The temporal paradox of Hebbian learning and homeostatic plasticity
Introduction
More than half a century ago, Donald Hebb [1] laid down an enticing framework for the neurobiological basis of learning, which can be succinctly summarized in the well-known mantra, ‘neurons that fire together wire together’ [2]. However, such dynamics suffers from two inherent problems. First, Hebbian learning exhibits a positive feedback instability: those neurons that wire together will fire together more, leading to even stronger connectivity. Second, such dynamics alone would lead to all neurons in a recurrent circuit wiring together, precluding the possibility of rich patterns of variation in synaptic strength that can encode, through learning, the rich structure of experience. Two fundamental ingredients required to solve these problems are stabilization [3], which prevents runaway neural activity, and competition [4•, 5, 6•], in which the strengthening of a synapse may come at the expense of the weakening of others.
In theoretical models, competition and stability are often achieved by augmenting Hebbian plasticity with additional constraints [5, 7•, 3]. Such constraints are typically implemented by imposing upper limits on individual synaptic strengths, and by enforcing some constraint on biophysical variables, for example, the total synaptic strength or average neuronal activity [6•, 8, 7•, 9, 10, 11, 12]. In neurobiology, forms of plasticity exist which seemingly enforce such limits or constraints through synaptic scaling in response to firing rate perturbations [13, 14], or through stabilizing adjustments of the properties of plasticity in response to the recent synaptic history, a phenomenon known as homeostatic metaplasticity [15, 16, 6•, 11]. Overall, synaptic scaling and metaplasticity, as special cases of homeostatic mechanisms that operate over diverse spatiotemporal scales across neurobiology [17, 18, 19, 20, 21, 22], are considered key ingredients that contribute both stability and competition to Hebbian plasticity by directly affecting the fate of synaptic strength.
The defining characteristic of homeostatic plasticity is that it drives synaptic strengths so as to ensure a homeostatic set point [23, 24•], such as a specific neuronal firing rate or membrane potential. However, it is important that this constraint is implemented only on average, over long timescales, thereby allowing neuronal activity to fluctuate on shorter timescales, so that these neuronal activity fluctuations, which drive learning through Hebbian plasticity, can indeed reflect the structure of ongoing experience. This requisite separation of timescales is indeed observed experimentally; forms of Hebbian plasticity can be induced on the timescale of seconds to minutes [25, 26, 27, 28], whilst most forms of homeostatic synaptic plasticity operate over hours or days [14, 29, 24•]. This separation of timescales, however, raises a temporal paradox: homeostatic plasticity then may become too slow to stabilize the fast positive feedback instability of Hebbian learning. Indeed modeling studies that have attempted to use homeostatic plasticity mechanisms to stabilize Hebbian learning [11, 30, 31•, 32•, 33, 34] were typically required to speed up homeostatic plasticity to timescales that are orders of magnitude faster than those observed in experiments (Figure 1).
This temporal paradox could have two potential resolutions. First, the timescale of Hebbian plasticity, as captured by recent plasticity models fit directly to data from slice experiments [35, 28, 36, 37•, 38], may overestimate the rate of plasticity that actually occurs in vivo. This overestimate could arise from differences in slice and in vivo preps, or because complex nonlinear synaptic dynamics, both present in biological synapses and useful in learning and memory [39, 40, 41], are missing in most, but not all [42, 43, 44], data-driven models. While slow plasticity may be a realistic possibility in cortical areas exhibiting plastic changes over days [45, 46], it may not be a realistic resolution in other areas, like the hippocampus, which must rapidly encode new episodic information [47, 48]. The second potential resolution to the paradoxical separation of timescales between Hebbian and homeostatic plasticity may be the existence of as yet unidentified rapid compensatory processes (RCPs) that stabilize Hebbian learning. Below, we explore both the theoretical utility and potential neurobiological instantiations of these putative RCPs.
Section snippets
The temporal paradox of Hebbian and homeostatic plasticity
To understand the theoretical necessity for RCPs to stabilize Hebbian plasticity, it is useful to view a diversity of synaptic learning models through the unifying lens of control theory (Figure 2a). Here we can view the ‘fire together, wire together’ interplay of neuronal activity and Hebbian synaptic plasticity as an unstable dynamical system. Also, we can view a compensatory process as a feedback controller that observes some aspect of either neuronal activity or synaptic strength, and uses
Putative rapid compensatory processes
What putative RCPs could augment Hebbian plasticity with the requisite stability and competition? Here we focus on several possibilities, operating at either the network, the neuronal or the dendritic level (Figure 4a). However, we note that these possibilities are by no means exhaustive.
At the network level, recurrent or feedforward synaptic inhibition could influence and potentially stabilize plasticity at excitatory synapses directly. For instance, [74] demonstrated via dynamic-clamp that a
Conclusion
The trinity of Hebbian plasticity, competition and stability are presumed to be crucial for effective learning and memory. However, a detailed theoretical and empirical understanding of how these diverse elements conspire to functionally shape neurobiological circuits is still missing. Here we have focused on one striking difference between existing models and neurobiology: the paradoxical separation of timescales between Hebbian and homeostatic plasticity. In models, such a separation of
Conflict of interest statement
Nothing declared.
References and recommended reading
Papers of particular interest, published within the period of review, have been highlighted as:
• of special interest
Acknowledgements
FZ was supported by the SNSF (Swiss National Science Foundation). SG was supported by the Burroughs Wellcome, Sloan, McKnight, Simons and James S. McDonnell Foundations and the Office of Naval Research. WG was supported for this work by the European Research Council under grant agreement number 268689 (MultiRules) and by the European Community's Seventh Framework Program under grant no. 604102 (Human Brain Project).
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