R.S. Sreenivas

Mikihisa Yuasa, Huy T. Tran, Ramavarapu S. Sreenivas

Understanding a \textit{reinforcement learning} policy, which guides state-to-action mappings to maximize rewards, necessitates an accompanying explanation for human comprehension. In this paper, we introduce a set of \textit{linear temporal logic} formulae designed to provide explanations for policies, and an algorithm for searching through those formulae for the one that best explains a given policy. Our focus is on explanations that elucidate both the ultimate objectives accomplished by the policy and the prerequisite conditions it upholds throughout its execution. The effectiveness of our proposed approach is illustrated through a simulated game of capture-the-flag and a car-parking environment,

Marius F. R. Juston, Ramavarapu S. Sreenivas, Dustin Nottage et al.

We analyze initialization dynamics for LDLT-based $\mathcal{L}$-Lipschitz layers by deriving the exact marginal output variance when the underlying parameter matrix $W_0\in \mathbb{R}^{m\times n}$ is initialized with IID Gaussian entries $\mathcal{N}(0,σ^2)$. The Wishart distribution, $S=W_0W_0^\top\sim\mathcal{W}_m(n,σ^2 \boldsymbol{I}_m)$, used for computing the output marginal variance is derived in closed form using expectations of zonal polynomials via James' theorem and a Laplace-integral expansion of $(α\boldsymbol{I}_m+S)^{-1}$. We develop an Isserlis/Wick-based combinatorial expansion for $\operatorname{\mathbb{E}}\left[\operatorname{tr}(S^k)\right]$ and provide explicit truncated moments up to $k=10$, which yield accurate series approximations for small-to-moderate $σ^2$. Monte Carlo experiments confirm the theoretical estimates. Furthermore, empirical analysis was performed to quantify that, using current He or Kaiming initialization with scaling $1/\sqrt{n}$, the output variance is $0.41$, whereas the new parameterization with $10/ \sqrt{n}$ for $α=1$ results in an output variance of $0.9$. The findings clarify why deep $\mathcal{L}$-Lipschitz networks suffer rapid information loss at initialization and offer practical prescriptions for choosing initialization hyperparameters to mitigate this effect. However, using the Higgs boson classification dataset, a hyperparameter sweep over optimizers, initialization scale, and depth was conducted to validate the results on real-world data, showing that although the derivation ensures variance preservation, empirical results indicate He initialization still performs better.

Marius F. R. Juston, Ramavarapu S. Sreenivas, Dustin Nottage et al.

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz constant in neural networks has emerged as an essential area of research to enhance adversarial robustness and network certifiability. This paper presents a rigorous approach to the general design of $\mathcal{L}$-Lipschitz deep residual networks using a Linear Matrix Inequality (LMI) framework. Initially, the ResNet architecture was reformulated as a cyclic tridiagonal LMI, and closed-form constraints on network parameters were derived to ensure $\mathcal{L}$-Lipschitz continuity; however, using a new $LDL^\top$ decomposition approach for certifying LMI feasibility, we extend the construction of $\mathcal{L}$-Lipchitz networks to any other nonlinear architecture. Our contributions include a provable parameterization methodology for constructing Lipschitz-constrained residual networks and other hierarchical architectures. Cholesky decomposition is also used for efficient parameterization. These findings enable robust network designs applicable to adversarial robustness, certified training, and control systems. The $LDL^\top$ formulation is shown to be a tight relaxation of the SDP-based network, maintaining full expressiveness and achieving 3\%-13\% accuracy gains over SLL Layers on 121 UCI data sets.

Logan Courtney, Ramavarapu Sreenivas

Many methods for learning from video sequences involve temporally processing 2D CNN features from the individual frames or directly utilizing 3D convolutions within high-performing 2D CNN architectures. The focus typically remains on how to incorporate the temporal processing within an already stable spatial architecture. This work constructs an MNIST-based video dataset with parameters controlling relevant facets of common video-related tasks: classification, ordering, and speed estimation. Models trained on this dataset are shown to differ in key ways depending on the task and their use of 2D convolutions, 3D convolutions, or convolutional LSTMs. An empirical analysis indicates a complex, interdependent relationship between the spatial and temporal dimensions with design choices having a large impact on a network's ability to learn the appropriate spatiotemporal features.

Logan Courtney, Ramavarapu Sreenivas

This paper explores the use of convolution LSTMs to simultaneously learn spatial- and temporal-information in videos. A deep network of convolutional LSTMs allows the model to access the entire range of temporal information at all spatial scales of the data. We describe our experiments involving convolution LSTMs for lipreading that demonstrate the model is capable of selectively choosing which spatiotemporal scales are most relevant for a particular dataset. The proposed deep architecture also holds promise in other applications where spatiotemporal features play a vital role without having to specifically cater the design of the network for the particular spatiotemporal features existent within the problem. For the Lip Reading in the Wild (LRW) dataset, our model slightly outperforms the previous state of the art (83.4% vs. 83.0%) and sets the new state of the art at 85.2% when the model is pretrained on the Lip Reading Sentences (LRS2) dataset.