovery. Building upon ``one-shot'' approaches in NAS, we propose a novel algorithm that we call CoNAS by merging ideas from one-shot approaches with a techniques for learning low-degree sparse Boolean polynomials. We provide theoretical analysis on the number of validation error measurements. Finally, we validate our approach on several datasets and discover novel architectures hitherto unreported, achieving competitive (or better) results in both performance and search time compared to the existing NAS approaches.

Chris Cannella, Jie Ding, Mohammadreza Soltani et al.

In this work, we introduce a new procedure for applying Restricted Boltzmann Machines (RBMs) to missing data inference tasks, based on linearization of the effective energy function governing the distribution of observations. We compare the performance of our proposed procedure with those obtained using existing reconstruction procedures trained on incomplete data. We place these performance comparisons within the context of the perception-distortion trade-off observed in other data reconstruction tasks, which has, until now, remained unexplored in tasks relying on incomplete training data.

Minsu Cho, Mohammadreza Soltani, Chinmay Hegde

Neural Architecture Search remains a very challenging meta-learning problem. Several recent techniques based on parameter-sharing idea have focused on reducing the NAS running time by leveraging proxy models, leading to architectures with competitive performance compared to those with hand-crafted designs. In this paper, we propose an iterative technique for NAS, inspired by algorithms for learning low-degree sparse Boolean functions. We validate our approach on the DARTs search space (Liu et al., 2018b) and NAS-Bench-201 (Yang et al., 2020). In addition, we provide theoretical analysis via upper bounds on the number of validation error measurements needed for reliable learning, and include ablation studies to further in-depth understanding of our technique.

Mohammadreza Soltani, Swayambhoo Jain, Abhinav Sambasivan

Recently, Generative Adversarial Networks (GANs) have emerged as a popular alternative for modeling complex high dimensional distributions. Most of the existing works implicitly assume that the clean samples from the target distribution are easily available. However, in many applications, this assumption is violated. In this paper, we consider the observation setting when the samples from target distribution are given by the superposition of two structured components and leverage GANs for learning the structure of the components. We propose two novel frameworks: denoising-GAN and demixing-GAN. The denoising-GAN assumes access to clean samples from the second component and try to learn the other distribution, whereas demixing-GAN learns the distribution of the components at the same time. Through extensive numerical experiments, we demonstrate that proposed frameworks can generate clean samples from unknown distributions, and provide competitive performance in tasks such as denoising, demixing, and compressive sensing.

Mohammadreza Soltani, Chinmay Hegde

In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. 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 \emph{condition number} of the optimum. In this paper, we provide a novel algorithmic framework that achieves the best of both worlds: asymptotically as fast as factorization methods, while requiring no dependency on the condition number. We instantiate our general framework for three important matrix estimation problems that impact several practical applications; (i) a \emph{nonlinear} variant of affine rank minimization, (ii) logistic PCA, and (iii) precision matrix estimation in probabilistic graphical model learning. We then derive explicit bounds on the sample complexity as well as the running time of our approach, and show that it achieves the best possible bounds for both cases. We also provide an extensive range of experimental results, and demonstrate that our algorithm provides a very attractive tradeoff between estimation accuracy and running time.

Viraj Shah, Mohammadreza Soltani, Chinmay Hegde

We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to compressive sensing-based signal and image acquisition systems. Our techniques can be potentially useful for reducing the measurement complexity of high dynamic range (HDR) imaging systems, with little loss in reconstruction quality. Several numerical experiments on real data demonstrate the effectiveness of our approach.

Mohammadreza Soltani, Chinmay Hegde

We consider the demixing problem of two (or more) structured high-dimensional vectors from a limited number of nonlinear observations where this nonlinearity is due to either a periodic or an aperiodic function. We study certain families of structured superposition models, and propose a method which provably recovers the components given (nearly) $m = \mathcal{O}(s)$ samples where $s$ denotes the sparsity level of the underlying components. This strictly improves upon previous nonlinear demixing techniques and asymptotically matches the best possible sample complexity. We also provide a range of simulations to illustrate the performance of the proposed algorithms.

Mohammadreza Soltani, Chinmay Hegde

We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this paper, we focus on the estimation of the low-rank component, which encodes the effect of marginalization over the latent variables. We introduce fast, proper learning algorithms for this problem. In contrast with existing approaches, our algorithms are manifestly non-convex. We support their efficacy via a rigorous theoretical analysis, and show that our algorithms match the best possible in terms of sample complexity, while achieving computational speed-ups over existing methods. We complement our theory with several numerical experiments.

Mohammadreza Soltani, Chinmay Hegde

We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous theoretical analysis. We show that the proposed algorithms enjoy linear convergence and that their sample complexity is independent of the condition number of the unknown true low-rank matrix. By leveraging recent advances in low-rank matrix approximation techniques, we show that our algorithms achieve computational speed-ups over existing methods. Finally, we complement our theory with some numerical experiments.

Mohammadreza Soltani, Chinmay Hegde

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.

Mohammadreza Soltani, Chinmay Hegde

We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an algorithm that stably estimate the underlying components under general \emph{structured sparsity} assumptions on these components. Specifically, we show that for certain types of structured superposition models, our method provably recovers the components given merely $n = \mathcal{O}(s)$ samples where $s$ denotes the number of nonzero entries in the underlying components. Moreover, our method achieves a fast (linear) convergence rate, and also exhibits fast (near-linear) per-iteration complexity for certain types of structured models. We also provide a range of simulations to illustrate the performance of the proposed algorithm.

Mohammadreza Soltani, Chinmay Hegde

We study the problem of demixing a pair of sparse signals from noisy, nonlinear observations of their superposition. Mathematically, we consider a nonlinear signal observation model, $y_i = g(a_i^Tx) + e_i, \ i=1,\ldots,m$, where $x = Φw+Ψz$ denotes the superposition signal, $Φ$ and $Ψ$ are orthonormal bases in $\mathbb{R}^n$, and $w, z\in\mathbb{R}^n$ are sparse coefficient vectors of the constituent signals, and $e_i$ represents the noise. Moreover, $g$ represents a nonlinear link function, and $a_i\in\mathbb{R}^n$ is the $i$-th row of the measurement matrix, $A\in\mathbb{R}^{m\times n}$. Problems of this nature arise in several applications ranging from astronomy, computer vision, and machine learning. In this paper, we make some concrete algorithmic progress for the above demixing problem. Specifically, we consider two scenarios: (i) the case when the demixing procedure has no knowledge of the link function, and (ii) the case when the demixing algorithm has perfect knowledge of the link function. In both cases, we provide fast algorithms for recovery of the constituents $w$ and $z$ from the observations. Moreover, we support these algorithms with a rigorous theoretical analysis, and derive (nearly) tight upper bounds on the sample complexity of the proposed algorithms for achieving stable recovery of the component signals. We also provide a range of numerical simulations to illustrate the performance of the proposed algorithms on both real and synthetic signals and images.