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Artificial neural networks (ANNs) with recurrence and self-attention have been shown to be Turing-complete (TC). However, existing work has shown that these ANNs require multiple turns or unbounded computation time, even with unbounded precision in weights, in order to recognize TC grammars. However, under constraints such as fixed or bounded precision neurons and time, ANNs without memory are shown to struggle to recognize even context-free languages. In this work, we extend the theoretical foundation for the $2^{nd}$-order recurrent network ($2^{nd}$ RNN) and prove there exists a class of a $2^{nd}$ RNN that is Turing-complete with bounded time. This model is capable of directly encoding a transition table into its recurrent weights, enabling bounded time computation and is interpretable by design. We also demonstrate that $2$nd order RNNs, without memory, under bounded weights and time constraints, outperform modern-day models such as vanilla RNNs and gated recurrent units in recognizing regular grammars. We provide an upper bound and a stability analysis on the maximum number of neurons required by $2$nd order RNNs to recognize any class of regular grammar. Extensive experiments on the Tomita grammars support our findings, demonstrating the importance of tensor connections in crafting computationally efficient RNNs. Finally, we show $2^{nd}$ order RNNs are also interpretable by extraction and can extract state machines with higher success rates as compared to first-order RNNs. Our results extend the theoretical foundations of RNNs and offer promising avenues for future explainable AI research.

Ranking and selection (R&S), which aims to select the best alternative with the largest mean performance from a finite set of alternatives, is a classic research topic in simulation optimization. Recently, considerable attention has turned towards the large-scale variant of the R&S problem which involves a large number of alternatives. Ideal large-scale R&S procedures should be sample optimal, i.e., the total sample size required to deliver an asymptotically non-zero probability of correct selection (PCS) grows at the minimal order (linear order) in the number of alternatives, but not many procedures in the literature are sample optimal. Surprisingly, we discover that the na\"ive greedy procedure, which keeps sampling the alternative with the largest running average, performs strikingly well and appears sample optimal. To understand this discovery, we develop a new boundary-crossing perspective and prove that the greedy procedure is indeed sample optimal. We further show that the derived PCS lower bound is asymptotically tight for the slippage configuration of means with a common variance. Moreover, we propose the explore-first greedy (EFG) procedure and its enhanced version (EFG$^+$ procedure) by adding an exploration phase to the na\"ive greedy procedure. Both procedures are proven to be sample optimal and consistent. Last, we conduct extensive numerical experiments to empirically understand the performance of our greedy procedures in solving large-scale R&S problems.

Multi-genre speaker recognition is becoming increasingly popular due to its ability to better represent the complexities of real-world applications. However, a major challenge is the significant shift in the distribution of speaker vectors across different genres. While distribution alignment is a common approach to address this challenge, previous studies have mainly focused on aligning a source domain with a target domain, and the performance of multi-genre data is unknown. This paper presents a comprehensive study of mainstream distribution alignment methods on multi-genre data, where multiple distributions need to be aligned. We analyze various methods both qualitatively and quantitatively. Our experiments on the CN-Celeb dataset show that within-between distribution alignment (WBDA) performs relatively better. However, we also found that none of the investigated methods consistently improved performance in all test cases. This suggests that solely aligning the distributions of speaker vectors may not fully address the challenges posed by multi-genre speaker recognition. Further investigation is necessary to develop a more comprehensive solution.

We prove upper and lower bounds for the threshold of the q-overlap-k-Exact cover problem. These results are motivated by the one-step replica symmetry breaking approach of Statistical Physics, and the hope of using an approach based on that of Mezard et al. (2005) to rigorously prove that for some values of the order parameter the overlap distribution of k-Exact Cover has discontinuous support.

Human perception inherently operates in a multimodal manner. Similarly, as machines interpret the empirical world, their learning processes ought to be multimodal. The recent, remarkable successes in empirical multimodal learning underscore the significance of understanding this paradigm. Yet, a solid theoretical foundation for multimodal learning has eluded the field for some time. While a recent study by Lu (2023) has shown the superior sample complexity of multimodal learning compared to its unimodal counterpart, another basic question remains: does multimodal learning also offer computational advantages over unimodal learning? This work initiates a study on the computational benefit of multimodal learning. We demonstrate that, under certain conditions, multimodal learning can outpace unimodal learning exponentially in terms of computation. Specifically, we present a learning task that is NP-hard for unimodal learning but is solvable in polynomial time by a multimodal algorithm. Our construction is based on a novel modification to the intersection of two half-spaces problem.

We provide the first convergence guarantee for full black-box variational inference (BBVI), also known as Monte Carlo variational inference. While preliminary investigations worked on simplified versions of BBVI (e.g., bounded domain, bounded support, only optimizing for the scale, and such), our setup does not need any such algorithmic modifications. Our results hold for log-smooth posterior densities with and without strong log-concavity and the location-scale variational family. Also, our analysis reveals that certain algorithm design choices commonly employed in practice, particularly, nonlinear parameterizations of the scale of the variational approximation, can result in suboptimal convergence rates. Fortunately, running BBVI with proximal stochastic gradient descent fixes these limitations, and thus achieves the strongest known convergence rate guarantees. We evaluate this theoretical insight by comparing proximal SGD against other standard implementations of BBVI on large-scale Bayesian inference problems.

Elections repeat commonly after a fixed time interval, ranging from months to years. This results in limitations on governance since elected candidates or policies are difficult to remove before the next elections, if needed, and allowed by the corresponding law. Participants may decide (through a public deliberation) to change their choices but have no opportunity to vote for these choices before the next elections. Another issue is the peak-end effect, where the judgment of voters is based on how they felt a short time before the elections. To address these issues, we propose Always on Voting (AoV) -- a repetitive voting framework that allows participants to vote and change elected candidates or policies without waiting for the next elections. Participants are permitted to privately change their vote at any point in time, while the effect of their change is manifested at the end of each epoch, whose duration is shorter than the time between two main elections. To thwart the problem of peak-end effect in epochs, the ends of epochs are randomized and made unpredictable, while preserved within soft bounds. These goals are achieved using the synergy between a Bitcoin puzzle oracle, verifiable delay function, and smart contracts.

This volume contains the proceedings of the 7th Working Formal Methods Symposium, which was held at the University of Bucharest, September 21-22, 2023.

A resource leak occurs when a program fails to free some finite resource after it is no longer needed. Such leaks are a significant cause of real-world crashes and performance problems. Recent work proposed an approach to prevent resource leaks based on checking resource management specifications. A resource management specification expresses how the program allocates resources, passes them around, and releases them; it also tracks the ownership relationship between objects and resources, and aliasing relationships between objects. While this specify-and-verify approach has several advantages compared to prior techniques, the need to manually write annotations presents a significant barrier to its practical adoption. This paper presents a novel technique to automatically infer a resource management specification for a program, broadening the applicability of specify-and-check verification for resource leaks. Inference in this domain is challenging because resource management specifications differ significantly in nature from the types that most inference techniques target. Further, for practical effectiveness, we desire a technique that can infer the resource management specification intended by the developer, even in cases when the code does not fully adhere to that specification. We address these challenges through a set of inference rules carefully designed to capture real-world coding patterns, yielding an effective fixed-point-based inference algorithm. We have implemented our inference algorithm in two different systems, targeting programs written in Java and C#. In an experimental evaluation, our technique inferred 85.5% of the annotations that programmers had written manually for the benchmarks. Further, the verifier issued nearly the same rate of false alarms with the manually-written and automatically-inferred annotations.

Deep Convolutional Neural Networks (CNNs) are a special type of Neural Networks, which have shown state-of-the-art results on various competitive benchmarks. The powerful learning ability of deep CNN is largely achieved with the use of multiple non-linear feature extraction stages that can automatically learn hierarchical representation from the data. Availability of a large amount of data and improvements in the hardware processing units have accelerated the research in CNNs and recently very interesting deep CNN architectures are reported. The recent race in deep CNN architectures for achieving high performance on the challenging benchmarks has shown that the innovative architectural ideas, as well as parameter optimization, can improve the CNN performance on various vision-related tasks. In this regard, different ideas in the CNN design have been explored such as use of different activation and loss functions, parameter optimization, regularization, and restructuring of processing units. However, the major improvement in representational capacity is achieved by the restructuring of the processing units. Especially, the idea of using a block as a structural unit instead of a layer is gaining substantial appreciation. This survey thus focuses on the intrinsic taxonomy present in the recently reported CNN architectures and consequently, classifies the recent innovations in CNN architectures into seven different categories. These seven categories are based on spatial exploitation, depth, multi-path, width, feature map exploitation, channel boosting and attention. Additionally, it covers the elementary understanding of the CNN components and sheds light on the current challenges and applications of CNNs.