A locked $t$-omino tiling is a grid tiling by $t$-ominoes such that, if you remove any pair of tiles, the only way to fill in the remaining space with $t$-ominoes is to use the same two tiles in the exact same configuration as before. We exclude degenerate cases where there is only one tiling overall due to small dimensions. Locked $t$-omino tilings arise as obstructions to widely used political redistricting algorithms in a grid model of redistricting. It is a classic (and straightforward) result that finite grids do not admit locked 2-omino tilings. In this paper, we construct explicit locked 3-, 4-, and 5-omino tilings of grids of various sizes. While 3-omino tilings are plentiful, 4- and 5-omino tilings are remarkably elusive. Using an exhaustive computational search, we completely enumerate all locked tilings on grid sizes up to $20 \times 20$, and all symmetric locked tilings on grid sizes up to $35 \times 35$. We find only a single 4-omino tiling (on the $10 \times 10$ grid) and a small handful of 5-omino tilings (only on $20 \times 20$ grids and larger). Finally, we construct a family of infinite periodic locked $t$-omino tilings with unbounded $t$ for both square and triangular grid lattices.
In this paper, we study the weighted stochastic matching problem. Let $G=(V, E)$ be a given edge-weighted graph and let its realization $\mathcal{G}$ be a random subgraph of $G$ that includes each edge $e\in E$ independently with a known probability $p_e$. The goal in this problem is to pick a sparse subgraph $Q$ of $G$ without prior knowledge of $G$'s realization, such that the maximum weight matching among the realized edges of $Q$ (i.e. the subgraph $Q\cap \mathcal{G}$) in expectation approximates the maximum weight matching of the entire realization $\mathcal{G}$. Attaining any constant approximation ratio for this problem requires selecting a subgraph of max-degree $\Omega(1/p)$ where $p=\min_{e\in E} p_e$. On the positive side, there exists a $(1-\epsilon)$-approximation algorithm by Behnezhad and Derakhshan, albeit at the cost of max-degree having exponential dependence on $1/p$. Within the $\text{poly}(1/p)$ regime, however, the best-known algorithm achieves a $0.536$ approximation ratio due to Dughmi, Kalayci, and Patel improving over the $0.501$ approximation algorithm by Behnezhad, Farhadi, Hajiaghayi, and Reyhani. In this work, we present a 0.68 approximation algorithm with $O(1/p)$ queries per vertex, which is asymptotically tight. This is even an improvement over the best-known approximation ratio of $2/3$ for unweighted graphs within the $\text{poly}(1/p)$ regime due to Assadi and Bernstein. The $2/3$ approximation ratio is proven tight in the presence of a few correlated edges in $\mathcal{G}$, indicating that surpassing the $2/3$ barrier should rely on the independent realization of edges. Our analysis involves reducing the problem to designing a randomized matching algorithm on a given stochastic graph with some variance-bounding properties.
Blockchain protocols typically aspire to run in the permissionless setting, in which nodes are owned and operated by a large number of diverse and unknown entities, with each node free to start or stop running the protocol at any time. This setting is more challenging than the traditional permissioned setting, in which the set of nodes that will be running the protocol is fixed and known at the time of protocol deployment. The goal of this paper is to provide a framework for reasoning about the rich design space of blockchain protocols and their capabilities and limitations in the permissionless setting. We propose a hierarchy of settings with different "degrees of permissionlessness", specified by the amount of knowledge that a protocol has about the current participants: These are the fully permissionless, dynamically available and quasi-permissionless settings. The paper also proves several results illustrating the utility of our analysis framework for reasoning about blockchain protocols in these settings. For example: (1) In the fully permissionless setting, even with synchronous communication and with severe restrictions on the total size of the Byzantine players, every deterministic protocol for Byzantine agreement has a non-terminating execution. (2) In the dynamically available and partially synchronous setting, no protocol can solve the Byzantine agreement problem with high probability, even if there are no Byzantine players at all. (3) In the quasi-permissionless and partially synchronous setting, by contrast, assuming a bound on the total size of the Byzantine players, there is a deterministic protocol solving state machine replication. (4) In the quasi-permissionless and synchronous setting, every proof-of-stake state machine replication protocol that uses only time-malleable cryptographic primitives is vulnerable to long-range attacks.
Interactive Natural Language Processing (iNLP) has emerged as a novel paradigm within the field of NLP, aimed at addressing limitations in existing frameworks while aligning with the ultimate goals of artificial intelligence. This paradigm considers language models as agents capable of observing, acting, and receiving feedback iteratively from external entities. Specifically, language models in this context can: (1) interact with humans for better understanding and addressing user needs, personalizing responses, aligning with human values, and improving the overall user experience; (2) interact with knowledge bases for enriching language representations with factual knowledge, enhancing the contextual relevance of responses, and dynamically leveraging external information to generate more accurate and informed responses; (3) interact with models and tools for effectively decomposing and addressing complex tasks, leveraging specialized expertise for specific subtasks, and fostering the simulation of social behaviors; and (4) interact with environments for learning grounded representations of language, and effectively tackling embodied tasks such as reasoning, planning, and decision-making in response to environmental observations. This paper offers a comprehensive survey of iNLP, starting by proposing a unified definition and framework of the concept. We then provide a systematic classification of iNLP, dissecting its various components, including interactive objects, interaction interfaces, and interaction methods. We proceed to delve into the evaluation methodologies used in the field, explore its diverse applications, scrutinize its ethical and safety issues, and discuss prospective research directions. This survey serves as an entry point for researchers who are interested in this rapidly evolving area and offers a broad view of the current landscape and future trajectory of iNLP.
Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.
Adversarial attack is a technique for deceiving Machine Learning (ML) models, which provides a way to evaluate the adversarial robustness. In practice, attack algorithms are artificially selected and tuned by human experts to break a ML system. However, manual selection of attackers tends to be sub-optimal, leading to a mistakenly assessment of model security. In this paper, a new procedure called Composite Adversarial Attack (CAA) is proposed for automatically searching the best combination of attack algorithms and their hyper-parameters from a candidate pool of \textbf{32 base attackers}. We design a search space where attack policy is represented as an attacking sequence, i.e., the output of the previous attacker is used as the initialization input for successors. Multi-objective NSGA-II genetic algorithm is adopted for finding the strongest attack policy with minimum complexity. The experimental result shows CAA beats 10 top attackers on 11 diverse defenses with less elapsed time (\textbf{6 $\times$ faster than AutoAttack}), and achieves the new state-of-the-art on $l_{\infty}$, $l_{2}$ and unrestricted adversarial attacks.
As a field of AI, Machine Reasoning (MR) uses largely symbolic means to formalize and emulate abstract reasoning. Studies in early MR have notably started inquiries into Explainable AI (XAI) -- arguably one of the biggest concerns today for the AI community. Work on explainable MR as well as on MR approaches to explainability in other areas of AI has continued ever since. It is especially potent in modern MR branches, such as argumentation, constraint and logic programming, planning. We hereby aim to provide a selective overview of MR explainability techniques and studies in hopes that insights from this long track of research will complement well the current XAI landscape. This document reports our work in-progress on MR explainability.
In this paper, we present an accurate and scalable approach to the face clustering task. We aim at grouping a set of faces by their potential identities. We formulate this task as a link prediction problem: a link exists between two faces if they are of the same identity. The key idea is that we find the local context in the feature space around an instance (face) contains rich information about the linkage relationship between this instance and its neighbors. By constructing sub-graphs around each instance as input data, which depict the local context, we utilize the graph convolution network (GCN) to perform reasoning and infer the likelihood of linkage between pairs in the sub-graphs. Experiments show that our method is more robust to the complex distribution of faces than conventional methods, yielding favorably comparable results to state-of-the-art methods on standard face clustering benchmarks, and is scalable to large datasets. Furthermore, we show that the proposed method does not need the number of clusters as prior, is aware of noises and outliers, and can be extended to a multi-view version for more accurate clustering accuracy.
Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different learning objectives. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results on these tasks, and consistently outperforms baselines on these tasks.
We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.
This paper discusses and demonstrates the outcomes from our experimentation on Image Captioning. Image captioning is a much more involved task than image recognition or classification, because of the additional challenge of recognizing the interdependence between the objects/concepts in the image and the creation of a succinct sentential narration. Experiments on several labeled datasets show the accuracy of the model and the fluency of the language it learns solely from image descriptions. As a toy application, we apply image captioning to create video captions, and we advance a few hypotheses on the challenges we encountered.