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Presynaptic modulation as fast synaptic switching: state-dependent modulation of task performance

Neuromodulatory receptors in presynaptic position have the ability to suppress synaptic transmission for seconds to minutes when fully engaged. This effectively alters the synaptic strength of a connection. Much work on neuromodulation has rested on the assumption that these effects are uniform at every neuron. However, there is considerable evidence to suggest that presynaptic regulation may be in effect synapse-specific. This would define a second"weight modulation"matrix, which reflects presynaptic receptor efficacy at a given site. Here we explore functional consequences of this hypothesis. By analyzing and comparing the weight matrices of networks trained on different aspects of a task, we identify the potential for a low complexity"modulation matrix", which allows to switch between differently trained subtasks while retaining general performance characteristics for the task. This means that a given network can adapt itself to different task demands by regulating its release of neuromodulators. Specifically, we suggest that (a) a network can provide optimized responses for related classification tasks without the need to train entirely separate networks and (b) a network can blend a"memory mode"which aims at reproducing memorized patterns and a"novelty mode"which aims to facilitate classification of new patterns. We relate this work to the known effects of neuromodulators on brain-state dependent processing.


I. INTRODUCTION
Neuromodulators (NM's) such as dopamine, serotonin or acetylcholine have the capacity to activate presynaptic receptors, located at axon boutons and involved in the regulation of both glutamate and GABA release [1], [2], [3]. For the most part, these receptors depress synaptic transmission when they become activated by a strong neuromodulatory signal. Neuromodulatory signals are generated by phasic increases of firing of e.g. dopamine or serotonin neurons (located in central brain areas such as the ventral tegmental area or dorsal raphe) and their effects generally last for seconds to minutes [4], [5], [6].
The plasticity expressed by NM receptors points to a targeted regulation at specific presynaptic sites [7], [8]. This means that the capacity for synaptic depression upon engagement of a NM receptor will be different for each synapse. The amount of change in synaptic strength is governed by the distribution and efficacy of presynaptic receptors at a given time. Plasticity in the distribution of NM receptors happens on a similar time-scale as long-term potentiation (hours for induction, days to weeks at least for retention). Thus the distribution of receptors at a presynaptic site is capable of reflecting experience on a similar time-scale as long-term potentiation, which influences the strength of glutamatergic transmission [9]. This paper explores the functional significance of presynaptic neuromodulatory receptors and their localization.
We choose conventional, fully trained neural networks as experimental material. Even though work in computational neuroscience during the past decade has shifted the focus within its major paradigm towards the investigation of precision in spike timing and the importance of short-term variability in synaptic transmission, network plasticity is still for the most part modelled by long-term potentiation as a way to set synaptic weights.
Thus the mechanisms for network plasticity are essentially the same in both artificial and biological networks, even though tighter constraints on architecture and a limited precision of synaptic weights need to be imposed on biological models.
We have therefore opted for conventionally trained neural networks as starting points for an investigation on how presynaptic modulation of synaptic weights may affect the function of biological networks in a state-dependent way.
Behavioral evidence shows that neuromodulators affect performance on recognition and learning tasks in ways that are clearly measurable yet difficult to conceptualize [10], [11]. For instance, dopamine and noradrenaline have been linked to the ideas of "attention", "arousal", "novelty" and "reward". Mathematically, they are usually analysed as regulating a single global parameter. This may guide reinforcement learning [12], set thresholds for signal detection [13] or alter the level of (recurrent) connectivity [14]. Here we propose an alternative mathematical model, the existence of a second matrix of stored values designed to be subtracted or added to the primary matrix. Obviously, the computational power expressed by weight modulation goes considerably beyond that of a global parameter. However, we also aim to show that the idea of weight modulation, which is synapse-specific and experience-dependent, is entirely compatible with the generalized notion of a subtle modulation of task execution which leaves basic performance intact. Thus we provide a theoretical basis towards further conceptualizing the role of neuromodulators in neural processing and the regulation of brain state.

II. FUNCTION OF PRESYNAPTIC NM RECEPTORS
Synapse-specific modulation of neural transmission means that a given weight matrix may be switched to a different but related one upon engagement of presynaptic receptors. More precisely, this "switch" will be often gradual, leading to a blending of stored weight values in at least two matrices.
(Since there are a number of different presynaptic receptors, each targeted by a different substance, the brain may operate with several modulation matrices. Alternatively, we might define a single matrix for the extreme values when all receptors are engaged, and the look at the various intermediate states. This question is not further addressed in this paper, rather all experiments are carried out with a single modulation matrix).
Since these effects are global on a short time scale throughout the brain, much work on neuromodulation has rested on the assumption that these effects are also uniform at each neuron or synapse. But recently, experimental evidence has emerged to the effect that NM receptors may indeed be individually regulated by a host of intracellular pathways and gene expression mechanisms [7], [8], overlapping with the mechanisms that guide glutamatergic strength (such as AMPA receptor regulation).
The activation of presynaptic NM receptors may be conceptualized as fast switching of synaptic weights -where "fast" refers to the time required to produce a strong neuromodulatory signal in response to a specific stimulus (approximately 100 ms) ( Figure 1). The change will usually last for several seconds to minutes, with termination of the effect being tightly regulated by a number of complex factors such as re-uptake mechanisms, continuing firing of NM neurons and excitation levels of the neuron (e.g. calcium and cAMP-levels).
Synaptic switching can be realized by introducing a second matrix that can be used to reset specific weights in a primary matrix. Physiologically, this corresponds to the capacity of local regulation of NM receptor activation by both transporter and receptor placement and efficacy. In this way, both depression and release from depression of fast glutamatergic/GABAergic signalling can be realized by the neural system.
Fast synaptic switching allows specific modulations of task performance in trained neural networks.
These modulations become specifically interesting when we are faced with a task or aspects of task performance, which cannot be solved by a single optimal distribution of weights.
For instance, a set of weights that classifies one set of patterns well may be less well adapted for another set of patterns. In this case, rather than choosing a weight matrix that covers both patterns in a suboptimal way, or learning and maintaining two separate networks for each set of patterns, the brain's solution may have been to combine different weight sets within a single network, and provide stimulusspecific switching between them. Rather than training different networks from scratch, the brain may thus reduce training complexity on highly related tasks. This will work when a basic performance on each aspect of the task is guaranteed with either weight distribution. Furthermore, if the weights are similar and derived from each other, incomplete switches (blends) will produce intermediate results without disrupting basic task performance. In a similar vein, the brain's answer to the problem of how to store patterns precisely for memorization but also in a more generalized, noisy fashion to facilitate classification of novel patterns may have been to accommodate both: a set of weights that closely represents a specific pattern set, and modifications to this weight matrix to obtain a looser fit, and promote generalization. In this paper we present two specific examples for task modification that can be realized by synaptic switching between two weight sets each optimized for a specific aspect of the task. The application is taken from the realm of face identification and recognition of emotional expressions of faces. The examples presented are very simple and designed to exemplify the principle of weight modulation rather than present a technical solution. They are primarily meant to illustrate the computational power of presynaptic receptors, once we accept the notion that the localization of NM receptors may be functionally regulated, rather than uniformly distributed.

III. MODULATION OF TASK PERFORMANCE
In the first example, we classify a set of patterns in a combined task (face identification and recognition of emotional expression) by supervised learning. We show that the performance of the network for each of the subtasks separately can be improved beyond the maximum performance for the whole task. Even though this means that performance for the other subtask goes down and the combined error level remains constant, we have identified a situation, where basic task performance is guaranteed and synaptic switching allows an allocation of precision in memory to one rather than the other task. Thus a network can adapt itself towards a focus on face identification or a focus on emotional recognition by engaging a neuromodulatory signal that subtly alters the weight distribution.
We created a network based on an input representation for a face image and trained on both face identification and recognition of emotional expression.
The data were taken from a publicly accessible database [15]. 53 different persons were used, and three different emo-tions (neutral, smiling, crying) were contained in the set (159 different patterns). Images were scaled and normalized to a size of 20x20 pixels which comprised the input of the network. For task A (identification), the output consisted in 6 bits coding for 53 classes, for task B (emotional recognition), the output consisted in 3 bits coding for each emotional expression. A general backpropagation algorithm was used to obtain weight matrices for a network with architecture 400x80x9 trained on both tasks simultaneously. After 4000 iterations of the training set we receive a fairly constant result of approximately 73% (face ID) and 86% (emotional recognition) correctness. (see Table I  The weight matrix is then stored and copied twice. One copy is further trained on only subtask A, the other on subtask B. This improves performance considerably for either task A or B, and results in small losses in the task not trained (s. Table  I, network A and network B).
The reduction of training complexity compared to training and storing two different networks may not seem significant in the case of a back-propagation trained neural network. But for a living neural system which takes hours to days to change individual synaptic weights, the issue of training time (not storage area) is a huge problem. Furthermore the advantage of having a coarse, roughly correct system which undergoes subtle modulation as needed in contrast to a set of highly specialized modules cannot be overestimated.
In a technical sense, whenever we are dealing with a situation, where a sequential focus on subtasks occurs, but a basic level of performance needs to be maintained at all times, this technique of "weight splitting" into two different, but similar sets of weights will optimize performance beyond the level of a single set of weights and a generalized combined ability.
We may analyze the complexity of the mechanism by a weight difference map for networks A and B (Figure 2). Very small differences in weight (< 0.03) are not shown.
This results in a picture with significant differences only in certain columns rather than others (the figure shows a cutout from the complete network).
We can see that the differences involve selected synapses and are fairly local, clustering in certain regions of the input space. The source units, connected to these sites of strongest discrepancy are are shown in Figure 3, on a 20x20 layout. In particular, weights encoding features for the eye and mouth region are affected by changes in the task setting.
This means that the given example has a low complexity in the additional training needed for the switching mechanism.

. Source Units for Strongest Weight Difference between Tasks A and B
We may also compare the hidden representations for selected patterns.  Figure 4, left panel shows the representations that result from superimposing all patterns with "smiling" face expression, the right panel shows the representations for all patterns for face id #23. In both cases, we see that the representation is similar, but not identical for networks A and B. This creates a situation, where blending of two networks can be applied without losing basic performance (s. IV). In contrast, the effort involved in training two different networks independently with essentially highly similar outcomes would not be justified.
Another reason for applying synaptic switching rather than continued training of a combinatory task consists in the assumption that we cannot substitute panel 1, B (optimal) into panel 2, B (suboptimal) without affecting panel 2 A (optimal) as well. A mathematical analysis of the "restriction of optimality" will help to establish this empirical observation. This should show that certain feature nodes are specifically affected and cannot exist in a single "best" position independent of the task that they are used for.

IV. MODULATION OF GENERALIZATION PERFORMANCE
Another modulation that can be implemented with the help of synaptic switching concerns the trade-off between pattern storage and generalization. Generally, training a network with optimization for the error level for storing a pattern may lead to "overfitting", i.e. a decrease in generalization performance, when the learned discriminant becomes too irregular. A number of techniques have been proposed to influence the degree of generalization vs. the storage of patterns (e.g. "early stopping", "weight decay" [16]). This trade-off is generally regarded to be resolved at the discretion of the modeller in accordance with task requirements.
Here we attempt to show that the brain may have implemented this design decision with the help of neuromodulation. The basic idea that neuromodulation may regulate trade-off between pattern storage and novel classification has been pioneered by Hasselmo [17], where the self-organization of feedforward connections was described as benefiting from suppression of strongly modified intrinsic connections associated with specific prior learning. The mechanism proposed here is more general, but a state-dependent modulation of learning vs. storage optimization seems to be one of the tasks of neuromodulation.
We select a training and a test set from the face identification problem. The training set consists of 100 patterns (2 for each face) and the test set of 50 patterns (1 for each face randomly selected).
Using a weight-decay backpropagation algorithm, we first obtain a network which performs well on the training set and minimizes the error in generalization (see Table II, network A, 1500 iterations, architecture of the network is 400-10-3).  Then, we perform additional training (without weight decay) to improve the network's capability to recall the training data (network B, additional 4000 iterations). This training results in 98% correct identification of the faces in the training set, but slightly decreases the generalization performance. By this method, as in the previous example, we obtain two different networks that are highly similar but different enough in selected synaptic weights to subtly alter task performance.
The comparison of the difference in weights between the two networks is shown in Figure 5. There is no clearly discernible structure to the weight difference diagram, thus we would expect complexity to be higher in this case. An interesting possibility that is supported by the physiological evidence is partial weight modulation. There are essentially two different mechanisms for that, some combination of which probably occurs in the brain. One mechanism assumes a partial activation of receptor sites by a limited increase of neuromodulator availability. This would result in a linear change of weight values. The other mechanism assumes that only a percentage of receptor sites are activated fully -other receptors being decoupled or desensitized. This would result in a potentially skewed change in weight values. Figure 6 shows the effects of both techniques on performance measures for the generalization-storage trade-off. Endpoints of the trajectories for storage and generalization are given by the values in Table II. Interestingly, shutting off a percentage of the receptors leads to fluctuations in performance (dashed line), while the linear interpolation approximates a corresponding linear change in performance (continuous line). We can see that the variance for the generalizing network is lower (1.2) than for the storing network (2.0). This is in accordance with the observation that weight decay helps in achieving better generalization. Physiologically, weight modulation may have the side effect of decreasing the range of synaptic strengths. Here we can see that this feature may have been applied in a functionally useful way by the brain.
Similarly, we may compare the firing rate distribution for both networks (Figure 8). This shows that the network optimized for storage has more neurons with low activation than the network which has been optimized for generalization. Again, this may point to a focusing of activation on selected neurons and less distributed activity in the network, which is a result that is compatible with neuromodulatory alterations of network activity.

V. CONCLUSION
In general, neuromodulators define brain state and alter neural processing according to current needs of the organism. Often it is assumed that the effects of NM are uniform at all synapses. In this sense, the modulation mediated by e.g. dopamine receptors depends only on a global signal, namely phasic increase of dopamine neuron firing and release. Accordingly, the function of neuromodulation has been linked to general, unspecific alterations in processing mode, such as increased signal-to-noise ratio, vigilance or arousal [18], (p.225-226), a general reinforcement signal [19], (p. 339-340) or increased recurrent connectivity [14], [20].
Here we show that the experimental evidence which supports localized responses greatly enhances the computational power associated with neuromodulation.
In particular, the technique of fast synaptic switching to a second weight matrix can be applied to increase performance levels of related tasks individually. We have applied this to classification of faces according to identity versus recognition of an emotional expression and to the memorization of face images versus the ability to classify novel images.
The basic idea of fast synaptic switching is not novel. A related form of synaptic switching within a neural processing network has been explored in the context of the "dynamic link architecture" [21], [22], [23]. The dynamic link architecture has been mostly used for the extraction and storage of invariants in perceptual processing. Its possible link to the physiological substrate of neuromodulation has not been explicitly explored. But the dynamic link architecture incorporates techniques for learning not only the primary weight matrix, but also a secondary matrix which stores information on the target weights that undergo switching. Our work has not addressed the question of a "learning rule" for the weight modulation matrix, i.e. the placement of presynaptic receptors. Rather we have explicitly constructed complete, fully trained weight matrices by conventional means, and explored the consequences of being able to blend or switch them by neuromodulatory signals. We have however made the observation that the complexity of learning can be expressed by the number of receptors that have to be placed.
We have taken care to ensure that the results are compatible with the forms of state-dependent processing which have been documented as behavioral modifications due to neuromodulatory function. Subtle alterations in task performance due to engagement of neuromodulator receptors provide a form of adaptivity that ensures basic performance but allows task-specific optimization. We feel that this description of neuromodulatory function provides a framework for further experimental and theoretical studies.