J. Schmidhuber. Adaptive decomposition of time. In T. Kohonen, K. Makisara, O. Simula, and J. Kangas, editors, Arti cial Neural Networks, pages 909-914. Elsevier Science Publishers B.V., NorthHolland, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....P : fP 1 ; P 2 g SZ according to Figure 2. Learning for S is now performed by propagating the error back through the trained evaluators E 1 and E 2 (gradients are calculated, weights not changed) Desired output values are b 1 = b 2 = 1, indicating known paths from P 1 to SZ, and from SZ to P 2 [17]. Using this principle the following experiment was conducted. A neural controller was teached to control 20 step trajectories from start to goal positions in between the unit square. One step length was less than 0.05, in each of the directions N ,W ,S,E. The controller was trained with 100.000 ....

J.H. Schmidhuber. Adaptive decomposition of time. In T. Kohonen, K. Makisara, O. Simula, and J. Kangas, editors, Artificial Neural Networks. Proceedings of the 1991 International Conference on Artificial Neural Networks (ICANN-91) Espoo, Finland, pages 909--914. Amsterdam: Elsevier Publishers B.V., North-Holland, June 1991.

....100 papers on diverse topics including fine arts [96] and the nature of surprises [97] Apparently he even founded a religion [94] Most of his articles, however, are about machines that learn from experience. I have started to compile an incomplete list of references to work by him and his lab [117, 116, 39, 50, 40, 42, 43, 41, 52, 49, 56, 44, 54, 47, 48, 51, 53, 57, 46, 68, 45, 55, 69, 64, 65, 59, 66, 58, 67, 60, 63, 61, 73, 71, 79, 70, 74, 62, 72, 75, 78, 82, 80, 76, 81, 77, 84, 89, 88, 94, 87, 85, 96, 83, 100, 86, 90, 99, 91, 93, 105, 119, 95, 92, 97, 120, 118, 98, 125, 130, 129, 126, 128, 124, 123, 122, 131, 127, 35, 34, 36, 38, 32, 33, 37, 27, 28, 25, 24, 22, 23, 15, 9, 21, 10, 16, 26, 17, 18, 6, 7, 8, 13, 11, 20, 19, 14, 12, 115, 114, 121, 30, 106, 108, 107, 29, 31, 109, 110, 111, 112, 113, 5, 101, 103, 104, 4, 3, 2, 1, 102]. Hopefully I ll be able to add missing entries soon. Future work will concentrate on categorizing related papers and establishing common threads. ....

J. Schmidhuber. Adaptive decomposition of time. In T. Kohonen, K. Makisara, O. Simula, and J. Kangas, editors, Artificial Neural Networks, pages 909--914. Elsevier Science Publishers B.V., North-Holland, 1991.

.... from the very first network are sent to a higher level network which in turn predict its next input operating on a slower, self organizing time scale (Schmidhuber, 1992a; 1992b; for a variation of this idea in which unexpected states are identified by a network that predicts its own error see Schmidhuber, 1991). 1.2 A self organizing hierarchy of prediction and segmentation layers In this paper we propose an approach based on a hierarchy of prediction layers (Figure 1) which try to predict the next internal states of the lower layers (or of the sensory motor states in the case of the very first ....

Schmidhuber, J. (1991). Adaptive decomposition of time. In Kohonen, Maekisara, Simula, Kangas (Eds.), Artificial Neural Networks, North-Holland: Elsevier.

....and direct trajectory does not exist (b = 0) Next we need a subgoal generation function S : P 2 P : fP 1 ; P 2 g SG, an other standard backpropagation network. In order to train the subgoal generation network we couple it with two copies of an already trained evaluation network (figure 1 [3]) For a specific start P 1 and a goal P 2 a subgoal SG should be produced, that yields b 1 ; b 2 (1 Gamma ) indicating known paths from P 1 to SG, and from SG to P 2 . This can be achieved by propagating the error back through the trained evaluators E 1 and E 2 (gradients are calculated, ....

J. H. Schmidhuber. Adaptive decomposition of time. In T. Kohonen, K. Makisara, O. Simula, and J. Kangas, editors, Artificial Neural Networks. Proceedings of the 1991 International Conference on Artificial Neural Networks (ICANN-91) Espoo, Finland. Amsterdam: Elsevier Publishers B.V., North-Holland, June 1991.

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J. Schmidhuber. Adaptive decomposition of time. In T. Kohonen, K. Makisara, O. Simula, and J. Kangas, editors, Arti cial Neural Networks, pages 909-914. Elsevier Science Publishers B.V., NorthHolland, 1991.

....time than P s . With the known learning algorithms, the higher level predictor will have less difficulties in learning to predict the critical inputs than the lower level predictor. This method [4] will lead to a hierarchy of predictors and is related to the recent chunking method described in [2]. Here it should be mentioned that with many practical tasks there is no need for unique representations of time steps [4] Often a multi level predictor hierarchy will be the fastest and safest way of learning to deal with sequences with multi level temporal structure (e.g speech) Experiments ....

J. Schmidhuber. Adaptive decomposition of time. In T. Kohonen, K. Makisara, O. Simula, and J. Kangas, editors, Artificial Neural Networks, pages 909--914. Elsevier Science Publishers B.V., NorthHolland, 1991.

....at time t is the real vector o C (t) fC (i C (t) hC (t) where the real vector hC (t) is the internal state of C. At time t there is a target output dC (t) for the confidence module. dC (t) should provide information about how reliable M s prediction o M (t) can be expected to be [8] 5] [7]. In what follows, v j is the jth component of a vector v, E denotes the expectation operator, dim(x) denotes the dimensionality of vector x, j c j denotes the absolute value of scalar c, P (A j B) denotes the conditional probability of A given B, and E(A j B) denotes the conditional ....

....oA (t) ffi x(t) and dM (t) x(t 1) where oA (t) is the output vector of a controller A at time t, ffi is the concatenation operator, and x(t) is the environmental input at time t. In general, o A (t) influences the state of the environment. Therefore it may have an influence on x(t 1) In [7] confidence modules have been successfully applied to the problem of meaningful hierarchical sequence chunking. This section (which provides the major contribution of this paper) describes how they can help to make the construction of a world model more efficient. We define curiosity as the desire ....

[Article contains additional citation context not shown here]

J. Schmidhuber. Adaptive decomposition of time. In T. Kohonen, K. Makisara, O. Simula, and J. Kangas, editors, Artificial Neural Networks, pages 909--914. Elsevier Science Publishers B.V., NorthHolland, 1991.

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Schmidhuber, J. (1991). Adaptive decomposition of time. In Kohonen, T., Makisara, K., Simula, O., and Kangas, J., editors, Artificial Neural Networks, pages 909--914. Elsevier Science Publishers B.V., North-Holland.

No context found.

Schmidhuber, J. H. (1991a). Adaptive decomposition of time. In Kohonen, T., Makisara, K., Simula, O., and Kangas, J., editors, Artificial Neural Networks, pages 909--914. Elsevier Science Publishers B.V., North-Holland.

....the algorithm presented here (by means of Euler discretization) Many typical environments produce input sequences that have both local and more global temporal structure. For instance, input sequences are often hierarchically organized (e.g. speech) In such cases, sequence composing algorithms (Schmidhuber, 1991) (Schmidhuber, 1992) can provide superior alternatives to pure gradient based algorithms. 1 ACKNOWLEDGEMENTS Thanks to Mike Mozer, Bernd Schurmann, and Daniel Prelinger for providing useful comments on an earlier draft of this paper. ....

Schmidhuber, J. H. (1991). Adaptive decomposition of time. In Kohonen, T., Makisara, K., Simula, O., and Kangas, J., editors, Artificial Neural Networks, pages 909--914. Elsevier Science Publishers B.V., North-Holland.

....that tend to have both local and more global temporal structure. For instance, often input sequences are hierarchically organized (e.g. speech) But, the algorithm described above (as well as the previous algorithms) do not try to learn to divide and conquer . Sequence composing algorithms [3] [4] can provide superior alternatives. ....

J. H. Schmidhuber. Adaptive decomposition of time. In O. Simula, editor, Proceedings of the International Conference on Artificial Neural Networks ICANN 91, to appear. Elsevier Science Publishers B.V., 1991.

....no need to store all the i(t k ) k = 1; l, it suffices to store only those components of the i(t k ) that were not correctly predicted. The above principle will be referred to as the principle of history compression . In an informal manner, it has been formulated in [25] 24] 19] and [27]. Now consider a second higher level discrete time predictor whose state at time t k ; k 2 fl; lg is described by an environmental input vector i C (t k ) t k ffi i(t k ) an internal state vector hC (t k ) and an output vector oC (t k ) Here ffi is the concatenation operator. ....

....fewer inputs over time than P s . With the known learning algorithms, the higher level predictor will have less difficulties in learning to predict the critical inputs than the lower level predictor. This method will lead to a hierarchy of predictors and is related to the method described in [27]. There are at least two important differences between the approach described in [27] and the approach described herein. One difference is the criterion for creating a new level in the hierarchy: With [27] this criterion is based on measuring the reliability of the predictor s predictions. The ....

[Article contains additional citation context not shown here]

J. H. Schmidhuber. Adaptive decomposition of time. In O. Simula, editor, Proceedings of the International Conference on Artificial Neural Networks ICANN 91, to appear. Elsevier Science Publishers B.V., 1991.

....at time t is the real vector oC (t) fC (i C (t) hC (t) where the real vector hC (t) is the internal state of C. At time t there is a target output dC (t) for the confidence module. dC (t) should provide information about how reliable M s prediction oM (t) can be expected to be [10] 8] [9]. In what follows, v j is the jth component of a vector v, E denotes the expectation operator, dim(x) denotes the dimensionality of vector x, j c j denotes the absolute value of scalar c, P (A j B) denotes the conditional probability of A given B, and E(A j B) denotes the conditional ....

....= oA (t)ffix(t) and dM (t) x(t 1) where oA (t) is the output vector of a controller A at time t, ffi is the concatenation operator, and x(t) is the environmental input at time t. In general, oA (t) influences the state of the environment. Therefore it may have an influence on x(t 1) In [9] confidence modules have been successfully applied to the problem of meaningful hierarchical sequence chunking. The next subsection describes how they can be used for supporting controller learning. The next subsection is not essential for the central contribution of this paper (which can be found ....

[Article contains additional citation context not shown here]

J. H. Schmidhuber. Adaptive decomposition of time. In O. Simula, editor, Proceedings of the International Conference on Artificial Neural Networks ICANN 91, to appear. Elsevier Science Publishers B.V., 1991.

....of structuring all kinds of sequences of events and or actions into parts that belong together . It is the problem of deciding what a good sub program is, which its initial conditions are, and when it ends. The dividing problem has to do with unsupervised learning. It has been adressed in [10] [11], and [12] The conquering problem is to select from many available sub programs and to combine them in a way that allows to reach a given goal state. In the sequel the conquering problem will be isolated and studied under the assumption that the dividing problem is already solved. In ....

J. H. Schmidhuber. Adaptive decomposition of time. In O. Simula, editor, Proceedings of the International Conference on Artificial Neural Networks ICANN 91. Elsevier Science Publishers B.V., 1991.

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