Abstract
Artificial neural networks are remarkably adept at sensory processing, sequence learning and reinforcement learning, but are limited in their ability to represent variables and data structures and to store data over long timescales, owing to the lack of an external memory. Here we introduce a machine learning model called a differentiable neural computer (DNC), which consists of a neural network that can read from and write to an external memory matrix, analogous to the random-access memory in a conventional computer. Like a conventional computer, it can use its memory to represent and manipulate complex data structures, but, like a neural network, it can learn to do so from data. When trained with supervised learning, we demonstrate that a DNC can successfully answer synthetic questions designed to emulate reasoning and inference problems in natural language. We show that it can learn tasks such as finding the shortest path between specified points and inferring the missing links in randomly generated graphs, and then generalize these tasks to specific graphs such as transport networks and family trees. When trained with reinforcement learning, a DNC can complete a moving blocks puzzle in which changing goals are specified by sequences of symbols. Taken together, our results demonstrate that DNCs have the capacity to solve complex, structured tasks that are inaccessible to neural networks without external read–write memory.
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Acknowledgements
We thank D. Silver, M. Botvinick and S. Legg for reviewing the paper prior to submission; P. Dayan, D. Wierstra, G. Hinton, J. Dean, N. Kalchbrenner, J. Veness, I. Sutskever, V. Mnih, A. Mnih, D. Kumaran, N. de Freitas, L. Sifre, R. Pascanu, T. Lillicrap, J. Rae, A. Senior, M. Denil, T. Kocisky, A. Fidjeland, K. Gregor, A. Lerchner, C. Fernando, D. Rezende, C. Blundell and N. Heess for discussions; J. Besley for legal assistance; the rest of the DeepMind team for support and encouragement; and Transport for London for allowing us to reproduce portions of the London Underground map.
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Contributions
A.G. and G.W. conceived the project. A.G., G.W., M.R., T.H., I.D., S.G. and E.G. implemented networks and tasks. A.G., G.W., M.R., T.H., A.G.-B., T.R. and J.A. performed analysis. M.R., T.H., I.D., E.G., K.M.H., C.S., P.B., K.K. and D.H. contributed ideas. A.C. prepared graphics. A.G., G.W., M.R., T.H., S.G., A.P.B., Y.Z., G.O. and K.K. performed experiments. A.G., G.W., H.K., K.K. and D.H. managed the project. A.G., G.W., M.R., T.H., K.K. and D.H. wrote the paper.
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Reviewer Information Nature thanks Y. Bengio, J. McClelland and the other anonymous reviewer(s) for their contribution to the peer review of this work.
Extended data figures and tables
Extended Data Figure 1 Dynamic memory allocation.
We trained the DNC on a copy problem, in which a series of 10 random sequences was presented as input. After each input sequence was presented, it was recreated as output. Once the output was generated, that input sequence was not needed again and could be erased from memory. We used a DNC with a feedforward controller and a memory of 10 locations—insufficient to store all 50 input vectors with no overwriting. The goal was to test whether the memory allocation system would be used to free and re-use locations as needed. As shown by the read and write weightings, the same locations are repeatedly used. The free gate is active during the read phases, meaning that locations are deallocated immediately after they are read from. The allocation gate is active during the write phases, allowing the deallocated locations to be re-used.
Extended Data Figure 2 Altering the memory size of a trained network.
A DNC trained on the traversal task with 256 memory locations was tested while varying the number of memory locations and graph triples. The heat map shows the fraction of traversals of length 1–10 performed perfectly by the network, out of a batch of 100. There is a clear correspondence between the number of triples in the graph and the number of memory locations required to solve the task, reflecting our earlier analysis (Fig. 3) that suggests that DNC writes each triple to a separate location in memory. The network appears to exploit all available memory, regardless of how much memory it was trained with. This supports our claim that memory is independent of processing in a DNC, and points to large-scale applications such as knowledge graph processing.
Extended Data Figure 3 Probability of achieving optimal solution.
a, DNC. With 10 goals, the performance of a DNC network with respect to satisfying constraints in minimal time as the minimum number of moves to a goal and the number of constraints in a goal are varied. Performance was highest with a large number of constraints in each goal. b, The performance of an LSTM on the same test.
Extended Data Figure 4 Effect of link matrix sparsity on performance.
We trained the DNC on a copy problem, for which a sequence of length 1–100 of size-6 random binary vectors was given as input, and an identical sequence was then required as output. A feedforward controller was used to ensure that the sequences could not be stored in the controller state. The faint lines show error curves for 20 randomly initialized runs with identical hyper-parameters, with link matrix sparsity switched off (pink), sparsity used with K = 5 (green) and with the link matrix disabled altogether (blue). The bold lines show the mean curve for each setting. The error rate is the fraction of sequences copied with no mistakes out of a batch of 100. There does not appear to be any systematic difference between no sparsity and K = 5. We observed similar behaviour for values of K between 2 and 20 (plots omitted for clarity). The task cannot easily be solved without the link matrix because the input sequence has to be recovered in the correct order. Note the abrupt drops in error for the networks with link matrices: these are the points at which the system learns a copy algorithm that generalizes to longer sequences.
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Supplementary information
Supplementary Information
This file contains a glossary of symbols and the complete equations. (PDF 85 kb)
Shortest Path Visualisation
This video shows a DNC successfully finding the shortest path between two nodes in a randomly generated graph. By decoding the memory usage of the DNC (as in Fig. 3) we were able to determine which edges were stored in the memory locations it was reading from and writing to at each timestep. The edges being read are shown in pink on the left, while the edges being written are shown in green on the right; the colour saturation indicates the relative strength of the operation. During the initial query phase, the DNC receives the labels for the start and end goal ("390" and "040" respectively). During the ten step planning phase it attempts to determine the shortest path. During this time it repeatedly reads edges close to or along the path, which are indicated by the grey shaded nodes. Beginning with edges attached to the start and end node, it appears to move further afield as the phase progresses. At the same time it writes to several of the edge locations, perhaps marking those edges as visited. Finally, during the answer phase, it successively reads the outgoing edges from the nodes along the shortest path, allowing it to correctly answer the query. (MOV 2604 kb)
Mini-SHRDLU Visualisation
This video shows a DNC successfully performing a reasoning problem in a blocks world. A sequence of letter-labeled goals (S, K, R, Q, E) is presented to the network one step at a time. Each goal consists of a sequence of defining constraints, presented one constraint per time-step. For example, S is: 6 below 2 (6b2); 2 right of 5 (2r5); 6 right of 1 (6r1); 5 above 1 (5a1). On the right, the write head edits the memory, writing information about the goals down. Ultimately, the DNC is commanded to satisfy goal \Q", which it does subsequently by using the read heads to inspect the locations containing goal Q. The constraints constituting goal \Q" are shown below, and the final board position is correct. (MOV 5292 kb)
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Graves, A., Wayne, G., Reynolds, M. et al. Hybrid computing using a neural network with dynamic external memory. Nature 538, 471–476 (2016). https://doi.org/10.1038/nature20101
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