A Framework for Quantum Finite-State Languages with Density Mapping

A quantum finite-state automaton (QFA) is a theoretical model designed to simulate the evolution of a quantum system with finite memory in response to sequential input strings. We define the language of a QFA as the set of strings that lead the QFA to an accepting state when processed from its initial state. QFAs exemplify how quantum computing can achieve greater efficiency compared to classical computing. While being one of the simplest quantum models, QFAs are still notably challenging to construct from scratch due to the preliminary knowledge of quantum mechanics required for superimposing unitary constraints on the automata. Furthermore, even when QFAs are correctly assembled, the limitations of a current quantum computer may cause fluctuations in the simulation results depending on how an assembled QFA is translated into a quantum circuit. We present a framework that provides a simple and intuitive way to build QFAs and maximize the simulation accuracy. Our framework relies on two methods: First, it offers a predefined construction for foundational types of QFAs that recognize special languages MOD and EQU. They play a role of basic building blocks for more complex QFAs. In other words, one can obtain more complex QFAs from these foundational automata using standard language operations. Second, we improve the simulation accuracy by converting these QFAs into quantum circuits such that the resulting circuits perform well on noisy quantum computers. Our framework is available at https://github.com/sybaik1/qfa-toolkit.

ATHENA: Mathematical Reasoning with Thought Expansion

Solving math word problems depends on how to articulate the problems, the lens through which models view human linguistic expressions. Real-world settings count on such a method even more due to the diverse practices of the same mathematical operations. Earlier works constrain available thinking processes by limited prediction strategies without considering their significance in acquiring mathematical knowledge. We introduce Attention-based THought Expansion Network Architecture (ATHENA) to tackle the challenges of real-world practices by mimicking human thought expansion mechanisms in the form of neural network propagation. A thought expansion recurrently generates the candidates carrying the thoughts of possible math expressions driven from the previous step and yields reasonable thoughts by selecting the valid pathways to the goal. Our experiments show that ATHENA achieves a new state-of-the-art stage toward the ideal model that is compelling in variant questions even when the informativeness in training examples is restricted.

Neuro-Symbolic Regex Synthesis Framework via Neural Example Splitting

Due to the practical importance of regular expressions (regexes, for short), there has been a lot of research to automatically generate regexes from positive and negative string examples. We tackle the problem of learning regexes faster from positive and negative strings by relying on a novel approach called `neural example splitting'. Our approach essentially split up each example string into multiple parts using a neural network trained to group similar substrings from positive strings. This helps to learn a regex faster and, thus, more accurately since we now learn from several short-length strings. We propose an effective regex synthesis framework called `SplitRegex' that synthesizes subregexes from `split' positive substrings and produces the final regex by concatenating the synthesized subregexes. For the negative sample, we exploit pre-generated subregexes during the subregex synthesis process and perform the matching against negative strings. Then the final regex becomes consistent with all negative strings. SplitRegex is a divided-and-conquer framework for learning target regexes; split (=divide) positive strings and infer partial regexes for multiple parts, which is much more accurate than the whole string inferring, and concatenate (=conquer) inferred regexes while satisfying negative strings. We empirically demonstrate that the proposed SplitRegex framework substantially improves the previous regex synthesis approaches over four benchmark datasets.

LST: Lexicon-Guided Self-Training for Few-Shot Text Classification

Self-training provides an effective means of using an extremely small amount of labeled data to create pseudo-labels for unlabeled data. Many state-of-the-art self-training approaches hinge on different regularization methods to prevent overfitting and improve generalization. Yet they still rely heavily on predictions initially trained with the limited labeled data as pseudo-labels and are likely to put overconfident label belief on erroneous classes depending on the first prediction. To tackle this issue in text classification, we introduce LST, a simple self-training method that uses a lexicon to guide the pseudo-labeling mechanism in a linguistically-enriched manner. We consistently refine the lexicon by predicting confidence of the unseen data to teach pseudo-labels better in the training iterations. We demonstrate that this simple yet well-crafted lexical knowledge achieves 1.0-2.0% better performance on 30 labeled samples per class for five benchmark datasets than the current state-of-the-art approaches.

ALP: Data Augmentation using Lexicalized PCFGs for Few-Shot Text Classification

Data augmentation has been an important ingredient for boosting performances of learned models. Prior data augmentation methods for few-shot text classification have led to great performance boosts. However, they have not been designed to capture the intricate compositional structure of natural language. As a result, they fail to generate samples with plausible and diverse sentence structures. Motivated by this, we present the data Augmentation using Lexicalized Probabilistic context-free grammars (ALP) that generates augmented samples with diverse syntactic structures with plausible grammar. The lexicalized PCFG parse trees consider both the constituents and dependencies to produce a syntactic frame that maximizes a variety of word choices in a syntactically preservable manner without specific domain experts. Experiments on few-shot text classification tasks demonstrate that ALP enhances many state-of-the-art classification methods. As a second contribution, we delve into the train-val splitting methodologies when a data augmentation method comes into play. We argue empirically that the traditional splitting of training and validation sets is sub-optimal compared to our novel augmentation-based splitting strategies that further expand the training split with the same number of labeled data. Taken together, our contributions on the data augmentation strategies yield a strong training recipe for few-shot text classification tasks.