The Enhanced Rise and Delayed Fall of Memory in a Model of Synaptic Integration: Extension to Discrete State Synapses

Elliott, Terry

doi:10.1162/neco_a_00867

Cited by 9 publications

(33 citation statements)

References 56 publications

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“…We note that 768/π 4 ≈ 7.88 ≈ 8 and therefore also 32/π 4 ≈ 0.33 ≈ 1/3, so these SNR lifetimes are quite insensitive to the choice of Ω. We have obtained the results for C & L before (Elliott, 2016a). The C & L model has also been extensively studied by previous authors, although purely in an SNR context.…”

Section: Snr Memory Lifetimesmentioning

confidence: 61%

“…An MFPT approach to memory lifetimes overcomes many of the difficulties of an SNR approach and shows that the latter is only asymptotically valid in the limit of a large number of synapses (Elliott, 2014). We have also observed in simulation that conditions on the number of states of synaptic strength that appear to optimise SNR memory lifetimes are not respected by MFPT lifetimes, suggesting that such optimality conditions are artifacts of the SNR approach (Elliott, 2016a).…”

Section: Introductionmentioning

confidence: 76%

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First Passage Time Memory Lifetimes for Simple, Multistate Synapses

Elliott

2017

Neural Computation

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Memory models based on synapses with discrete and bounded strengths store new memories by forgetting old ones. Memory lifetimes in such memory systems may be defined in a variety of ways. A mean first passage time (MFPT) definition overcomes much of the arbitrariness and many of the problems associated with the more usual signal-to-noise ratio (SNR) definition. We have previously computed MFPT lifetimes for simple, binary-strength synapses that lack internal, plasticity-related states. In simulation we have also seen that for multistate synapses, optimality conditions based on SNR lifetimes are absent with MFPT lifetimes, suggesting that such conditions may be artifactual. Here we extend our earlier work by computing the entire first passage time (FPT) distribution for simple, multistate synapses, from which all statistics including the MFPT lifetime may be extracted. For this, we develop a Fokker-Planck equation using the jump moments for perceptron activation. Two models are considered that satisfy a particular eigenvector condition that this approach requires. In these models, MFPT lifetimes do not exhibit optimality conditions, while in one but not the other, SNR lifetimes do exhibit optimality. Thus, not only are such optimality conditions artifacts of the SNR approach, but they are also strongly model-dependent. By examining the variance in the FPT distribution, we may identify regions in which memory storage is subject to high variability, although MFPT lifetimes are nevertheless robustly positive.In such regions, SNR lifetimes are typically (defined to be) zero. FPT-defined memory lifetimes therefore provide an analytically superior approach and also have the virtue of being directly related to a neuron's firing properties.2

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Section: Snr Memory Lifetimesmentioning

confidence: 61%

Section: Introductionmentioning

confidence: 76%

First Passage Time Memory Lifetimes for Simple, Multistate Synapses

Elliott

2017

Neural Computation

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“…Conversely, simple stochastic updater synapses that lack internal states are relatively easy to study. By integrating out internal synaptic states and working purely in terms of transitions in synaptic strength, we have shown in earlier work that we can often derive exact results that would otherwise be quite difficult, if not impossible, to obtain by other means (Elliott, 2010b(Elliott, , 2016a. Furthermore, this change of perspective often affords far greater theoretical insight by stripping away the microscopic details and bringing into sharp focus the macroscopic dynamics.…”

Section: Discussionmentioning

confidence: 95%

“…An examination of MFPT-defined memory lifetimes with complex synapses reveals that network-size effects or optimality conditions are absent, in contrast to memory lifetimes defined by SNRs (Elliott, 2016a). Although we have only examined this issue with filter-based synapses here, this difference between MFPT and SNR memory lifetimes appears to be present in other models of complex synapses (unpublished observations).…”

Section: Discussionmentioning

confidence: 99%

“…We have previously shown that considerable analytical progress and much dynamical insight can be achieved by integrating out synapses' internal states and working explicitly with their changes in strengths (Elliott, 2010b(Elliott, , 2016a. Here, therefore, by focusing only on processes that lead to changes in synaptic strength, we show that the dynamics of complex synapses may be effectively reduced to those of simple synapses for the purposes of studying memory lifetimes.…”

Section: Introductionmentioning

confidence: 90%

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Mean First Passage Memory Lifetimes by Reducing Complex Synapses to Simple Synapses

Elliott

2017

Neural Computation

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Memory models that store new memories by forgetting old ones have memory lifetimes that are rather short and grow only logarithmically in the number of synapses. Attempts to overcome these deficits include "complex" models of synaptic plasticity in which synapses possess internal states governing the expression of synaptic plasticity. Integrate-and-express, filter-based models of synaptic plasticity propose that synapses act as low-pass filters, integrating plasticity induction signals before expressing synaptic plasticity. Such mechanisms enhance memory lifetimes, leading to an initial rise in the memory signal that is in radical contrast to other related, but non-integrative memory models. Because of the complexity of models with internal synaptic states, however, their dynamics can be more difficult to extract compared to "simple" models that lack internal states. Here, we show that by focusing only on processes that lead to changes in synaptic strength, we can integrate out internal synaptic states and effectively reduce complex synapses to simple synapses.For binary-strength synapses, these simplified dynamics then allow us to work directly in the transitions in perceptron activation induced by memory storage rather than in the underlying transitions in synaptic configurations. This permits us to write down master and Fokker-Planck equations that may be simplified under certain, well-defined approximations. These methods allow us to see that memory based on synaptic filters can be viewed as an initial transient that leads to memory signal rise, followed by the emergence of OrnsteinUhlenbeck-like dynamics that return the system to equilibrium. We may use this approach to compute mean first passage time-defined memory lifetimes for complex models of memory storage.2

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Modeling Emergent Dynamics Arising from Synaptic Tagging and Capture at the Network Level

Luboeinski,

Tetzlaff

2024

Synaptic Tagging and Capture

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The Enhanced Rise and Delayed Fall of Memory in a Model of Synaptic Integration: Extension to Discrete State Synapses

Cited by 9 publications

References 56 publications

First Passage Time Memory Lifetimes for Simple, Multistate Synapses

First Passage Time Memory Lifetimes for Simple, Multistate Synapses

Mean First Passage Memory Lifetimes by Reducing Complex Synapses to Simple Synapses

Modeling Emergent Dynamics Arising from Synaptic Tagging and Capture at the Network Level

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