Using a statistical mechanical formalism we calculate the evidence, generalisation error and consistency measure for a linear perceptron trainedand tested on a set of examples generated by a non linear teacher. The teacher is said to be unrealisable because the student can never model it without error. Our model allows us to interpolate between the known case of a linear teacher, and an unrealisable, nonlinearteacher. A comparison of the hyperparameters which maximise the evidence with those that optimise the performance measuresreveals that, in the nonlinear case, the evidence procedure is a misleading guide to optimising performance. Finally, we explore the extent to which the evidence procedure is unreliable and find that, despite being sub-optimal, in some circumstances it might be a useful method for fixing the hyperparameters. 1 INTRODUCTION The analysis of supervised learning or learning from examples is a major field of research within neural networks.

"How We Know Universals: The Perception Their first paper made many intellectual waves--which are still spreading, 50 years later. They had claimed that the truth or falsity of any (computable) proposition could, in with AI, for it's difficult to say just principle, be computed by a simple type of The future of psychology, they good a date as any, however, is 1943--almost said, consisted of the design of various sorts exactly half a century ago. This In that year, Warren McCulloch (a psychiatrist, novel methodology, and the nascent technology cybernetician, philosopher, and poet) associated with it, promised to show just and Walter Pitts (a research student in mathematics) how mind is grounded in mechanism. Much of this was "logical" in nature result was a heady brew, which explicitly and developed into what's known as classical, promised to revolutionize psychology and or symbolic, AI. But some was what is nowadays philosophy--and which, in the event, revolutionized called connectionist, studying networks technology too. In the late 1980s, however, it McCulloch and Pitts' paper ("A Logical Calculus blossomed--hitting the newsstands with of the Ideas Immanent in Nervous rash promises of "brainlike" computers just Activity") concentrated on how propositions around the corner. But both these forms of AI expressible in logic could be computed by share the same historical roots. Those nets consisted of So much for pedigree. But does a mere halfcentury cells passing inhibitory and excitatory messages of work count as a pedigree? Might it between them and acting as what computer rather be a mere blip, an unfortunate academic scientists (soon afterwards) called "and-mutation with no real intellectual fitness?

Surely, scientific arguments Still, a full literature search of citations They are trivial, that is, when compared have their own special logic. of Rescher's 1977 monograph, to the defeasibility of open-textured Cavalli-Sforza has for a while been Dialectics, reveals no useful formal concepts, the logic of which interested in Toulmin's own attempts extension or clarification of the logical remains unanalyzed (says McCarty, to apply his work on argument to system prior to Brewka.

The traditional reliability design methods are imperfect because the designed systems aim at fewer faults, but once a fault happens, the systems might hard fail. To solve this problem, we present a self-maintenance machine (SMM), one that can maintain its functions flexibly even though faults occur. To achieve the capabilities of diagnosing and repair planning, a model-based approach that uses qualitative physics was proposed. Regarding the repair-executing capability, control-type repair strategy was followed. A prototype of the SMM was developed, and it succeeded in maintaining its functions if the structure did not change. However, the prototype revealed the following problems when its reasoning system was used with a commercial product as embedded software: (1) poor performance of the reasoning system, (2) system size that was too large, (3) low adaptability to environmental changes, and (4) roughness of qualitative repair operations. To solve these problems, we proposed new reasoning method based on virtual cases and fuzzy qualitative values. This methodology is one of knowledge compilation, which gives better reasoning performance and can deal with real-world applications such as the SMM. By using this method, we finally developed a commercial photocopier that has self-maintainability and is more robust against faults. The commercial version has been supplied worldwide as a product of Mita Industrial Co., Ltd., since April 1994.

OPUS is a branch and bound search algorithm that enables efficient admissible search through spaces for which the order of search operator application is not significant. The algorithm's search efficiency is demonstrated with respect to very large machine learning search spaces. The use of admissible search is of potential value to the machine learning community as it means that the exact learning biases to be employed for complex learning tasks can be precisely specified and manipulated. OPUS also has potential for application in other areas of artificial intelligence, notably, truth maintenance.

In the area of inductive learning, generalization is a main operation, and the usual definition of induction is based on logical implication. Recently there has been a rising interest in clausal representation of knowledge in machine learning. Almost all inductive learning systems that perform generalization of clauses use the relation theta-subsumption instead of implication. The main reason is that there is a well-known and simple technique to compute least general generalizations under theta-subsumption, but not under implication. However generalization under theta-subsumption is inappropriate for learning recursive clauses, which is a crucial problem since recursion is the basic program structure of logic programs. We note that implication between clauses is undecidable, and we therefore introduce a stronger form of implication, called T-implication, which is decidable between clauses. We show that for every finite set of clauses there exists a least general generalization under T-implication. We describe a technique to reduce generalizations under implication of a clause to generalizations under theta-subsumption of what we call an expansion of the original clause. Moreover we show that for every non-tautological clause there exists a T-complete expansion, which means that every generalization under T-implication of the clause is reduced to a generalization under theta-subsumption of the expansion.

Characteristic models are an alternative, model based, representation for Horn expressions. It has been shown that these two representations are incomparable and each has its advantages over the other. It is therefore natural to ask what is the cost of translating, back and forth, between these representations. Interestingly, the same translation questions arise in database theory, where it has applications to the design of relational databases. This paper studies the computational complexity of these problems. Our main result is that the two translation problems are equivalent under polynomial reductions, and that they are equivalent to the corresponding decision problem. Namely, translating is equivalent to deciding whether a given set of models is the set of characteristic models for a given Horn expression. We also relate these problems to the hypergraph transversal problem, a well known problem which is related to other applications in AI and for which no polynomial time algorithm is known. It is shown that in general our translation problems are at least as hard as the hypergraph transversal problem, and in a special case they are equivalent to it.

This paper studies the problem of ergodicity of transition probability matrices in Markovian models, such as hidden Markov models (HMMs), and how it makes very difficult the task of learning to represent long-term context for sequential data. This phenomenon hurts the forward propagation of long-term context information, as well as learning a hidden state representation to represent long-term context, which depends on propagating credit information backwards in time. Using results from Markov chain theory, we show that this problem of diffusion of context and credit is reduced when the transition probabilities approach 0 or 1, i.e., the transition probability matrices are sparse and the model essentially deterministic. The results found in this paper apply to learning approaches based on continuous optimization, such as gradient descent and the Baum-Welch algorithm.

The first session aimed to set the component being tested. The stage for the day's discussion by focusing variation in all three of these contexts on the issues surrounding the will lead to different types of and Verification of Knowledge-use of formal specification techniques The first paper, by Formal Specifications to Design Intelligence (AAAI-94) in Seattle, Lance Miller of SAIC, was entitled Verifiable Hybrid KBS" by Rose Gamble, Washington, marked the seventh This paper provided a with its specification, and (2) the The 1994 workshop was significant basis for the comparison of validation refinement of formal specifications in that there was a definitive move in and verification techniques to for their implementation. O'Leary, from the lows the possibility of constraining techniques for validating certain University of Southern California, the experts' choices to ensure that properties of KBSs. A paper by presented a paper on the relationship any new knowledge added is valid Alun Preece, Cliff Gossner, and T. between errors and size in KBSs. This and that the knowledge base structure Radhakrishnan (all from the University paper is among the first to address ensures the knowledge is of Aberdeen, Scotland) considered this important issue.

Analogy has a rich history in Western civilization. Over the centuries, it has become reified in that analogical reasoning has sometimes been regarded as a fundamental cognitive process. In addition, it has become identified with a particular expressive format. The limitations of the modern view are illustrated by monster analogies, which show that analogy need not be regarded as something having a single form, format, or semantics. Analogy clearly does depend on the human ability to create and use well-defined or analytic formats for laying out propositions that express or imply meanings and perceptions. Beyond this dependence, research in cognitive science suggests that analogy relies on a number of genuinely fundamental cognitive capabilities, including semantic flexibility, the perception of resemblances and of distinctions, imagination, and metaphor. Extant symbolic models of analogical reasoning have various sorts of limitation, yet each model presents some important insights and plausible mechanisms. I argue that future efforts could be aimed at integration. This aim would include the incorporation of contextual information, the construction of semantic bases that are dynamic and knowledge rich, and the incorporation of multiple approaches to the problems of inference constraint.