Skewing the Perceptron: Modeling the Importance of System-Level Manipulation When Investigating Long-Term Potentiation

Manipulation of learning processes in the brain has proven to be experimentally challenging. Various studies have focused on specific components of Long-Term Potentiation (LTP), attempting to systematically regulate the learning progress through manipulation of its proposed elements. The manipulation of such elements is thought to result in a proportional change in the efficacy of the whole system. Based on the inadequate results of this approach, we hypothesized that changes implemented to a fraction of synapses in a network represented an incomplete investigation of LTP function. We further hypothesized that in order to successfully manipulate learning output, whole systems must be manipulated whether working with a single synapse or a neural network. We chose a relatively simple and easily applied model, the perceptron, to simulate the effects of strengthening synaptic connections between neurons, as in learning. We expected that following the learning phase, systematic changes to a fraction of synaptic weights would jeopardize the perceptron’s ability to recall the learned patterns. Indeed, fractional changes of the weight distribution caused more errors in the retrieval of patterns. However, when the entire distribution was altered, error in pattern retrieval was absent. Introduction The connections between neurons have been shown to grow in strength (i.e. synaptic weight) in response to long trains of high frequency stimulation, or the temporal pairing of two or more stimulating signals (Kessels and Manilow, 2009; Bliss and Lømo, 1973). Such an input-dependant change in the properties of neuron communication is the definition of LongTerm Potentiation (LTP), a leading theory of memory formation and recall in the brain. LTP involves many complex cellular steps, coordinated between the preand postsynaptic neurons in ways that are yet not fully understood. Following induction of LTP, synapses exhibiting the increased weight values characteristic of this type of learning tend to transmit signals more readily when stimulated. A higher firing probability is subsequently observed throughout the affected pathways (Blundon and Zakharenko, 2008; Smolen, 2007). The changes in pathway activity resulting from LTP represent the specific tuning of neural response to a familiar (or learned) stimulus. Studies have shown that neurons within the Medial Temporal Cortex of the mammalian brain are more responsive to familiar stimuli, showing either an increase or a decrease in their firing efficacy (Squire et al. 2009). Although this is good evidence for learning, it is not yet clear how this is manifested in memory retrieval. We can however speculate from this evidence that cells which have undergone increases in synaptic weight (as in learning) do develop recall ability, as a function of the increased synaptic strength. Various studies have attempted to access the effects of altering synaptic strength via genetic and pharmacological manipulations in an effort to change either the outcome of the learning process, or retrieval ability following learning (Shunsuke et al, 2009; Tao-Cheng et al, 2001; Eichenbaum, 1996). Although LTP is a multicomponent process, these studies have suggested the presence of key constituents in synaptic weight increase. Experimenters have labeled various cellular steps as rate limiting steps, and attempted to either upor downregulate their activity to cause associated changes in memory systems both in vivo and in vitro. These studies have lead to very few conclusive results, suggesting that the underlying assumption, that singular key components exist within LTP systems, is inaccurate. The single-layer perceptron (Rosenblatt, 1958) allows the basic modeling of a neural network, similar to those found in the Medial Temporal Cortex. It is a theoretical model capable of simulated learning of associations between independent patterns by adjusting the connections of its network in a way representative of LTP. The 2 Journal of Young Investigators April 2010 network connections are collectively represented by a matrix of weight values, each value representing connection strength. The relative simplicity of this model in theory and application, together with its amenability to experimental manipulation, makes it a good platform from which to examine general trends in neuronal connectivity. Although it has been shown that the capabilities of feed-forward learning networks are limited (Minsky&Papert, 1969; Malinowski et al. 1995), trends which can be systematically isolated in the perceptron are valuable measures of influence over basic learning (Elizondo et al. 2007). Targeted manipulation of values in the weight matrix largely parallels previously mentioned biological experiments. Approaches in living systems have targeted synaptic weights through specific components of LTP, and in select cells within a network. Such manual increases in localized synaptic strength are presumably beneficial to the network, seeing as the overall efficiency of the system would be expected to increase. However, by altering a fraction of a network’s weight matrix by a constant factor, we expected to simulate the incomplete strengthening of a network and produce effects which mirror those observed in living systems. Using the perceptron program as a basis for supervised learning and subsequent retrieval of learned information, we hypothesized that experimental changes to the distribution of weight values after learning will cause associated changes in the state of the perceptron. We expect that these changes will reflect decreases in the efficiency of pattern retrieval. Materials and Methods In our configuration of the perceptron model (Figure 1.), input patterns are represented in groups of binomial values (0 and 1). Each input pattern is processed through the weight matrix during its transmission from an input node to an output node (nodes equivalent to pre and postsynaptic neurons). By this process it receives a strength value, assumed to be defined by the pattern’s familiarity (and later, its ability to be recalled). A total of 20 input patterns were multiplied across the weight matrix connecting the input and output nodes. The initial weights assigned to the weight matrix were randomly selected from a uniform distribution between -0.5 and +0.5. This random selection of values results in a Gaussian distribution of weights as suggested by the Central Limit Theorem. A fixed-threshold function was used to produce a binomial output from the range of values emerging from the weight matrix. The desired output of the perceptron is chosen by the experimenter and is independent of the input. The learning process takes place by comparing the input pattern to the desired pattern and developing the weight matrix according to the Delta rule formula so that the matrix may be tailored to link the input with the output. In this way the model is able to “learn” associations between independent stimuli solely by changing the strength of connections between its nodes (comparable to LTP-based learning). Figure 1. Schematic model representing the processing of 5 input patterns (in) arising from a series of 5 input nodes. The input patterns (composed of binary vectors) are compared to a predetermined “desired” output. Weight values (wn) are then applied to the inputs through algorithm in an effort to yield an output pattern similar to the desired output. The perceptron is able to learn patterns by adjusting these weights in order to render the desired and actual outputs identical. The memory of the input or stimulus is thereby stored in the array of updated weight values. The error rate observed in perceptron performance is defined as the percentage of incorrectly retrieved patterns over many successive trials. The update (ΔWj) required to resolve the error between the present and the desired states of the perceptron was computed, and gradually resolved using the Delta rule: ( )Xi Yj Uj Wj − = Δ α The learning rate (α) was chosen as 0.1 in accordance with previous protocol (Rojas, 1996). The rule requires the distance between the desired output (Uj) and the present state (Yj) be multiplied by both α and the i input (Xi). Delta rule 2 Journal of Young Investigators April 2010 updating is characterized by a gradient descent in the error rate of the perceptron as it learns a new pattern. Following primary training of the perceptron we made systematic increases (factor of 2) to the “learned” weight matrix by initially altering 100 weight values (out of total 4000=2.5%) and increasing the number of changed weights by increments of 100, up to the point of altering the entire matrix. We operationally defined each stepwise increase in the number of altered weights as one incremental condition, for a total of 40 conditions. Following each change to the learned matrix, we tested the recall ability of the perceptron. To measure the ability of the perceptron to recall the information it had learned, we presented the initial patterns and processed them through the transformed weight matrix, generating an output. The deviation of the generated output was compared to the desired memory and recorded as error rate. Mean error rate was plotted for the 100 iterations in the 40 conditions. All experiments were performed within a network consisting of 20 input nodes and 20 corresponding output nodes. These were fully interconnected by 4000 modeled synaptic connections. Results Initial perceptron learning took place successfully and the program was able to store all associations between the patterns introduced and desired outputs within the weight matrix. The 40 incremental changes to this established matrix then produced a function of mean error rates reminiscent of a parabolic shape. As illustrated by the curve in figure 2, the program begins at a state of perfect recall, meaning that the perceptron was able to associate all previously learned patterns. Therefore no