arXiv subjects

Jeremias Sulam

Publications and source records attributed to Jeremias Sulam.

At least 37 records · Page 2Linked to original sources

arXiv2023

Sparsity-aware generalization theory for deep neural networks

Deep artificial neural networks achieve surprising generalization abilities that remain poorly understood. In this paper, we present a new approach to analyzing generalization for deep feed-forward ReLU networks that takes advantage of the degree of sparsity that is achieved in the hidden layer activations. By developing a framework that accounts for this reduced effective model size for each input sample, we are able to show fundamental trade-offs between sparsity and generalization. Importantly, our results make no strong assumptions about the degree of sparsity achieved by the model, and it improves over recent norm-based approaches. We illustrate our results numerically, demonstrating non-vacuous bounds when coupled with data-dependent priors in specific settings, even in over-parametrized models.

cs.LG↗

arXiv2023

Estimating and Controlling for Equalized Odds via Sensitive Attribute Predictors

As the use of machine learning models in real world high-stakes decision settings continues to grow, it is highly important that we are able to audit and control for any potential fairness violations these models may exhibit towards certain groups. To do so, one naturally requires access to sensitive attributes, such as demographics, gender, or other potentially sensitive features that determine group membership. Unfortunately, in many settings, this information is often unavailable. In this work we study the well known \emph{equalized odds} (EOD) definition of fairness. In a setting without sensitive attributes, we first provide tight and computable upper bounds for the EOD violation of a predictor. These bounds precisely reflect the worst possible EOD violation. Second, we demonstrate how one can provably control the worst-case EOD by a new post-processing correction method. Our results characterize when directly controlling for EOD with respect to the predicted sensitive attributes is -- and when is not -- optimal when it comes to controlling worst-case EOD. Our results hold under assumptions that are milder than previous works, and we illustrate these results with experiments on synthetic and real datasets.

cs.LG↗

arXiv2023

Understanding Noise-Augmented Training for Randomized Smoothing

Randomized smoothing is a technique for providing provable robustness guarantees against adversarial attacks while making minimal assumptions about a classifier. This method relies on taking a majority vote of any base classifier over multiple noise-perturbed inputs to obtain a smoothed classifier, and it remains the tool of choice to certify deep and complex neural network models. Nonetheless, non-trivial performance of such smoothed classifier crucially depends on the base model being trained on noise-augmented data, i.e., on a smoothed input distribution. While widely adopted in practice, it is still unclear how this noisy training of the base classifier precisely affects the risk of the robust smoothed classifier, leading to heuristics and tricks that are poorly understood. In this work we analyze these trade-offs theoretically in a binary classification setting, proving that these common observations are not universal. We show that, without making stronger distributional assumptions, no benefit can be expected from predictors trained with noise-augmentation, and we further characterize distributions where such benefit is obtained. Our analysis has direct implications to the practical deployment of randomized smoothing, and we illustrate some of these via experiments on CIFAR-10 and MNIST, as well as on synthetic datasets.

cs.LG↗

arXiv2023

Fourier Diffusion Models: A Method to Control MTF and NPS in Score-Based Stochastic Image Generation

Score-based stochastic denoising models have recently been demonstrated as powerful machine learning tools for conditional and unconditional image generation. The existing methods are based on a forward stochastic process wherein the training images are scaled to zero over time and white noise is gradually added such that the final time step is approximately zero-mean identity-covariance Gaussian noise. A neural network is then trained to approximate the time-dependent score function, or the gradient of the logarithm of the probability density, for that time step. Using this score estimator, it is possible to run an approximation of the time-reversed stochastic process to sample new images from the training data distribution. These score-based generative models have been shown to out-perform generative adversarial neural networks using standard benchmarks and metrics. However, one issue with this approach is that it requires a large number of forward passes of the neural network. Additionally, the images at intermediate time steps are not useful, since the signal-to-noise ratio is low. In this work we present a new method called Fourier Diffusion Models which replaces the scalar operations of the forward process with shift-invariant convolutions and the additive white noise with additive stationary noise. This allows for control of MTF and NPS at intermediate time steps. Additionally, the forward process can be crafted to converge to the same MTF and NPS as the measured images. This way, we can model continuous probability flow from true images to measurements. In this way, the sample time can be used to control the tradeoffs between measurement uncertainty and generative uncertainty of posterior estimates. We compare Fourier diffusion models to existing scalar diffusion models and show that they achieve a higher level of performance and allow for a smaller number of time steps.

physics.med-ph↗

arXiv2023

Adversarial robustness of sparse local Lipschitz predictors

This work studies the adversarial robustness of parametric functions composed of a linear predictor and a non-linear representation map. % that satisfies certain stability condition. Our analysis relies on \emph{sparse local Lipschitzness} (SLL), an extension of local Lipschitz continuity that better captures the stability and reduced effective dimensionality of predictors upon local perturbations. SLL functions preserve a certain degree of structure, given by the sparsity pattern in the representation map, and include several popular hypothesis classes, such as piece-wise linear models, Lasso and its variants, and deep feed-forward \relu networks. % are sparse local Lipschitz. We provide a tighter robustness certificate on the minimal energy of an adversarial example, as well as tighter data-dependent non-uniform bounds on the robust generalization error of these predictors. We instantiate these results for the case of deep neural networks and provide numerical evidence that supports our results, shedding new insights into natural regularization strategies to increase the robustness of these models.

cs.LG↗

arXiv2022

Weakly Supervised Learning Significantly Reduces the Number of Labels Required for Intracranial Hemorrhage Detection on Head CT

Modern machine learning pipelines, in particular those based on deep learning (DL) models, require large amounts of labeled data. For classification problems, the most common learning paradigm consists of presenting labeled examples during training, thus providing strong supervision on what constitutes positive and negative samples. This constitutes a major obstacle for the development of DL models in radiology--in particular for cross-sectional imaging (e.g., computed tomography [CT] scans)--where labels must come from manual annotations by expert radiologists at the image or slice-level. These differ from examination-level annotations, which are coarser but cheaper, and could be extracted from radiology reports using natural language processing techniques. This work studies the question of what kind of labels should be collected for the problem of intracranial hemorrhage detection in brain CT. We investigate whether image-level annotations should be preferred to examination-level ones. By framing this task as a multiple instance learning problem, and employing modern attention-based DL architectures, we analyze the degree to which different levels of supervision improve detection performance. We find that strong supervision (i.e., learning with local image-level annotations) and weak supervision (i.e., learning with only global examination-level labels) achieve comparable performance in examination-level hemorrhage detection (the task of selecting the images in an examination that show signs of hemorrhage) as well as in image-level hemorrhage detection (highlighting those signs within the selected images). Furthermore, we study this behavior as a function of the number of labels available during training. Our results suggest that local labels may not be necessary at all for these tasks, drastically reducing the time and cost involved in collecting and curating datasets.

cs.CV↗

arXiv2022

DeepSTI: Towards Tensor Reconstruction using Fewer Orientations in Susceptibility Tensor Imaging

Susceptibility tensor imaging (STI) is an emerging magnetic resonance imaging technique that characterizes the anisotropic tissue magnetic susceptibility with a second-order tensor model. STI has the potential to provide information for both the reconstruction of white matter fiber pathways and detection of myelin changes in the brain at mm resolution or less, which would be of great value for understanding brain structure and function in healthy and diseased brain. However, the application of STI in vivo has been hindered by its cumbersome and time-consuming acquisition requirement of measuring susceptibility induced MR phase changes at multiple (usually more than six) head orientations. This complexity is enhanced by the limitation in head rotation angles due to physical constraints of the head coil. As a result, STI has not yet been widely applied in human studies in vivo. In this work, we tackle these issues by proposing an image reconstruction algorithm for STI that leverages data-driven priors. Our method, called DeepSTI, learns the data prior implicitly via a deep neural network that approximates the proximal operator of a regularizer function for STI. The dipole inversion problem is then solved iteratively using the learned proximal network. Experimental results using both simulation and in vivo human data demonstrate great improvement over state-of-the-art algorithms in terms of the reconstructed tensor image, principal eigenvector maps and tractography results, while allowing for tensor reconstruction with MR phase measured at much less than six different orientations. Notably, promising reconstruction results are achieved by our method from only one orientation in human in vivo, and we demonstrate a potential application of this technique for estimating lesion susceptibility anisotropy in patients with multiple sclerosis.

eess.IV↗

arXiv2022

Fast Hierarchical Games for Image Explanations

As modern complex neural networks keep breaking records and solving harder problems, their predictions also become less and less intelligible. The current lack of interpretability often undermines the deployment of accurate machine learning tools in sensitive settings. In this work, we present a model-agnostic explanation method for image classification based on a hierarchical extension of Shapley coefficients--Hierarchical Shap (h-Shap)--that resolves some of the limitations of current approaches. Unlike other Shapley-based explanation methods, h-Shap is scalable and can be computed without the need of approximation. Under certain distributional assumptions, such as those common in multiple instance learning, h-Shap retrieves the exact Shapley coefficients with an exponential improvement in computational complexity. We compare our hierarchical approach with popular Shapley-based and non-Shapley-based methods on a synthetic dataset, a medical imaging scenario, and a general computer vision problem, showing that h-Shap outperforms the state of the art in both accuracy and runtime. Code and experiments are made publicly available.

cs.CV↗

arXiv2022

Label Cleaning Multiple Instance Learning: Refining Coarse Annotations on Single Whole-Slide Images

Annotating cancerous regions in whole-slide images (WSIs) of pathology samples plays a critical role in clinical diagnosis, biomedical research, and machine learning algorithms development. However, generating exhaustive and accurate annotations is labor-intensive, challenging, and costly. Drawing only coarse and approximate annotations is a much easier task, less costly, and it alleviates pathologists' workload. In this paper, we study the problem of refining these approximate annotations in digital pathology to obtain more accurate ones. Some previous works have explored obtaining machine learning models from these inaccurate annotations, but few of them tackle the refinement problem where the mislabeled regions should be explicitly identified and corrected, and all of them require a -- often very large -- number of training samples. We present a method, named Label Cleaning Multiple Instance Learning (LC-MIL), to refine coarse annotations on a single WSI without the need of external training data. Patches cropped from a WSI with inaccurate labels are processed jointly within a multiple instance learning framework, mitigating their impact on the predictive model and refining the segmentation. Our experiments on a heterogeneous WSI set with breast cancer lymph node metastasis, liver cancer, and colorectal cancer samples show that LC-MIL significantly refines the coarse annotations, outperforming state-of-the-art alternatives, even while learning from a single slide. Moreover, we demonstrate how real annotations drawn by pathologists can be efficiently refined and improved by the proposed approach. All these results demonstrate that LC-MIL is a promising, light-weight tool to provide fine-grained annotations from coarsely annotated pathology sets.

cs.CV↗

arXiv2022

Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms

Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfields of applied statistics. While several results have characterized the recovery error of the principal eigenvectors, these are typically in spectral or Frobenius norms. In this paper, we provide entrywise $\ell_{2,\infty}$ bounds for Sparse PCA under a general high-dimensional subgaussian design. In particular, our results hold for any algorithm that selects the correct support with high probability, those that are sparsistent. Our bound improves upon known results by providing a finer characterization of the estimation error, and our proof uses techniques recently developed for entrywise subspace perturbation theory.

math.ST↗

arXiv2021

Deciphering antibody affinity maturation with language models and weakly supervised learning

In response to pathogens, the adaptive immune system generates specific antibodies that bind and neutralize foreign antigens. Understanding the composition of an individual's immune repertoire can provide insights into this process and reveal potential therapeutic antibodies. In this work, we explore the application of antibody-specific language models to aid understanding of immune repertoires. We introduce AntiBERTy, a language model trained on 558M natural antibody sequences. We find that within repertoires, our model clusters antibodies into trajectories resembling affinity maturation. Importantly, we show that models trained to predict highly redundant sequences under a multiple instance learning framework identify key binding residues in the process. With further development, the methods presented here will provide new insights into antigen binding from repertoire sequences alone.

q-bio.BM↗

arXiv2021

A Geometric Analysis of Neural Collapse with Unconstrained Features

We provide the first global optimization landscape analysis of $Neural\;Collapse$ -- an intriguing empirical phenomenon that arises in the last-layer classifiers and features of neural networks during the terminal phase of training. As recently reported by Papyan et al., this phenomenon implies that ($i$) the class means and the last-layer classifiers all collapse to the vertices of a Simplex Equiangular Tight Frame (ETF) up to scaling, and ($ii$) cross-example within-class variability of last-layer activations collapses to zero. We study the problem based on a simplified $unconstrained\;feature\;model$, which isolates the topmost layers from the classifier of the neural network. In this context, we show that the classical cross-entropy loss with weight decay has a benign global landscape, in the sense that the only global minimizers are the Simplex ETFs while all other critical points are strict saddles whose Hessian exhibit negative curvature directions. In contrast to existing landscape analysis for deep neural networks which is often disconnected from practice, our analysis of the simplified model not only does it explain what kind of features are learned in the last layer, but it also shows why they can be efficiently optimized in the simplified settings, matching the empirical observations in practical deep network architectures. These findings could have profound implications for optimization, generalization, and robustness of broad interests. For example, our experiments demonstrate that one may set the feature dimension equal to the number of classes and fix the last-layer classifier to be a Simplex ETF for network training, which reduces memory cost by over $20\%$ on ResNet18 without sacrificing the generalization performance.

cs.LG↗

arXiv2021

Adversarial Robustness of Supervised Sparse Coding

Several recent results provide theoretical insights into the phenomena of adversarial examples. Existing results, however, are often limited due to a gap between the simplicity of the models studied and the complexity of those deployed in practice. In this work, we strike a better balance by considering a model that involves learning a representation while at the same time giving a precise generalization bound and a robustness certificate. We focus on the hypothesis class obtained by combining a sparsity-promoting encoder coupled with a linear classifier, and show an interesting interplay between the expressivity and stability of the (supervised) representation map and a notion of margin in the feature space. We bound the robust risk (to $\ell_2$-bounded perturbations) of hypotheses parameterized by dictionaries that achieve a mild encoder gap on training data. Furthermore, we provide a robustness certificate for end-to-end classification. We demonstrate the applicability of our analysis by computing certified accuracy on real data, and compare with other alternatives for certified robustness.

cs.LG↗

arXiv2020

Conformal Symplectic and Relativistic Optimization

Arguably, the two most popular accelerated or momentum-based optimization methods in machine learning are Nesterov's accelerated gradient and Polyaks's heavy ball, both corresponding to different discretizations of a particular second order differential equation with friction. Such connections with continuous-time dynamical systems have been instrumental in demystifying acceleration phenomena in optimization. Here we study structure-preserving discretizations for a certain class of dissipative (conformal) Hamiltonian systems, allowing us to analyze the symplectic structure of both Nesterov and heavy ball, besides providing several new insights into these methods. Moreover, we propose a new algorithm based on a dissipative relativistic system that normalizes the momentum and may result in more stable/faster optimization. Importantly, such a method generalizes both Nesterov and heavy ball, each being recovered as distinct limiting cases, and has potential advantages at no additional cost.

math.OC↗

arXiv2020

Recovery and Generalization in Over-Realized Dictionary Learning

In over two decades of research, the field of dictionary learning has gathered a large collection of successful applications, and theoretical guarantees for model recovery are known only whenever optimization is carried out in the same model class as that of the underlying dictionary. This work characterizes the surprising phenomenon that dictionary recovery can be facilitated by searching over the space of larger over-realized models. This observation is general and independent of the specific dictionary learning algorithm used. We thoroughly demonstrate this observation in practice and provide an analysis of this phenomenon by tying recovery measures to generalization bounds. In particular, we show that model recovery can be upper-bounded by the empirical risk, a model-dependent quantity and the generalization gap, reflecting our empirical findings. We further show that an efficient and provably correct distillation approach can be employed to recover the correct atoms from the over-realized model. As a result, our meta-algorithm provides dictionary estimates with consistently better recovery of the ground-truth model.

cs.LG↗

arXiv2020

Learning to solve TV regularized problems with unrolled algorithms

Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the $\ell_1$-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually solved using iterative algorithms such as proximal gradient descent, primal-dual algorithms or ADMM. However, such methods can require a very large number of iterations to converge to a suitable solution. In this paper, we accelerate such iterative algorithms by unfolding proximal gradient descent solvers in order to learn their parameters for 1D TV regularized problems. While this could be done using the synthesis formulation, we demonstrate that this leads to slower performances. The main difficulty in applying such methods in the analysis formulation lies in proposing a way to compute the derivatives through the proximal operator. As our main contribution, we develop and characterize two approaches to do so, describe their benefits and limitations, and discuss the regime where they can actually improve over iterative procedures. We validate those findings with experiments on synthetic and real data.

math.OC↗

arXiv2020

Learned Proximal Networks for Quantitative Susceptibility Mapping

Quantitative Susceptibility Mapping (QSM) estimates tissue magnetic susceptibility distributions from Magnetic Resonance (MR) phase measurements by solving an ill-posed dipole inversion problem. Conventional single orientation QSM methods usually employ regularization strategies to stabilize such inversion, but may suffer from streaking artifacts or over-smoothing. Multiple orientation QSM such as calculation of susceptibility through multiple orientation sampling (COSMOS) can give well-conditioned inversion and an artifact free solution but has expensive acquisition costs. On the other hand, Convolutional Neural Networks (CNN) show great potential for medical image reconstruction, albeit often with limited interpretability. Here, we present a Learned Proximal Convolutional Neural Network (LP-CNN) for solving the ill-posed QSM dipole inversion problem in an iterative proximal gradient descent fashion. This approach combines the strengths of data-driven restoration priors and the clear interpretability of iterative solvers that can take into account the physical model of dipole convolution. During training, our LP-CNN learns an implicit regularizer via its proximal, enabling the decoupling between the forward operator and the data-driven parameters in the reconstruction algorithm. More importantly, this framework is believed to be the first deep learning QSM approach that can naturally handle an arbitrary number of phase input measurements without the need for any ad-hoc rotation or re-training. We demonstrate that the LP-CNN provides state-of-the-art reconstruction results compared to both traditional and deep learning methods while allowing for more flexibility in the reconstruction process.

eess.IV↗

arXiv2020

Deep Learning in Protein Structural Modeling and Design

Deep learning is catalyzing a scientific revolution fueled by big data, accessible toolkits, and powerful computational resources, impacting many fields including protein structural modeling. Protein structural modeling, such as predicting structure from amino acid sequence and evolutionary information, designing proteins toward desirable functionality, or predicting properties or behavior of a protein, is critical to understand and engineer biological systems at the molecular level. In this review, we summarize the recent advances in applying deep learning techniques to tackle problems in protein structural modeling and design. We dissect the emerging approaches using deep learning techniques for protein structural modeling, and discuss advances and challenges that must be addressed. We argue for the central importance of structure, following the "sequence -> structure -> function" paradigm. This review is directed to help both computational biologists to gain familiarity with the deep learning methods applied in protein modeling, and computer scientists to gain perspective on the biologically meaningful problems that may benefit from deep learning techniques.

q-bio.BM↗