Polynomial Learnability and Locality of Formal Grammars

We apply a complexity theoretic notion of feasible learnability called polynomial learnability to the evaluation of grammatical formalisms for linguistic description. We show that a novel, nontrivial constraint on the degree of locality of grammars allows not only context free languages but also a rich class of mildly context sensitive languages to be polynomially learnable. We discuss possible implications of this result to the theory of natural language acquisition

Feasible Learnability of Formal Grammars and the Theory of Natural Language Acquisition

We propose to apply a complexity theoretic notion of feasible learnability called polynomial learnability to the evaluation of grammatical formalisms for linguistic description. Polynomial learnability was originally defined by Valiant in the context of boolean concept learning and subsequently generalized by Blumer et al. to infinitary domains. We give a clear, intuitive exposition of this notion of learnability and what characteristics of a collection of languages may or may not help feasible learnability under this paradigm. In particular, we present a novel, nontrivial constraint on the degree of locality of grammars which allows a rich class of mildly context sensitive languages to be feasibly learnable. We discuss possible implications of this observation to the theory of natural language acquisition

Polynomial Learnability of Semilinear Sets

We characterize learnability and non-learnability of subsets of Nm called \u27semilinear sets\u27, with respect to the distribution-free learning model of Valiant. In formal language terms, semilinear sets are exactly the class of \u27letter-counts\u27 (or Parikh-images) of regular sets. We show that the class of semilinear sets of dimensions 1 and 2 is learnable, when the integers are encoded in unary. We complement this result with negative results of several different sorts, relying on hardness assumptions of varying degrees - from P ≠ NP and RP ≠ NP to the hardness of learning DNF. We show that the minimal consistent concept problem is NP-complete for this class, verifying the non-triviality of our learnability result. We also show that with respect to the binary encoding of integers, the corresponding \u27prediction\u27 problem is already as hard as that of DNF, for a class of subsets of Nm much simpler than semilinear sets. The present work represents an interesting class of countably infinite concepts for which the questions of learnability have been nearly completely characterized. In doing so, we demonstrate how various proof techniques developed by Pitt and Valiant [14], Blumer et al. [3], and Pitt and Warmuth [16] can be fruitfully applied in the context of formal languages

Global network structure of dominance hierarchy of ant workers

Dominance hierarchy among animals is widespread in various species and believed to serve to regulate resource allocation within an animal group. Unlike small groups, however, detection and quantification of linear hierarchy in large groups of animals are a difficult task. Here, we analyse aggression-based dominance hierarchies formed by worker ants in Diacamma sp. as large directed networks. We show that the observed dominance networks are perfect or approximate directed acyclic graphs, which are consistent with perfect linear hierarchy. The observed networks are also sparse and random but significantly different from networks generated through thinning of the perfect linear tournament (i.e., all individuals are linearly ranked and dominance relationship exists between every pair of individuals). These results pertain to global structure of the networks, which contrasts with the previous studies inspecting frequencies of different types of triads. In addition, the distribution of the out-degree (i.e., number of workers that the focal worker attacks), not in-degree (i.e., number of workers that attack the focal worker), of each observed network is right-skewed. Those having excessively large out-degrees are located near the top, but not the top, of the hierarchy. We also discuss evolutionary implications of the discovered properties of dominance networks.Comment: 5 figures, 2 tables, 4 supplementary figures, 2 supplementary table

Black-Box Anomaly Attribution

When the prediction of a black-box machine learning model deviates from the true observation, what can be said about the reason behind that deviation? This is a fundamental and ubiquitous question that the end user in a business or industrial AI application often asks. The deviation may be due to a sub-optimal black-box model, or it may be simply because the sample in question is an outlier. In either case, one would ideally wish to obtain some form of attribution score -- a value indicative of the extent to which an input variable is responsible for the anomaly. In the present paper we address this task of ``anomaly attribution,'' particularly in the setting in which the model is black-box and the training data are not available. Specifically, we propose a novel likelihood-based attribution framework we call the ``likelihood compensation (LC),'' in which the responsibility score is equated with the correction on each input variable needed to attain the highest possible likelihood. We begin by showing formally why mainstream model-agnostic explanation methods, such as the local linear surrogate modeling and Shapley values, are not designed to explain anomalies. In particular, we show that they are ``deviation-agnostic,'' namely, that their explanations are blind to the fact that there is a deviation in the model prediction for the sample of interest. We do this by positioning these existing methods under the unified umbrella of a function family we call the ``integrated gradient family.'' We validate the effectiveness of the proposed LC approach using publicly available data sets. We also conduct a case study with a real-world building energy prediction task and confirm its usefulness in practice based on expert feedback

鎮信流茶道理念「知足」の現代的意義

拡大しつづける現代社会にとって、いま最も必要とされるのは「知足」の理念ではなかろうか。本稿では、「足るを知」らなくなってしまった現状とその現状に対する危惧を素描しようとした。また、鎮信流茶道理念「知足」の必要性の背景にも迫ってみた。As it continues to expand, what the contemporary society needs most is the idea of Chisoku-to learn to be satisfied with what is given. This article outlines the present state of society where we became unable to subscribe to the notion of Chisoku, and misgivings about such a situation. It also investigates into what is behind the necessity of the idea of chisoku - the key concept in the chinshin School of tea ceremony