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In a recent paper Wunderlich and Pehle introduced the EventProp algorithm that enables training spiking neural networks by gradient descent on exact gradients. In this paper we present extensions of EventProp to support a wider class of loss functions and an implementation in the GPU enhanced neuronal networks framework which exploits sparsity. The GPU acceleration allows us to test EventProp extensively on more challenging learning benchmarks. We find that EventProp performs well on some tasks but for others there are issues where learning is slow or fails entirely. Here, we analyse these issues in detail and discover that they relate to the use of the exact gradient of the loss function, which by its nature does not provide information about loss changes due to spike creation or spike deletion. Depending on the details of the task and loss function, descending the exact gradient with EventProp can lead to the deletion of important spikes and so to an inadvertent increase of the loss and decrease of classification accuracy and hence a failure to learn. In other situations the lack of knowledge about the benefits of creating additional spikes can lead to a lack of gradient flow into earlier layers, slowing down learning. We eventually present a first glimpse of a solution to these problems in the form of `loss shaping', where we introduce a suitable weighting function into an integral loss to increase gradient flow from the output layer towards earlier layers.

Consider the semigroup of random walk on a complete graph, which we call the Potts semigroup. Diaconis and Saloff-Coste computed the maximum of the ratio of the relative entropy and the Dirichlet form obtaining the constant $\alpha_2$ in the $2$-log-Sobolev inequality ($2$-LSI). In this paper, we obtain the best possible non-linear inequality relating entropy and the Dirichlet form (i.e., $p$-NLSI, $p\ge1$). As an example, we show $\alpha_1 = 1+\frac{1+o(1)}{\log k}$. By integrating the $1$-NLSI we obtain the new strong data processing inequality (SDPI), which in turn allows us to improve results of Mossel and Peres on reconstruction thresholds for Potts models on trees. A special case is the problem of reconstructing color of the root of a $k$-colored tree given knowledge of colors of all the leaves. We show that to have a non-trivial reconstruction probability the branching number of the tree should be at least $$\frac{\log k}{\log k - \log(k-1)} = (1-o(1))k\log k.$$ This recovers previous results (of Sly and Bhatnagar et al.) in (slightly) more generality, but more importantly avoids the need for any coloring-specialized arguments. Similarly, we improve the state-of-the-art on the weak recovery threshold for the stochastic block model with $k$ balanced groups, for all $k\ge 3$. To further show the power of our method, we prove optimal non-reconstruction results for a broadcasting on trees model with Gaussian kernels, closing a gap left open by Eldan et al. These improvements advocate information-theoretic methods as a useful complement to the conventional techniques originating from the statistical physics.

It is known that the exact form of the Burrows-Wheeler-Transform (BWT) of a string collection depends, in most implementations, on the input order of the strings in the collection. Reordering strings of an input collection affects the number of equal-letter runs $r$, arguably the most important parameter of BWT-based data structures, such as the FM-index or the $r$-index. Bentley, Gibney, and Thankachan [ESA 2020] introduced a linear-time algorithm for computing the permutation of the input collection which yields the minimum number of runs of the resulting BWT. In this paper, we present the first tool that guarantees a Burrows-Wheeler-Transform with minimum number of runs (optBWT), by combining i) an algorithm that builds the BWT from a string collection (either SAIS-based [Cenzato et al., SPIRE 2021] or BCR [Bauer et al., CPM 2011]); ii) the SAP array data structure introduced in [Cox et al., Bioinformatics, 2012]; and iii) the algorithm by Bentley et al. We present results both on real-life and simulated data, showing that the improvement achieved in terms of $r$ with respect to the input order is significant and the overhead created by the computation of the optimal BWT negligible, making our tool competitive with other tools for BWT-computation in terms of running time and space usage. In particular, on real data the optBWT obtains up to 31 times fewer runs with only a $1.39\times$ slowdown. Source code is available at //github.com/davidecenzato/optimalBWT.git.

Credit assignment problem of neural networks refers to evaluating the credit of each network component to the final outputs. For an untrained neural network, approaches to tackling it have made great contributions to parameter update and model revolution during the training phase. This problem on trained neural networks receives rare attention, nevertheless, it plays an increasingly important role in neural network patch, specification and verification. Based on Koopman operator theory, this paper presents an alternative perspective of linear dynamics on dealing with the credit assignment problem for trained neural networks. Regarding a neural network as the composition of sub-dynamics series, we utilize step-delay embedding to capture snapshots of each component, characterizing the established mapping as exactly as possible. To circumvent the dimension-difference problem encountered during the embedding, a composition and decomposition of an auxiliary linear layer, termed minimal linear dimension alignment, is carefully designed with rigorous formal guarantee. Afterwards, each component is approximated by a Koopman operator and we derive the Jacobian matrix and its corresponding determinant, similar to backward propagation. Then, we can define a metric with algebraic interpretability for the credit assignment of each network component. Moreover, experiments conducted on typical neural networks demonstrate the effectiveness of the proposed method.

Clustering with outliers is one of the most fundamental problems in Computer Science. Given a set $X$ of $n$ points and two integers $k$ and $m$, the clustering with outliers aims to exclude $m$ points from $X$ and partition the remaining points into $k$ clusters that minimizes a certain cost function. In this paper, we give a general approach for solving clustering with outliers, which results in a fixed-parameter tractable (FPT) algorithm in $k$ and $m$, that almost matches the approximation ratio for its outlier-free counterpart. As a corollary, we obtain FPT approximation algorithms with optimal approximation ratios for $k$-Median and $k$-Means with outliers in general metrics. We also exhibit more applications of our approach to other variants of the problem that impose additional constraints on the clustering, such as fairness or matroid constraints.

Prior work has looked at applying reinforcement learning and imitation learning approaches to autonomous driving scenarios, but either the safety or the efficiency of the algorithm is compromised. With the use of control barrier functions embedded into the reinforcement learning policy, we arrive at safe policies to optimize the performance of the autonomous driving vehicle. However, control barrier functions need a good approximation of the model of the car. We use probabilistic control barrier functions as an estimate of the model uncertainty. The algorithm is implemented as an online version in the CARLA (Dosovitskiy et al., 2017) Simulator and as an offline version on a dataset extracted from the NGSIM Database. The proposed algorithm is not just a safe ramp merging algorithm but a safe autonomous driving algorithm applied to address ramp merging on highways.

We propose a conservative energy method based on neural networks with subdomains for solving variational problems (CENN), where the admissible function satisfying the essential boundary condition without boundary penalty is constructed by the radial basis function (RBF), particular solution neural network, and general neural network. The loss term is the potential energy, optimized based on the principle of minimum potential energy. The loss term at the interfaces has the lower order derivative compared to the strong form PINN with subdomains. The advantage of the proposed method is higher efficiency, more accurate, and less hyperparameters than the strong form PINN with subdomains. Another advantage of the proposed method is that it can apply to complex geometries based on the special construction of the admissible function. To analyze its performance, the proposed method CENN is used to model representative PDEs, the examples include strong discontinuity, singularity, complex boundary, non-linear, and heterogeneous problems. Furthermore, it outperforms other methods when dealing with heterogeneous problems.

Safety constraints and optimality are important, but sometimes conflicting criteria for controllers. Although these criteria are often solved separately with different tools to maintain formal guarantees, it is also common practice in reinforcement learning to simply modify reward functions by penalizing failures, with the penalty treated as a mere heuristic. We rigorously examine the relationship of both safety and optimality to penalties, and formalize sufficient conditions for safe value functions (SVFs): value functions that are both optimal for a given task, and enforce safety constraints. We reveal this structure by examining when rewards preserve viability under optimal control, and show that there always exists a finite penalty that induces a safe value function. This penalty is not unique, but upper-unbounded: larger penalties do not harm optimality. Although it is often not possible to compute the minimum required penalty, we reveal clear structure of how the penalty, rewards, discount factor, and dynamics interact. This insight suggests practical, theory-guided heuristics to design reward functions for control problems where safety is important.

Temporal Action Localization (TAL) aims to predict both action category and temporal boundary of action instances in untrimmed videos, i.e., start and end time. Fully-supervised solutions are usually adopted in most existing works, and proven to be effective. One of the practical bottlenecks in these solutions is the large amount of labeled training data required. To reduce expensive human label cost, this paper focuses on a rarely investigated yet practical task named semi-supervised TAL and proposes an effective active learning method, named AL-STAL. We leverage four steps for actively selecting video samples with high informativeness and training the localization model, named \emph{Train, Query, Annotate, Append}. Two scoring functions that consider the uncertainty of localization model are equipped in AL-STAL, thus facilitating the video sample rank and selection. One takes entropy of predicted label distribution as measure of uncertainty, named Temporal Proposal Entropy (TPE). And the other introduces a new metric based on mutual information between adjacent action proposals and evaluates the informativeness of video samples, named Temporal Context Inconsistency (TCI). To validate the effectiveness of proposed method, we conduct extensive experiments on two benchmark datasets THUMOS'14 and ActivityNet 1.3. Experiment results show that AL-STAL outperforms the existing competitors and achieves satisfying performance compared with fully-supervised learning.

Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.