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Title: ∇-Prox: Differentiable Proximal Algorithm Modeling for Large-Scale Optimization
Tasks across diverse application domains can be posed as large-scale optimization problems, these include graphics, vision, machine learning, imaging, health, scheduling, planning, and energy system forecasting. Independently of the application domain, proximal algorithms have emerged as a formal optimization method that successfully solves a wide array of existing problems, often exploiting problem-specific structures in the optimization. Although model-based formal optimization provides a principled approach to problem modeling with convergence guarantees, at first glance, this seems to be at odds with black-box deep learning methods. A recent line of work shows that, when combined with learning-based ingredients, model-based optimization methods are effective, interpretable, and allow for generalization to a wide spectrum of applications with little or no extra training data. However, experimenting with such hybrid approaches for different tasks by hand requires domain expertise in both proximal optimization and deep learning, which is often error-prone and time-consuming. Moreover, naively unrolling these iterative methods produces lengthy compute graphs, which when differentiated via autograd techniques results in exploding memory consumption, making batch-based training challenging. In this work, we introduce ∇-Prox, a domain-specific modeling language and compiler for large-scale optimization problems using differentiable proximal algorithms. ∇-Prox allows users to specify optimization objective functions of unknowns concisely at a high level, and intelligently compiles the problem into compute and memory-efficient differentiable solvers. One of the core features of ∇-Prox is its full differentiability, which supports hybrid model- and learning-based solvers integrating proximal optimization with neural network pipelines. Example applications of this methodology include learning-based priors and/or sample-dependent inner-loop optimization schedulers, learned with deep equilibrium learning or deep reinforcement learning. With a few lines of code, we show ∇-Prox can generate performant solvers for a range of image optimization problems, including end-to-end computational optics, image deraining, and compressive magnetic resonance imaging. We also demonstrate ∇-Prox can be used in a completely orthogonal application domain of energy system planning, an essential task in the energy crisis and the clean energy transition, where it outperforms state-of-the-art CVXPY and commercial Gurobi solvers. more »« less
Most modern commodity imaging systems we use directly for photography—or indirectly rely on for downstream applications—employ optical systems of multiple lenses that must balance deviations from perfect optics, manufacturing constraints, tolerances, cost, and footprint. Although optical designs often have complex interactions with downstream image processing or analysis tasks, today’s compound optics are designed in isolation from these interactions. Existing optical design tools aim to minimize optical aberrations, such as deviations from Gauss’ linear model of optics, instead of application-specific losses, precluding joint optimization with hardware image signal processing (ISP) and highly parameterized neural network processing. In this article, we propose an optimization method for compound optics that lifts these limitations. We optimize entire lens systems jointly with hardware and software image processing pipelines, downstream neural network processing, and application-specific end-to-end losses. To this end, we propose a learned, differentiable forward model for compound optics and an alternating proximal optimization method that handles function compositions with highly varying parameter dimensions for optics, hardware ISP, and neural nets. Our method integrates seamlessly atop existing optical design tools, such as Zemax . We can thus assess our method across many camera system designs and end-to-end applications. We validate our approach in an automotive camera optics setting—together with hardware ISP post processing and detection—outperforming classical optics designs for automotive object detection and traffic light state detection. For human viewing tasks, we optimize optics and processing pipelines for dynamic outdoor scenarios and dynamic low-light imaging. We outperform existing compartmentalized design or fine-tuning methods qualitatively and quantitatively, across all domain-specific applications tested.
Terris, Matthieu; Dabbech, Arwa; Tang, Chao; Wiaux, Yves(
, Monthly Notices of the Royal Astronomical Society)
ABSTRACT
We introduce a new class of iterative image reconstruction algorithms for radio interferometry, at the interface of convex optimization and deep learning, inspired by plug-and-play methods. The approach consists in learning a prior image model by training a deep neural network (DNN) as a denoiser, and substituting it for the handcrafted proximal regularization operator of an optimization algorithm. The proposed AIRI (‘AI for Regularization in radio-interferometric Imaging’) framework, for imaging complex intensity structure with diffuse and faint emission from visibility data, inherits the robustness and interpretability of optimization, and the learning power and speed of networks. Our approach relies on three steps. First, we design a low dynamic range training data base from optical intensity images. Secondly, we train a DNN denoiser at a noise level inferred from the signal-to-noise ratio of the data. We use training losses enhanced with a non-expansiveness term ensuring algorithm convergence, and including on-the-fly data base dynamic range enhancement via exponentiation. Thirdly, we plug the learned denoiser into the forward–backward optimization algorithm, resulting in a simple iterative structure alternating a denoising step with a gradient-descent data-fidelity step. We have validated AIRI against clean, optimization algorithms of the SARA family, and a DNN trained to reconstruct the image directly from visibility data. Simulation results show that AIRI is competitive in imaging quality with SARA and its unconstrained forward–backward-based version uSARA, while providing significant acceleration. clean remains faster but offers lower quality. The end-to-end DNN offers further acceleration, but with far lower quality than AIRI.
Multiple-surface segmentation in optical coherence tomography (OCT) images is a challenging problem, further complicated by the frequent presence of weak image boundaries. Recently, many deep learning-based methods have been developed for this task and yield remarkable performance. Unfortunately, due to the scarcity of training data in medical imaging, it is challenging for deep learning networks to learn the global structure of the target surfaces, including surface smoothness. To bridge this gap, this study proposes to seamlessly unify a U-Net for feature learning with a constrained differentiable dynamic programming module to achieve end-to-end learning for retina OCT surface segmentation to explicitly enforce surface smoothness. It effectively utilizes the feedback from the downstream model optimization module to guide feature learning, yielding better enforcement of global structures of the target surfaces. Experiments on Duke AMD (age-related macular degeneration) and JHU MS (multiple sclerosis) OCT data sets for retinal layer segmentation demonstrated that the proposed method was able to achieve subvoxel accuracy on both datasets, with the mean absolute surface distance (MASD) errors of 1.88 ± 1.96μmand 2.75 ± 0.94μm, respectively, over all the segmented surfaces.
Jean-Paul, S.; Elseify, T.; Obeid, I.; Picone, J.(
, IEEE Signal Processing in Medicine and Biology Symposium (SPMB))
Obeid, I.; Selesnik, I.; Picone, J.
(Ed.)
The Neuronix high-performance computing cluster allows us to conduct extensive machine learning experiments on big data [1]. This heterogeneous cluster uses innovative scheduling technology, Slurm [2], that manages a network of CPUs and graphics processing units (GPUs). The GPU farm consists of a variety of processors ranging from low-end consumer grade devices such as the Nvidia GTX 970 to higher-end devices such as the GeForce RTX 2080. These GPUs are essential to our research since they allow extremely compute-intensive deep learning tasks to be executed on massive data resources such as the TUH EEG Corpus [2]. We use TensorFlow [3] as the core machine learning library for our deep learning systems, and routinely employ multiple GPUs to accelerate the training process.
Reproducible results are essential to machine learning research. Reproducibility in this context means the ability to replicate an existing experiment – performance metrics such as error rates should be identical and floating-point calculations should match closely. Three examples of ways we typically expect an experiment to be replicable are: (1) The same job run on the same processor should produce the same results each time it is run. (2) A job run on a CPU and GPU should produce identical results. (3) A job should produce comparable results if the data is presented in a different order. System optimization requires an ability to directly compare error rates for algorithms evaluated under comparable operating conditions. However, it is a difficult task to exactly reproduce the results for large, complex deep learning systems that often require more than a trillion calculations per experiment [5]. This is a fairly well-known issue and one we will explore in this poster.
Researchers must be able to replicate results on a specific data set to establish the integrity of an implementation. They can then use that implementation as a baseline for comparison purposes. A lack of reproducibility makes it very difficult to debug algorithms and validate changes to the system. Equally important, since many results in deep learning research are dependent on the order in which the system is exposed to the data, the specific processors used, and even the order in which those processors are accessed, it becomes a challenging problem to compare two algorithms since each system must be individually optimized for a specific data set or processor. This is extremely time-consuming for algorithm research in which a single run often taxes a computing environment to its limits. Well-known techniques such as cross-validation [5,6] can be used to mitigate these effects, but this is also computationally expensive.
These issues are further compounded by the fact that most deep learning algorithms are susceptible to the way computational noise propagates through the system. GPUs are particularly notorious for this because, in a clustered environment, it becomes more difficult to control which processors are used at various points in time. Another equally frustrating issue is that upgrades to the deep learning package, such as the transition from TensorFlow v1.9 to v1.13, can also result in large fluctuations in error rates when re-running the same experiment. Since TensorFlow is constantly updating functions to support GPU use, maintaining an historical archive of experimental results that can be used to calibrate algorithm research is quite a challenge. This makes it very difficult to optimize the system or select the best configurations.
The overall impact of all of these issues described above is significant as error rates can fluctuate by as much as 25% due to these types of computational issues. Cross-validation is one technique used to mitigate this, but that is expensive since you need to do multiple runs over the data, which further taxes a computing infrastructure already running at max capacity.
GPUs are preferred when training a large network since these systems train at least two orders of magnitude faster than CPUs [7]. Large-scale experiments are simply not feasible without using GPUs. However, there is a tradeoff to gain this performance. Since all our GPUs use the NVIDIA CUDA® Deep Neural Network library (cuDNN) [8], a GPU-accelerated library of primitives for deep neural networks, it adds an element of randomness into the experiment. When a GPU is used to train a network in TensorFlow, it automatically searches for a cuDNN implementation. NVIDIA’s cuDNN implementation provides algorithms that increase the performance and help the model train quicker, but they are non-deterministic algorithms [9,10]. Since our networks have many complex layers, there is no easy way to avoid this randomness. Instead of comparing each epoch, we compare the average performance of the experiment because it gives us a hint of how our model is performing per experiment, and if the changes we make are efficient.
In this poster, we will discuss a variety of issues related to reproducibility and introduce ways we mitigate these effects. For example, TensorFlow uses a random number generator (RNG) which is not seeded by default. TensorFlow determines the initialization point and how certain functions execute using the RNG. The solution for this is seeding all the necessary components before training the model. This forces TensorFlow to use the same initialization point and sets how certain layers work (e.g., dropout layers). However, seeding all the RNGs will not guarantee a controlled experiment. Other variables can affect the outcome of the experiment such as training using GPUs, allowing multi-threading on CPUs, using certain layers, etc.
To mitigate our problems with reproducibility, we first make sure that the data is processed in the same order during training. Therefore, we save the data from the last experiment and to make sure the newer experiment follows the same order. If we allow the data to be shuffled, it can affect the performance due to how the model was exposed to the data. We also specify the float data type to be 32-bit since Python defaults to 64-bit. We try to avoid using 64-bit precision because the numbers produced by a GPU can vary significantly depending on the GPU architecture [11-13]. Controlling precision somewhat reduces differences due to computational noise even though technically it increases the amount of computational noise.
We are currently developing more advanced techniques for preserving the efficiency of our training process while also maintaining the ability to reproduce models. In our poster presentation we will demonstrate these issues using some novel visualization tools, present several examples of the extent to which these issues influence research results on electroencephalography (EEG) and digital pathology experiments and introduce new ways to manage such computational issues.
Shen, Guoyao; Hao, Boran; Li, Mengyu; Farris, Chad W.; Paschalidis, Ioannis Ch.; Anderson, Stephan W.; Zhang, Xin(
, APL Machine Learning)
The application of compressed sensing (CS)-enabled data reconstruction for accelerating magnetic resonance imaging (MRI) remains a challenging problem. This is due to the fact that the information lost in k-space from the acceleration mask makes it difficult to reconstruct an image similar to the quality of a fully sampled image. Multiple deep learning-based structures have been proposed for MRI reconstruction using CS, in both the k-space and image domains, and using unrolled optimization methods. However, the drawback of these structures is that they are not fully utilizing the information from both domains (k-space and image). Herein, we propose a deep learning-based attention hybrid variational network that performs learning in both the k-space and image domains. We evaluate our method on a well-known open-source MRI dataset (652 brain cases and 1172 knee cases) and a clinical MRI dataset of 243 patients diagnosed with strokes from our institution to demonstrate the performance of our network. Our model achieves an overall peak signal-to-noise ratio/structural similarity of 40.92 ± 0.29/0.9577 ± 0.0025 (fourfold) and 37.03 ± 0.25/0.9365 ± 0.0029 (eightfold) for the brain dataset, 31.09 ± 0.25/0.6901 ± 0.0094 (fourfold) and 29.49 ± 0.22/0.6197 ± 0.0106 (eightfold) for the knee dataset, and 36.32 ± 0.16/0.9199 ± 0.0029 (20-fold) and 33.70 ± 0.15/0.8882 ± 0.0035 (30-fold) for the stroke dataset. In addition to quantitative evaluation, we undertook a blinded comparison of image quality across networks performed by a subspecialty trained radiologist. Overall, we demonstrate that our network achieves a superior performance among others under multiple reconstruction tasks.
@article{osti_10438192,
place = {Country unknown/Code not available},
title = {∇-Prox: Differentiable Proximal Algorithm Modeling for Large-Scale Optimization},
url = {https://par.nsf.gov/biblio/10438192},
DOI = {10.1145/3592144},
abstractNote = {Tasks across diverse application domains can be posed as large-scale optimization problems, these include graphics, vision, machine learning, imaging, health, scheduling, planning, and energy system forecasting. Independently of the application domain, proximal algorithms have emerged as a formal optimization method that successfully solves a wide array of existing problems, often exploiting problem-specific structures in the optimization. Although model-based formal optimization provides a principled approach to problem modeling with convergence guarantees, at first glance, this seems to be at odds with black-box deep learning methods. A recent line of work shows that, when combined with learning-based ingredients, model-based optimization methods are effective, interpretable, and allow for generalization to a wide spectrum of applications with little or no extra training data. However, experimenting with such hybrid approaches for different tasks by hand requires domain expertise in both proximal optimization and deep learning, which is often error-prone and time-consuming. Moreover, naively unrolling these iterative methods produces lengthy compute graphs, which when differentiated via autograd techniques results in exploding memory consumption, making batch-based training challenging. In this work, we introduce ∇-Prox, a domain-specific modeling language and compiler for large-scale optimization problems using differentiable proximal algorithms. ∇-Prox allows users to specify optimization objective functions of unknowns concisely at a high level, and intelligently compiles the problem into compute and memory-efficient differentiable solvers. One of the core features of ∇-Prox is its full differentiability, which supports hybrid model- and learning-based solvers integrating proximal optimization with neural network pipelines. Example applications of this methodology include learning-based priors and/or sample-dependent inner-loop optimization schedulers, learned with deep equilibrium learning or deep reinforcement learning. With a few lines of code, we show ∇-Prox can generate performant solvers for a range of image optimization problems, including end-to-end computational optics, image deraining, and compressive magnetic resonance imaging. We also demonstrate ∇-Prox can be used in a completely orthogonal application domain of energy system planning, an essential task in the energy crisis and the clean energy transition, where it outperforms state-of-the-art CVXPY and commercial Gurobi solvers.},
journal = {ACM Transactions on Graphics},
volume = {42},
number = {4},
author = {Lai, Zeqiang and Wei, Kaixuan and Fu, Ying and Härtel, Philipp and Heide, Felix},
}
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