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Ramin Hasani

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9 papers

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NeurIPS Conference 2023 Conference Paper

Gigastep - One Billion Steps per Second Multi-agent Reinforcement Learning

Mathias Lechner
lianhao yin
Tim Seyde
Tsun-Hsuan Johnson Wang
Wei Xiao
Ramin Hasani
Joshua Rountree
Daniela Rus

Multi-agent reinforcement learning (MARL) research is faced with a trade-off: it either uses complex environments requiring large compute resources, which makes it inaccessible to researchers with limited resources, or relies on simpler dynamics for faster execution, which makes the transferability of the results to more realistic tasks challenging. Motivated by these challenges, we present Gigastep, a fully vectorizable, MARL environment implemented in JAX, capable of executing up to one billion environment steps per second on consumer-grade hardware. Its design allows for comprehensive MARL experimentation, including a complex, high-dimensional space defined by 3D dynamics, stochasticity, and partial observations. Gigastep supports both collaborative and adversarial tasks, continuous and discrete action spaces, and provides RGB image and feature vector observations, allowing the evaluation of a wide range of MARL algorithms. We validate Gigastep's usability through an extensive set of experiments, underscoring its role in widening participation and promoting inclusivity in the MARL research community.

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NeurIPS Conference 2023 Conference Paper

On the Size and Approximation Error of Distilled Datasets

Alaa Maalouf
Murad Tukan
Noel Loo
Ramin Hasani
Mathias Lechner
Daniela Rus

Dataset Distillation is the task of synthesizing small datasets from large ones while still retaining comparable predictive accuracy to the original uncompressed dataset. Despite significant empirical progress in recent years, there is little understanding of the theoretical limitations/guarantees of dataset distillation, specifically, what excess risk is achieved by distillation compared to the original dataset, and how large are distilled datasets? In this work, we take a theoretical view on kernel ridge regression (KRR) based methods of dataset distillation such as Kernel Inducing Points. By transforming ridge regression in random Fourier features (RFF) space, we provide the first proof of the existence of small (size) distilled datasets and their corresponding excess risk for shift-invariant kernels. We prove that a small set of instances exists in the original input space such that its solution in the RFF space coincides with the solution of the original data. We further show that a KRR solution can be generated using this distilled set of instances which gives an approximation towards the KRR solution optimized on the full input data. The size of this set is linear in the dimension of the RFF space of the input set or alternatively near linear in the number of effective degrees of freedom, which is a function of the kernel, number of data points, and the regularization parameter $\lambda$. The error bound of this distilled set is also a function of $\lambda$. We verify our bounds analytically and empirically.

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NeurIPS Conference 2022 Conference Paper

Efficient Dataset Distillation using Random Feature Approximation

Noel Loo
Ramin Hasani
Alexander Amini
Daniela Rus

Dataset distillation compresses large datasets into smaller synthetic coresets which retain performance with the aim of reducing the storage and computational burden of processing the entire dataset. Today's best performing algorithm, \textit{Kernel Inducing Points} (KIP), which makes use of the correspondence between infinite-width neural networks and kernel-ridge regression, is prohibitively slow due to the exact computation of the neural tangent kernel matrix, scaling $O(|S|^2)$, with $|S|$ being the coreset size. To improve this, we propose a novel algorithm that uses a random feature approximation (RFA) of the Neural Network Gaussian Process (NNGP) kernel which reduces the kernel matrix computation to $O(|S|)$. Our algorithm provides at least a 100-fold speedup over KIP and can run on a single GPU. Our new method, termed an RFA Distillation (RFAD), performs competitively with KIP and other dataset condensation algorithms in accuracy over a range of large-scale datasets, both in kernel regression and finite-width network training. We demonstrate the effectiveness of our approach on tasks involving model interpretability and privacy preservation.

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NeurIPS Conference 2022 Conference Paper

Evolution of Neural Tangent Kernels under Benign and Adversarial Training

Noel Loo
Ramin Hasani
Alexander Amini
Daniela Rus

Two key challenges facing modern deep learning is mitigating deep networks vulnerability to adversarial attacks, and understanding deep learning's generalization capabilities. Towards the first issue, many defense strategies have been developed, with the most common being Adversarial Training (AT). Towards the second challenge, one of the dominant theories that has emerged is the Neural Tangent Kernel (NTK) -- a characterization of neural network behavior in the infinite-width limit. In this limit, the kernel is frozen and the underlying feature map is fixed. In finite-widths however, there is evidence that feature learning happens at the earlier stages of the training (kernel learning) before a second phase where the kernel remains fixed (lazy training). While prior work has aimed at studying adversarial vulnerability through the lens of the frozen infinite-width NTK, there is no work which studies adversarial robustness of NTK during training. In this work, we perform an empirical study of the evolution of the NTK under standard and adversarial training, aiming to disambiguate the effect of adversarial training on kernel learning and lazy training. We find under adversarial training, the NTK rapidly converges to a different kernel (and feature map) than standard training. This new kernel provides adversarial robustness, even when non-robust training is performed on top of it. Furthermore, we find that adversarial training on top of a fixed kernel can yield a classifier with $76. 1\%$ robust accuracy under PGD attacks with $\varepsilon = 4/255$ on CIFAR-10.

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AAAI Conference 2022 Conference Paper

GoTube: Scalable Statistical Verification of Continuous-Depth Models

Sophie A. Gruenbacher
Mathias Lechner
Ramin Hasani
Daniela Rus
Thomas A. Henzinger
Scott A. Smolka
Radu Grosu

We introduce a new statistical verification algorithm that formally quantifies the behavioral robustness of any timecontinuous process formulated as a continuous-depth model. Our algorithm solves a set of global optimization (Go) problems over a given time horizon to construct a tight enclosure (Tube) of the set of all process executions starting from a ball of initial states. We call our algorithm GoTube. Through its construction, GoTube ensures that the bounding tube is conservative up to a desired probability and up to a desired tightness. GoTube is implemented in JAX and optimized to scale to complex continuous-depth neural network models. Compared to advanced reachability analysis tools for timecontinuous neural networks, GoTube does not accumulate overapproximation errors between time steps and avoids the infamous wrapping effect inherent in symbolic techniques. We show that GoTube substantially outperforms state-of-theart verification tools in terms of the size of the initial ball, speed, time-horizon, task completion, and scalability on a large set of experiments. GoTube is stable and sets the stateof-the-art in terms of its ability to scale to time horizons well beyond what has been previously possible.

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NeurIPS Conference 2021 Conference Paper

Causal Navigation by Continuous-time Neural Networks

Charles Vorbach
Ramin Hasani
Alexander Amini
Mathias Lechner
Daniela Rus

Imitation learning enables high-fidelity, vision-based learning of policies within rich, photorealistic environments. However, such techniques often rely on traditional discrete-time neural models and face difficulties in generalizing to domain shifts by failing to account for the causal relationships between the agent and the environment. In this paper, we propose a theoretical and experimental framework for learning causal representations using continuous-time neural networks, specifically over their discrete-time counterparts. We evaluate our method in the context of visual-control learning of drones over a series of complex tasks, ranging from short- and long-term navigation, to chasing static and dynamic objects through photorealistic environments. Our results demonstrate that causal continuous-time deep models can perform robust navigation tasks, where advanced recurrent models fail. These models learn complex causal control representations directly from raw visual inputs and scale to solve a variety of tasks using imitation learning.

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AAAI Conference 2021 Conference Paper

Liquid Time-constant Networks

Ramin Hasani
Mathias Lechner
Alexander Amini
Daniela Rus
Radu Grosu

We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system’s dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i. e. , liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics, and compute their expressive power by the trajectory length measure in a latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs.

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AAAI Conference 2021 Conference Paper

On the Verification of Neural ODEs with Stochastic Guarantees

Sophie Grunbacher
Ramin Hasani
Mathias Lechner
Jacek Cyranka
Scott A. Smolka
Radu Grosu

We show that Neural ODEs, an emerging class of timecontinuous neural networks, can be verified by solving a set of global-optimization problems. For this purpose, we introduce Stochastic Lagrangian Reachability (SLR), an abstraction-based technique for constructing a tight Reachtube (an over-approximation of the set of reachable states over a given time-horizon), and provide stochastic guarantees in the form of confidence intervals for the Reachtube bounds. SLR inherently avoids the infamous wrapping effect (accumulation of over-approximation errors) by performing local optimization steps to expand safe regions instead of repeatedly forward-propagating them as is done by deterministic reachability methods. To enable fast local optimizations, we introduce a novel forward-mode adjoint sensitivity method to compute gradients without the need for backpropagation. Finally, we establish asymptotic and non-asymptotic convergence rates for SLR.

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NeurIPS Conference 2021 Conference Paper

Sparse Flows: Pruning Continuous-depth Models

Lucas Liebenwein
Ramin Hasani
Alexander Amini
Daniela Rus

Continuous deep learning architectures enable learning of flexible probabilistic models for predictive modeling as neural ordinary differential equations (ODEs), and for generative modeling as continuous normalizing flows. In this work, we design a framework to decipher the internal dynamics of these continuous depth models by pruning their network architectures. Our empirical results suggest that pruning improves generalization for neural ODEs in generative modeling. We empirically show that the improvement is because pruning helps avoid mode-collapse and flatten the loss surface. Moreover, pruning finds efficient neural ODE representations with up to 98% less parameters compared to the original network, without loss of accuracy. We hope our results will invigorate further research into the performance-size trade-offs of modern continuous-depth models.

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