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A novel algorithm, called semantic line combination detector (SLCD), to find an optimal combination of semantic lines is proposed in this paper. It processes all lines in each line combination at once to assess the overall harmony of the lines. First, we generate various line combinations from reliable lines. Second, we estimate the score of each line combination and determine the best one. Experimental results demonstrate that the proposed SLCD outperforms existing semantic line detectors on various datasets. Moreover, it is shown that SLCD can be applied effectively to three vision tasks of vanishing point detection, symmetry axis detection, and composition-based image retrieval. Our codes are available at //github.com/Jinwon-Ko/SLCD.

Recent work (Xu et al., 2020) has suggested that numeral systems in different languages are shaped by a functional need for efficient communication in an information-theoretic sense. Here we take a learning-theoretic approach and show how efficient communication emerges via reinforcement learning. In our framework, two artificial agents play a Lewis signaling game where the goal is to convey a numeral concept. The agents gradually learn to communicate using reinforcement learning and the resulting numeral systems are shown to be efficient in the information-theoretic framework of Regier et al. (2015); Gibson et al. (2017). They are also shown to be similar to human numeral systems of same type. Our results thus provide a mechanistic explanation via reinforcement learning of the recent results in Xu et al. (2020) and can potentially be generalized to other semantic domains.

We first elucidate various fundamental properties of optimal adversarial predictors: the structure of optimal adversarial convex predictors in terms of optimal adversarial zero-one predictors, bounds relating the adversarial convex loss to the adversarial zero-one loss, and the fact that continuous predictors can get arbitrarily close to the optimal adversarial error for both convex and zero-one losses. Applying these results along with new Rademacher complexity bounds for adversarial training near initialization, we prove that for general data distributions and perturbation sets, adversarial training on shallow networks with early stopping and an idealized optimal adversary is able to achieve optimal adversarial test error. By contrast, prior theoretical work either considered specialized data distributions or only provided training error guarantees.

Guessing random additive noise decoding (GRAND) is a recently proposed decoding paradigm particularly suitable for codes with short length and high rate. Among its variants, ordered reliability bits GRAND (ORBGRAND) exploits soft information in a simple and effective fashion to schedule its queries, thereby allowing efficient hardware implementation. Compared with maximum likelihood (ML) decoding, however, ORBGRAND still exhibits noticeable performance loss in terms of block error rate (BLER). In order to improve the performance of ORBGRAND while still retaining its amenability to hardware implementation, a new variant of ORBGRAND termed RS-ORBGRAND is proposed, whose basic idea is to reshuffle the queries of ORBGRAND so that the expected number of queries is minimized. Numerical simulations show that RS-ORBGRAND leads to noticeable gains compared with ORBGRAND and its existing variants, and is only 0.1dB away from ML decoding, for BLER as low as $10^{-6}$.

The Stochastic Gradient Langevin Dynamics (SGLD) are popularly used to approximate Bayesian posterior distributions in statistical learning procedures with large-scale data. As opposed to many usual Markov chain Monte Carlo (MCMC) algorithms, SGLD is not stationary with respect to the posterior distribution; two sources of error appear: The first error is introduced by an Euler--Maruyama discretisation of a Langevin diffusion process, the second error comes from the data subsampling that enables its use in large-scale data settings. In this work, we consider an idealised version of SGLD to analyse the method's pure subsampling error that we then see as a best-case error for diffusion-based subsampling MCMC methods. Indeed, we introduce and study the Stochastic Gradient Langevin Diffusion (SGLDiff), a continuous-time Markov process that follows the Langevin diffusion corresponding to a data subset and switches this data subset after exponential waiting times. There, we show the exponential ergodicity of SLGDiff and that the Wasserstein distance between the posterior and the limiting distribution of SGLDiff is bounded above by a fractional power of the mean waiting time. We bring our results into context with other analyses of SGLD.

This research explores the application of Large Language Models (LLMs) for automating the extraction of requirement-related legal content in the food safety domain and checking legal compliance of regulatory artifacts. With Industry 4.0 revolutionizing the food industry and with the General Data Protection Regulation (GDPR) reshaping privacy policies and data processing agreements, there is a growing gap between regulatory analysis and recent technological advancements. This study aims to bridge this gap by leveraging LLMs, namely BERT and GPT models, to accurately classify legal provisions and automate compliance checks. Our findings demonstrate promising results, indicating LLMs' significant potential to enhance legal compliance and regulatory analysis efficiency, notably by reducing manual workload and improving accuracy within reasonable time and financial constraints.

Assembly Calculus (AC), proposed by Papadimitriou et al., aims to reproduce advanced cognitive functions through simulating neural activities, with several applications based on AC having been developed, including a natural language parser proposed by Mitropolsky et al. However, this parser lacks the ability to handle Kleene closures, preventing it from parsing all regular languages and rendering it weaker than Finite Automata (FA). In this paper, we propose a new bionic natural language parser (BNLP) based on AC and integrates two new biologically rational structures, Recurrent Circuit and Stack Circuit which are inspired by RNN and short-term memory mechanism. In contrast to the original parser, the BNLP can fully handle all regular languages and Dyck languages. Therefore, leveraging the Chomsky-Sch \H{u}tzenberger theorem, the BNLP which can parse all Context-Free Languages can be constructed. We also formally prove that for any PDA, a Parser Automaton corresponding to BNLP can always be formed, ensuring that BNLP has a description ability equal to that of PDA and addressing the deficiencies of the original parser.

Evolutionary algorithms (EAs) have achieved remarkable success in tackling complex combinatorial optimization problems. However, EAs often demand carefully-designed operators with the aid of domain expertise to achieve satisfactory performance. In this work, we present the first study on large language models (LLMs) as evolutionary combinatorial optimizers. The main advantage is that it requires minimal domain knowledge and human efforts, as well as no additional training of the model. This approach is referred to as LLM-driven EA (LMEA). Specifically, in each generation of the evolutionary search, LMEA instructs the LLM to select parent solutions from current population, and perform crossover and mutation to generate offspring solutions. Then, LMEA evaluates these new solutions and include them into the population for the next generation. LMEA is equipped with a self-adaptation mechanism that controls the temperature of the LLM. This enables it to balance between exploration and exploitation and prevents the search from getting stuck in local optima. We investigate the power of LMEA on the classical traveling salesman problems (TSPs) widely used in combinatorial optimization research. Notably, the results show that LMEA performs competitively to traditional heuristics in finding high-quality solutions on TSP instances with up to 20 nodes. Additionally, we also study the effectiveness of LLM-driven crossover/mutation and the self-adaptation mechanism in evolutionary search. In summary, our results reveal the great potentials of LLMs as evolutionary optimizers for solving combinatorial problems. We hope our research shall inspire future explorations on LLM-driven EAs for complex optimization challenges.

We develop a novel approach for efficiently applying variational quantum linear solver (VQLS) in context of structured sparse matrices. Such matrices frequently arise during numerical solution of partial differential equations which are ubiquitous in science and engineering. Conventionally, Pauli basis is used for linear combination of unitary (LCU) decomposition of the underlying matrix to facilitate the evaluation the global/local VQLS cost functions. However, Pauli basis in worst case can result in number of LCU terms that scale quadratically with respect to the matrix size. We show that by using an alternate basis one can better exploit the sparsity and underlying structure of matrix leading to number of tensor product terms which scale only logarithmically with respect to the matrix size. Given this new basis is comprised of non-unitary operators, we employ the concept of unitary completion to design efficient quantum circuits for computing the global/local VQLS cost functions. We compare our approach with other related concepts in the literature including unitary dilation and measurement in Bell basis, and discuss its pros/cons while using VQLS applied to Heat equation as an example.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.