Ehsan Saleh

Ehsan Saleh, Saba Ghaffari, Timothy Bretl et al.

In this paper, we present a policy gradient method that avoids exploratory noise injection and performs policy search over the deterministic landscape. By avoiding noise injection all sources of estimation variance can be eliminated in systems with deterministic dynamics (up to the initial state distribution). Since deterministic policy regularization is impossible using traditional non-metric measures such as the KL divergence, we derive a Wasserstein-based quadratic model for our purposes. We state conditions on the system model under which it is possible to establish a monotonic policy improvement guarantee, propose a surrogate function for policy gradient estimation, and show that it is possible to compute exact advantage estimates if both the state transition model and the policy are deterministic. Finally, we describe two novel robotic control environments -- one with non-local rewards in the frequency domain and the other with a long horizon (8000 time-steps) -- for which our policy gradient method (TDPO) significantly outperforms existing methods (PPO, TRPO, DDPG, and TD3). Our implementation with all the experimental settings is available at https://github.com/ehsansaleh/code_tdpo

Ehsan Saleh, Saba Ghaffari, Timothy Bretl et al.

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for training. As a result, accurate evaluation may be impractical, and we show that naive approximations at replacing these integrals with unbiased estimates lead to biased loss functions and solutions. To overcome this bias, we investigate three types of potential solutions: the deterministic sampling approaches, the double-sampling trick, and the delayed target method. We consider three classes of PDEs for benchmarking; one defining Poisson problems with singular charges and weak solutions of up to 10 dimensions, another involving weak solutions on electro-magnetic fields and a Maxwell equation, and a third one defining a Smoluchowski coagulation problem. Our numerical results confirm the existence of the aforementioned bias in practice and also show that our proposed delayed target approach can lead to accurate solutions with comparable quality to ones estimated with a large sample size integral. Our implementation is open-source and available at https://github.com/ehsansaleh/btspinn.

Saba Ghaffari, Ehsan Saleh, Alexander G. Schwing et al.

Protein design, a grand challenge of the day, involves optimization on a fitness landscape, and leading methods adopt a model-based approach where a model is trained on a training set (protein sequences and fitness) and proposes candidates to explore next. These methods are challenged by sparsity of high-fitness samples in the training set, a problem that has been in the literature. A less recognized but equally important problem stems from the distribution of training samples in the design space: leading methods are not designed for scenarios where the desired optimum is in a region that is not only poorly represented in training data, but also relatively far from the highly represented low-fitness regions. We show that this problem of "separation" in the design space is a significant bottleneck in existing model-based optimization tools and propose a new approach that uses a novel VAE as its search model to overcome the problem. We demonstrate its advantage over prior methods in robustly finding improved samples, regardless of the imbalance and separation between low- and high-fitness samples. Our comprehensive benchmark on real and semi-synthetic protein datasets as well as solution design for physics-informed neural networks, showcases the generality of our approach in discrete and continuous design spaces. Our implementation is available at https://github.com/sabagh1994/PGVAE.

Saba Ghaffari, Ehsan Saleh, David Forsyth et al.

Learning accurate classifiers for novel categories from very few examples, known as few-shot image classification, is a challenging task in statistical machine learning and computer vision. The performance in few-shot classification suffers from the bias in the estimation of classifier parameters; however, an effective underlying bias reduction technique that could alleviate this issue in training few-shot classifiers has been overlooked. In this work, we demonstrate the effectiveness of Firth bias reduction in few-shot classification. Theoretically, Firth bias reduction removes the $O(N^{-1})$ first order term from the small-sample bias of the Maximum Likelihood Estimator. Here we show that the general Firth bias reduction technique simplifies to encouraging uniform class assignment probabilities for multinomial logistic classification, and almost has the same effect in cosine classifiers. We derive an easy-to-implement optimization objective for Firth penalized multinomial logistic and cosine classifiers, which is equivalent to penalizing the cross-entropy loss with a KL-divergence between the uniform label distribution and the predictions. Then, we empirically evaluate that it is consistently effective across the board for few-shot image classification, regardless of (1) the feature representations from different backbones, (2) the number of samples per class, and (3) the number of classes. Finally, we show the robustness of Firth bias reduction, in the case of imbalanced data distribution. Our implementation is available at https://github.com/ehsansaleh/firth_bias_reduction

Ehsan Saleh, Saba Ghaffari, Jeffrey H. Curtis et al.

Aerosol-cloud--radiation interactions remain among the most uncertain components of the Earth's climate system, in partdue to the high dimensionality of aerosol state representations and the difficulty of obtaining complete \textit{in situ} measurements. Addressing these challenges requires methods that distill complex aerosol properties into compact yet physically meaningful forms. Generative autoencoder models provide such a pathway. We present a framework for learning deep variational autoencoder (VAE) models of speciated mass and number concentration distributions, which capture detailed aerosol size-composition characteristics. By compressing hundreds of original dimensions into ten latent variables, the approach enables efficient storage and processing while preserving the fidelity of key diagnostics, including cloud condensation nuclei (CCN) spectra, optical scattering and absorption coefficients, and ice nucleation properties. Results show that CCN spectra are easiest to reconstruct accurately, optical properties are moderately difficult, and ice nucleation properties are the most challenging. To improve performance, we introduce a preprocessing optimization strategy that avoids repeated retraining and yields latent representations resilient to high-magnitude Gaussian noise, boosting accuracy for CCN spectra, optical coefficients, and frozen fraction spectra. Finally, we propose a novel realism metric -- based on the sliced Wasserstein distance between generated samples and a held-out test set -- for optimizing the KL divergence weight in VAEs. Together, these contributions enable compact, robust, and physically meaningful representations of aerosol states for large-scale climate applications.