Infinite Gray code has been introduced by Tsuiki as a redundancy-free representation of the reals. In applications the signed digit representation is mostly used which has maximal redundancy. Tsuiki presented a functional program converting signed digit code into infinite Gray code. Moreover, he showed that infinite Gray code can effectively be converted into signed digit code, but the program needs to have some non-deterministic features (see also H. Tsuiki, K. Sugihara, "Streams with a bottom in functional languages"). Berger and Tsuiki reproved the result in a system of formal first-order intuitionistic logic extended by inductive and co-inductive definitions, as well as some new logical connectives capturing concurrent behaviour. The programs extracted from the proofs are exactly the ones given by Tsuiki. In order to do so, co-inductive predicates $\bS$ and $\bG$ are defined and the inclusion $\bS \subseteq \bG$ is derived. For the converse inclusion the new logical connectives are used to introduce a concurrent version $\S_{2}$ of $S$ and $\bG \subseteq \bS_{2}$ is shown. What one is looking for, however, is an equivalence proof of the involved concepts. One of the main aims of the present paper is to close the gap. A concurrent version $\bG^{*}$ of $\bG$ and a modification $\bS^{*}$ of $\bS_{2}$ are presented such that $\bS^{*} = \bG^{*}$. A crucial tool in U. Berger, H. Tsuiki, "Intuitionistic fixed point logic" is a formulation of the Archimedean property of the real numbers as an induction principle. We introduce a concurrent version of this principle which allows us to prove that $\bS^{*}$ and $\bG^{*}$ coincide. A further central contribution is the extension of the above results to the hyperspace of non-empty compact subsets of the reals.
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We propose the use of conversational GPT models for easy and quick few-shot text classification in the financial domain using the Banking77 dataset. Our approach involves in-context learning with GPT-3.5 and GPT-4, which minimizes the technical expertise required and eliminates the need for expensive GPU computing while yielding quick and accurate results. Additionally, we fine-tune other pre-trained, masked language models with SetFit, a recent contrastive learning technique, to achieve state-of-the-art results both in full-data and few-shot settings. Our findings show that querying GPT-3.5 and GPT-4 can outperform fine-tuned, non-generative models even with fewer examples. However, subscription fees associated with these solutions may be considered costly for small organizations. Lastly, we find that generative models perform better on the given task when shown representative samples selected by a human expert rather than when shown random ones. We conclude that a) our proposed methods offer a practical solution for few-shot tasks in datasets with limited label availability, and b) our state-of-the-art results can inspire future work in the area.
The introduction of ChatGPT and the subsequent improvement of Large Language Models (LLMs) have prompted more and more individuals to turn to the use of ChatBots, both for information and assistance with decision-making. However, the information the user is after is often not formulated by these ChatBots objectively enough to be provided with a definite, globally accepted answer. Controversial topics, such as "religion", "gender identity", "freedom of speech", and "equality", among others, can be a source of conflict as partisan or biased answers can reinforce preconceived notions or promote disinformation. By exposing ChatGPT to such debatable questions, we aim to understand its level of awareness and if existing models are subject to socio-political and/or economic biases. We also aim to explore how AI-generated answers compare to human ones. For exploring this, we use a dataset of a social media platform created for the purpose of debating human-generated claims on polemic subjects among users, dubbed Kialo. Our results show that while previous versions of ChatGPT have had important issues with controversial topics, more recent versions of ChatGPT (gpt-3.5-turbo) are no longer manifesting significant explicit biases in several knowledge areas. In particular, it is well-moderated regarding economic aspects. However, it still maintains degrees of implicit libertarian leaning toward right-winged ideals which suggest the need for increased moderation from the socio-political point of view. In terms of domain knowledge on controversial topics, with the exception of the "Philosophical" category, ChatGPT is performing well in keeping up with the collective human level of knowledge. Finally, we see that sources of Bing AI have slightly more tendency to the center when compared to human answers. All the analyses we make are generalizable to other types of biases and domains.
Bug fixing holds significant importance in software development and maintenance. Recent research has made notable progress in exploring the potential of large language models (LLMs) for automatic bug fixing. However, existing studies often overlook the collaborative nature of bug resolution, treating it as a single-stage process. To overcome this limitation, we introduce a novel stage-wise framework named STEAM in this paper. The objective of STEAM is to simulate the interactive behavior of multiple programmers involved in various stages across the bug's life cycle. Taking inspiration from bug management practices, we decompose the bug fixing task into four distinct stages: bug reporting, bug diagnosis, patch generation, and patch verification. These stages are performed interactively by LLMs, aiming to imitate the collaborative abilities of programmers during the resolution of software bugs. By harnessing the collective contribution, STEAM effectively enhances the bug-fixing capabilities of LLMs. We implement STEAM by employing the powerful dialogue-based LLM -- ChatGPT. Our evaluation on the widely adopted bug-fixing benchmark demonstrates that STEAM has achieved a new state-of-the-art level of bug-fixing performance.
In the conventional successive cancellation (SC) decoder for polar codes, all the future bits to be estimated later are treated as random variables. However, polar codes inevitably involve frozen bits, and their concatenated coding schemes also include parity bits (or dynamic frozen bits) causally generated from the past bits estimated earlier. We refer to the frozen and parity bits located behind a target decoding bit as its future constraints (FCs). Although the values of FCs are deterministic given the past estimates, they have not been exploited in the conventional SC-based decoders, not leading to optimality. In this paper, we propose SC-check (SCC) and belief propagation SCC (BP-SCC) decoding algorithms in order to leverage FCs in decoding. We further devise an improved tree search technique based on stack-based backjumping (SBJ) to solve dynamic constraint satisfaction problems (CSPs) formulated by FCs. Over the binary erasure channel (BEC), numerical results show that a combination of the BP-SCC algorithm and the SBJ tree search technique achieves the erasure recovery performance close to the dependence testing (DT) bound, a bound of achievable finite-length performance.
The industrial Internet of Things (IIoT) and network slicing (NS) paradigms have been envisioned as key enablers for flexible and intelligent manufacturing in the industry 4.0, where a myriad of interconnected machines, sensors, and devices of diversified quality of service (QoS) requirements coexist. To optimize network resource usage, stakeholders in the IIoT network are encouraged to take pragmatic steps towards resource sharing. However, resource sharing is only attractive if the entities involved are able to settle on a fair exchange of resource for remuneration in a win-win situation. In this paper, we design an economic model that analyzes the multilateral strategic trading interactions between sliced tenants in IIoT networks. We formulate the resource pricing and purchasing problem of the seller and buyer tenants as a cooperative Stackelberg game. Particularly, the cooperative game enforces collaboration among the buyer tenants by coalition formation in order to strengthen their position in resource price negotiations as opposed to acting individually, while the Stackelberg game determines the optimal policy optimization of the seller tenants and buyer tenant coalitions. To achieve a Stackelberg equilibrium (SE), a multi-agent deep reinforcement learning (MADRL) method is developed to make flexible pricing and purchasing decisions without prior knowledge of the environment. Simulation results and analysis prove that the proposed method achieves convergence and is superior to other baselines, in terms of utility maximization.
The Natural Language Processing(NLP) community has been using crowd sourcing techniques to create benchmark datasets such as General Language Understanding and Evaluation(GLUE) for training modern Language Models such as BERT. GLUE tasks measure the reliability scores using inter annotator metrics i.e. Cohens Kappa. However, the reliability aspect of LMs has often been overlooked. To counter this problem, we explore a knowledge-guided LM ensembling approach that leverages reinforcement learning to integrate knowledge from ConceptNet and Wikipedia as knowledge graph embeddings. This approach mimics human annotators resorting to external knowledge to compensate for information deficits in the datasets. Across nine GLUE datasets, our research shows that ensembling strengthens reliability and accuracy scores, outperforming state of the art.
The quality of text-to-image generation is continuously improving, yet the boundaries of its applicability are still unclear. In particular, refinement of the text input with the objective of achieving better results - commonly called prompt engineering - so far seems to have not been geared towards work with pre-existing texts. We investigate whether text-to-image generation and prompt engineering could be used to generate basic illustrations of popular fairytales. Using Midjourney v4, we engage in action research with a dual aim: to attempt to generate 5 believable illustrations for each of 5 popular fairytales, and to define a prompt engineering process that starts from a pre-existing text and arrives at an illustration of it. We arrive at a tentative 4-stage process: i) initial prompt, ii) composition adjustment, iii) style refinement, and iv) variation selection. We also discuss three reasons why the generation model struggles with certain illustrations: difficulties with counts, bias from stereotypical configurations and inability to depict overly fantastic situations. Our findings are not limited to the specific generation model and are intended to be generalisable to future ones.
While language models are powerful and versatile, they often fail to address highly complex problems. This is because solving complex problems requires deliberate thinking, which has been only minimally guided during training. In this paper, we propose a new method called Cumulative Reasoning (CR), which employs language models in a cumulative and iterative manner to emulate human thought processes. By decomposing tasks into smaller components, CR streamlines the problem-solving process, rendering it both more manageable and effective. For logical inference tasks, CR consistently outperforms existing methods with an improvement up to 9.3%, and achieves the astonishing accuracy of 98.04% on the curated FOLIO wiki dataset. In the context of the Game of 24, CR achieves an accuracy of 98%, which signifies a substantial enhancement of 24% over the previous state-of-the-art method. Finally, on the MATH dataset, we establish new state-of-the-art results with 58.0% overall accuracy, surpassing the previous best approach by a margin of 4.2%, and achieving 43% relative improvement on the hardest level 5 problems (22.4% to 32.1%). Code is available at //github.com/iiis-ai/cumulative-reasoning.
Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.
Deep Learning algorithms have achieved the state-of-the-art performance for Image Classification and have been used even in security-critical applications, such as biometric recognition systems and self-driving cars. However, recent works have shown those algorithms, which can even surpass the human capabilities, are vulnerable to adversarial examples. In Computer Vision, adversarial examples are images containing subtle perturbations generated by malicious optimization algorithms in order to fool classifiers. As an attempt to mitigate these vulnerabilities, numerous countermeasures have been constantly proposed in literature. Nevertheless, devising an efficient defense mechanism has proven to be a difficult task, since many approaches have already shown to be ineffective to adaptive attackers. Thus, this self-containing paper aims to provide all readerships with a review of the latest research progress on Adversarial Machine Learning in Image Classification, however with a defender's perspective. Here, novel taxonomies for categorizing adversarial attacks and defenses are introduced and discussions about the existence of adversarial examples are provided. Further, in contrast to exisiting surveys, it is also given relevant guidance that should be taken into consideration by researchers when devising and evaluating defenses. Finally, based on the reviewed literature, it is discussed some promising paths for future research.
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