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In the past, the field of drum source separation faced significant challenges due to limited data availability, hindering the adoption of cutting-edge deep learning methods that have found success in other related audio applications. In this manuscript, we introduce StemGMD, a large-scale audio dataset of isolated single-instrument drum stems. Each audio clip is synthesized from MIDI recordings of expressive drums performances using ten real-sounding acoustic drum kits. Totaling 1224 hours, StemGMD is the largest audio dataset of drums to date and the first to comprise isolated audio clips for every instrument in a canonical nine-piece drum kit. We leverage StemGMD to develop LarsNet, a novel deep drum source separation model. Through a bank of dedicated U-Nets, LarsNet can separate five stems from a stereo drum mixture faster than real-time and is shown to significantly outperform state-of-the-art nonnegative spectro-temporal factorization methods.

Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern, especially for short block lengths. While neural decoders have recently demonstrated their advantage over classical decoding techniques, the neural design of the codes remains a challenge. In this work, we propose for the first time a unified encoder-decoder training of binary linear block codes. To this end, we adapt the coding setting to support efficient and differentiable training of the code for end-to-end optimization over the order two Galois field. We also propose a novel Transformer model in which the self-attention masking is performed in a differentiable fashion for the efficient backpropagation of the code gradient. Our results show that (i) the proposed decoder outperforms existing neural decoding on conventional codes, (ii) the suggested framework generates codes that outperform the {analogous} conventional codes, and (iii) the codes we developed not only excel with our decoder but also show enhanced performance with traditional decoding techniques.

In the field of computer vision, the numerical encoding of 3D surfaces is crucial. It is classical to represent surfaces with their Signed Distance Functions (SDFs) or Unsigned Distance Functions (UDFs). For tasks like representation learning, surface classification, or surface reconstruction, this function can be learned by a neural network, called Neural Distance Function. This network, and in particular its weights, may serve as a parametric and implicit representation for the surface. The network must represent the surface as accurately as possible. In this paper, we propose a method for learning UDFs that improves the fidelity of the obtained Neural UDF to the original 3D surface. The key idea of our method is to concentrate the learning effort of the Neural UDF on surface edges. More precisely, we show that sampling more training points around surface edges allows better local accuracy of the trained Neural UDF, and thus improves the global expressiveness of the Neural UDF in terms of Hausdorff distance. To detect surface edges, we propose a new statistical method based on the calculation of a $p$-value at each point on the surface. Our method is shown to detect surface edges more accurately than a commonly used local geometric descriptor.

Placement of electromagnetic signal emitting devices, such as light sources, has important usage in for signal coverage tasks. Automatic placement of these devices is challenging because of the complex interaction of the signal and environment due to reflection, refraction and scattering. In this work, we iteratively improve the placement of these devices by interleaving device placement and sensing actions, correcting errors in the model of the signal propagation. To this end, we propose a novel factor-graph based belief model which combines the measurements taken by the robot and an analytical light propagation model. This model allows accurately modelling the uncertainty of the light propagation with respect to the obstacles, which greatly improves the informative path planning routine. Additionally, we propose a method for determining when to re-plan the emitter placements to balance a trade-off between information about a specific configuration and frequent updating of the configuration. This method incorporates the uncertainty from belief model to adaptively determine when re-configuration is needed. We find that our system has a 9.8% median error reduction compared to a baseline system in simulations in the most difficult environment. We also run on-robot tests and determine that our system performs favorably compared to the baseline.

In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. However, timing constraints are important in many applications like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time temporal equilibrium logic, in which temporal operators are constrained by intervals over natural numbers. The resulting Metric Equilibrium Logic provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. To this end, we define a translation of metric formulas into monadic first-order formulas and give a correspondence between their models in Metric Equilibrium Logic and Monadic Quantified Equilibrium Logic, respectively. Interestingly, our translation provides a blue print for implementation in terms of ASP modulo difference constraints.

The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.

Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.

In many important graph data processing applications the acquired information includes both node features and observations of the graph topology. Graph neural networks (GNNs) are designed to exploit both sources of evidence but they do not optimally trade-off their utility and integrate them in a manner that is also universal. Here, universality refers to independence on homophily or heterophily graph assumptions. We address these issues by introducing a new Generalized PageRank (GPR) GNN architecture that adaptively learns the GPR weights so as to jointly optimize node feature and topological information extraction, regardless of the extent to which the node labels are homophilic or heterophilic. Learned GPR weights automatically adjust to the node label pattern, irrelevant on the type of initialization, and thereby guarantee excellent learning performance for label patterns that are usually hard to handle. Furthermore, they allow one to avoid feature over-smoothing, a process which renders feature information nondiscriminative, without requiring the network to be shallow. Our accompanying theoretical analysis of the GPR-GNN method is facilitated by novel synthetic benchmark datasets generated by the so-called contextual stochastic block model. We also compare the performance of our GNN architecture with that of several state-of-the-art GNNs on the problem of node-classification, using well-known benchmark homophilic and heterophilic datasets. The results demonstrate that GPR-GNN offers significant performance improvement compared to existing techniques on both synthetic and benchmark data.

Graphs, which describe pairwise relations between objects, are essential representations of many real-world data such as social networks. In recent years, graph neural networks, which extend the neural network models to graph data, have attracted increasing attention. Graph neural networks have been applied to advance many different graph related tasks such as reasoning dynamics of the physical system, graph classification, and node classification. Most of the existing graph neural network models have been designed for static graphs, while many real-world graphs are inherently dynamic. For example, social networks are naturally evolving as new users joining and new relations being created. Current graph neural network models cannot utilize the dynamic information in dynamic graphs. However, the dynamic information has been proven to enhance the performance of many graph analytical tasks such as community detection and link prediction. Hence, it is necessary to design dedicated graph neural networks for dynamic graphs. In this paper, we propose DGNN, a new {\bf D}ynamic {\bf G}raph {\bf N}eural {\bf N}etwork model, which can model the dynamic information as the graph evolving. In particular, the proposed framework can keep updating node information by capturing the sequential information of edges, the time intervals between edges and information propagation coherently. Experimental results on various dynamic graphs demonstrate the effectiveness of the proposed framework.

This paper is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. We assume no math knowledge beyond what you learned in calculus 1, and provide links to help you refresh the necessary math where needed. Note that you do not need to understand this material before you start learning to train and use deep learning in practice; rather, this material is for those who are already familiar with the basics of neural networks, and wish to deepen their understanding of the underlying math. Don't worry if you get stuck at some point along the way---just go back and reread the previous section, and try writing down and working through some examples. And if you're still stuck, we're happy to answer your questions in the Theory category at forums.fast.ai. Note: There is a reference section at the end of the paper summarizing all the key matrix calculus rules and terminology discussed here. See related articles at //explained.ai