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Schema formation in a neural population subspace underlies learning-to-learn in flexible sensorimotor problem-solving


Learning-to-learn, a progressive speedup of learning while solving a series of similar problems, represents a core process of knowledge acquisition that draws attention in both neuroscience and artificial intelligence. To investigate its underlying brain mechanism, we trained a recurrent neural network model on arbitrary sensorimotor mappings known to depend on the prefrontal cortex. The network displayed an exponential time course of accelerated learning. The neural substrate of a schema emerges within a low-dimensional subspace of population activity; its reuse in new problems facilitates learning by limiting connection weight changes. Our work highlights the weight-driven modifications of the vector field, which determines the population trajectory of a recurrent network and behavior. Such plasticity is especially important for preserving and reusing the learned schema in spite of undesirable changes of the vector field due to the transition to learning a new problem; the accumulated changes across problems account for the learning-to-learn dynamics.

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Fig. 1: RNNs trained on delayed sensorimotor association problems exhibit learning-to-learn.
Fig. 2: Neural representations of decision and choice are shared across problems.
Fig. 3: Manifold perturbations reveal that reusing the schematic decision manifold facilitates learning.
Fig. 4: Learned trajectories emerge from VFCs.
Fig. 5: Weight-driven and state-driven VFCs differentially contribute to population activity change.
Fig. 6: The magnitude of recurrent weight changes explains both the magnitude of the weight-driven VFC and the number of trials to learn a problem.
Fig. 7: Accumulation of weight changes progressively improves invariance of existing representations to learning.
Fig. 8: Learning-to-learn is a process with three time scales.

Data availability

Data files, including pre-trained networks, are available for further analyses on GitHub ( in Python and MATLAB readable formats.

Code availability

All training and analysis codes are available on GitHub (


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We thank A. L. Fairhall, I. Skelin, J. J. Lin, B. Doiron, G. R. Yang, N. Y. Masse, U. P. Obilinovic, L. Y. Tian, D. V. Buonomano, J. Jaramillo, J. E. Fitzgerald and H. Sompolinksy for fruitful discussions and Y. Liu, K. Berlemont, A. Battista and P. Theodoni for critical comments on the manuscript. This work was supported by National Institute of Health U-19 program grant 5U19NS107609-03 and Office of Naval Research grant N00014-23-1-2040.

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B.P., D.J.F., E.A.B. and X.-J.W. designed the study. V.G. performed the research. V.G. and X.-J.W. wrote the manuscript.

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Correspondence to Xiao-Jing Wang.

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Goudar, V., Peysakhovich, B., Freedman, D.J. et al. Schema formation in a neural population subspace underlies learning-to-learn in flexible sensorimotor problem-solving. Nat Neurosci 26, 879–890 (2023).

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