Hippocampal replay is not a simple recapitulation of recent experience, with awake replay often unrolling in reverse temporal order upon receipt of reward, in a manner dependent on reward magnitude. These findings have led to the proposal that replay serves to update values in accordance with reinforcement learning theories. We argue that there may be a more parsimonious account of these observations involving simple associations between contexts and experiences: During wakefulness, animals associate experiences with the contexts in which they are encoded, in a manner modulated by the salience of each experience. During periods of quiescence, replay emerges when contextual cues trigger a cascade of reactivations driven by the reinstatement of each memory’s encoding context, which in turn facilitates memory consolidation. Our theory unifies numerous replay phenomena, including findings that reinforcement learning models fail to account for.

We explore a recurrent neural network model of counting based on the differentiable recurrent attentional model of Gregor et al. (2015). Our results reveal that the model can learn to count the number of items in a display, pointing to each of the items in turn and producing the next item in the count sequence at each step, then saying ‘done’ when there are no more blobs to count. The model thus demonstrates that the ability to learn to count does not depend on special knowledge relevant to the counting task. We find that the model’s ability to count depends on how well it has learned to point to each successive item in the array, underscoring the importance of coordination of the visuospatial act of pointing with the recitation of the count list. The model learns to count items in a display more quickly if it has previously learned to touch all the items in such a display correctly, capturing the relationship between touching and counting noted by Alibali and DiRusso. In such cases it achieves performance sometimes thought to result from a semantic induction of the ‘cardinality principle’. Yet the errors that it makes have similarities with the patterns seen in human children’s counting errors, consistent with idea that children rely on graded and somewhat variable mechanisms similar to our neural networks.

Researchers exploring mathematical abilities have proposed that humans and animals possess an approximate number system (ANS) that enables them to estimate numerosities in visual displays. Experimental data shows that estimation responses exhibit a constant coefficient of variation (CV: ratio of variability of the estimates to their mean) for numerosities larger than four, and a constant CV has been taken as a signature characteristic of the innate ANS. For numerosities up to four, however, humans often produce error-free responses, suggesting the presence of estimation mechanisms distinct from the ANS specialized for this ‘subitizing range’. We explored whether a constant CV might arise from learning in generic neural networks using widely-used neural network learning procedures. We find that our networks exhibit a flat CV for numerosities larger than 4, but do not do so robustly for smaller numerosities. Our findings are consistent with the idea that estimation for numbers larger than 4 may not require innate specialization for number, while also supporting the view that a process different from the one we model may underlie estimation responses for the smallest numbers.

Distributed representations, in which information is encodedin overlapping populations of neuronal units, are essential tothe remarkable success of artificial neural networks (ANNs) inmany domains, and have been posited to be employed through-out the brain, especially in neocortex. A fundamental signatureof ANNs employing distributed representations is that learningrequires exposure to information in an interleaved order; expo-sure to new information in a blocked order tends to overwriteprior knowledge (i.e., ’catastrophic interference’). Because itis difficult to match human learning to the learning conditionsof these networks, it is not known whether human learning ex-hibits these properties, which, if true, would implicate use ofsimilar representations. To test this, we leveraged a recent pro-posal that parts of the hippocampus host distributed represen-tations of the kind typically ascribed to neocortex, and adopteda hippocampally dependent task that contrasts the effects of in-terleaved versus blocked learning on a short timescale. Exper-iments 1a and 1b demonstrate that interleaved exposure facili-tates the rapid perception of shared structure across items. Ex-periment 2 shows that only interleaved exposure permits use-ful inference when item associations need to be inferred basedon statistical regularities. Together, these results demonstratethe power of interleaved learning and implicate the use of dis-tributed representations in human rapid learning of structuredinformation.