According to the dominant computational approach in cognitive science, cognitive agents are digital computers; according to the alternative approach, they are dynamical systems. This target article attempts to articulate and support the dynamical hypothesis. The dynamical hypothesis has two major components: the nature hypothesis (cognitive agents are dynamical systems) and the knowledge hypothesis (cognitive agents can be understood dynamically). A wide range of objections to this hypothesis can be rebutted. The conclusion is that cognitive systems may well be dynamical systems, (...) and only sustained empirical research in cognitive science will determine the extent to which that is true. (shrink)

Advocates of dynamical systems theory (DST) sometimes employ revolutionary rhetoric. In an attempt to clarify how DST models differ from others in cognitive science, I focus on two issues raised by DST: the role for representations in mental models and the conception of explanation invoked. Two features of representations are their role in standing-in for features external to the system and their format. DST advocates sometimes claim to have repudiated the need for stand-ins in DST models, but I argue that (...) they are mistaken. Nonetheless, DST does offer new ideas as to the format of representations employed in cognitive systems. With respect to explanation, I argue that some DST models are better seen as conforming to the covering-law conception of explanation than to the mechanistic conception of explanation implicit in most cognitive science research. But even here, I argue, DST models are a valuable complement to more mechanistic cognitive explanations. (shrink)

Van Gelder (1995) has recently spearheaded a movement to challenge the dominance of connectionist and classicist models in cognitive science. The dynamical conception of cognition is van Gelder's replacement for the computation bound paradigms provided by connectionism and classicism. He relies on the Watt governor to fulfill the role of a dynamicist Turing machine and claims that the Motivational Oscillatory Theory (MOT) provides a sound empirical basis for dynamicism. In other words, the Watt governor is to be the theoretical exemplar (...) of the class of systems necessary for cognition and MOT is an empirical instantiation of that class. However, I shall argue that neither the Watt governor nor MOT successfully fulfill these prescribed roles. This failure, along with van Gelder's peculiar use of the concept of computation and his struggle with representationalism, prevent him from providing a convincing alternative to current cognitive theories. (shrink)

In a recent series of publications, dynamicist researchers have proposed a new conception of cognitive functioning. This conception is intended to replace the currently dominant theories of connectionism and symbolicism. The dynamicist approach to cognitive modeling employs concepts developed in the mathematical field of dynamical systems theory. They claim that cognitive models should be embedded, low-dimensional, complex, described by coupled differential equations, and non-representational. In this paper I begin with a short description of the dynamicist project and its role as (...) a cognitive theory. Subsequently, I determine the theoretical commitments of dynamicists, critically examine those commitments and discuss current examples of dynamicist models. In conclusion, I determine dynamicism's relation to symbolicism and connectionism and find that the dynamicist goal to establish a new paradigm has yet to be realized. (shrink)

This paper advocates explicitness about the type of entity to be considered as content- bearing in connectionist systems; it makes a positive proposal about how vehicles of content should be individuated; and it deploys that proposal to argue in favour of representation in connectionist systems. The proposal is that the vehicles of content in some connectionist systems are clusters in the state space of a hidden layer. Attributing content to such vehicles is required to vindicate the standard explanation for some (...) classificatory networks’ ability to generalise to novel samples their correct classification of the samples on which they were trained. (shrink)

Fodor's and Pylyshyn's stand on systematicity in thought and language has been debated and criticized. Van Gelder and Niklasson, among others, have argued that Fodor and Pylyshyn offer no precise definition of systematicity. However, our concern here is with a learning based formulation of that concept. In particular, Hadley has proposed that a network exhibits strong semantic systematicity when, as a result of training, it can assign appropriate meaning representations to novel sentences (both simple and embedded) which contain words in (...) syntactic positions they did not occupy during training. The experience of researchers indicates that strong systematicity in any form is difficult to achieve in connectionist systems.Herein we describe a network which displays strong semantic systematicity in response to Hebbian, connectionist training. During training, two-thirds of all nouns are presented only in a single syntactic position (either as grammatical subject or object). Yet, during testing, the network correctly interprets thousands of sentences containing those nouns in novel positions. In addition, the network generalizes to novel levels of embedding. Successful training requires a, corpus of about 1000 sentences, and network training is quite rapid. The architecture and learning algorithms are purely connectionist, but classical insights are discernible in one respect, viz, that complex semantic representations spatially contain their semantic constituents. However, in other important respects, the architecture is distinctly non-classical. (shrink)

Fodor and Pylyshyn's critique of connectionism has posed a challenge to connectionists: Adequately explain such nomological regularities as systematicity and productivity without postulating a "language of thought" (LOT). Some connectionists like Smolensky took the challenge very seriously, and attempted to meet it by developing models that were supposed to be non-classical. At the core of these attempts lies the claim that connectionist models can provide a representational system with a combinatorial syntax and processes sensitive to syntactic structure. They are not (...) implementation models because, it is claimed, the way they obtain syntax and structure sensitivity is not "concatenative," hence "radically different" from the way classicists handle them. In this paper, I offer an analysis of what it is to physically satisfy/realize a formal system. In this context, I examine the minimal truth-conditions of LOT Hypothesis. From my analysis it will follow that concatenative realization of formal systems is irrelevant to LOTH since the very notion of LOT is indifferent to such an implementation level issue as concatenation. I will conclude that to the extent to which they can explain the law-like cognitive regularities, a certain class of connectionist models proposed as radical alternatives to the classical LOT paradigm will in fact turn out to be LOT models, even though new and potentially very exciting ones. (shrink)

This paper offers both a theoretical and an experimental perspective on the relationship between connectionist and Classical (symbol-processing) models. Firstly, a serious flaw in Fodor and Pylyshyn’s argument against connectionism is pointed out: if, in fact, a part of their argument is valid, then it establishes a conclusion quite different from that which they intend, a conclusion which is demonstrably false. The source of this flaw is traced to an underestimation of the differences between localist and distributed representation. It has (...) been claimed that distributed representations cannot support systematic operations, or that if they can, then they will be mere implementations of traditional ideas. This paper presents experimental evidence against this conclusion: distributed representations can be used to support direct structure-sensitive operations, in a man- ner quite unlike the Classical approach. Finally, it is argued that even if Fodor and Pylyshyn’s argument that connectionist models of compositionality must be mere implementations were correct, then this would still not be a serious argument against connectionism as a theory of mind. (shrink)

More than a decade ago, philosopher John Searle started a long-running controversy with his paper “Minds, Brains, and Programs” (Searle, 1980a), an attack on the ambitious claims of artificial intelligence (AI). With his now famous _Chinese Room_ argument, Searle claimed to show that despite the best efforts of AI researchers, a computer could never recreate such vital properties of human mentality as intentionality, subjectivity, and understanding. The AI research program is based on the underlying assumption that all important aspects of (...) human cognition may in principle be captured in a computational model. This assumption stems from the belief that beyond a certain level, implementational details are irrelevant to cognition. According to this belief, neurons, and biological wetware in general, have no preferred status as the substrate for a mind. As it happens, the best examples of minds we have at present have arisen from a carbon-based substrate, but this is due to constraints of evolution and possibly historical accidents, rather than to an absolute metaphysical necessity. As a result of this belief, many cognitive scientists have chosen to focus not on the biological substrate of the mind, but instead on the abstract causal structure_ _that the mind embodies (at an appropriate level of abstraction). The view that it is abstract causal structure that is essential to mentality has been an implicit assumption of the AI research program since Turing (1950), but was first articulated explicitly, in various forms, by Putnam (1960), Armstrong (1970) and Lewis (1970), and has become known as _functionalism_. From here, it is a very short step to _computationalism_, the view that computational structure is what is important in capturing the essence of mentality. This step follows from a belief that any abstract causal structure can be captured computationally: a belief made plausible by the Church–Turing Thesis, which articulates the power. (shrink)

Mental imagery (varieties of which are sometimes colloquially refered to as “visualizing,” “seeing in the mind's eye,” “hearing in the head,” “imagining the feel of,” etc.) is quasi-perceptual experience; it resembles perceptual experience, but occurs in the absence of the appropriate external stimuli. It is also generally understood to bear intentionality (i.e., mental images are always images of something or other), and thereby to function as a form of mental representation. Traditionally, visual mental imagery, the most discussed variety, was thought (...) to be caused by the presence of picturelike representations (mental images) in the mind, soul, or brain, but this is no longer universally accepted. (shrink)

Prior to the twentieth century, theories of knowledge were inherently perceptual. Since then, developments in logic, statis- tics, and programming languages have inspired amodal theories that rest on principles fundamentally different from those underlying perception. In addition, perceptual approaches have become widely viewed as untenable because they are assumed to implement record- ing systems, not conceptual systems. A perceptual theory of knowledge is developed here in the context of current cognitive science and neuroscience. During perceptual experience, association areas in the (...) brain capture bottom-up patterns of activation in sensory-motor areas. Later, in a top-down manner, association areas partially reactivate sensory-motor areas to implement perceptual symbols. The stor- age and reactivation of perceptual symbols operates at the level of perceptual components – not at the level of holistic perceptual expe- riences. Through the use of selective attention, schematic representations of perceptual components are extracted from experience and stored in memory (e.g., individual memories of green, purr, hot). As memories of the same component become organized around a com- mon frame, they implement a simulator that produces limitless simulations of the component (e.g., simulations of purr). Not only do such simulators develop for aspects of sensory experience, they also develop for aspects of proprioception (e.g., lift, run) and introspec- tion (e.g., compare, memory, happy, hungry). Once established, these simulators implement a basic conceptual system that represents types, supports categorization, and produces categorical inferences. These simulators further support productivity, propositions, and ab- stract concepts, thereby implementing a fully functional conceptual system. Productivity results from integrating simulators combinato- rially and recursively to produce complex simulations. Propositions result from binding simulators to perceived individuals to represent type-token relations. Abstract concepts are grounded in complex simulations of combined physical and introspective events. Thus, a per- ceptual theory of knowledge can implement a fully functional conceptual system while avoiding problems associated with amodal sym- bol systems. Implications for cognition, neuroscience, evolution, development, and artificial intelligence are explored. (shrink)

A comprehensive introduction to the Language of Though Hypothesis (LOTH) accessible to general audiences. LOTH is an empirical thesis about thought and thinking. For their explication, it postulates a physically realized system of representations that have a combinatorial syntax (and semantics) such that operations on representations are causally sensitive only to the syntactic properties of representations. According to LOTH, thought is, roughly, the tokening of a representation that has a syntactic (constituent) structure with an appropriate semantics. Thinking thus consists in (...) syntactic operations defined over representations. Most of the arguments for LOTH derive their strength from their ability to explain certain empirical phenomena like productivity, systematicity of thought and thinking. (shrink)

I argue that analogue mental representations possess a canonical decomposition into privileged constituents from which they compose. I motivate this suggestion, and rebut arguments to the contrary, through reflection on the approximate number system, whose representations are widely expected to have an analogue format. I then argue that arguments for the compositionality and constituent structure of these analogue representations generalize to other analogue mental representations posited in the human mind, such as those in early vision and visual imagery.

Each of our theories of mental representation provides some insight into how the mind works. However, these insights often seem incompatible, as the debates between symbolic, dynamical, emergentist, sub-symbolic, and grounded approaches to cognition attest. Mental representations—whatever they are—must share many features with each of our theories of representation, and yet there are few hypotheses about how a synthesis could be possible. Here, I develop a theory of the underpinnings of symbolic cognition that shows how sub-symbolic dynamics may give rise (...) to higher-level cognitive representations of structures, systems of knowledge, and algorithmic processes. This theory implements a version of conceptual role semantics by positing an internal universal representation language in which learners may create mental models to capture dynamics they observe in the world. The theory formalizes one account of how truly novel conceptual content may arise, allowing us to explain how even elementary logical and computational operations may be learned from a more primitive basis. I provide an implementation that learns to represent a variety of structures, including logic, number, kinship trees, regular languages, context-free languages, domains of theories like magnetism, dominance hierarchies, list structures, quantification, and computational primitives like repetition, reversal, and recursion. This account is based on simple discrete dynamical processes that could be implemented in a variety of different physical or biological systems. In particular, I describe how the required dynamics can be directly implemented in a connectionist framework. The resulting theory provides an “assembly language” for cognition, where high-level theories of symbolic computation can be implemented in simple dynamics that themselves could be encoded in biologically plausible systems. (shrink)

Several approaches to implementing symbol-like representations in neurally plausible models have been proposed. These approaches include binding through synchrony, “mesh” binding, and conjunctive binding. Recent theoretical work has suggested that most of these methods will not scale well, that is, that they cannot encode structured representations using any of the tens of thousands of terms in the adult lexicon without making implausible resource assumptions. Here, we empirically demonstrate that the biologically plausible structured representations employed in the Semantic Pointer Architecture approach (...) to modeling cognition do scale appropriately. Specifically, we construct a spiking neural network of about 2.5 million neurons that employs semantic pointers to successfully encode and decode the main lexical relations in WordNet, which has over 100,000 terms. In addition, we show that the same representations can be employed to construct recursively structured sentences consisting of arbitrary WordNet concepts, while preserving the original lexical structure. We argue that these results suggest that semantic pointers are uniquely well-suited to providing a biologically plausible account of the structured representations that underwrite human cognition. (shrink)

Philosophy and Memory Traces defends two theories of autobiographical memory. One is a bewildering historical view of memories as dynamic patterns in fleeting animal spirits, nervous fluids which rummaged through the pores of brain and body. The other is new connectionism, in which memories are 'stored' only superpositionally, and reconstructed rather than reproduced. Both models, argues John Sutton, depart from static archival metaphors by employing distributed representation, which brings interference and confusion between memory traces. Both raise urgent issues about control (...) of the personal past, and about relations between self and body. Sutton demonstrates the role of bizarre body fluids in moral physiology, as philosophers from Descartes and Locke to Coleridge struggled to control their own innards and impose cognitive discipline on 'the phantasmal chaos of association'. Going on to defend connectionism against Fodor and critics of passive mental representations, he shows how problems of the self are implicated in cognitive science. (shrink)

Despite the considerable attention that the systematicity argument has enjoyed, it is worthwhile examining the argument within the context of similar explanatory arguments from the history of science. This kind of analysis helps show that Connectionism, qua Connectionism, really does not have an explanation of systematicity. Second, and more surprisingly, one finds that the systematicity argument sets such a high explanatory standard that not even Classicism can explain the systematicity of thought.

This paper introduces a special issue of Cognitive Science initiated on the 25th anniversary of the publication of Parallel Distributed Processing (PDP), a two-volume work that introduced the use of neural network models as vehicles for understanding cognition. The collection surveys the core commitments of the PDP framework, the key issues the framework has addressed, and the debates the framework has spawned, and presents viewpoints on the current status of these issues. The articles focus on both historical roots and contemporary (...) developments in learning, optimality theory, perception, memory, language, conceptual knowledge, cognitive control, and consciousness. Here we consider the approach more generally, reviewing the original motivations, the resulting framework, and the central tenets of the underlying theory. We then evaluate the impact of PDP both on the field at large and within specific subdomains of cognitive science and consider the current role of PDP models within the broader landscape of contemporary theoretical frameworks in cognitive science. Looking to the future, we consider the implications for cognitive science of the recent success of machine learning systems called “deep networks”—systems that build on key ideas presented in the PDP volumes. (shrink)

This article addresses the ability of Parallel Distributed Processing (PDP) networks to generate stagewise cognitive development in accordance with Piaget's theory of cognitive epigenesis. We carried out a replication study of the simulation experiments by McClelland (1989) and McClelland and Jenkins (1991) in which a PDP network learns to solve balance scale problems. In objective tests motivated from catastrophe theory, a mathematical theory of transitions in epigenetical systems, no evidence for stage transitions in network performance was found. It is concluded (...) that PDP networks lack the ability to recover the positive outcomes of analogous catastrophe analyses of real cognitive developmental data. In an attempt to further characterize the learning behaviour of PDP networks, we carried out a second simulation study using the discrimination‐shift paradigm. The results thus obtained indicate that PDP learning is compatible with the learning of stimulus‐response relationships, not with the acquisition of mediating rules such as conceived in (neo‐)Piagetian theory. In closing, we speculate about the feasibility of simulating stagewise development with alternative network architectures. (shrink)

The computational paradigm, which has dominated psychology and artificial intelligence since the cognitive revolution, has been a source of intense debate. Recently, several cognitive scientists have argued against this paradigm, not by objecting to computation, but rather by objecting to the notion of representation. Our analysis of these objections reveals that it is not the notion of representation per se that is causing the problem, but rather specific properties of representations as they are used in various psychological theories. Our analysis (...) suggests that all theorists accept the idea that cognitive processing involves internal information-carrying states that mediate cognitive processing. These mediating states are a superordinate category of representations. We discuss five properties that can be added to mediating states and examine their importance in various cognitive models. Finally, three methodological lessons are drawn from our analysis and discussion. (shrink)

[Edited from Conclusion section:] We have looked at various challenging issues to do with getting connectionism to cope with high-level cognitive activities such a reasoning and natural language understanding. The issues are to do with various facets of generalization that are not commonly noted. We have been concerned in particular with the special forms these issues take in the arena of propositional attitude processing. The main problems we have looked at are: (1) The need to construct explicit representations of generalizations, (...) not just generalize correctly to individual cases; (2) The need to be able to match two or more complex short-term information structures, to enable rapid generalization from recent examples rather than from long-term memories; (3) The need to represent and reason with anomalous combinations of concepts; (4) The need to perform embedded reasoning. This presents special problems for systems using non-concatenative representations (as in mainstream connectionist approaches). We also touched on vague quantification in attitude report complements. Neither this topic nor that of analogies between short-term structures (point 2) has been adequately addressed in the symbolic framework, let alone in connectionism. -/- The opportunities and problems covered are put forward as things worth being optimistic about or pessimistic about, respectively. They are not put forward as decisive arguments for or against connectionism. The hope is that this chapter contributes to a greater understanding of the connectionist/symbolist gap by presenting some unusual issues and by throwing new light on some well known ones. (shrink)

This paper is a commentary on the target article by Lokendra Shastri & Venkat Ajjanagadde [S&A]: “From simple associations to systematic reasoning: A connectionist representation of rules, variables and dynamic bindings using temporal synchrony” in same issue of the journal, pp.417–451. -/- It puts S&A's temporal-synchrony binding method in a broader context, comments on notions of pointing and other ways of associating information - in both computers and connectionist systems - and mentions types of reasoning that are a challenge to (...) S&A's system (amongst many other connectionist systems, recognizing that S&A's is much more capable as regards reasoning than most other contemporary systems). (shrink)

In this article, I survey the integrated connectionist/symbolic (ICS) cognitive architecture in which higher cognition must be formally characterized on two levels of description. At the microlevel, parallel distributed processing (PDP) characterizes mental processing; this PDP system has special organization in virtue of which it can be characterized at the macrolevel as a kind of symbolic computational system. The symbolic system inherits certain properties from its PDP substrate; the symbolic functions computed constitute optimization of a well-formedness measure called Harmony. The (...) most important outgrowth of the ICS research program is optimality theory (Prince & Smolensky, 1993/2004), an optimization based grammatical theory that provides a formal theory of cross-linguistic typology. Linguistically, Harmony maximization corresponds to minimization of markedness or structural ill-formedness. Cognitive explanation in ICS requires the collaboration of symbolic and connectionist principles. ICS is developed in detail in Smolensky and Legendre (2006a); this article is a précis of and guide to those volumes. (shrink)

Vector-based models of word meaning have become increasingly popular in cognitive science. The appeal of these models lies in their ability to represent meaning simply by using distributional information under the assumption that words occurring within similar contexts are semantically similar. Despite their widespread use, vector-based models are typically directed at representing words in isolation, and methods for constructing representations for phrases or sentences have received little attention in the literature. This is in marked contrast to experimental evidence (e.g., in (...) sentential priming) suggesting that semantic similarity is more complex than simply a relation between isolated words. This article proposes a framework for representing the meaning of word combinations in vector space. Central to our approach is vector composition, which we operationalize in terms of additive and multiplicative functions. Under this framework, we introduce a wide range of composition models that we evaluate empirically on a phrase similarity task. (shrink)

Over the last quarter century, the dominant tendency in comparative cognitive psychology has been to emphasize the similarities between human and nonhuman minds and to downplay the differences as (Darwin 1871). In the present target article, we argue that Darwin was mistaken: the profound biological continuity between human and nonhuman animals masks an equally profound discontinuity between human and nonhuman minds. To wit, there is a significant discontinuity in the degree to which human and nonhuman animals are able to approximate (...) the higher-order, systematic, relational capabilities of a physical symbol system (PSS) (Newell 1980). We show that this symbolic-relational discontinuity pervades nearly every domain of cognition and runs much deeper than even the spectacular scaffolding provided by language or culture alone can explain. We propose a representational-level specification as to where human and nonhuman animals' abilities to approximate a PSS are similar and where they differ. We conclude by suggesting that recent symbolic-connectionist models of cognition shed new light on the mechanisms that underlie the gap between human and nonhuman minds. (shrink)

Arguably no concept is more fundamental to science than that of causality, for investigations into cases of existence, persistence, and change in the natural world are largely investigations into the causes of these phenomena. Yet the metaphysics and epistemology of causality remain unclear. For example, the ontological categories of the causal relata have been taken to be objects (Hume 1739), events (Davidson 1967), properties (Armstrong 1978), processes (Salmon 1984), variables (Hitchcock 1993), and facts (Mellor 1995). (For convenience, causes and effects (...) will usually be understood as events in what follows.) Complicating matters, causal relations may be singular (Socrates’s drinking hemlock caused Socrates’s death) or general (Drinking hemlock causes death); hence the relata might be tokens (e.g., instances of properties) or types (e.g., types of events) of the category in question. Other questions up for grabs are: Are singular causes metaphysically and/or epistemologically prior to general causes or vice versa (or neither)? What grounds the intuitive asymmetry of the causal relation? Are macro-causal relations reducible to micro-causal relations? And perhaps most importantly: Are causal facts (e.g., the holding of causal relations) reducible to non-causal facts (e.g., the holding of certain spatiotemporal relations)? (shrink)

[This is an earlier (1997), much longer and more detailed version of my entry on LOTH in the _Stanford Encyclopedia of Philosophy_] The Language of Thought Hypothesis (LOTH) is an empirical thesis about thought and thinking. For their explication, it postulates a physically realized system of representations that have a combinatorial syntax (and semantics) such that operations on representations are causally sensitive only to the syntactic properties of representations. According to LOTH, thought is, roughly, the tokening of a representation that (...) has a syntactic (constituent) structure with an appropriate semantics. Thinking thus consists in syntactic operations defined over representations. Most of the arguments for LOTH derive their strength from their ability to explain certain empirical phenomena like productivity, systematicity of thought and thinking. (shrink)

Multiple explanatory frameworks may be required to provide an adequate account of human cognition. This paper embeds the classical account within a neural network framework, exploring the encoding of syntacticallystructured objects over the synchronicdiachronic characteristics of networks. Synchronic structure is defined in terms of temporal binding and the superposition of states. To accommodate asymmetric relations, synchronic structure is subject to the type uniqueness constraint. The nature of synchronic structure is shown to underlie Xbar theory that characterizes the phrasal structure of (...) human languages. The derivation differentiates core Xbar properties from languagespecific properties. (shrink)

The past decade has witnessed the emergence of a novel stance on semantic representation, and its relationship to context sensitivity. Connectionist-minded philosophers, including Clark and van Gelder, have espoused the merits of viewing hidden-layer, context-sensitive representations as possessing semantic content, where this content is partially revealed via the representations'' position in vector space. In recent work, Bodén and Niklasson have incorporated a variant of this view of semantics within their conception of semantic systematicity. Moreover, Bodén and Niklasson contend that they (...) have produced experimental results which not only satisfy a kind of context-based, semantic systematicity, but which, to the degree that reality permits, effectively deals with challenges posed by Fodor and Pylyshyn (1988), and Hadley (1994a). The latter challenge involved well-defined criteria for strong semantic systematicity. This paper examines the relevant claims and experiments of Bodén and Niklasson. It is argued that their case fatally involves two fallacies of equivocation; one concerning ''semantic content'' and the other concerning ''novel test sentences''. In addition, it is argued that their ultimate construal of context sensitive semantics contains serious confusions. These confusions are also found in certain publications dealing with "latent semantic analysis". Thus, criticisms presented here have relevance beyond the work of Bodén and Niklasson. (shrink)

Figure 1: A pr ototyp ical exa mple of a three-layer feed forward network, used by Plunkett and M archm an (1 991 ) to simulate learning the past-tense of En glish verbs. The inpu t units encode representations of the three phonemes of the present tense of the artificial words used in this simulation. Th e netwo rk is trained to produce a representation of the phonemes employed in the past tense form and the suffix (/d/, /ed/, or /t/) (...) used on regular verbs. To run the network, each input unit is assigned an activation value o f 0 or 1 , dep ending on whethe r the featu re is present or not. Eac h input unit is conne cted to each of the 30 hidden units by a we ighted conn ection and p rovid es an inp ut to each hidden unit equal to the product of the input unit's activation and the weight. Each hidd en unit's activation is then determined by summing ov er the va lues co ming fro m each inp ut unit to deter mine a netinput, and then applying a non-linear function (e.g., the logistic function 1/(1+e^netinput). Th is whole proced ure is. (shrink)