First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper focuses on how to choose optimal training examples for people learning to discriminate categories. The authors develop an optimal teacher model that selects training examples in order to minimize generalization error, assuming that people make classification decisions in accordance with the GCM, a widely used categorization model. They test their model with an experiment and find that the best teacher is one that assumes that people have a limited memory capacity that only allows them to retrieve a few previous examples to compare to a new item. This teacher chooses idealized training sets rather than representative ones.

Unlike regular models, these very simple models--often referred to as toy models--are not required to be linked to the real world through structural similarity or resemblance relations. They are not meant to be approximations of the target world system, and in some cases, they are not even required to be representational. In semantic terms, they do not accurately map onto their targets. Despite these limitations, they are still useful in understanding theoretical concepts and possible configurations of the target system. Paradigmatic examples of toy models include Boyle's law and the Ising model in physics, the Lotka-Volterra model in population ecology, and the Schelling model in the social sciences (Weisberg, 2013). In recent years, philosophers of science have become interested in toy models (Grüne-Yanoff, 2009; Luczak, 2017; Reutlinger et al., 2018; Frigg & Nguyen, 2017; Nguyen, 2020). The main purpose of this literature is to explore the nature of these models and examine how they perform their epistemic function. Despite lacking the regular descriptive and predictive features of full-scale scientific models, they often offer an elementary understanding of a phenomenon. Their definitions of "toy model" differ as well as their assessment of the importance of representation in modelling generally, but they all agree that toy models play an important epistemic role in scientific research, exploration, and pedagogy.

Explainable AI (xAI) methods are important for establishing trust in using black-box models. However, recent criticism has mounted against current xAI methods that they disagree, are necessarily false, and can be manipulated, which has started to undermine the deployment of black-box models. Rudin (2019) goes so far as to say that we should stop using black-box models altogether in high-stakes cases because xAI explanations "must be wrong". However, strict fidelity to the truth is historically not a desideratum in science. Idealizations -- the intentional distortions introduced to scientific theories and models -- are commonplace in the natural sciences and are seen as a successful scientific tool. Thus, it is not falsehood qua falsehood that is the issue. In this paper, I outline the need for xAI research to engage in idealization evaluation. Drawing on the use of idealizations in the natural sciences and philosophy of science, I introduce a novel framework for evaluating whether xAI methods engage in successful idealizations or deceptive explanations (SIDEs). SIDEs evaluates whether the limitations of xAI methods, and the distortions that they introduce, can be part of a successful idealization or are indeed deceptive distortions as critics suggest. I discuss the role that existing research can play in idealization evaluation and where innovation is necessary. Through a qualitative analysis we find that leading feature importance methods and counterfactual explanations are subject to idealization failure and suggest remedies for ameliorating idealization failure.

In our recently proposed Integrated Finite Element Neural Network (I-FENN) framework (Pantidis and Mobasher, 2023) we showcased how PINNs can be deployed on a finite element-level basis to swiftly approximate a state variable of interest, and we applied it in the context of non-local gradient-enhanced damage mechanics. In this paper, we enhance the rigour and performance of I-FENN by focusing on two crucial aspects of its PINN component: a) the error convergence analysis and b) the hyperparameter-performance relationship. Guided by the available theoretical formulations in the field, we introduce a systematic numerical approach based on a novel set of holistic performance metrics to answer both objectives. In the first objective, we explore in detail the convergence of the PINN training error and the global error against the network size and the training sample size. We demonstrate a consistent converging behavior of the two error types for any investigated combination of network complexity, dataset size and choice of hyperparameters, which empirically proves the conformance of the PINN setup and implementation to the available convergence theories. In the second objective, we establish an a-priori knowledge of the hyperparameters which favor higher predictive accuracy, lower computational effort, and the least chances of arriving at trivial solutions. The analysis leads to several outcomes that contribute to the better performance of I-FENN, and fills a long-standing gap in the PINN literature with regards to the numerical convergence of the network errors while accounting for commonly used optimizers (Adam and L-BFGS). The proposed analysis method can be directly extended to other ML applications in science and engineering. The code and data utilized in the analysis are posted publicly to aid the reproduction and extension of this research.

First, it is a brain dump: too long, epsilon-baked, and unpolished. Second, it is not obviously relevant to the topic of this site. Third, parts are more technical than most readers would want. However, a quick, bad post may be better than none. This post was prompted by discussions about Bayesianism and the LessWrong rationalist community, with Scott Alexander, Catharine G. Evans, muflax, and St. Rev. (among others). They are each brilliant, quirky, articulate, and fascinating; consider following them online! They might disagree with much of this post, though, and are not implicated in its defects.] This site concerns ways of thinking about some particularly important things: purpose, self, ethics, authority, and meaning, for instance. My aim is to point out common mistakes in thinking about those things, and how to do better. I enjoy thinking about thinking. That's one reason I spent a dozen years in artificial intelligence research. To make a computer think, you'd need to understand how you think. So AI research is a way of thinking about thinking that forces you to be specific. It calls your bluff if you think you understand thinking, but don't. I thought a lot about how to do AI. 1 In 1988, I put together "How to do research at the MIT AI Lab," a guide for graduate students. Although I edited it, it was a collaboration of many people. There are now many similar guides, some of them better, but this was the first.

I begin by considering examples of practical reasoning. In the remainder of the paper, I try to say something about what Example 8. Playing soccer. Soccer is like table tennis, but a logical approach that begins to do justice to the subject with the added dimension of teamwork and the need to might be like. This task was selected as a benchmark problem in robotics, and has been extensively Example 1. Ordering a meal at a restaurant. Here, the problem is deciding what to eat and drink. Typing an email message, Even if the only relevant factors are price and preferences composing it as you go along, starts perhaps with a general about food, the number of possible combinations is very idea of what to say.

One of the challenges of multiagent decision making is that the behavior needed to maximize utility can depend on what other agents choose to do: sometimes there is no "right" answer in the absence of knowledge of how opponents will act. The Nash equilibrium is a sensible choice of behavior because it represents a mutual best response. But, even when there is a unique equilibrium, other players are under no obligation to take part in it. This observation has been forcefully illustrated in the behavioral economics community where repeated experiments have shown individuals playing Nash equilibria and performing badly as a result. In this paper, we show how to apply a tool from behavioral economics called the Cognitive Hierarchy (CH) to the design of agents in general sum games. We attack the recently introduced ``Lemonade Game'' and show how the results of an open competition are well explained by CH. We believe this game, and perhaps many other similar games, boils down to predicting how deeply other agents in the game will be reasoning. An agent that does not reason enough risks being exploited by its opponents, while an agent that reasons too much may not be able to interact productively with its opponents. We demonstrate these ideas by presenting empirical results using agents from the competition and idealizations arising from a CH analysis.

T1. Let S1 be the set of equivalence classes of S0 with respect to N, and