Image processing and becoming conscious of its result Mitja Peruš BION Institute; Stegne 21; SLO-1000 Ljubljana; Slovenia Phone & fax:+386-1-513-1147; mitia.perus@uni-lj.si: http://www.bion.si/mitja.htm Keywords: image processing, brain, vision, striate cortex = VI, consciousness, quantum associative net, Pribram Received: March7, 2001 Based on the Holonomic Brain Theory by Kari Pribram and relaled models, an inlegraled model of conscious image processing is proposed. It optimally incorporates conlemporary limited knowledge starling from a sys(ematic search for fit between existing computational models, and between available experimental data, and between data and models. Since we are not yet able to tackle qualitative conscious experience directly, processes for making an image (or result of image processing, respectively) conscious are discussed. A quantum implementalion of holography-like processing of images in the striate cortex (VI) is proposed using a computational model called quantum associative netivork. The input to the guantum net could be the Gabor wavelets, together with their coefficients, which are infomax-constrained spectral and sparse neural codes produced in the convolutional cascade along the retino-geniculo-slriale visual pathway using ihe receptive fields as determined by dendritic processes. Perceptual projections are used as argumeiit for holography-like and quanlum essence of visual phenomena, because classically (neurally) al one they could not be produced in such a quality. Level-invariant image attractors are argued to be representations to become conscious in/by a subject, after a similar stimulus has triggered the wave-function collapse (i.e., recall from memory). Auxiliary representations for simultaneous subconscious processing, based on phase-information, for associative vision-based cognition are proposed lo be Gabor \vavelets (i.e., spectral codes in VI receptive fields, or dendritic trees, respectively) and their coefficients (i.e., sparse codes in activities ofVl neurons). Introduction Aims and sources. This paper provides an information-theoretic integrative model of conscious image processing "having the kernel" in the striate cortex (named also the primary visual cortex or V]). Beside of an attempt to present a model that is an optimal compromise of bioIogically-plausible ingredients and relevant information-processing features needed for describing image processing in man, this study is interested in the problem how the residt of image processing (the image representation) becomes conscious, i.e. how we become conscious of the perceived image. The model is based on several earlier presentations of antecedent and accompanying physiological processes (Peruš, 2000b) and of Information transfer and transformation along the visual pathway from the retina over the optic nerve and through the lateral geniculate nucleiis (LGN) (Weiiky & Katz, 1999) to VI (Peruš, 2001). To provide a ground for the present study, a large body of neurophysiologicai, psychophysica!, biocybernetical, neuropsychological, and other theoretical, experimental and simulation-based literature on vision (incl. reviews in: Kandel et al., 1991; Kosslyn & Andersen, 1992; Arbib, 1995) has been systematica]ly studied, analyzed and compared in search for a synthesis (where possible). These data as well as several relevant models have been considered (Peruš, 2000a) in the context of Kari Pribram's (1991) Holonomic Brain Theory. Many informative complementarities were found (Peruš, 2000a, 2001). The present paper thus suggests a new comprehensive model of (conscious) image processing, while ali the contextual processes - like visual attention and memory (Crick, 1984; Bickle et al., 1999; Vidyasagar, 1999; Wurtz et al., 1980; Desimone, 1996; Goldman-Rakič, 1996), stereopsis (DeAngelis, 2000; Porrill et al., 1999; Poggio et al , 1985), segmentation of figure from background (Sompolinsky & Tsodyks, 1994), perceptual binding (Roelfsema, 1998; Lee & Blake, 1999a,b) and imagery (Kosslyn, 1988) - have been integratively considered in auxiliary literature (Peruš, 2000a,b, 2001). Early visual processing: infoniax. Along the retino-geniculo-striate pathway (De Yoe & Van Essen, 1988; Livingstone & Hubel, 1988), a cascade of encoding / decoding processes, or convolutional processes, respectively, ensures optimal Information pre­processing and encoding of images into various representations needed for visual cognition. Such preprocessing and encoding are realized, as psychophysical evidence (Wainwright, 1999; van Hateren, 1992) shows, so that Information is maximally preserved, as is also imitated by the so-called "infomca" models of artitlcial neural net (ANN) processing. Many of them generate so-called sparse codes where an oligarchy of units is active in encoding the entire image, but the majority is inactive. It was realized (Peruš, 2001) that the infomax­models, like the Independent Component Analysis (ICA) by Bell & Sejnowski (1995, 1996, 1997) and sparseness-maximization net by Olshausen & Field (1996a,b; 1997), outperform the ciassicai Hebbian or Principal Component Analysis (PCA) models (Haken, 1991, 1996), because they incorporate phase information, or higher-order statistics, respectively. ]nfomax-models were shown to give much more biologically-plausible outputs (receptive-field profiles'), but a biologicaily­plausible implementation on the "hardware"-level is possible (for now) only for the Olshausen & Field net, not for the Bell & Sejnovvski net. Relations between the Olshausen & Field (1996a,b) net and MacLennan's (1999) dendritic field computation model were found (Peruš, 2001), which indicate a possibility of dendritic implementation of the Olshausen & Field net. However, dendritic processing "following the Olshausen & Field algorithm" would be strongly constrained by sparseness-maximization process which could originate from the lateral inhibition or from top-down (i.e., corticofugal) influences (e.g., Pribram in Dubois, 2000b; Montero, 2000; Mclntosh et al., 1999; Moran & Desimone, 1985).^ Gabor vvavelets. Since the oscillatory-dynamic phase-processing is experimentally supported (Gray et al., 1989; Baird, 1990; Pribram, 1971, 1991; Wang, 1999; IVIannion & Taylor, 1992; Schempp, 1993, 1994, 1995; Sompolinsky & Tsodyks, 1994), a question arose whether ICA infomax-processing, or at least the sparsification process, might be realized virtualiy, i.e. on a "software"-level (higher-order attractor dynaiTiics). ICA-like infomax processing shapes the receptive-field profiles into Gabor wavelets, and these are then convoluted with the sensory inputs (Pribram & Carlton, 1986). The infomax processing is thus vievved as an information-saving preprocessing procedure for optimal encoding into Gabor vvavelets (also by other ICA models like: Harpur & Prager, 1996; Hyvarinen & Oja, 1998; Levvicki & Olshausen, 1999; cf, van Hateren & Ruderman, 1998). As will be shown, infomax-based (appropriately weighted) Gabor wavelets are spectral image-representations (van Hateren & van der Schaaf, 1998) which are involved in convolution (during perceptual processing), or in interference, or in othsr phase-Hebbian processes (during pictorial cognitive processing and ' A receplive field of a neuron is everytliing (or the whole surrounding space or netvvork, respectively) that influences its output afler ali the inputs have entered it along its own dendritic tree. The receptive-field's profile is a mathematical function describing the effcct of transformations upon neuron's inputs (the "vveights" of inputs) before the axonal output is "calculated". ^ A "sparsification pressure" is imposed on dendritic (and maybe also on neuronal) processing in order to get maximally sparse codes. Biological realization of sparsification is unknown. It might originate in virtual higher-level attractor structures (the "software" Icvel), maybe in a similar way as in Haken (1991). The second hypothesis, i.e. that lateral inhibition forces sparsification, is reflected in Pribram's (1998a) words: "[...] As the dendritic field can be described in terms of a spacetime constraint on a sinusoid - such as the Gabor elementary function, the constraint is embodied in the inhibitory surround of the field." M. Peruš associations). Phase-Hebb learning rule, i.e. the Hebb correlation-rule with phase-differences (because complex-valued activities are correlated or convoluted) (cf, Sutherland, 1990; Peruš & Dey, 2000; Spencer, 2001), is a name I coined for the following expression for "holography-like" memory-storage into so-called connections (or weights, or interactions, respectively) Jij betvveen "units" / and^': JIJ = Ek Aik Ajk exp(i((p,k-(Pjk)). A is the activity-amplitude of a "unit", (p is its phase of oscillation; k is the eigenstate which represents a pattern or image. Quantuiti implementation. In Peruš (1996, 1997a, 1998a) mathematical analogies in holographic, associative artificial-neural-net, spin-system and quantum-interference processes which could be harnessed for parallel-distributed information processing were systematically presented. Possible (biological) implementations of these processes were indicated. Furthermore, the Quantum Associative Network, an original computational model by Peruš (in Wang et al., 1998), was presented as a possible core-model for holonomic associative image processing in Peruš (2000a). Possibility for such a quantum image processing implies that the image, vvhich is recognized by the quantum associative net, becomes the "object of our conscious experience". This hypothesis results from numerous indications (e.g., Gosvvami, 1990; Hameroff et al., 1994—1998; Lockwood, 1989; Rakič et al., 1997; Stapp, 1993; Peruš, 1997b) that consciousness is essentially related to quantum processes. The comparative neuro-quantum study, and original derivation of the model of quanturn associative net from the simulated neural-net formalism, are presented in detail in Peruš (2000c). Some resulting novel suggestions for flexible image processing (e.g., "fuzzification" harnessing "quasi-orthogonar' structure of data) are described in Peruš & Dey (2000) (cf., Kainen, 1992; Kainen & Kurkova, 1993; Kurkova & Kainen, 1996). 2 Attempt ofan integrated model of image processing in VI , and beyond Introduction to the model. The holonomic theory (Pribram, 1991) of the retino-geniculo-striate image processing (Pribram & Carlton, 1986; Peruš, 2000a) ušes Gabor wavelets as "\veighting"- or "filtering"-functions vvhile performing convolution with the retinal image. The result of this Gabor transform is a spectral image-representation in VI. This, roughly hologram-like, representation in VI is then reconstructed by an inverse Gabor-transform into the spatial representation in V2, probably. Thus, the topoIogically­correct "image" (cf, Tootell, 1998) is recovered in inverted form in V2. The overlapped Gabor vvavelets, which are used in image processing in VI , describe the receptive-field CONSCIOU S IMAG E PROCESSING . profiles of VI neurons (Daugman, 1985, 1988) which realize the Gabor transform using their dendritic trees (cf, Berger et al., 1990, 1992; Artun et al., 1998). Gabor wavelets were shaped by an ICA-like process. Peruš (2001, 2000a) stated the reasons why it is good to prefer the Olshausen & Field (1996a,b, 1997) sparseness-maximization process over the ICA-variant of Bell & Sejnovvski (1995, 1996, 1997) for the implementation-model of shaping the Gabor wavelets g (i.e., the independent components Y) and especially determining their coefficients s (i.e., the amplitudes or sparse codes of the independent components of input-images). The Gabor coefficients are updated much more rapidly than the Gabor vvavelets. Coefficients change with each new input image, but the Gabor receptive fields adapt in a longer term - after a lot of different images have been presented. In fact, they adapt slowly ali the time, but substantial change is seen after a while. Frotn Gabor receptive fields to vvavelets. A Gabor elementary function g has two roles in modeling vision which seem to be somewhat different. First, it is used as a description of the receptive-field profile, i.e. of the "weighting" which the synapto-dendritic net imposes on ali the inputs to a neuron. Second, it is used as a Gabor wavelet which represents the encoding of an independent component of input-images. Of course, both roles have the same origin (a sort of ICA) and "are two sides of the same coin". However, the consequence of infomax-processing manifesls in different places: in the receptive-field profile which "lies hidden" in the synapto-dendritic net, and in the Gabor wavelet which propagates to other brain areas and gets involved in further holography-like processing there. Namely, if the receptive field is Gabor-shaped, then it gives Gabor­shaped outputs, or at least something similar or generalized, on a later stage. These Gabor vvavelets might be of another sort - e.g., time-dependent or spectral.^ This effect (i.e., Gabor wavelets produced because/out of Gabor receptive fields) is more clearly evident if the retinal input is made uniform (i.e., "white noise" or Ganzfeld). This is related to well-known observations that an uniform stimulation triggers a system's response which is a sort of internal "expectation" (or a "hallucination", respectively) of the filtering system (e.g., MacLennan in Pribram, 1993, p. 189). Sorts of representations. In principle, there are two sorts of representations in VI available for further brain processing: the spectral "compound of images", or equivalently, the sparse assembly of codes (the so-called sparse codes) representing or "weighting" the independent components extracted from a collection of images. The first representation (independent component) is hidden in VI dendritic fields; the second ' They retain Ihe same form, but vvilli different intcrpretation of coordinate-axes. The Gabor \vavelet in spectral representation sce in Daugman & Downing (in Arbib, 1995). This Fourier transform of the original Gabor profile is expressed in the same functional form as the original spatial Gabor "vvavelet", but with the spectral («) and spatial {x) variables interchanged. Informatica 2 5 (2001) 575-49 2 57 7 representation (sparse coding) is encoded in activities of VI-neurons (cf, Pribram et al., 1981). After the spectral representation of VI has been inverse-Gabor-transformed in the connections between VI and V2, the retinal image re-emerges in V2. Thus, the usual image, as once originally fallen on the retina, should be reconstructed (turned upside-down, maybe also somewhat "deformed") in V2 or nearby. This "image" is then the third available representation. Why three representations? (Cf, Kirvelis in Dubois, 2000b.) We could suppose that the spectral (Gabor wavelet) representation is for perceptual image processing in VI . The sparse-code (Gabor coefficient) representation is for robust, rough encoding needed for automatic, immediate, reflex actions — they are unconscious and probably realized by neural circuits alone (dendrites just transmit the signals, do not process them). The "image" representation in V2 is used for the usual phenomenal conscious experience. Let me explain. When a person is, say, involved in conversation, (s)he sees another person and at the same time processes a lot of Information —- e.g., "decodes" the other-person's body-language, not to mention more multi-modal and symbolic cognitive processes like understanding of vvords and thinking about the topic. The person sees the other one in full phenomenal integrity and quality ali the time, vvithout interruptions of the Information processing (understanding body-language and spoken language, thoughts, etc.) going on in the background. For the seemingly-direct "realistic" experience of the environmental image, as conscious process offers it, the V2 space-time "image" is needed (more in Pribram, 1998a). For the abundant accompanying apperceptual processing (e.g., Luria, 1983; Stillings et al., 1995), which is unconscious and abstract, the spectral representation is needed (Pribram, 1997b). I will suppose that the "image" is also needed for additional processing, mainly limited to visual cognition, which ušes associative processing that is more similar to holography than the perceptual spectral processing is. From edge- to object-perception. Edges of object-forms are the first level of invariance or perceptual constancy and can be detected by linear transformations, like those in ICA. Incorporation of phase processing essentially improves results, as the Bell & Sejnowski and Olshausen & Field simulations demonstrate. However, finding transformations that are invariant to shifting, scaling and rotation of object-patterns, are mainly an open problem for ICA (Lee after Bell & Sejnovvski, 1997). These transformations were with certain success tackled with generalized Hebbian models using Fourier-preprocessing (e.g., Haken, 1991) and by other non-infomax specialized models. ICA seems to be a good model for image (pre)processing, but not necessarily for object perception (which is well distinguished from image processing by the holonomic theory and other models of vision, and this has psycho­physioIogical reasons) (e.g., see Wallis & Biilthoff, 1999). Object recognition, based on search for perceptual invariances, might need a combination of ICA and associative processing (a successful example is: Bartlett & Sejnovvski, 1997; cf. also Gray et al., 1997), probably in attractor-networks which manifest gestalt-like structures (Luccio, 1993; Peruš & Ečimovič, 1998). Phase-Hebbian associations take over. Peruš (2001) thinks that visual associative processes of VI, after perceptual preprocessing has been finished (ICA has generated Gabor wavelets and Gabor coefficients, and the Gabor transform using convolution has produced spectral responses of VI simple cells), could be well realized by a Hebbian (e.g., Churchiand & Sejnovvski, 1992; Gardner, 1993) or phase-Hebbian mechanism. The second one, which is most similar to holography, has much more chances for good performance. These models may in some respect be less efficient than other phase-processing models, vvhich are not phase-Hebbian, like ICA and MacLennan's (in Pribram, 1993) dendritic model as far as it has similarities with the Olshausen & Field (1996a,b) model. But the phase-Hebbian models have a peculiar symmetry vvhich makes them fundamental and close to physics. So, 1 believe, there is a division of labor. Other models (ICA, convolution-models, Kohonen's Self-Organizing Maps) "do the hard job " first. After their processing vvith nonlinear moments (like sparsification) is finished, the phase-Hebbian associative dynamics start the "fine job". Phase-Hebbian models have an ability to construct rich multi-level attractor-structures. In this, they can go beyond Hebbian models vvhich are already successful in flexible attractor-dynamics (Haken, 1991; Peruš & Ečimovič, 1998). Attractor processing. For secondary visual processing (i.e., e.g., object perception, from VI to V2, and beyond it), processing vvith attractors is unavoidable (Peruš, 2000b, 2001). Pribram (1971, 1991) also says that cortical processing ušes largely parallel-distributed and redundant representations. The model, vvhich realizes this most directly and is also the best ANN embodiment of holography (cf, Psaltis et al., 1990), is sketched as foUovvs. In simple vvords, the vvhole netvvork of units vvith their connections encodes numerous "images" simultaneousIy: In the weight-matrix (encoded in the array of connections / junctions), there is the content-addressable associative memory. In the configuration-vector (encoded in the set of units), there is the "image" vvhich is currently processed (vvhich "vve are conscions of) . Each vector of activity-configurations, vvhich represents an "image", acts as an attractor of network's dynamics, because it is at the minimum of its potential vvell — as in the Hopfield model (details in: Peruš & Ečimovič, 1998; Peruš, 2000d). In the matrix of connections (or "hologram"), not the vvhole patterns or images are stored. Merely pair­vvise (auto)correlations of ali previously-input images are stored. With other vvords, condensed Information about (dis)agreements among aH image-parts of ali the vvatched images is encoded so that it is parallelly­distributed across the vvhole matrix. This is sufficient for reconstruction of an image from the memorized image­ti^aces if a recall-key (i.e., a nevv, similar input pattern) is presented to the array of connectionist units (formal M. Peruš neurons) of the netvvork. The interaction of these units across the connections is modeled by multiplication of the vector of units' states vvith the matrix of inter-unit connections (details in: Peruš & Ečimovič, 1998). Quantum net as the inner processor. The essential point is that processing of the Quantum Associative Network (Peruš in Wang et al., 1998; Peruš & Dey, 2000), as derived from ANN in Peruš (2000c) based on analogies of Peruš (1996, 1997a, 1998), realizes the attractor-dynamics, associative processing and image recognition in a "compact" and effective way. It is progressive that Hebbian processing is enriched vvith phase-processing. Because this model can be quantum-implemented in a natural way, it is, for novv, hard to imagine anything more fundamental, more holographic, more effective, and hypothetically more directly linked to conscious experience, in the sense of associative processing. Processing similar to that of quantum associative net might take plače in VI and partially also maybe in V2. The quantum associative net can process, by interference, various kinds of eigen-vvave-functions (eigen-images). They can be Gabor vvavelets. Gabor vvavelets are very similar to the natural quantum vvave­packets (MacLennan in Pribram, 1993). The Gabor vvavelet, originally proposed by the "discoverer" of holography D. Gabor in 1946, is a sequence of vvaves under a fixed gaussian envelope vvhile the frequency of the vvave inside the envelope varies for different cases. Such a vvavelet is eguivalent to a family of Weyl-Heisenberg coherent wave-packets used in guantum physics (Lee, 1996). This observation allovvs me to relate infomax image-processing vvith quantum-implemented holography-like associative processing vvith attractors ­in the quantum associative net. Peruš & Dey (2000) present interference-processing in the quantum associative net using the plane-vvaves for image-bearing eigen-vvave-functions — for simplicity, although efficient. This is the most usual / basic quantum-type holography. Interfering Gabor wavelels could enable more sophisticated, maximally information-preserving processing, in accord vvith the holonomic theory. Associative basis for visual cognition. The uniformity of (neo)cortical structure (Ebdon, 1993; details in Burnod, 1990) allovvs the use of phase-Hebbian associative models for a rough (but maybe the best available) approximation of global (neo)cortical processing (cf, hovvever, Ingber, 1998; Komer et al., 1999) vvhich is at roots of visual cognition (cf, Clement et al., 1999; Pribram, 1997a). The proper modeling combination, 1 suppose, vvould be: ICA-constrained convoliitional preprocessing up to VI, followed by fractal-based associative processing in (neojcortical neural, dendritic and quantum attractor networks — one within another inside VI. My hypothesis is that the multi-level phase-Hebbian associative processing, having the quantum associative net as the most deep/inner leve! (for novv), is currently the most convenient one for cognitive manipulations of images or, rather, objectforms, as performed probably in the inferior temporal cortex (ITC) CONSCIOUS IMAGE PROCESSING. (cf, Miyashita & Chang, 1988; Fuster & Jervey, 1982; Mishkin et al , 1983; Perret & Oram, 1998). ITC is specialized for prototype-converging recognition or comprehension of objects, including discriminations and choices resulting from it (Pribram, 1971). Global associations and •context-searches are necessary during search of the right prototype. In accord with Rainer & Miller (2000), Riesenhuber & Poggio (2000) argue that the prefrontal cortex finishes the object-recognition started by ITC. They write on p. 1202: "In anterior ITC, invariances to object-based transformations, such as rotation in depth, illumination and so forth, is achieved by pooling together the appropriate view-tuned cells for each object." Then Riesenhuber & Poggio (2000, Fig. 3 caption) continue: "The stages up to the object-centered units probably encompass V1 to anterior ITC. The last stage of task-dependent modules may be located in the prefrontal cortex." These modules are needed for tasks like object-identification, -discrimination and -categorization, they say before. Experiments of Rainer & Miller (2000) on object recognition in the prefrontal cortex showed that familiar objects activate fewer neurons than novel objects do, but these neurons are more narrowly tuned. Such a sparse representation of a familiar object is also more robust to degradation (made after the learning period) of a newly-posed stimulus-object. Based on ITC inputs (in vision), the prefrontal cortex is the region most important for the so-called working memory used in cognition. Present models use Hopfield-net-produced Hebbian* attractors for working-memory representations and attractor dynamics for (visual) cognition. 1 believe, generalization of these models (which were used in: Peruš & Ečimovič, 1998; Peruš, 2000d) by incorporating phase-processing (i.e., using the phase-Hebb rule) and implementing it in dendritic or/and quantum networks would be more appropriate. It should be emphasized once again that image processing and subsequent object recognition could be possible only because of "the hard job done" by I CA and the perceptual convolutional cascade. They provided Gabor wavelets (cf., Potzsch et al., 1996) and spectral representations of images which are stili used in many higher cortical areas for more abstract processing (i.e., processing vvithout the topologically-correct pictorial representation - the usual image). Volition-, "l"-based control- and symbolic processing are examples of abstract processing. On the other hand, operations of visual cognition — like imagery, mental manipulations of objects, visual modeling or planning (e.g., vividly imagining how to drive from A to B) (review in Baars, 1997) — could have cortical implementation based on the quantum associative net, especially if these processes are performed consciously. This fits the Crick and Koch (in Hameroff, 1996) hypothesis that we begin to be conscious of visual processing in V2 and beyond (encompassing visual cognition based on cooperation of ITC and the prefrontal cortex). "' Details on neurophysiological bases of Mcbbian memor>'-slorage see in: Gardner (1993), Abbot & Nelson (2000), Bear (1996). Informatica 25 (2001) 575-492 579 3 Addition of conscious experience and quantum processes into consideration From dendrites to conscious experience. The following citate from Pribram (1971, p. 105) summarizes the view vvhich has been later elaborated by the holonomic theory: "Neural impulses and slow potentials are two kinds of processes that could function reciprocally. A simple hypothesis would State that the more efficient the processing of arrival patterns into departure patterns, the shorter the duration of the design formed by the slow potential junctional microstructure. Once habit and habituation have occurred, behavior becomes "reflex" — meanvvhile the more or less persistent designs of slow potential patterns are coordinate with awareness. This view carries a corollary, wz. that nerve impulse patterns per se and the behavior they generale are unavailable to immediate awareness. [...] In short, nerve impulses arriving at junctions generale a slow potential microstructure. The design of this microstructure interacts with that already present by virtue of the spontaneous activity of the nervous system and its previous "experience". The interaction is enhanced by inhibitory processes and the vvhole procedure produces effects akin to the interference patterns resulting from the interaction of simultaneously occurring wave fronts. The slow potential microstructures act thus as analogue cross-correlation devices to produce new figures from vvhich the patterns of departure of nerve impulses are iniciated. The rapidly--paced changes in avvareness could vvell reflect the duration of the correlation process." Discussion on sorts of representation in section 2 seems to fit this citate. Sparse-coding assemblies of neurons (i.e., just few neurons fire, and this is enough for encoding entire images) serve in reflexes vvithout avvareness. The second representations of images, the Gabor wavelets, interfere in the (sub)dendritic microstructure. The correlation process, hidden in subcellular or quantum (as 1 prefer) interference, could also be accompanied by awareness. The final result of interference processing, the conscious image, would be reconstructed after the coUapse of quantum (or at least quantum-like) wave-function. In support for his hypothesis on junctional electric activity as the substrate for awareness, Pribram (1971, 1995) mentions that using biofeedback subjects can discriminate a-EEG waves in their brain by "feeling them as pleasantly relaxed avvareness". He also cites Libefs findings that stimulation-produced avvareness occurs in patients 0.5-5 seconds after the relevant brain-area has been stimulated — as if some electrical state would have to be built before the patients can experience anything. Neural and quantuin "sides" of dendrites. lnfomax-processing is probably based in dendritic-y;6er netvvorks or/and neural circuits - on the (sub)cellular level, not quantum. VI image processing and subsequent visual associations are probably realized by quantum-based dendritic «i/croprocesses. Dendritic processing thus combines two levels. Its macroscopic fiber-part is involved, under some top-down influences probably, in shaping the Gabor receptive-field profiles by specific collective dynamics of dendritic trees of many neurons that criss-cross. Its microscopic membrane-"bioplasma" part (in the patches or "holes" in-between the criss­crossed dendritic fibers beneath their membranes) implements the holography-hke image-processing, as will be described in section 6, but probably by interfering a sort of Gabor vvavelets instead of plane-waves. Wavelets could be naturally rooted in quantum background. Why fractal-like inulti-level processing. Systematic observations show that brain structures repeat roughly on many levels or scales like in a fractal. Why such a (seeming?) redundancy? The ansvver is probably: flexibility, adaptability and universality. Pribram (1971, 1991) observes that patterns shaped or learned in one part (area, level) can be transferred to another part (area, level) of the brain. One perceives an image, can recall it, manipulate it in imagination, one can use it to guide and control motor action directed toward its object (the image of achievement). In Pribram's example, one can dravv a circie with a pencil on a paper or wall using fingers of a hand or even of a foot, or one can put the pencil in the mouth. The same pattern (circie) can be proditced (drawn) in different circumslances using differenl body-actions and different brain areas. Even different levels of the tissue are needed: microscopic for processing, macroscopic for execution of action. To mobilize a muscle, amplification of (sub)neural signals is necessary - thafs why neurons are needed also, not just dendrites and quantum systeins. Neurons are cells - like the muscle cells are also. Since Nature is multi-scale, body and brain also have to be multi-scale to handle it. The many levels therefore have to cooperate fluently, so they must be compatible in information exchange. Patterns as global information therefore have to be able to travel from one level to another. This is realizable by fractal-like dynamics that is intrinsic to coiTiplex (bio)systems anyway. How the inter-level or inter-scale transfer of patterns or images is realized is much harder to find out than to realize that this is indeed happening (J. Anderson). Attractors are very probably those emergent virtual structures which can "travel across the brain". They are the bioinformational or PDP (parallel­distributed processing) correlate of gestalts — each represents an invariant information-unit (percept). An attractor, a primitive "ghost in the machine", is rooted in a network-state, but changes its substrate-elements (Peruš & Ečimovič, 1998) like the electric current changes its underlying crystal structure or like (water) waves change (water) molecules while propagating. M. Peruš 4 Quantum associative network model Essentials. A verbal (partially metaphoric) description of processing in the quantum associative net, in comparison to holography, will now be given (mathematical details in Peruš, 2000a,c). The processing of quantum associative net is a sort of hoIography, if one is allovved to use the term outside classical optics, since the net interferes quantum waves. In fact, the quantum associative net is a quantum-mechanics-based mathematical model which can be computationally simulated (cf., Zak & Williams, 1998). No reasons have up to now been found why the model could not be impiemented in a real quantum-physical system. The model also needs specific input-output transformations, therefore it is an informational model as much as it is a physical one. Interpretadon of states. The quantum associative net is the core of basic quantum mechanics (in Feynman's interpretation) which is put into an inlelligible interaction with the environment (visual field). This is new: the input-output dynamics. Another essential new thing is that eigen-wave-fiinctions (i.e., the basic, natural quantum states - they are often particles-waves, but not necessary) are harnessed to encode some information like an image. An intelligent being must be there which interacts with the system in such a way that the input-, output- and internal (memory) states represent some meaningful information for the being. His interpretation "transforms " an ordinary guantum system into an information-processing system as soon as he is satisfied with the input-to-output transformations. Let us assume so. (It is like in the čase of a round piece of wood "becoming" a wheel if put in a proper context - the axis, other vvheels, upper plate, etc.) Inputs. Image processing can be done during the holographic process (Pribram, 1991). It works perfectly and simply, as aH physicists and opticians know (Hariharan, 1996). It is natural in holography (as well as photography and any other optics) that the light encodes the 3-dimensional form of an object by specific modulation (i.e., shaping) of amplitudes, frequencies and phases of its waves (rays). So, it is possible to encode complicated object-forms into usual electro-magnetic waves — even with perfect resolution when the code is being reconstructed. We thus have: objects, their codes or representations (in a medium), and we need object-to­code transformations (encoding) and, finally, code-to­object transformations (decoding or reconstruction). Because holography works vvith ali sorts of waves, the information-carrying waves can be quantum waves. This inight bring new capabilities, but not eliminate the classical ones. Hence, the input-waves can be plane-waves, mathernatically described by equation y/^i?,t) = A^(P,t)exp{i(p^(r,t)) (1), or the input-waves can be Gabor wavelets (inade of "increasing and decreasing waves under a gaussian envelope"). {y/'\s the wave-function, A is its amplitude,

^2>^' (2), k=l describes the quantum hologram. Its essential mernory­ "traces" are phase-differences in the exponent (cf, Ahn et al., 2000). Matrix G is at the same time the carrier and transformer of waves. G is the quantum-holographic memory which is active - performs associations "through itself. G describes the "self-organizing internal restructuring" of the quantum system by "internal interactions between its (seeming) parts", i.e. by self- interference. It should be emphasized here that this is not an interaction in the sense of chemical or quantum- particle (nuclear, subnuclear) reaction, but in the sense of mutual mechanical (or electrodynamic / optical) influence or re-arrangement on a quantum level. In the language of quantum informatics, G describes a compound. (The "deeper, holistic" quantum fields incorporate entanglements, where parts which have once interacted cannot be really separated any more, but just seemingly. See experiment by Aspect et al., 1982.) Compounds can be "un-mixed" like the images can be reconstructed from the hologram (memory). Associative processing. The matrix / hologram / propagator G describes phase-relationships between "infinitely"-small parts of the waves vvhich were "mixed". This is associative meniory, which also acts like a "turbine" for associative "computing". Each Informatica 25 (2001) 575^92 581 quantum wave (//• "flovvs through the C-turbine", and this changes both the G and the wave. In mathematical description: '^'(''2 > ^2) = \\Gif, ,t„r^ .t^ yY{r, ,t,)dP, dt, (3). This implies, because equation (2) should be inserted into equation (3) to replace G, that (and how, why) waves iff change G and G changes waves }jf. This is called the coupled dynamics of the quantum system — it is a "self­holography" triggered by our inputs. We call it associative processing, because it is realized by "projecting" the quantum eigen-state or -wave "through the associative memory or hologram" G. Initial quantum-encoded informational state (\|/in) is thus transformed into an associated quantum-encoded informational state (Voul) ­ Image recognition by wave-function collapse. If we want to recall a memory, or to reconstruct a stored image out of C, respectively, we have to present a part of the image or a similar image (the memory-"key") to the system (i|/in). The similarity activates matching of relations, encoded in phases, and thus selectively associates the "key" with the most similar stored image vvhich then "comes out of the mixture" (i.e., G) in a clearly-reconstructed form. This is described by the follovving sequence of equations: = |[E L Wk(AyYk(^2WXr„t,)dr,^ =(f^,(r,m^,o^y,(^2)+-+ {^Wp{r,y'i''ir„t,)dF,y,(r,) = Ay/,if,) + B (4) vvhere A=\ ("extracted image") and 5=0 ("noise"). 1 can claim that this quantuiTi process, called "\vave-function collapse", is typically holographic in the framework of quantum associative nets (details in Peruš, 1997a). 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