However, for many applications this formulation is insufficient.

Neural networks are emerging as a tool for scalable data-driven simulation of high-dimensional dynamical systems, especially in settings where numerical methods are infeasible or computationally expensive. Notably, it has been shown that incorporating domain symmetries in deterministic neural simulators can substantially improve their accuracy, sample efficiency, and parameter efficiency. However, to incorporate symmetries in probabilistic neural simulators that can simulate stochastic phenomena, we need a model that produces equivariant distributions over trajectories, rather than equivariant function approximations. In this paper, we propose Equivariant Probabilistic Neural Simulation (EPNS), a framework for autoregressive probabilistic modeling of equivariant distributions over system evolutions. We use EPNS to design models for a stochastic n-body system and stochastic cellular dynamics. Our results show that EPNS considerably outperforms existing neural network-based methods for probabilistic simulation. More specifically, we demonstrate that incorporating equivariance in EPNS improves simulation quality, data efficiency, rollout stability, and uncertainty quantification. We conclude that EPNS is a promising method for efficient and effective data-driven probabilistic simulation in a diverse range of domains.

However, for many applications this formulation is insufficient.

Accurate quantification of both aleatoric and epistemic uncertainties is essential when deploying Graph Neural Networks (GNNs) in high-stakes applications such as drug discovery and financial fraud detection, where reliable predictions are critical. Although Evidential Deep Learning (EDL) efficiently quantifies uncertainty using a Dirichlet distribution over predictive probabilities, existing EDL-based GNN (EGNN) models require modifications to the network architecture and retraining, failing to take advantage of pre-trained models. We propose a plug-and-play framework for uncertainty quantification in GNNs that works with pre-trained models without the need for retraining. Our Evidential Probing Network (EPN) uses a lightweight Multi-Layer-Perceptron (MLP) head to extract evidence from learned representations, allowing efficient integration with various GNN architectures. We further introduce evidence-based regularization techniques, referred to as EPN-reg, to enhance the estimation of epistemic uncertainty with theoretical justifications. Extensive experiments demonstrate that the proposed EPN-reg achieves state-of-the-art performance in accurate and efficient uncertainty quantification, making it suitable for real-world deployment.

Neural networks are emerging as a tool for scalable data-driven simulation of high-dimensional dynamical systems, especially in settings where numerical methods are infeasible or computationally expensive. Notably, it has been shown that incorporating domain symmetries in deterministic neural simulators can substantially improve their accuracy, sample efficiency, and parameter efficiency. However, to incorporate symmetries in probabilistic neural simulators that can simulate stochastic phenomena, we need a model that produces equivariant distributions over trajectories, rather than equivariant function approximations. In this paper, we propose Equivariant Probabilistic Neural Simulation (EPNS), a framework for autoregressive probabilistic modeling of equivariant distributions over system evolutions. We use EPNS to design models for a stochastic n-body system and stochastic cellular dynamics.

We aim at capturing high-order statistics of feature vectors formed by a neural network, and propose end-to-end second- and higher-order pooling to form a tensor descriptor. Tensor descriptors require a robust similarity measure due to low numbers of aggregated vectors and the burstiness phenomenon, when a given feature appears more/less frequently than statistically expected. The Heat Diffusion Process (HDP) on a graph Laplacian is closely related to the Eigenvalue Power Normalization (EPN) of the covariance/autocorrelation matrix, whose inverse forms a loopy graph Laplacian. We show that the HDP and the EPN play the same role, i.e., to boost or dampen the magnitude of the eigenspectrum thus preventing the burstiness. We equip higher-order tensors with EPN which acts as a spectral detector of higher-order occurrences to prevent burstiness. We also prove that for a tensor of order r built from d dimensional feature descriptors, such a detector gives the likelihood if at least one higher-order occurrence is 'projected' into one of binom(d,r) subspaces represented by the tensor; thus forming a tensor power normalization metric endowed with binom(d,r) such 'detectors'. For experimental contributions, we apply several second- and higher-order pooling variants to action recognition, provide previously not presented comparisons of such pooling variants, and show state-of-the-art results on HMDB-51, YUP++ and MPII Cooking Activities.

Neural networks are emerging as a tool for scalable data-driven simulation of high-dimensional dynamical systems, especially in settings where numerical methods are infeasible or computationally expensive. Notably, it has been shown that incorporating domain symmetries in deterministic neural simulators can substantially improve their accuracy, sample efficiency, and parameter efficiency. However, to incorporate symmetries in probabilistic neural simulators that can simulate stochastic phenomena, we need a model that produces equivariant distributions over trajectories, rather than equivariant function approximations. In this paper, we propose Equivariant Probabilistic Neural Simulation (EPNS), a framework for autoregressive probabilistic modeling of equivariant distributions over system evolutions. We use EPNS to design models for a stochastic n-body system and stochastic cellular dynamics. Our results show that EPNS considerably outperforms existing neural network-based methods for probabilistic simulation. More specifically, we demonstrate that incorporating equivariance in EPNS improves simulation quality, data efficiency, rollout stability, and uncertainty quantification. We conclude that EPNS is a promising method for efficient and effective data-driven probabilistic simulation in a diverse range of domains.

Today, deep learning is increasingly applied in security-critical situations such as autonomous driving and medical diagnosis. Despite its success, the behavior and robustness of deep networks are not fully understood yet, posing a significant risk. In particular, researchers recently found that neural networks are overly confident in their predictions, even on data they have never seen before. To tackle this issue, one can differentiate two approaches in the literature. One accounts for uncertainty in the predictions, while the second estimates the underlying density of the training data to decide whether a given input is close to the training data, and thus the network is able to perform as expected.In this thesis, we investigate the capabilities of EBMs at the task of fitting the training data distribution to perform detection of out-of-distribution (OOD) inputs. We find that on most datasets, EBMs do not inherently outperform other density estimators at detecting OOD data despite their flexibility. Thus, we additionally investigate the effects of supervision, dimensionality reduction, and architectural modifications on the performance of EBMs. Further, we propose Energy-Prior Network (EPN) which enables estimation of various uncertainties within an EBM for classification, bridging the gap between two approaches for tackling the OOD detection problem. We identify a connection between the concentration parameters of the Dirichlet distribution and the joint energy in an EBM. Additionally, this allows optimization without a held-out OOD dataset, which might not be available or costly to collect in some applications. Finally, we empirically demonstrate that Energy-Prior Network (EPN) is able to detect OOD inputs, datasets shifts, and adversarial examples. Theoretically, EPN offers favorable properties for the asymptotic case when inputs are far from the training data.

Carlos Gaitan, the CEO and Co-founder of Benchmark Labs a leading provider of AI & IoT-driven weather forecasting solutions for the agriculture, energy, and insurance sectors joins Enterprise Radio. Dr. Gaitan is the Co-founder and CEO of Benchmark Labs. He did his doctoral studies at the University of British Columbia (Vancouver, Canada) working with William Hsieh in machine learning applications in the environmental sciences. He also holds a Bachelor degree in Civil Engineering and a Master degree in Hydrosystems from the Pontificia Universidad Javeriana (Bogota, Colombia). He is an elected member of the American Meteorological Society's (AMS) Artificial Intelligence Committee.

Babak Hodjat was the Vice President of and a specialist in the field of artificial intelligence and machine learning joins Enterprise Radio. Hodjat is the author of the book "The Konar and the Apple". Babak Hodjat is Vice President of Evolutionary AI at Cognizant, and former co-founder and CEO of Sentient Technologies. He is responsible for the core technology behind the world's largest distributed artificial intelligence system. Babak was also the founder of the world's first AI-driven hedge fund, Sentient Investment Management.