Working memory requires information about external stimuli to be represented in the brain even after those stimuli go away. This information is encoded in the activities of neurons, and neural activities change over timescales of tens of milliseconds. Information in working memory, however, is retained for tens of seconds, suggesting the question of how time-varying neural activities maintain stable representations. Prior work shows that, if the neural dynamics are in the `  null space' of the representation - so that changes to neural activity do not affect the downstream read-out of stimulus information - then information can be retained for periods much longer than the time-scale of individual-neuronal activities. The prior work, however, requires precisely constructed synaptic connectivity matrices, without explaining how this would arise in a biological neural network. To identify mechanisms through which biological networks can self-organize to learn  memory function, we derived biologically plausible synaptic plasticity rules that dynamically modify the connectivity matrix to enable information storing. Networks implementing this plasticity rule can successfully learn to form memory representations even if only 10% of the synapses are plastic, they are robust to synaptic noise, and they can represent information about multiple stimuli. Working memory is a key cognitive function, and it relies on us retaining representations of external stimuli even after they go away. Stimulus-specific elevated firing rates have been observed in the prefrontal cortex during the delay period of working memory tasks, and are the main neural correlates of working memory BID6 BID7 . Perturbations to the delay period neural activities cause changes in the animal's subsequent report of the remembered stimulus representation BID12 BID19 . These elevated delay-period firing rates are not static but have time-varying dynamics with activities changing over timescales of tens of milliseconds BID0 BID18 ), yet information can be retained for tens of seconds FIG0 . This suggests the question of how time-varying neural activities keep representing the same information.Prior work from BID5 shows that, if the neural dynamics are in the "null space" of the representation -so that changes to neural activity do not affect the downstream read-out of stimulus information -then information can be retained for periods much longer than the timescale of individual neuronal activities (called the FEVER model; FIG0 . That model has a severe fine-tuning problem, discussed below. We identified a synaptic plasticity mechanism that overcomes this fine-tuning problem, enabling neural networks to learn to form stable representations.While the dynamics of neurons in the FEVER model match that which is observed in the monkey prefrontal cortex during a working memory task BID16 , the model itself requires that the network connectivity matrix have one or more eigenvalues very near to unity. According to the Gershgorin Circle Theorem, this will almost surely not happen in randomly-connected networks: fine-tuned connectivity is needed. BID5 suggest a mechanism of Hebbian learning by which this connectivity can be learned. That mechanism requires the read-out weights to form a 'tight frame' , which will not necessarily be true in biological circuits. Thus, the prior work leaves it unknown how synaptic plasticity can form and/or maintain functional working memory networks. Here, we identify biologically plausible synaptic plasticity rules that can solve this fine-tuning problem without making strong assumptions like 'tight frame' representations. Our plasticity rules dynamically re-tune the connectivity matrix to enable persistent representations of When presented with an external stimulus, s, neural activity patterns initially encode an internal representation of that stimulus,ŝ(t=0). These neural activity patterns change over time on timescales of tens of milliseconds, and yet somehow the same information is stored for up to tens of seconds. (B) While the firing rates, r i (t), change over time, information about stimulus,ŝ(t), can be remain unchanged as long as the projection of the firing rates onto the "read-out" vector d, remains constant BID5 .stimulus information. We specifically address parametric working memory, where the requirement is to remember continuous values describing several different variables or dimensions such as spatial locations or sound frequencies. For example, in the oculomotor delayed response task, subjects must remember the location of a target during a delay period BID6 . We perform experiments to demonstrate that networks using these plasticity rules are able to store information about multiple stimuli, work even if only a fraction of the synapses are tuned, and are robust to synaptic noise. We also show that these networks improve over time with multiple presented stimuli, and that the learning rules work within densely or sparsely connected networks. We derived biologically plausible synaptic plasticity rules through which networks self-organize to store information in working memory. Networks implementing these plasticity rules are robust to synaptic noise, to having only some of the synapses updated, and to partial connectivity. These networks can store multiple stimuli and have increased performance after previous training. We suggest two candidate sources for the global error signal necessary for the plasticity rule, and demonstrate that our networks can learn to store stimulus information while satisfying the added requirements imposed by these biological mechanisms. This flexibility suggests that other types of synaptic plasticity updates may also be able to organize working memory circuits.The results presented here were obtained for networks of 100 neurons -as opposed to larger networks -to speed up the simulations. Tests on networks with 10,000 neurons show that the update rule works in larger networks. The optimal learning rate, η, decreases as the network size increases. Aside from network size, a potential caveat in using a rate-based network model is losing information about spike-timing dependency. A future direction would be to create a spike-based model and determine what, if anything, must be adjusted to account for spike timing, and for the discretization that spiking neurons entail for the information shared between cells.Along with understanding how information is stored in working memory, this work may have implications in training recurrent neural networks (RNNs). Machine learning algorithms are generally unrealistic from a biological perspective: most rely on non-local synaptic updates or symmetric synapses. We show that recurrent networks can learn to store information using biologically plausible synaptic plasticity rules which require local information plus a global error signal (or signals), that can be calculated on the apical dendrite or via neuromodulators. This same setup could be utilized in RNNs to make them more biologically realistic. This would let us better understand how the brain learns, and could lead to novel biomimetic technologies: prior work on biologically realistic machine learning algorithms has led to hardware devices that use on-chip learning BID11 BID20 . Synaptically local updates do not have to be coordinated over all parts of the chip, enabling simpler and more efficient hardware implementations.
We derived biologically plausible synaptic plasticity learning rules for a recurrent neural network to store stimulus representations.  A neural network model consisting of recurrently connected neurons and one or more redouts which aims to retain some output over time. This paper presents a self-organizing memory mechanism in a neural model, and introduces an objective function that minimizes changes in the signal to be memorized.