به حداقل رساندن هزینه در طول تکامل شبیه سازی شبکه های عصبی زوج منجر به عدم تقارن و تخصص شدن

Motivated by specialization (lateralization) that occurs in corresponding left and right regions of the cerebral cortex, several past computational models have studied conditions under which functional specialization can arise during learning due to underlying asymmetries in paired neural networks. However, these past studies have not addressed the basic issue of how such underlying asymmetries arise in the first place. As an initial step in addressing this issue, we investigated the hypothesis that underlying asymmetries will appear in paired neural networks during a simulated evolutionary process when fitness is based not only on maximizing performance, but also on minimizing various ‘costs’ such as energy consumption, neural connection weights, and response times. Simulated evolution under these conditions consistently produced networks with left–right asymmetries in region size, excitability and plasticity. These underlying asymmetries were often synergistic, leading to subsequent functional lateralization during network training. While our computational models are too simple for these results to be directly extrapolated to real nervous systems, they provide support for the hypothesis that brain asymmetries and lateralization in biological nervous systems may be a consequence of cost minimization present during evolution, and are the first computational demonstration of emergent population lateralization

Hemispheric specialization is said to occur when one cerebral hemisphere develops to perform a task better than the other. Well known examples include lateralization in the human brain of language, handedness and visuospatial processing ( Cook, 2002, Davidson and Hugdahl, 1995 and Hellige, 1993). For instance, in roughly 95% of adult people, the left cerebral hemisphere largely controls language, so the left hemisphere is said to be dominant for language, and language to be lateralized to the left hemisphere, in these individuals. Hemispheric specializations such as vocalization and motor preferences have also been demonstrated in animals such as rodents, birds and primates ( Bradshaw and Rogers, 1993, Hellige, 1993 and Rogers and Andrew, 2002). An important distinction in this regard is between individual lateralization, such as occurs in a single person or animal, versus population lateralization, in which lateralization not only occurs in individuals, but also to the same side in the population of individuals under consideration. For example, people exhibit population lateralization to the left hemisphere for language and handedness as noted above, while birds exhibit population lateralization for bird song. In contrast, some species of lobsters develop strong individual ‘handedness’ (one claw develops to be a strong crusher, the other a more diminutive cutter) but there is no population lateralization: roughly 50% of such lobsters are left dominant and 50% right dominant (Govind, 1989). In spite of over a century of experimental investigation, the underlying causes of hemispheric specialization remain poorly understood and controversial. Many underlying asymmetries, involving neuroanatomic, cytoarchitectonic, developmental, biochemical and physiological factors, have been identified in the brain, including left–right cortical differences in size, excitability, and concentrations of important neurotransmitters (for reviews, see Davidson and Hugdahl, 1995 and Hellige, 1993). However, it is currently not clear which of these asymmetries actually are relevant to lateralization. Further, since bilateral symmetry evolved in early nervous systems in association with the appearance of forward locomotion (Lawrenz-Miller, 1977), and since it conveys certain apparent advantages (Provins, 1997), it is unclear what selective advantage would accrue on an evolutionary scale to individuals having superimposed asymmetries (Provins, 1997). Another factor, hemispheric interactions via connecting pathways between left and right hemispheres such as the corpus callosum, may also play a significant although currently unproven role ( Cook, 1986 and Hellige, 1993). Given the above uncertainties, a substantial number of computational models of emergent cerebral specialization and hemispheric interactions have been created over the last 15 years (recently reviewed in (Reggia & Levitan, 2003)). Typically, such neural network models consist of corresponding left and right cerebral regions, often connected to each other via simulated corpus callosum connections, that undergo a learning period involving alterations in synaptic connection strengths (Anninos and Cook, 1988, Cook, 1986, Cook and Beech, 1990, Jacobs and Kosslyn, 1994, Levitan and Reggia, 2000, Reggia et al., 1998, Reggia and Levitan, 2003, Ringo et al., 1994, Shevtsova and Reggia, 1999 and Shkuro et al., 2000). These computational studies have shown, for example, that lateralization to a simulated hemispheric region will occur during learning if that region is larger, learns faster, or is more active, and that inhibitory interhemispheric connections lead to more pronounced lateralization. None of these past neural models, including our own, have used evolutionary computation methods. Conversely, while there have been many studies investigating the evolution of artificial neural networks (e.g. Porto, 1997 and Ruppin, 2002), none of these latter studies has involved the issue of cerebral lateralization. In the research described in this current paper, we extend past computational modeling work by considering a different question: Why might the presence of underlying hemispheric asymmetries be beneficial to the brain from an evolutionary point of view? We work within the framework illustrated in Fig. 1. Unlike the past computational studies of hemispheric specialization described above, which start with an assumed underlying structural/functional asymmetry (i.e. they model solely the right half of Fig. 1), we evolve the parameters in a genetic representation of interacting left and right neural network regions to see if underlying asymmetries will emerge from the evolutionary process, and subsequently during learning/development lead to behavioral specialization (in other words, we model both the evolutionary and the learning processes of Fig. 1). However, we do not directly designate individual neural networks to be fit based on the presence or absence of underlying asymmetries or lateralization. Instead, we specifically examine the hypothesis that adaptive neural networks will evolve to became asymmetrical if they must not only learn to perform well during a developmental period (i.e. learn to minimize their error as they adapt to their environment via synaptic changes), but must also at the same time minimize (a) their energy consumption, (b) their weighted connectivity, or (c) their response time. As we discuss later, energy consumption, weighted connectivity, and response time have previously been suggested to be very important plausible constraints on evolution of organisms in natural environments, motivating their selection for study here. We explore through computational experiments whether these factors, which are not obviously related to neural network asymmetries or specialization a priori, can lead to simulated evolution of asymmetric neural networks that, in turn, lead to lateralization of function during subsequent neural network learning. To our knowledge, this is the first computational study to examine simulated evolution of underlying hemispheric region asymmetries rather than assuming their a priori occurrence1, and the first to examine emergent population lateralization as well as individual lateralization.

In this study, we examined the impact of incorporating various costs (constraints) into the fitness function guiding the evolution of neural networks composed of paired left and right modules. The specific costs used were inspired by factors postulated previously by others to exert important influences on brain evolution: minimizing brain metabolic energy expenditure (Gibbons, 1998), connectivity between neural elements (Cherniak, 1994), and response times (Rogers, 2000). Networks with lower values for these costs possessed a selective survival advantage in our model. These networks were free to evolve over time to be left–right symmetric or asymmetric in terms of region size, excitability, plasticity, and other parameters. Such asymmetries in biological nervous systems have been suggested to be the underlying basis of left–right brain specializations (e.g. handedness and language in humans (Hellige, 1993)) that appear during brain development. Our simulated evolutionary process did not directly determine fitness based upon network symmetries/asymmetries. Fitness was based solely on a network’s task performance and the minimizing of energy/activity, connection weights, or response time. The primary finding of this study was that substantial underlying network asymmetries very often arose whenever both maximizing performance and minimizing network costs guided the evolutionary process. This finding was very robust: it occurred in the most fit individuals in every genetic algorithm run regardless of which specific cost (energy consumption, network connection weights, or response time) was involved. It did not occur nearly as much in the two control experiments where fitness was based solely on performance, and thus is attributable to the influences of cost minimization during simulated evolution. Further, the underlying network asymmetries that appeared involved region size, region excitability and connection plasticity, typically all in the same network. These multiple asymmetries were often synergistic and reinforcing, leading to the appearance of substantial individual lateralization during learning. Given the presence of evolved underlying network asymmetries, such lateralization would be expected to appear subsequently during learning based on previous non-evolutionary computational modeling studies ( Levitan and Reggia, 2000, Reggia et al., 1998, Shevtsova and Reggia, 1999 and Shkuro et al., 2000). Why should synergistic asymmetries arise when costs as well as performance guide the evolutionary process? Plausible suggestions can be made concerning why the networks discovered by the genetic algorithm in this study are at least good solutions to the problem. To understand these suggestions, it is important to note that evolution and learning influenced network fitness in different ways. The genetic algorithm could only influence broad, top level aspects of a network (regional sizes, plasticity, etc.) while learning could only influence changes in individual connection weights. Further, in the experimental runs, the genetic algorithm was trying both to maximize performance and to minimize some cost factor, while the learning algorithm was driven to maximize only performance regardless of its impact on any costs. Thus, the evolutionary process had to discover ways to minimize costs that would not be undone by subsequent learning that occurred prior to fitness assessment. In this context, the strategies for cost minimization discovered by the genetic algorithm appear to be quite reasonable. When minimizing energy consumption, evolving underlying asymmetries favoring one side led to strong lateralization to that dominant side, while the other side was almost inactive during processing. This inactivity caused a marked reduction in total ‘energy consumption’ (the non-dominant side had low activity) while performance was maximized by learning using just the dominant side. The networks evolved while minimizing the sum of weight magnitudes on outgoing subcortical/cortical connections can be understood in a similar fashion. The evolutionary process preferred one side to be larger and have higher activation, making it learn faster and contribute more to accuracy. At the same time, since learning generally tends to increase the magnitude of connection weights, the learning rate was lower on this dominant side so that most weights in the network were kept relatively small and the total sum of weights in the network stayed relatively low. Such a strategy explains the ‘paradoxical asymmetry’ in learning rates favoring the non-dominant side (Fig. 5, bottom left; input-to-subcortical weights did not participate in this paradoxical asymmetry as they did not factor into the cost function of Eq. (6)). Finally, the networks produced while minimizing both error and response time naturally evolved to minimize the number of relaxation cycles for subcortical and cortical layers. While less marked than with the other cost factors above, lateralization still occurred fairly consistently due to evolved asymmetries in learning rates, maximum activation levels, and region sizes. Presumably, the evolutionary process discovered that, in the context of little time for interactions and coordination between left and right regions, allowing one side to dominate during learning produced lower performance error and thus higher fitness overall. Such a result is especially interesting in that recent studies with an animal model of lateralization have shown lateralization to be associated with faster speed in predator detection (Rogers, 2000) supporting the concept that lateralization and fast response times may be related. In addition to individual lateralization, runs of the genetic algorithm in the comparative experiments also consistently led to population lateralization where almost all of the networks forming a population were lateralized to the same side. To our knowledge, this is the first computational study to demonstrate the emergence of population lateralization. It occurred due to the well known convergence properties of genetic algorithms. Once a highly fit, asymmetric and lateralized individual network appeared, it was more likely to be selected for reproduction, so its characteristics rapidly permeated throughout the population. Such a result supports the view that the specific side of population lateralization of an inherited asymmetry that conveys an advantage is arbitrary and based on chance events early in the evolutionary process. This is consistent with our observation of the emergence of population lateralization sometimes to the left, and sometimes to the right, in different runs of the genetic algorithm under the same fitness criteria. What do these results suggest about the origins of biological brain asymmetries? Although not without controversy, there is substantial evidence today that underlying cerebral asymmetries have evolved in the human brain, and that they contribute to the emergence of behavioral lateralization such as occurs with handedness and language (Bradshaw and Rogers, 1993, Corballis, 1989, Geschwind et al., 2002, Hellige, 1993 and Iaccino, 1993). Perhaps most intriguing is the recent identification in some animals of specific genes determining right–left asymmetries in heart and other organs (Meyers and Martin, 1999 and Ryan et al., 1998) and suggestions that such genes might influence the development of brain asymmetries (Bisgrove, Essner, & Yost, 2000). However, it has remained unclear what advantages accrue to an individual with hemispheric specialization that could be guiding the evolutionary process: “For in the course of human evolution, the inception of any inborn bias for right-handedness or left-brainedness would have been unlikely to persist unless it bestowed on the possessor some selective survival advantage. If it did, what is it?” (Provins, 1997, p. 555). Our model is, of course, too limited to be directly extrapolated to real nervous systems, or to provide a firm answer to such questions. It was necessarily small and simple for computational tractability, and the evolutionary process used does not capture the complexities of natural evolution. That said, the striking and consistent results we obtained are intriguing. They indicate that some neural networks consisting of left and right processing pathways, when subjected to cost minimization pressures as well as performance pressures, evolve preferentially to produce asymmetric pathways. This provides support for the hypothesis that cost minimization may be a fundamental underlying factor of asymmetries in real biological nervous systems. Further, since the assumptions underlying our model are not specific to the human brain, these results imply that our model predicts that underlying left–right asymmetries and behavioral lateralization should occur in non-human animals too. There is extensive and growing evidence that this is often the case ( Bradshaw and Rogers, 1993, Hellige, 1993 and Rogers and Andrew, 2002), including recent discoveries that in non-human primates the cerebral homologs of human brain language areas are usually larger on the left than the right, just as in humans ( Cantalupo and Hopkins, 2001 and Gannon et al., 1998). Our simulations produced less clear results concerning the nature of cross–midline connections between ‘subcortical regions’ and between ‘cortical regions’. There is a long-standing and ongoing controversy over whether each cerebral hemisphere exerts primarily an excitatory versus an inhibitory influence on the opposite hemisphere via callosal connections (Cook, 1986, Cook and Beech, 1990, Reggia et al., 2001a and Reggia et al., 2001b). Different runs of the genetic algorithm produced cross–midline subcortical connections that ranged from ineffective/absent to strongly inhibitory; excitatory subcortical connections were generally not created. Evolved callosal connections were generally weaker and more varied in sign, being either excitatory or inhibitory. Overall, the results suggest that the simulated evolutionary process in comparative experiments consistently selected for inhibitory cross–midline subcortical influences and favored relatively weaker callosal influences of either sign (most often excitatory). These results are especially interesting in the context of recent non-evolutionary computational studies that have presented the view that excitatory callosal influences plus inhibitory subcortical cross–midline influences provide the best fit to a broad range of experimental data (Reggia et al., 2001a and Reggia et al., 2001b). The very limited nature of our model points the way towards possible future studies with more elaborate and realistic models. For example, we have dealt with only a single network architecture, and with a small pattern classification performance task. Thus it will be important to determine the generality of the results obtained here: do they carry over to larger recurrent networks, other tasks, and more realistic evolutionary processes? During the last few years contemporary evolutionary computation methods have increasingly been used to explore hypotheses about how brain/cognitive evolution may have occurred. For example, recent studies have examined the simulated evolution of neural networks ranging from ‘command neurons’ in simple nervous systems (Aharonov-Barki, Beker, & Ruppin, 2001) to human cortical columnar circuitry (Ayers & Reggia, 2001), and behavioral issues such as the evolution of food-finding strategies (Nolfi, Elman, & Parisi, 1994), animal signaling (Arita and Koyama, 1998, MacLennan and Burghardt, 1994 and Wagner et al., 2003) and human language (Cangelosi and Parisi, 1998 and Kvasnicka and Pospichal, 1999). Along with this current study, such investigations indicate a promising and increasingly important role for simulated evolution of neural networks in better understanding of the nature of real nervous systems.