Author name cluster

Adeel Pervez

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

8 papers

1 author row

ICML Conference 2025 Conference Paper

Mechanistic PDE Networks for Discovery of Governing Equations

Adeel Pervez
Efstratios Gavves
Francesco Locatello

We present Mechanistic PDE Networks – a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in neural network hidden representations. The represented PDEs are then solved and decoded for specific tasks. The learned PDE representations naturally express the spatiotemporal dynamics in data in neural network hidden space, enabling increased modeling power. Solving the PDE representations in a compute and memory-efficient way, however, is a significant challenge. We develop a native, GPU-capable, parallel, sparse and differentiable multigrid solver specialized for linear partial differential equations that acts as a module in Mechanistic PDE Networks. Leveraging the PDE solver we propose a discovery architecture that can discovers nonlinear PDEs in complex settings, while being robust to noise. We validate PDE discovery on a number of PDEs including reaction-diffusion and Navier-Stokes equations.

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ICLR Conference 2025 Conference Paper

Scalable Mechanistic Neural Networks

Jiale Chen 0004
Dingling Yao
Adeel Pervez
Dan Alistarh
Francesco Locatello

We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems. Source code is available at https://github.com/IST-DASLab/ScalableMNN.

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ICML Conference 2024 Conference Paper

Mechanistic Neural Networks for Scientific Machine Learning

Adeel Pervez
Francesco Locatello
Stratis Gavves

This paper presents Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential equations as representations, revealing the underlying dynamics of data and enhancing interpretability and efficiency in data modeling. Central to our approach is a novel Relaxed Linear Programming Solver (NeuRLP) inspired by a technique that reduces solving linear ODEs to solving linear programs. This integrates well with neural networks and surpasses the limitations of traditional ODE solvers enabling scalable GPU parallel processing. Overall, Mechanistic Neural Networks demonstrate their versatility for scientific machine learning applications, adeptly managing tasks from equation discovery to dynamic systems modeling. We prove their comprehensive capabilities in analyzing and interpreting complex scientific data across various applications, showing significant performance against specialized state-of-the-art methods. Source code is available at https: //github. com/alpz/mech-nn.

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ICLR Conference 2023 Conference Paper

Differentiable Mathematical Programming for Object-Centric Representation Learning

Adeel Pervez
Phillip Lippe
Efstratios Gavves

We propose topology-aware feature partitioning into $k$ disjoint partitions for given scene features as a method for object-centric representation learning. To this end, we propose to use minimum $s$-$t$ graph cuts as a partitioning method which is represented as a linear program. The method is topologically aware since it explicitly encodes neighborhood relationships in the image graph. To solve the graph cuts our solution relies on an efficient, scalable, and differentiable quadratic programming approximation. Optimizations specific to cut problems allow us to solve the quadratic programs and compute their gradients significantly more efficiently compared with the general quadratic programming approach. Our results show that our approach is scalable and outperforms existing methods on object discovery tasks with textured scenes and objects.

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ICLR Conference 2023 Conference Paper

Scalable Subset Sampling with Neural Conditional Poisson Networks

Adeel Pervez
Phillip Lippe
Efstratios Gavves

A number of problems in learning can be formulated in terms of the basic primitive of sampling $k$ elements out of a universe of $n$ elements. This subset sampling operation cannot directly be included in differentiable models and approximations are essential. Current approaches take an \emph{order sampling} approach to sampling subsets and depend on differentiable approximations of the Top-$k$ operator for selecting the largest $k$ elements from a set. We present a simple alternative method for sampling subsets based on \emph{conditional Poisson sampling}. Unlike order sampling approaches, the parallel complexity of the proposed method is independent of the subset size which makes the method scalable to large subset sizes. We adapt the procedure to make it efficient and amenable to discrete gradient approximations for use in differentiable models. Furthermore, the method also allows the subset size parameter $k$ to be differentiable. We demonstrate our approach on model explanation, image sub-sampling and stochastic $k$-nearest neighbor tasks outperforming existing methods in accuracy, efficiency and scalability.

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ICLR Conference 2022 Conference Paper

Stability Regularization for Discrete Representation Learning

Adeel Pervez
Efstratios Gavves

We present a method for training neural network models with discrete stochastic variables. The core of the method is \emph{stability regularization}, which is a regularization procedure based on the idea of noise stability developed in Gaussian isoperimetric theory in the analysis of Gaussian functions. Stability regularization is method to make the output of continuous functions of Gaussian random variables close to discrete, that is binary or categorical, without the need for significant manual tuning. The method allows control over the extent to which a Gaussian function's output is close to discrete, thus allowing for continued flow of gradient. The method can be used standalone or in combination with existing continuous relaxation methods. We validate the method in a broad range of experiments using discrete variables including neural relational inference, generative modeling, clustering and conditional computing.

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ICML Conference 2021 Conference Paper

Spectral Smoothing Unveils Phase Transitions in Hierarchical Variational Autoencoders

Adeel Pervez
Efstratios Gavves

Variational autoencoders with deep hierarchies of stochastic layers have been known to suffer from the problem of posterior collapse, where the top layers fall back to the prior and become independent of input. We suggest that the hierarchical VAE objective explicitly includes the variance of the function parameterizing the mean and variance of the latent Gaussian distribution which itself is often a high variance function. Building on this we generalize VAE neural networks by incorporating a smoothing parameter motivated by Gaussian analysis to reduce higher frequency components and consequently the variance in parameterizing functions and show that this can help to solve the problem of posterior collapse. We further show that under such smoothing the VAE loss exhibits a phase transition, where the top layer KL divergence sharply drops to zero at a critical value of the smoothing parameter that is similar for the same model across datasets. We validate the phenomenon across model configurations and datasets.

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ICML Conference 2020 Conference Paper

Low Bias Low Variance Gradient Estimates for Boolean Stochastic Networks

Adeel Pervez
Taco Cohen
Efstratios Gavves

Stochastic neural networks with discrete random variables are an important class of models for their expressiveness and interpretability. Since direct differentiation and backpropagation is not possible, Monte Carlo gradient estimation techniques are a popular alternative. Efficient stochastic gradient estimators, such Straight-Through and Gumbel-Softmax, work well for shallow stochastic models. Their performance, however, suffers with hierarchical, more complex models. We focus on stochastic networks with Boolean latent variables. To analyze such networks, we introduce the framework of harmonic analysis for Boolean functions to derive an analytic formulation for the bias and variance in the Straight-Through estimator. Exploiting these formulations, we propose \emph{FouST}, a low-bias and low-variance gradient estimation algorithm that is just as efficient. Extensive experiments show that FouST performs favorably compared to state-of-the-art biased estimators and is much faster than unbiased ones.

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