We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly produce a single satisfying assignment. Our first CSP solver, called Perturbed Blief Propagation, smoothly interpolates two well-known inference procedures; it starts as BP and ends as a Gibbs sampler, which produces a single sample from the set of solutions. Moreover we apply a similar perturbation scheme to SP to produce another CSP solver, Perturbed Survey Propagation. Experimental results on random and real-world CSPs show that Perturbed BP is often more successful and at the same time tens to hundreds of times more efficient than standard BP guided decimation. Perturbed BP also compares favorably with state-of-the-art SP-guided decimation, which has a computational complexity that generally scales exponentially worse than our method (wrt the cardinality of variable domains and constraints). Furthermore, our experiments with random satisfiability and coloring problems demonstrate that Perturbed SP can outperform SP-guided decimation, making it the best incomplete random CSP-solver in difficult regimes.

We consider a set of probabilistic functions of some input variables as a representation of the inputs. We present bounds on how informative a representation is about input data. We extend these bounds to hierarchical representations so that we can quantify the contribution of each layer towards capturing the information in the original data. The special form of these bounds leads to a simple, bottom-up optimization procedure to construct hierarchical representations that are also maximally informative about the data. This optimization has linear computational complexity and constant sample complexity in the number of variables. These results establish a new approach to unsupervised learning of deep representations that is both principled and practical. We demonstrate the usefulness of the approach on both synthetic and real-world data.

Biology seems to be a science in its own right, or set of sciences having common aims, and so it should have its own language and explanatory concepts; yet when any specifically biological concept is suggested and used as an explanatory concept it seems to be unsatisfactory and even mystical. There are many biological concepts of this kind: Purpose, Drive, elan vital, Entelechy, Gestalten.* Physicists and engineers seem, on the other hand, to have clearly defined concepts having great power within biology.

If ability to perform complex calculations were a sufficient criterion, then even a conventional digital computor could lay claim to more intelligence than any of usand perhaps we had better let it make away with the word and be done with it.

There is another and perhaps more profound Point. The nature of a trail is that it divides space into two sets, success (being on the trail) and failure (not being so). If you are in tne success set, you are near other points of success: that means success is correlateri.

Where the accountants have fallen down, however, is in their reluctance and sometimes inability to make intensive studies of different equipment and to specify their requirements for equipment. As one authority in the field of electronic data processing has pointed out, "Accountants, unlike engineers, take the equipment as given without bothering to specify their own particular needs." But after all things are taken into consideration, it is of primary importance that the personnel who are handling the details of the investigation have a good knowledge of the particular application to be studied. Executives in many companies have been dissatisfied with the help received from outsiders who are expert programmers and who know a lot about equipment, but who are unfamiliar with business systems. In some companies executives have found that their own personnel, who know the firm's particular data processing system, after three or four months of experience in which to grasp the logics of the computer and the intricacies of programming, are much more valuable than such outside experts.

For example, if the game is chess, the piece may be: king, rook, pawn... My aim was to realize a program playing several For some games, all men are of the same games.

A general game-playing program must know the rules of the particular playing game. These rules are: (1) an algorithm indicating the winning state; (2) an algorithm enumerating legal moves. A move gives a set of changes from the present situation. There are two means of giving these rules: (1) We can write a subroutine which recognizes if we have won and another which enumerates legal moves. Such a subroutine is a black box giving to the calling program the answer: 'you win' or'you do not win', or the list of legal moves. But it cannot know what is in that subroutine.

It creates some plans and tries to execute them. It analyses the situations deeper in the tree only if the plan fails. In that case it generates new plans correcting what is wrong in the old one. So, the program considers only natural branches of the tree. It can find combinations for which it is necessary to look more than twenty ply ahead. The paper describes the methods used for analyzing a situation and for modifying unsuccessful plans. Then we examine some results found by the program.

Rote learning.We can keep all the situations already found. With each situation we store an indication on its interest or the move which has to be played. Samuell gives an example of such an application. This can be done if there are not too many possible situations. Even in games where there are many possible situations, this method can be useful for the beginning or the end of the games. We can improve this method: if the rulesare the same for all the players, we can standardize the situations: we assume that it is always the same player who has to play; for instance, at chess, white. We just keep half of the possible situations. At Go Moku where there are two axes of symetry, we just keep a quarter of the situations. But even with these improvements, there are many cases where this method is not useful because there are too many situations. It is doubtful that we can have good results in the middle game 398 at chess with such methods. We can try to generalize what has been done in a situation to another similar situation. For example in the second situation we play the same move than in the first one. Waterman2 has written an interesting progrpi playing poker. Let us describe it roughly. A situation is described by the value of seven variables: value of the program's hand, amount of money in the pot, measure of conservative style by the opponent... The program defines a partition of the set of possible values of these variables. For instance: If our hand is excellent, bet low if the opponent tends to be a conservative player and has just bet low. The problem is to define wisely these subsets. This can be done by the program which improves progressively the quality of the partition. This method is good for poker and it obtained very good results. But it is difficult to see how we can use it in a game like chess. How could we evaluate the similarity between situations, such as in similar situations we have to play the same move? A different position of a pawn can destroy a combination.