Tatsuji Takahashi

A loosely symmetric model of cognition

Cognitive biases explaining human deviation from formal logic have been broadly studied. We here try to give a step toward the general formalism still missing, introducing a probabilistic formula for causal induction. It has symmetries reflecting human cognitive biases and shows extremely high correlation with the experimental results. We apply the formula to learning or decision-theoretic tasks, n-armed bandit problems. Searching for the best cause for reward, it exhibits an optimal property breaking the usual trade-off between speed and accuracy.

Cognitively inspired reinforcement learning architecture and its application to giant-swing motion control

Many algorithms and methods in artificial intelligence or machine learning were inspired by human cognition. As a mechanism to handle the exploration-exploitation dilemma in reinforcement learning, the loosely symmetric (LS) value function that models causal intuition of humans was proposed (Shinohara et al., 2007). While LS shows the highest correlation with causal induction by humans, it has been reported that it effectively works in multi-armed bandit problems that form the simplest class of tasks representing the dilemma. However, the scope of application of LS was limited to the reinforcement learning problems that have K actions with only one state (K-armed bandit problems). This study proposes LS-Q learning architecture that can deal with general reinforcement learning tasks with multiple states and delayed reward. We tested the learning performance of the new architecture in giant-swing robot motion learning, where uncertainty and unknown-ness of the environment is huge. In the test, the help of ready-made internal models or functional approximation of the state space were not given. The simulations showed that while the ordinary Q-learning agent does not reach giant-swing motion because of stagnant loops (local optima with low rewards), LS-Q escapes such loops and acquires giant-swing. It is confirmed that the smaller number of states is, in other words, the more coarse-grained the division of states and the more incomplete the state observation is, the better LS-Q performs in comparison with Q-learning. We also showed that the high performance of LS-Q depends comparatively little on parameter tuning and learning time. This suggests that the proposed method inspired by human cognition works adaptively in real environments.

The efficacy of symmetric cognitive biases in robotic motion learning

We propose an application of human-like decision-making to robotic motion learning. Human is known to have illogical symmetric cognitive biases that induce “if p then q” and “if not q then not p” from “if q then p.” The loosely symmetric Shinohara model quantitatively represents the tendencies (Shinohara et al. 2007). Previous studies one of the authors have revealed that an agent with the model used as the action value function shows great performance in n-armed bandit problems, because of the illogical biases. In this study, we apply the model to reinforcement learning with Q-learning algorithm. Testing the model on a simulated giant-swing robot, we have confirmed its efficacy in convergence speed increase and avoidance of local optimum.

Rule‐following as an Anticipatory Act: Interaction in Second Person and an Internal Measurement Model of Dialogue

We pursue anticipation in second person or normative anticipation. As the first step, we make the three concepts second person, internal measurement and asynchroneity clearer by introducing the velocity of logic νl and the velocity of communication νc, in the context of social communication. After proving anticipatory nature of rule‐following or language use in general via Kripke’s “rule‐following paradox,” we present a mathematical model expressing the internality essential to second person, taking advantage of equivalences and differences in the formal language theory. As a consequence, we show some advantages of negatively considered concepts and arguments by concretizing them into an elementary and explicit formal model. The time development of the model shows a self‐organizing property which never results if we adopt a third person stance.

Understanding Conditionals in the East: A Replication Study of Politzer et al. (2010) With Easterners

The new probabilistic approaches to the natural language conditional imply that there is a parallel relation between indicative conditionals (ICs) “if s then b” and conditional bets (CBs) “I bet

Robotic action acquisition with cognitive biases in coarse-grained state space

1 that if s then b” in two aspects. First, the probability of an IC and the probability of winning a CB are both the conditional probability, P(s|b). Second, both an IC and a CB have a third value “void” (neither true nor false, neither wins nor loses) when the antecedent is false (¬s). These aspects of the parallel relation have been found in Western participants. In the present study, we investigated whether this parallel is also present in Eastern participants. We replicated the study of Politzer et al. (2010) with Chinese and Japanese participants and made two predictions. First, Eastern participants will tend to engage in more holistic cognition and take all possible cases, including ¬s, into account when they judge the probability of conditional: Easterners may assess the probability of antecedent s out of all possible cases, P(s), and then may focus on consequent b out of s, P(b|s). Consequently, Easterners may judge the probability of the conditional, and of winning the bet, to be P(s) ∗ P(b|s) = P(s & b), and false/losing the bet as P(s) ∗ P(¬b|s) = P(s & ¬b). Second, Eastern participants will tend to be strongly affected by context, and they may not show parallel relationships between ICs and CBs. The results indicate no cultural differences in judging the false antecedent cases: Eastern participants judged false antecedent cases as not making the IC true nor false and as not being winning or losing outcomes. However, there were cultural differences when asked about the probability of a conditional. Consistent with our hypothesis, Eastern participants had a greater tendency to take all possible cases into account, especially in CBs. We discuss whether these results can be explained by a hypothesized tendency for Eastern people to think in more holistic and context-dependent terms than Western people.

Loosely symmetric reasoning to cope with the speed-accuracy trade-off

Some of the authors have previously proposed a cognitively inspired reinforcement learning architecture (LS-Q) that mimics cognitive biases in humans. LS-Q adaptively learns under uniform, coarse-grained state division and performs well without parameter tuning in a giant-swing robot task. However, these results were shown only in simulations. In this study, we test the validity of the LS-Q implemented in a robot in a real environment. In addition, we analyze the learning process to elucidate the mechanism by which the LS-Q adaptively learns under the partially observable environment. We argue that the LS-Q may be a versatile reinforcement learning architecture, which is, despite its simplicity, easily applicable and does not require well-prepared settings.

Symmetrizing object and meta levels organizes thinking

When we learn from unknown environment to collect reward, we face speed-accuracy trade-off for the decision-making that agents act. We will lose if we continue to act greedily, but we cannot maximize reward if we search continually. From experience, it is assumed that human beings act with some kind of standards to cope with trade-off. Hence, we focused symmetric reasoning that is kind of Illogical cognitive properties peculiar to human beings, as a valid solution for speed-accuracy tradeoff. In this study, we simulated the N armed bandit problem as a simple decision-making problem, using Loosely Symmetric model (LS) which is a model of flexibly and loosely symmetric reasoning. In addition, with theoretical consideration for LS and the the change of the reference point as an idea, we developed LS with Variable Reference (LSVR) as a newly improved model, and simulated this model. As a result, In case it has many choices, we confirmed that LSVR can collect overwhelming reward than UCB1 that is the excellent decision-making model used Go AI.

Correlation Detection with and without the Theory of Conditionals: A model update of Hattori & Oaksford (2007)

We present a single non-cellular finite automaton model first shown to exhibit self-organizing behavior with intermittency and criticality, through a self-referential process. We propose a method to make self-referential contradiction a dynamic process of interaction with the selves in first person and third person description. The process represents thinking as inner dialogue with the self in second person. The dynamic effect of the rewrite shows characters proper to internal measurement, disequilibration by equilibration and transfer of inconsistency to the neighborhood by local resolution of the inconsistency. As the result, the advent of contradiction is postponed by the rewrite. The duality of internal measurement subject prevents inner dialogue in second person from lapsing into monologue. Criticality of thinking process is expressed. A probabilistic interpretation of non-determinacy weakening oracle is the key.

A Tentative Assumption of Electroacoustic Music as an Enjoyable Music for Diverse People

We view observational causal induction as a statistical independence test under rarity assumption. This paper complements the two-stage theory of causal induction proposed by Hattori and Oaksford (2007) with a computational analysis. We show that their dual-factor heuristic (DFH) model has a rational account as the square root of the index of (non-)independence under extreme rarity assumption, contrary to the criticism that the DFH model is non-normative (e.g., Lu et al., 2008). We introduce a model that considers the proportion of assumed-to-be rare instances (pARIs), which is the probability of biconditionals (according to several theories of compound conditionals) and can be seen as a simplified version of the DFH model. While being a single conditional probability, pARIs approximates the non-independence measure, the square of DFH. In reproducing the meta-analysis in Hattori and Oaksford (2007), we confirm that pARIs and DFH have the same level of descriptive adequacy, and that the two models have the highest fit among more than 40 models. Then, we critically examine the computer simulations which were central to the rational analysis in Hattori and Oaksford (2007). We point out two problems in their simluations: samples in some of the simulations being restricted to generative ones, and in-definite values of models because of the small samples. In the light of especially the latter problem of definability, pARIs shows higher applicability.