Against inertia

Revised version added 12 March 2012In this paper I challenge the Inertial Theory of language change put forward by Longobardi (2001), which claims that syntactic change does not arise unless caused and that any such change must originate as an ‘interface phenomenon’. It is shown that these two claims and the resulting contention that ‘syntax, by itself, is diachronically completely inert’ (Longobardi 2001: 278), if construed as a substantive, falsifiable theory of diachrony, make predictions that are too strong, and that they cannot be reduced (as seems desirable) to properties of language acquisition. I also express doubt as to the utility and necessity of a methodological/heuristic principle of Inertia, broadly following Lass’s (1980) view of causality.This work was supported by AHRC doctoral award AH/H026924/1

The Causal-Neural Connection: Expressiveness, Learnability, and Inference

One of the central elements of any causal inference is an object called structural causal model (SCM), which represents a collection of mechanisms and exogenous sources of random variation of the system under investigation (Pearl, 2000). An important property of many kinds of neural networks is universal approximability: the ability to approximate any function to arbitrary precision. Given this property, one may be tempted to surmise that a collection of neural nets is capable of learning any SCM by training on data generated by that SCM. In this paper, we show this is not the case by disentangling the notions of expressivity and learnability. Specifically, we show that the causal hierarchy theorem (Thm. 1, Bareinboim et al., 2020), which describes the limits of what can be learned from data, still holds for neural models. For instance, an arbitrarily complex and expressive neural net is unable to predict the effects of interventions given observational data alone. Given this result, we introduce a special type of SCM called a neural causal model (NCM), and formalize a new type of inductive bias to encode structural constraints necessary for performing causal inferences. Building on this new class of models, we focus on solving two canonical tasks found in the literature known as causal identification and estimation. Leveraging the neural toolbox, we develop an algorithm that is both sufficient and necessary to determine whether a causal effect can be learned from data (i.e., causal identifiability); it then estimates the effect whenever identifiability holds (causal estimation). Simulations corroborate the proposed approach.Comment: 10 pages main body (53 total pages with references and appendix), 5 figures in main body (20 total figures including appendix

Borg’s Minimalism and the Problem of Paradox

According to Emma Borg, minimalism is (roughly) the view that natural language sentences have truth conditions, and that these truth conditions are fully determined by syntactic structure and lexical content. A principal motivation for her brand of minimalism is that it coheres well with the popular view that semantic competence is underpinned by the cognition of a minimal semantic theory. In this paper, I argue that the liar paradox presents a serious problem for this principal motivation. Two lines of response to the problem are discussed, and difficulties facing those responses are raised. I close by issuing a challenge: to construe the principal motivation for Borg’s version of minimalism in such a way so as to avoid the problem of paradox

Structure identification in relational data

This paper presents several investigations into the prospects for identifying meaningful structures in empirical data, namely, structures permitting effective organization of the data to meet requirements of future queries. We propose a general framework whereby the notion of identifiability is given a precise formal definition similar to that of learnability. Using this framework, we then explore if a tractable procedure exists for deciding whether a given relation is decomposable into a constraint network or a CNF theory with desirable topology and, if the answer is positive, identifying the desired decomposition. Finally, we address the problem of expressing a given relation as a Horn theory and, if this is impossible, finding the best k-Horn approximation to the given relation. We show that both problems can be solved in time polynomial in the length of the data

Are words easier to learn from infant- than adult-directed speech? A quantitative corpus-based investigation

We investigate whether infant-directed speech (IDS) could facilitate word form learning when compared to adult-directed speech (ADS). To study this, we examine the distribution of word forms at two levels, acoustic and phonological, using a large database of spontaneous speech in Japanese. At the acoustic level we show that, as has been documented before for phonemes, the realizations of words are more variable and less discriminable in IDS than in ADS. At the phonological level, we find an effect in the opposite direction: the IDS lexicon contains more distinctive words (such as onomatopoeias) than the ADS counterpart. Combining the acoustic and phonological metrics together in a global discriminability score reveals that the bigger separation of lexical categories in the phonological space does not compensate for the opposite effect observed at the acoustic level. As a result, IDS word forms are still globally less discriminable than ADS word forms, even though the effect is numerically small. We discuss the implication of these findings for the view that the functional role of IDS is to improve language learnability.Comment: Draf

Formal Modeling of Connectionism using Concurrency Theory, an Approach Based on Automata and Model Checking

This paper illustrates a framework for applying formal methods techniques, which are symbolic in nature, to specifying and verifying neural networks, which are sub-symbolic in nature. The paper describes a communicating automata [Bowman & Gomez, 2006] model of neural networks. We also implement the model using timed automata [Alur & Dill, 1994] and then undertake a verification of these models using the model checker Uppaal [Pettersson, 2000] in order to evaluate the performance of learning algorithms. This paper also presents discussion of a number of broad issues concerning cognitive neuroscience and the debate as to whether symbolic processing or connectionism is a suitable representation of cognitive systems. Additionally, the issue of integrating symbolic techniques, such as formal methods, with complex neural networks is discussed. We then argue that symbolic verifications may give theoretically well-founded ways to evaluate and justify neural learning systems in the field of both theoretical research and real world applications