arXiv subjects

Srinath Mahankali

Publications and source records attributed to Srinath Mahankali.

4 recordsLinked to original sources

arXiv2024

Random Latent Exploration for Deep Reinforcement Learning

We introduce Random Latent Exploration (RLE), a simple yet effective exploration strategy in reinforcement learning (RL). On average, RLE outperforms noise-based methods, which perturb the agent's actions, and bonus-based exploration, which rewards the agent for attempting novel behaviors. The core idea of RLE is to encourage the agent to explore different parts of the environment by pursuing randomly sampled goals in a latent space. RLE is as simple as noise-based methods, as it avoids complex bonus calculations but retains the deep exploration benefits of bonus-based methods. Our experiments show that RLE improves performance on average in both discrete (e.g., Atari) and continuous control tasks (e.g., Isaac Gym), enhancing exploration while remaining a simple and general plug-in for existing RL algorithms. Project website and code: https://srinathm1359.github.io/random-latent-exploration

cs.LG↗

arXiv2023

Randomly Initialized One-Layer Neural Networks Make Data Linearly Separable

Recently, neural networks have demonstrated remarkable capabilities in mapping two arbitrary sets to two linearly separable sets. The prospect of achieving this with randomly initialized neural networks is particularly appealing due to the computational efficiency compared to fully trained networks. This paper contributes by establishing that, given sufficient width, a randomly initialized one-layer neural network can, with high probability, transform two sets into two linearly separable sets without any training. Moreover, we furnish precise bounds on the necessary width of the neural network for this phenomenon to occur. Our initial bound exhibits exponential dependence on the input dimension while maintaining polynomial dependence on all other parameters. In contrast, our second bound is independent of input dimension, effectively surmounting the curse of dimensionality. The main tools used in our proof heavily relies on a fusion of geometric principles and concentration of random matrices.

cs.LG↗

arXiv2023

Norm-dependent convergence and stability of the inverse scattering series for diffuse and scalar waves

This work analyzes the forward and inverse scattering series for scalar waves based on the Helmholtz equation and the diffuse waves from the time-independent diffusion equation, which are important PDEs in various applications. Different from previous works, which study the radius of convergence for the forward and inverse scattering series, the stability, and the approximation error of the series under the $L^p$ norms, we study these quantities under the Sobolev $H^s$ norm, which associates with a general class of $L^2$-based function spaces. The $H^s$ norm has a natural spectral bias based on its definition in the Fourier domain: the case $s<0$ biases towards the lower frequencies, while the case $s>0$ biases towards the higher frequencies. We compare the stability estimates using different $H^s$ norms for both the parameter and data domains and provide a theoretical justification for the frequency weighting techniques in practical inversion procedures. We also provide numerical inversion examples to demonstrate the differences in the inverse scattering radius of convergence under different metric spaces.

math.AP↗

arXiv2021

The convexity of optimal transport-based waveform inversion for certain structured velocity models

Full--waveform inversion (FWI) is a method used to determine properties of the Earth from information on the surface. We use the squared Wasserstein distance (squared $W_2$ distance) as an objective function to invert for the velocity of seismic waves as a function of position in the Earth, and we discuss its convexity with respect to the velocity parameter. In one dimension, we consider constant, piecewise increasing, and linearly increasing velocity models as a function of position, and we show the convexity of the squared $W_2$ distance with respect to the velocity parameter on the interval from zero to the true value of the velocity parameter when the source function is a probability measure. Furthermore, we consider a two--dimensional model where velocity is linearly increasing as a function of depth and prove the convexity of the squared $W_2$ distance in the velocity parameter on large regions containing the true value. We discuss the convexity of the squared $W_2$ distance compared with the convexity of the squared $L^2$ norm, and we discuss the relationship between frequency and convexity of these respective distances. We also discuss multiple approaches to optimal transport for non--probability measures by first converting the wave data into probability measures.

physics.geo-ph↗