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Key Point Analysis (KPA), the summarization of multiple arguments into a concise collection of key points, continues to be a significant and unresolved issue within the field of argument mining. Existing models adapt a two-stage pipeline of clustering arguments or generating key points for argument clusters. This approach rely on semantic similarity instead of measuring the existence of shared key points among arguments. Additionally, it only models the intra-cluster relationship among arguments, disregarding the inter-cluster relationship between arguments that do not share key points. To address these limitations, we propose a novel approach for KPA with pairwise generation and graph partitioning. Our objective is to train a generative model that can simultaneously provide a score indicating the presence of shared key point between a pair of arguments and generate the shared key point. Subsequently, to map generated redundant key points to a concise set of key points, we proceed to construct an arguments graph by considering the arguments as vertices, the generated key points as edges, and the scores as edge weights. We then propose a graph partitioning algorithm to partition all arguments sharing the same key points to the same subgraph. Notably, our experimental findings demonstrate that our proposed model surpasses previous models when evaluated on both the ArgKP and QAM datasets.

In this expository note we show that the learning parities with noise (LPN) assumption is robust to weak dependencies in the noise distribution of small batches of samples. This provides a partial converse to the linearization technique of [AG11]. The material in this note is drawn from a recent work by the authors [GMR24], where the robustness guarantee was a key component in a cryptographic separation between reinforcement learning and supervised learning.

We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). Formally, we prove lower bounds against the accuracy of FPC-interpretations that map Unique Games instances (encoded as relational structures) to rational numbers giving the approximate fraction of constraints that can be satisfied. We prove two new FPC-inexpressibility results for Unique Games: the existence of a $(1/2, 1/3 + \delta)$-inapproximability gap, and inapproximability to within any constant factor. Previous recent work has established similar FPC-inapproximability results for a small handful of other problems. Our construction builds upon some of these ideas, but contains a novel technique. While most FPC-inexpressibility results are based on variants of the CFI-construction, ours is significantly different. We start with a graph of very large girth and label the edges with random affine vector spaces over $\mathbb{F}_2$ that determine the constraints in the two structures. Duplicator's strategy involves maintaining a partial isomorphism over a minimal tree that spans the pebbled vertices of the graph.

The general/finite PCTL satisfiability problem asks whether a given PCTL formula has a general/finite model. We show that the finite PCTL satisfiability problem is undecidable, and the general PCTL satisfiability problem is even highly undecidable (beyond the arithmetical hierarchy). Consequently, there are no sound deductive systems proving all generally/finitely valid PCTL formulae.

Foundation models such as GPT-4 are fine-tuned to avoid unsafe or otherwise problematic behavior, so that, for example, they refuse to comply with requests for help with committing crimes or with producing racist text. One approach to fine-tuning, called reinforcement learning from human feedback, learns from humans' expressed preferences over multiple outputs. Another approach is constitutional AI, in which the input from humans is a list of high-level principles. But how do we deal with potentially diverging input from humans? How can we aggregate the input into consistent data about ''collective'' preferences or otherwise use it to make collective choices about model behavior? In this paper, we argue that the field of social choice is well positioned to address these questions, and we discuss ways forward for this agenda, drawing on discussions in a recent workshop on Social Choice for AI Ethics and Safety held in Berkeley, CA, USA in December 2023.

While the success of edge and fog computing increased with the proliferation of the Internet of Things (IoT) solutions, such novel computing paradigm, that moves compute resources closer to the source of data and services, must address many challenges such as reducing communication overhead to/from datacenters, the latency to compute and receive results, as well as energy consumption at the mobile and IoT devices. fog-to-fog (f2f) cooperation has recently been proposed to increase the computation capacity at the network edge through cooperation across multiple stakeholders. In this paper we adopt an analytical approach to studying f2f cooperation paradigm. We highlight the benefits of using such new paradigm in comparison with traditional three-tier fog computing paradigms. We use a Continuous Time Markov Chain (CTMC) model for the N f2f cooperating nodes and cast cooperation as an optimization problem, which we solve using the proposed model.

Bayesian Neural Networks (BNNs) have become one of the promising approaches for uncertainty estimation due to the solid theorical foundations. However, the performance of BNNs is affected by the ability of catching uncertainty. Instead of only seeking the distribution of neural network weights by in-distribution (ID) data, in this paper, we propose a new Bayesian Neural Network with an Attached structure (ABNN) to catch more uncertainty from out-of-distribution (OOD) data. We first construct a mathematical description for the uncertainty of OOD data according to the prior distribution, and then develop an attached Bayesian structure to integrate the uncertainty of OOD data into the backbone network. ABNN is composed of an expectation module and several distribution modules. The expectation module is a backbone deep network which focuses on the original task, and the distribution modules are mini Bayesian structures which serve as attachments of the backbone. In particular, the distribution modules aim at extracting the uncertainty from both ID and OOD data. We further provide theoretical analysis for the convergence of ABNN, and experimentally validate its superiority by comparing with some state-of-the-art uncertainty estimation methods Code will be made available.

Large-language Models (LLMs) need to adopt Retrieval-Augmented Generation (RAG) to generate factual responses that are better suited to knowledge-based applications in the design process. We present a data-driven method to identify explicit facts of the form - head entity :: relationship :: tail entity from patented artefact descriptions. We train roBERTa Transformer-based sequence classification models using our proprietary dataset of 44,227 sentences. Upon classifying tokens in a sentence as entities or relationships, our method uses another classifier to identify specific relationship tokens for a given pair of entities. We compare the performances against linear classifiers and Graph Neural Networks (GNNs) that both incorporate BERT Transformer-based token embeddings to predict associations among the entities and relationships. We apply our method to 4,870 fan system related patents and populate a knowledge base that constitutes around 3 million facts. Using the knowledge base, we demonstrate retrieving generalisable and specific domain knowledge for contextualising LLMs.

We study the following Independent Stable Set problem. Let G be an undirected graph and M = (V(G),I) be a matroid whose elements are the vertices of G. For an integer k\geq 1, the task is to decide whether G contains a set S\subseteq V(G) of size at least k which is independent (stable) in G and independent in M. This problem generalizes several well-studied algorithmic problems, including Rainbow Independent Set, Rainbow Matching, and Bipartite Matching with Separation. We show that - When the matroid M is represented by the independence oracle, then for any computable function f, no algorithm can solve Independent Stable Set using f(k)n^{o(k)} calls to the oracle. - On the other hand, when the graph G is of degeneracy d, then the problem is solvable in time O((d+1)^kn), and hence is FPT parameterized by d+k. Moreover, when the degeneracy d is a constant (which is not a part of the input), the problem admits a kernel polynomial in k. More precisely, we prove that for every integer d\geq 0, the problem admits a kernelization algorithm that in time n^{O(d)} outputs an equivalent framework with a graph on dk^{O(d)} vertices. A lower bound complements this when d is part of the input: Independent Stable Set does not admit a polynomial kernel when parameterized by k+d unless NP \subseteq coNP/poly. This lower bound holds even when M is a partition matroid. - Another set of results concerns the scenario when the graph G is chordal. In this case, our computational lower bound excludes an FPT algorithm when the input matroid is given by its independence oracle. However, we demonstrate that Independent Stable Set can be solved in 2^{O(k)}||M||^{O(1)} time when M is a linear matroid given by its representation. In the same setting, Independent Stable Set does not have a polynomial kernel when parameterized by k unless NP\subseteq coNP/poly.

We propose a novel method for automatic reasoning on knowledge graphs based on debate dynamics. The main idea is to frame the task of triple classification as a debate game between two reinforcement learning agents which extract arguments -- paths in the knowledge graph -- with the goal to promote the fact being true (thesis) or the fact being false (antithesis), respectively. Based on these arguments, a binary classifier, called the judge, decides whether the fact is true or false. The two agents can be considered as sparse, adversarial feature generators that present interpretable evidence for either the thesis or the antithesis. In contrast to other black-box methods, the arguments allow users to get an understanding of the decision of the judge. Since the focus of this work is to create an explainable method that maintains a competitive predictive accuracy, we benchmark our method on the triple classification and link prediction task. Thereby, we find that our method outperforms several baselines on the benchmark datasets FB15k-237, WN18RR, and Hetionet. We also conduct a survey and find that the extracted arguments are informative for users.