Meraj Hashemizadeh

Meraj Hashemizadeh, Juan Ramirez, Rohan Sukumaran et al. · mila

Model pruning is a popular approach to enable the deployment of large deep learning models on edge devices with restricted computational or storage capacities. Although sparse models achieve performance comparable to that of their dense counterparts at the level of the entire dataset, they exhibit high accuracy drops for some data sub-groups. Existing methods to mitigate this disparate impact induced by pruning (i) rely on surrogate metrics that address the problem indirectly and have limited interpretability; or (ii) scale poorly with the number of protected sub-groups in terms of computational cost. We propose a constrained optimization approach that directly addresses the disparate impact of pruning: our formulation bounds the accuracy change between the dense and sparse models, for each sub-group. This choice of constraints provides an interpretable success criterion to determine if a pruned model achieves acceptable disparity levels. Experimental results demonstrate that our technique scales reliably to problems involving large models and hundreds of protected sub-groups.

Jose Gallego-Posada, Juan Ramirez, Meraj Hashemizadeh et al. · mila

Cooper is an open-source package for solving constrained optimization problems involving deep learning models. Cooper implements several Lagrangian-based first-order update schemes, making it easy to combine constrained optimization algorithms with high-level features of PyTorch such as automatic differentiation, and specialized deep learning architectures and optimizers. Although Cooper is specifically designed for deep learning applications where gradients are estimated based on mini-batches, it is suitable for general non-convex continuous constrained optimization. Cooper's source code is available at https://github.com/cooper-org/cooper.

Juan Ramirez, Ignacio Hounie, Juan Elenter et al. · mila

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance on every individual data point. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.

Juan Ramirez, Meraj Hashemizadeh, Simon Lacoste-Julien

Recent efforts to develop trustworthy AI systems with accountability guarantees have led to widespread use of machine learning formulations incorporating external requirements, or constraints. These requirements are often enforced via penalization--adding fixed-weight terms to the task loss. We argue this approach is fundamentally ill-suited since there may be no penalty coefficient that simultaneously ensures constraint satisfaction and optimal constrained performance, i.e., that truly solves the constrained problem. Moreover, tuning these coefficients requires costly trial-and-error, incurring significant time and computational overhead. We, therefore, advocate for broader adoption of tailored constrained optimization methods--such as the Lagrangian approach, which jointly optimizes the penalization "coefficients" (the Lagrange multipliers) and the model parameters. Such methods (i) truly solve the constrained problem and do so accountably, by clearly defining feasibility and verifying when it is achieved, (ii) eliminate the need for extensive penalty tuning, and (iii) integrate seamlessly with modern deep learning pipelines.

Meraj Hashemizadeh, Michelle Liu, Jacob Miller et al.

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models such as Tucker, tensor train (TT) and tensor ring (TR). However, identifying the best tensor network structure from data for a given task is challenging. In this work, we leverage the TN formalism to develop a generic and efficient adaptive algorithm to jointly learn the structure and the parameters of a TN from data. Our method is based on a simple greedy approach starting from a rank one tensor and successively identifying the most promising tensor network edges for small rank increments. Our algorithm can adaptively identify TN structures with small number of parameters that effectively optimize any differentiable objective function. Experiments on tensor decomposition, tensor completion and model compression tasks demonstrate the effectiveness of the proposed algorithm. In particular, our method outperforms the state-of-the-art evolutionary topology search [Li and Sun, 2020] for tensor decomposition of images (while being orders of magnitude faster) and finds efficient tensor network structures to compress neural networks outperforming popular TT based approaches [Novikov et al., 2015].