In this paper,wegeneralize thebound propagation procedure toallowtheaddition of arbitrary cutting plane constraints, including those involving relaxed integer variables that do not appear in existing bound propagation formulations.

Bound propagation methods, when combined with branch and bound, are among the most effective methods to formally verify properties of deep neural networks such as correctness, robustness, and safety. However, existing works cannot handle the general form of cutting plane constraints widely accepted in traditional solvers, which are crucial for strengthening verifiers with tightened convex relaxations. In this paper, we generalize the bound propagation procedure to allow the addition of arbitrary cutting plane constraints, including those involving relaxed integer variables that do not appear in existing bound propagation formulations. Our generalized bound propagation method, GCP-CROWN, opens up the opportunity to apply general cutting plane methods for neural network verification while benefiting from the efficiency and GPU acceleration of bound propagation methods. As a case study, we investigate the use of cutting planes generated by off-the-shelf mixed integer programming (MIP) solver.

Bound propagation methods, when combined with branch and bound, are among the most effective methods to formally verify properties of deep neural networks such as correctness, robustness, and safety. However, existing works cannot handle the general form of cutting plane constraints widely accepted in traditional solvers, which are crucial for strengthening verifiers with tightened convex relaxations. In this paper, we generalize the bound propagation procedure to allow the addition of arbitrary cutting plane constraints, including those involving relaxed integer variables that do not appear in existing bound propagation formulations. Our generalized bound propagation method, GCP-CROWN, opens up the opportunity to apply general cutting plane methods for neural network verification while benefiting from the efficiency and GPU acceleration of bound propagation methods. As a case study, we investigate the use of cutting planes generated by off-the-shelf mixed integer programming (MIP) solver.

Prompting is a flexible and adaptable way of providing instructions to a Large Language Model (LLM). Contextual prompts include context in the form of a document or dialogue along with the natural language instructions to the LLM, often constraining the LLM to restrict facts to that of the given context while complying with the instructions. Masking the context, it acts as template for prompts. In this paper, we present an iterative method to generate better templates using an LLM from an existing set of prompt templates without revealing the context to the LLM. Multiple methods of optimising prompts using the LLM itself are explored to check the effect of few shot sampling methods on iterative propagation while maintaining linguistic styles and syntax on optimisation of prompt templates, yielding a 103.87% improvement using the best performing method. Comparison of the results of multiple contextual tasks demonstrate the ability of LLMs to maintain syntax while learning to replicate linguistic styles. Additionally, the effect on the output with different methods of prompt template generation is shown.

The increasing prevalence of large-scale graphs poses a significant challenge for graph neural network training, attributed to their substantial computational requirements. In response, graph condensation (GC) emerges as a promising datacentric solution aiming to substitute the large graph with a small yet informative condensed graph to facilitate data-efficient GNN training. However, existing GC methods suffer from intricate optimization processes, necessitating excessive computing resources and training time. In this paper, we revisit existing GC optimization strategies and identify two pervasive issues therein: (1) various GC optimization strategies converge to class-level node feature matching between the original and condensed graphs, making the optimization target coarse-grained despite the complex computations; (2) to bridge the original and condensed graphs, existing GC methods rely on a Siamese graph network architecture that requires time-consuming bi-level optimization with iterative gradient computations. To overcome these issues, we propose an efficient, training-free GC framework termed Class-partitioned Graph Condensation (CGC), which refines the node feature matching from the class-to-class paradigm into a novel class-to-node paradigm. Remarkably, this refinement also simplifies the GC optimization as a class partition problem, which can be efficiently solved by any clustering methods. Moreover, CGC incorporates a pre-defined graph structure to enable a closed-form solution for condensed node features, eliminating the need for back-and-forth gradient descent in existing GC approaches without sacrificing accuracy. Extensive experiments demonstrate that CGC achieves state-of-the-art performance with a more efficient condensation process. For instance, compared with the seminal GC method (i.e., GCond), CGC condenses the largest Reddit graph within 10 seconds, achieving a 2,680 speedup and a 1.4% accuracy increase.

Due to the popularity of Graph Neural Networks (GNNs), various GNN-based methods have been designed to reason on knowledge graphs (KGs). An important design component of GNN-based KG reasoning methods is called the propagation path, which contains a set of involved entities in each propagation step. Existing methods use hand-designed propagation paths, ignoring the correlation between the entities and the query relation. In addition, the number of involved entities will explosively grow at larger propagation steps. In this work, we are motivated to learn an adaptive propagation path in order to filter out irrelevant entities while preserving promising targets. First, we design an incremental sampling mechanism where the nearby targets and layer-wise connections can be preserved with linear complexity. Second, we design a learning-based sampling distribution to identify the semantically related entities. Extensive experiments show that our method is powerful, efficient, and semantic-aware. The code is available at https://github.com/LARS-research/AdaProp.

Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the approximation error. In this paper, we develop a new approach for over-approximating the reachable sets of neural network dynamical systems using adaptive template polytopes. We use the singular value decomposition of linear layers along with the shape of the activation functions to adapt the geometry of the polytopes at each time step to the geometry of the true reachable sets. We then propose a branch-and-bound method to compute accurate over-approximations of the reachable sets by the inferred templates. We illustrate the utility of the proposed approach in the reachability analysis of linear systems driven by neural network controllers.

We present an end-to-end binaural audio rendering approach (Listen2Scene) for virtual reality (VR) and augmented reality (AR) applications. We propose a novel neural-network-based binaural sound propagation method to generate acoustic effects for 3D models of real environments. Any clean audio or dry audio can be convolved with the generated acoustic effects to render audio corresponding to the real environment. We propose a graph neural network that uses both the material and the topology information of the 3D scenes and generates a scene latent vector. Moreover, we use a conditional generative adversarial network (CGAN) to generate acoustic effects from the scene latent vector. Our network is able to handle holes or other artifacts in the reconstructed 3D mesh model. We present an efficient cost function to the generator network to incorporate spatial audio effects. Given the source and the listener position, our learning-based binaural sound propagation approach can generate an acoustic effect in 0.1 milliseconds on an NVIDIA GeForce RTX 2080 Ti GPU and can easily handle multiple sources. We have evaluated the accuracy of our approach with binaural acoustic effects generated using an interactive geometric sound propagation algorithm and captured real acoustic effects. We also performed a perceptual evaluation and observed that the audio rendered by our approach is more plausible as compared to audio rendered using prior learning-based sound propagation algorithms.

This paper develops a new nonlinear filter, called Moment-based Kalman Filter (MKF), using the exact moment propagation method. Existing state estimation methods use linearization techniques or sampling points to compute approximate values of moments. However, moment propagation of probability distributions of random variables through nonlinear process and measurement models play a key role in the development of state estimation and directly affects their performance. The proposed moment propagation procedure can compute exact moments for non-Gaussian as well as non-independent Gaussian random variables. Thus, MKF can propagate exact moments of uncertain state variables up to any desired order. MKF is derivative-free and does not require tuning parameters. Moreover, MKF has the same computation time complexity as the extended or unscented Kalman filters, i.e., EKF and UKF. The experimental evaluations show that MKF is the preferred filter in comparison to EKF and UKF and outperforms both filters in non-Gaussian noise regimes.