NATURE VOL. 323 9 OCTOBER 1986 LETTERSTO NATURE delineating the absolute indigeneity of amino acids in fossils. Arco, Exxon, Phillips Petroleum, Texaco Inc., The Upjohn Co. As AMS techniques are refined to handle smaller samples, it We also acknowledge the donors of the Petroleum Research may also become possible to date individual amino acid enan- Fund, administered by the American Chemical Society(grant tiomers by the C method. If one enantiomer is entirely derived 16144-AC2 to M.H.E., grant 14805-AC2 to S.A.M.) for support. from the other by racemization during diagenesis, the individual S.A.M. acknowledges NSERC(grant A2644) for partial support. D- and L-enantiomers for a given amino acid should have identical C ages. Received 19 May: accepted 15 July 1986 Older, more poorly preserved fossils may not always prove 1. Bada, J. L. & Protsch, R. Proc. natn. Acad. ScL U.S.A. 70, 1331-1334 (1973) amenable to the determination of amino acid indigeneity by the 2. Bada, J. L., Schroeder, R. A. & Carter, G. F. Science 184, 791-793(1974). stable isotope method, as the prospects for complete replace- 3. Boulton. G. S. et al Nature 298. 437-441(1982) 4. Wehmiller, J. F. in Quaternary Dating Methods (ed. Mahaney, W. C.) 171-193 (Elsevier ment of indigenous amino acids with non-indigenous amino Amsterdam. 1984). acids increases with time. As non-indigenous amino acids 5. Engel, M. H., Zumberge, J. E. & Nagy, B. Analyt. Biochem. 82, 415-422 (1977). 6. Bada, J. 1. A. Reu. Earth planet. Sci. 13, 241-268 (1985). undergo racemization, the enantiomers may have identical 7. Chisholm, B. S., Nelson, D. E. & Schwarcz, H. P. Science 216, 1131-1132(1982) isotopic compositions and still not be related to the original 8. Ambrose, S. H. & DeNiro, M. J. Nature 319,321-324(1986) organisms. Such a circumstance may, however, become easier 9. Macko, S. A., Estep, M. L. F., Hare, P. E. & Hoering, T. C. Yb. Carnegie Instn Wash. 82, 404-410(1983) to recognize as more information becomes available concerning 10. Hare, P. E. & Estep, M. L. F. Yb. Camegie Instn Wash. 82, 410-414 (1983) the distribution and stable isotopic composition of the amino 11. Engel, M. H. & Hare, P. E. in Chemistry and Biochemistry of the Amino Acids (ed. Barrett. G. C.) 462-479 (Chapman and Hall, London, 1985). acid constituents of modern representatives of fossil organisms 12. Johnstone, R. A. W. & Rose, M. E. in Chemistry and Biochemistry of the Amino Acids (ed. Also, AMS dates on individual amino acid enantiomers may Barrett, G. C.) 480-524(Chapman and Hall, London, 1985). in some cases, help to clarify indigeneity problems, in particular 13. Weinstein, S., Engel, M. H. & Hare, P. E. in Practical Protein Chemistry-A Handbook (ed. Darbre, A.)337-344 (Wiley, New York, 1986). when stratigraphic controls can be used to estimate a genera 14. Bada, J. L., Gillespie, R., Gowlett, J. A. J. & Hedges, R. E. M. Nature 312, 442-444(1984). age range for the fossil in question. 15. Mitterer, R. M. & Kriausakul, N. Org. Geochem. 7, 91-98(1984). 16. Williams, K. M. & Smith, G. G. Onigins Life 8, 91-144 (1977) Finally, the development of techniques for determining the 17. Engel, M. H. & Hare, P. E. Yb. Carnegie Instm Wash. 81, 425-430 (1982). stable isotopic composition of amino acid enantiomers may 18. Hare, P. E. Yb. Carnegie Instn Wash. 73, 576-581(1974). 19. Pillinger. C. T. Naure 296. 802 (1982) enable us to establish whether non-racemic amino acids in some 20. Neuberger, A. Ado. Protein Chem 4, 298-383(1948). carbonaceous meteorites2' are indigenous, or result in part fron 21. Engel, M. H. & Macko, S. A. Analyt. Chem. 56, 2598-2600(1984). 22. Dungworth. G. Chem. Geol 17, 135-153 (1976) terrestrial contamination. 23. Weinstein, S., Engel, M. H. & Hare, P. E. Analyt. Biochem. 121, 370-377(1982) M.H.E. thanks the NSF, Division of Earth Sciences (grant 24. Macko, S. A., Lee, W. Y. & Parker, P. L. J. exp. mar. Biol. Ecol 63, 145-149 (1982) EAR-8352055)and the following contributors to his Presidential 25. Macko, S. A., Estep, M. L. F. & Hoering, T. C. Yb. Carnegie Instn Wash. 81,413-417(1982). 26. Vallentyne, J. R. Geochim, cosmochim. Acta 28, 157-188(1964). Young Investigator Award for partial support of this research 27. Engel, M. H. & Nagy, B. Nature 296, 837-840(1982). Learning representations more difficult when we introduce hidden units whose actual or by back-propagating errors desired states are not specified by the task. (In perceptrons, there are 'feature analysers' between the input and output that are not true hidden units because their input connections are David E. Rumelhart*, Geoffrey E. Hintont fixed by hand, so their states are completely determined by the & Ronald J. Williams* input vector: they do not learn representations.) The learning procedure must decide under what circumstances the hidden * Institute for Cognitive Science, C-015, University of California, units should be active in order to help achieve the desired San Diego, La Jolla, California 92093. USA input-output behaviour. This amounts to deciding what these Department of Computer Science, Carnegie-Mellon University, units should represent. We demonstrate that a general purpose Pittsburgh, Philadelphia 15213, USA and relatively simple procedure is powerful enough to construct appropriate internal representations. The simplest form of the learning procedure is for layered We describe a new learning procedure, back-propagation, for networks which have a layer of input units at the bottom; any networks of neurone-like units. The procedure repeatedly adjusts number of intermediate layers; and a layer of output units at the weights of the connections in the network so as to minimize a the top. Connections within a layer or from higher to lower measure of the difference between the actual output vector of the layers are forbidden, but connections can skip intermediate net and the desired output vector. As a result of the weight layers. An input vector is presented to the network by setting adjustments, internal 'hidden' units which are not part of the input the states of the input units. Then the states of the units in each or output come to represent important features of the task domain. layer are determined by applying equations(1)and(2)to the and the regularities in the task are captured by the interactions connections coming from lower layers. All units within a layer of these units. The ability to create useful new features distin have their states set in parallel, but different layers have their guishes back-propagation from earlier, simpler methods such as states set sequentially, starting at the bottom and working the perceptron-convergence procedure'. upwards until the states of the output units are determined. There have been many attempts to design self-organizing The total input, x, to unit j is a linear function of the outputs, neural networks. The aim is to find a powerful synaptic y, of the units that are connected to j and of the weights, w modification rule that will allow an arbitrarily connected neural on these connections network to develop an internal structure that is appropriate for x=yW (1) a particular task domain. The task is specified by giving the desired state vector of the output units for each state vector of Units can be given biases by introducing an extra input to each the input units. If the input units are directly connected to the unit which always has a value of 1. The weight on this extra output units it is relatively easy to find learning rules that input is called the bias and is equivalent to a threshold of the iteratively adjust the relative strengths of the connections so as opposite sign. It can be treated just like the other weights. to progressively reduce the difference between the actual and A unit has a real-valued output, y, which is a non-linear desired output vectors. Learning becomes more interesting but function of its total input (2) tTo whom correspondence should be addressed 1+e 1986 Nature Publishing Group© Nature Publishing Group 1986