A fundamental problem in deep neural networks is toverify or certify that a trained network is robust, i.e. not susceptible to adversarial attacks [11, 29, 39].

We propose a novel perspective on varied-density clustering for high-dimensional data by framing it as a label propagation process in neighborhood graphs that adapt to local density variations. Our method formally connects density-based clustering with graph connectivity, enabling the use of efficient graph propagation techniques developed in network science. To ensure scalability, we introduce a density-aware neighborhood propagation algorithm and leverage advanced random projection methods to construct approximate neighborhood graphs. Our approach significantly reduces computational cost while preserving clustering quality. Empirically, it scales to datasets with millions of points in minutes and achieves competitive accuracy compared to existing baselines.

U-Nets are among the most widely used architectures in computer vision, renowned for their exceptional performance in applications such as image segmentation, denoising, and diffusion modeling. However, a theoretical explanation of the U-Net architecture design has not yet been fully established. This paper introduces a novel interpretation of the U-Net architecture by studying certain generative hierarchical models, which are tree-structured graphical models extensively utilized in both language and image domains. With their encoder-decoder structure, long skip connections, and pooling and up-sampling layers, we demonstrate how U-Nets can naturally implement the belief propagation denoising algorithm in such generative hierarchical models, thereby efficiently approximating the denoising functions. This leads to an efficient sample complexity bound for learning the denoising function using U-Nets within these models. Additionally, we discuss the broader implications of these findings for diffusion models in generative hierarchical models. We also demonstrate that the conventional architecture of convolutional neural networks (ConvNets) is ideally suited for classification tasks within these models. This offers a unified view of the roles of ConvNets and U-Nets, highlighting the versatility of generative hierarchical models in modeling complex data distributions across language and image domains.

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.

Up- propagation is an algorithm for inverting and learning neural network generative models Sensory input is processed by inverting a model that generates patterns from hidden variables using top down connections The inversion process is iterative utilizing a negative feedback loop that depends on an error signal propagated by bottom up connections The error signal is also used to learn the generative model from examples The algorithm is benchmarked against principal component analysis in experiments on images of handwritten digits .

Variational approximations are becoming a widespread tool for Bayesian learning of graphical models. We provide some theoret(cid:173) ical results for the variational updates in a very general family of conjugate-exponential graphical models. We show how the belief propagation and the junction tree algorithms can be used in the inference step of variational Bayesian learning. Applying these re(cid:173) sults to the Bayesian analysis of linear-Gaussian state-space models we obtain a learning procedure that exploits the Kalman smooth(cid:173) ing propagation, while integrating over all model parameters. We demonstrate how this can be used to infer the hidden state dimen(cid:173) sionality of the state-space model in a variety of synthetic problems and one real high-dimensional data set.

Propagators are central to the success of constraint programming, that is contracting functions removing values proven not to be in any solution of a given constraint. The literature contains numerous propagation algorithms, for many different constraints, and common to all these propagation algorithms is the notion of correctness: only values that appear in no solution to the respective constraint may be removed. In this paper half-checking propagators are introduced, for which the only requirements are that identified solutions (by the propagators) are actual solutions (to the corresponding constraints), and that the propagators are contracting. In particular, a half-checking propagator may remove solutions resulting in an incomplete solving process, but with the upside that (good) solutions may be found faster. Overall completeness can be obtained by running half-checking propagators as one component in a portfolio solving process. Half-checking propagators opens up a wider variety of techniques to be used when designing propagation algorithms, compared to what is currently available. A formal model for half-checking propagators is introduced, together with a detailed description of how to support such propagators in a constraint programming system. Three general directions for creating half-checking propagation algorithms are introduced, and used for designing new half-checking propagators for the cost-circuit constraint as examples. The new propagators are implemented in the Gecode system.

Up- propagation is an algorithm for inverting and learning neural network generative models Sensory input is processed by inverting a model that generates patterns from hidden variables using top down connections The inversion process is iterative utilizing a negative feedback loop that depends on an error signal propagated by bottom up connections The error signal is also used to learn the generative model from examples The algorithm is benchmarked against principal component analysis in experiments on images of handwritten digits . Papers published at the Neural Information Processing Systems Conference.

In many real-world machine learning problems, feature values are not readily available. To make predictions, some of the missing features have to be acquired, which can incur a cost in money, computational time, or human time, depending on the problem domain. This leads us to the problem of choosing which features to use at the prediction time. The chosen features should increase the prediction accuracy for a low cost, but determining which features will do that is challenging. The choice should take into account the previously acquired feature values as well as the feature costs. This paper proposes a novel approach to address this problem. The proposed approach chooses the most useful features adaptively based on how relevant they are for the prediction task as well as what the corresponding feature costs are. Our approach uses a generic neural network architecture, which is suitable for a wide range of problems. We evaluate our approach on three cost-sensitive datasets, including Yahoo! Learning to Rank Competition dataset as well as two health datasets. We show that our approach achieves high accuracy with a lower cost than the current state-of-the-art approaches.

Many common events in our daily life affect us in positive and negative ways. For example, going on vacation is typically an enjoyable event, while being rushed to the hospital is an undesirable event. In narrative stories and personal conversations, recognizing that some events have a strong affective polarity is essential to understand the discourse and the emotional states of the affected people. However, current NLP systems mainly depend on sentiment analysis tools, which fail to recognize many events that are implicitly affective based on human knowledge about the event itself and cultural norms. Our goal is to automatically acquire knowledge of stereotypically positive and negative events from personal blogs. Our research creates an event context graph from a large collection of blog posts and uses a sentiment classifier and semi-supervised label propagation algorithm to discover affective events. We explore several graph configurations that propagate affective polarity across edges using local context, discourse proximity, and event-event co-occurrence. We then harvest highly affective events from the graph and evaluate the agreement of the polarities with human judgements.