Hebbian Wiring Plasticity Generates Efficient Network Structures for Robust Inference with Synaptic Weight Plasticity

Ask your doctor and stroke association to clarify Hebbian synapses. Since plasticity is referred to, this is damned important for you to know how to construct and your doctor how to know when you are doing it right.  Don't let your doctor weasel out of answering.
http://journal.frontiersin.org/article/10.3389/fncir.2016.00041/full?

Naoki Hiratani^1,2* and Tomoki Fukai^2*

• ¹Department of Complexity Science and Engineering, The University of Tokyo, Kashiwa, Japan
• ²Laboratory for Neural Circuit Theory, RIKEN Brain Science Institute, Wako, Japan

In the adult mammalian cortex, a small fraction of spines are created and eliminated every day, and the resultant synaptic connection structure is highly nonrandom, even in local circuits. However, it remains unknown whether a particular synaptic connection structure is functionally advantageous in local circuits, and why creation and elimination of synaptic connections is necessary in addition to rich synaptic weight plasticity. To answer these questions, we studied an inference task model through theoretical and numerical analyses. We demonstrate that a robustly beneficial network structure naturally emerges by combining Hebbian-type synaptic weight plasticity and wiring plasticity. Especially in a sparsely connected network, wiring plasticity achieves reliable computation by enabling efficient information transmission. Furthermore, the proposed rule reproduces experimental observed correlation between spine dynamics and task performance.

Introduction

The amplitude of excitatory and inhibitory postsynaptic potentials (EPSPs and IPSPs), often referred to as synaptic weight, is considered a fundamental variable in neural computation (Bliss and Collingridge, 1993; Dayan and Abbott, 2005). In the mammalian cortex, excitatory synapses often show large variations in EPSP amplitudes (Song et al., 2005; Ikegaya et al., 2013; Buzsáki and Mizuseki, 2014), and the amplitude of a synapse can be stable over trials (Lefort et al., 2009) and time (Yasumatsu et al., 2008), enabling rich information capacity compared with that at binary synapses (Brunel et al., 2004; Hiratani et al., 2013). In addition, synaptic weight shows a wide variety of plasticity which depend primarily on the activity of presynaptic and postsynaptic neurons (Caporale and Dan, 2008; Feldman, 2009). Correspondingly, previous theoretical results suggest that under appropriate synaptic plasticity, a randomly connected network is computationally sufficient for various tasks (Maass et al., 2002; Ganguli and Sompolinsky, 2012).

On the other hand, it is also known that synaptic wiring plasticity and the resultant synaptic connection structure are crucial for computation in the brain (Chklovskii et al., 2004; Holtmaat and Svoboda, 2009). Elimination and creation of dendritic spines are active even in the brain of adult mammalians. In rodents, the spine turnover rate is up to 15% per day in sensory cortex (Holtmaat et al., 2005) and 5% per day in motor cortex (Zuo et al., 2005). Recent studies further revealed that spine dynamics are tightly correlated with the performance of motor-related tasks (Xu et al., 2009; Yang et al., 2009). Previous modeling studies suggest that wiring plasticity helps memory storage (Poirazi and Mel, 2001; Stepanyants et al., 2002; Knoblauch et al., 2010). However, in those studies, EPSP amplitude was often assumed to be a binary variable, and wiring plasticity was performed in a heuristic manner. Thus, it remains unknown what should be encoded by synaptic connection structure when synaptic weights have a rich capacity for representation, and how such a connection structure can be achieved through a local spine elimination and creation mechanism, which is arguably noisy and stochastic (Kasai et al., 2010).

To answer these questions, we constructed a theoretical model of an inference task. We first studied how sparse connectivity affects the performance of the network by analytic consideration and information theoretic evaluations. Then, we investigated how synaptic weights and connectivity should be organized to perform robust inference, especially under the presence of variability in the input structure. Based on these insights, we proposed a local unsupervised rule for wiring and synaptic weight plasticity. In addition, we demonstrated that connection structure and synaptic weight learn different components under a dynamic environment, enabling robust computation. Lastly, we investigated whether the model is consistent with various experimental results on spine dynamics.

More at link.