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Qualia: the geometry of integrated information.

Balduzzi D, Tononi G - PLoS Comput. Biol. (2009)

Bottom Line: Both active and inactive elements specify a quale, but elements that are inactivated do not.In principle, different aspects of experience may be classified as different shapes in Q, and the similarity between experiences reduces to similarities between shapes.Finally, specific qualities, such as the "redness" of red, while generated by a local mechanism, cannot be reduced to it, but require considering the entire quale.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychiatry, University of Wisconsin, Madison, WI, USA.

ABSTRACT
According to the integrated information theory, the quantity of consciousness is the amount of integrated information generated by a complex of elements, and the quality of experience is specified by the informational relationships it generates. This paper outlines a framework for characterizing the informational relationships generated by such systems. Qualia space (Q) is a space having an axis for each possible state (activity pattern) of a complex. Within Q, each submechanism specifies a point corresponding to a repertoire of system states. Arrows between repertoires in Q define informational relationships. Together, these arrows specify a quale -- a shape that completely and univocally characterizes the quality of a conscious experience. Phi -- the height of this shape -- is the quantity of consciousness associated with the experience. Entanglement measures how irreducible informational relationships are to their component relationships, specifying concepts and modes. Several corollaries follow from these premises. The quale is determined by both the mechanism and state of the system. Thus, two different systems having identical activity patterns may generate different qualia. Conversely, the same quale may be generated by two systems that differ in both activity and connectivity. Both active and inactive elements specify a quale, but elements that are inactivated do not. Also, the activation of an element affects experience by changing the shape of the quale. The subdivision of experience into modalities and submodalities corresponds to subshapes in Q. In principle, different aspects of experience may be classified as different shapes in Q, and the similarity between experiences reduces to similarities between shapes. Finally, specific qualities, such as the "redness" of red, while generated by a local mechanism, cannot be reduced to it, but require considering the entire quale. Ultimately, the present framework may offer a principled way for translating qualitative properties of experience into mathematics.

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Tangled concepts can generate more information about their inputsthan their atomic subconcepts.(A): An element extracts information from a set of four sensors. Ifthe input received by the sensor layer is pure noise (the maximumentropy distribution on24 = 16 possible firingpatterns) then the best a single element can do, on average, is toextract 1 bit of information. An efficient strategy is toCOPY the output of one of the sensors, so thatthe element generates a concept of the form ON/OFF.(B): An element that spikes if it receives a BAR:1100, 0110 or 0011. If a bar is presented, the 4 connectionstogether generate 2.4 bits of information, whereas the individualconnections generate 0.08 bits independently. For the 4 connectionsto generate more information as a whole than separately they must betangled: γ = 0.25 bits. Ifthe input pattern is not a bar, the element generates 0.3 bits, sothat it performs worse than the COPY, on average,on maxent noise. However, if bars are sufficiently common in theinput, then the element generates more information than aCOPY element. (C): Two elementsCOPY their inputs. This produces the maximumpossible average effective information (2 bits for 2 binaryelements) assuming the inputs are maxent distributed. The elementsare not tangled, γ = 0, andso the whole generates information equal to the sum of the parts.(D): A cartoon cortical area: a subsystem that receives more inputsthan there are elements. If there is some statistical structure tothe inputs (certain patterns are more common than others), thesystem can form concepts specific to the input structure. The 2binary elements shown generate 4 bits of information about the inputpattern, more than the elements taken individually (2.7 bits). Onaverage, using maxent, the 2 elements generate 1.8 bits, less thanthe COPY elements. However, if the inputs arestructured and so not maxent, the elements can generate moreinformation about other cortical areas than they should“by right” by tangling informationalrelationships into concepts and modes.
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pcbi-1000462-g013: Tangled concepts can generate more information about their inputsthan their atomic subconcepts.(A): An element extracts information from a set of four sensors. Ifthe input received by the sensor layer is pure noise (the maximumentropy distribution on24 = 16 possible firingpatterns) then the best a single element can do, on average, is toextract 1 bit of information. An efficient strategy is toCOPY the output of one of the sensors, so thatthe element generates a concept of the form ON/OFF.(B): An element that spikes if it receives a BAR:1100, 0110 or 0011. If a bar is presented, the 4 connectionstogether generate 2.4 bits of information, whereas the individualconnections generate 0.08 bits independently. For the 4 connectionsto generate more information as a whole than separately they must betangled: γ = 0.25 bits. Ifthe input pattern is not a bar, the element generates 0.3 bits, sothat it performs worse than the COPY, on average,on maxent noise. However, if bars are sufficiently common in theinput, then the element generates more information than aCOPY element. (C): Two elementsCOPY their inputs. This produces the maximumpossible average effective information (2 bits for 2 binaryelements) assuming the inputs are maxent distributed. The elementsare not tangled, γ = 0, andso the whole generates information equal to the sum of the parts.(D): A cartoon cortical area: a subsystem that receives more inputsthan there are elements. If there is some statistical structure tothe inputs (certain patterns are more common than others), thesystem can form concepts specific to the input structure. The 2binary elements shown generate 4 bits of information about the inputpattern, more than the elements taken individually (2.7 bits). Onaverage, using maxent, the 2 elements generate 1.8 bits, less thanthe COPY elements. However, if the inputs arestructured and so not maxent, the elements can generate moreinformation about other cortical areas than they should“by right” by tangling informationalrelationships into concepts and modes.

Mentions: Figure 13A shows a systemcomprising 4 input elements (sensors) and 1 output element (detector), whichimplements a COPY of one input element. In doing so, theCOPY element generates 1 bit of information, whether it fires or not, andspecifies a single informational relationship (q-arrow), corresponding tothe simplest possible concept: that things are one way rather than anotherway, just like the photodiode in Fig. 1. If the input is pure noise (themaximum entropy distribution on24 = 16 possible inputpatterns), then extracting 1 bit of information is indeed the best a singleelement can do. By contrast, the “BAR”element in Fig. 13B“integrates” information from 4 sensors. If the input is1100, 0110, or 0011, the BAR element fires, and generates 2.4 bits ofinformation, more than the COPY element. It can do so because theconnections it receives from the 4 sensors are tangled, meaning that jointlythey generate more information than the sum of the information generated byeach connection independently (0.08 bits each). The corresponding tangledinformational relationship(γ = 0.25 bits) corresponds to theconcept BAR. By contrast, when the input pattern is not a bar (13 patternsout of 16), the element generates 0.3 bits. On average, then, the BARelement performs worse than the COPY element on pure noise, but can dobetter, thanks to entanglement, if bars are a common statistical feature ofthe input, i.e. more common than other patterns. In general,“integrating” information through entanglement and theformation of concepts is an effective strategy to extract more informationfrom an input under the constraint of dimensionality reduction (here from 4inputs to 1 output), as long as the input has some statistical structure.Neurons are certainly well-suited to extracting information from their input[26], and they must perform extreme dimensionalityreduction, as they receive thousands of inputs but emit a single output.Indeed, it is frequently stated that neurons are wired to“integrate information.” The notion of entanglementprovides a precise formulation of this function.


Qualia: the geometry of integrated information.

Balduzzi D, Tononi G - PLoS Comput. Biol. (2009)

Tangled concepts can generate more information about their inputsthan their atomic subconcepts.(A): An element extracts information from a set of four sensors. Ifthe input received by the sensor layer is pure noise (the maximumentropy distribution on24 = 16 possible firingpatterns) then the best a single element can do, on average, is toextract 1 bit of information. An efficient strategy is toCOPY the output of one of the sensors, so thatthe element generates a concept of the form ON/OFF.(B): An element that spikes if it receives a BAR:1100, 0110 or 0011. If a bar is presented, the 4 connectionstogether generate 2.4 bits of information, whereas the individualconnections generate 0.08 bits independently. For the 4 connectionsto generate more information as a whole than separately they must betangled: γ = 0.25 bits. Ifthe input pattern is not a bar, the element generates 0.3 bits, sothat it performs worse than the COPY, on average,on maxent noise. However, if bars are sufficiently common in theinput, then the element generates more information than aCOPY element. (C): Two elementsCOPY their inputs. This produces the maximumpossible average effective information (2 bits for 2 binaryelements) assuming the inputs are maxent distributed. The elementsare not tangled, γ = 0, andso the whole generates information equal to the sum of the parts.(D): A cartoon cortical area: a subsystem that receives more inputsthan there are elements. If there is some statistical structure tothe inputs (certain patterns are more common than others), thesystem can form concepts specific to the input structure. The 2binary elements shown generate 4 bits of information about the inputpattern, more than the elements taken individually (2.7 bits). Onaverage, using maxent, the 2 elements generate 1.8 bits, less thanthe COPY elements. However, if the inputs arestructured and so not maxent, the elements can generate moreinformation about other cortical areas than they should“by right” by tangling informationalrelationships into concepts and modes.
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Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC2713405&req=5

pcbi-1000462-g013: Tangled concepts can generate more information about their inputsthan their atomic subconcepts.(A): An element extracts information from a set of four sensors. Ifthe input received by the sensor layer is pure noise (the maximumentropy distribution on24 = 16 possible firingpatterns) then the best a single element can do, on average, is toextract 1 bit of information. An efficient strategy is toCOPY the output of one of the sensors, so thatthe element generates a concept of the form ON/OFF.(B): An element that spikes if it receives a BAR:1100, 0110 or 0011. If a bar is presented, the 4 connectionstogether generate 2.4 bits of information, whereas the individualconnections generate 0.08 bits independently. For the 4 connectionsto generate more information as a whole than separately they must betangled: γ = 0.25 bits. Ifthe input pattern is not a bar, the element generates 0.3 bits, sothat it performs worse than the COPY, on average,on maxent noise. However, if bars are sufficiently common in theinput, then the element generates more information than aCOPY element. (C): Two elementsCOPY their inputs. This produces the maximumpossible average effective information (2 bits for 2 binaryelements) assuming the inputs are maxent distributed. The elementsare not tangled, γ = 0, andso the whole generates information equal to the sum of the parts.(D): A cartoon cortical area: a subsystem that receives more inputsthan there are elements. If there is some statistical structure tothe inputs (certain patterns are more common than others), thesystem can form concepts specific to the input structure. The 2binary elements shown generate 4 bits of information about the inputpattern, more than the elements taken individually (2.7 bits). Onaverage, using maxent, the 2 elements generate 1.8 bits, less thanthe COPY elements. However, if the inputs arestructured and so not maxent, the elements can generate moreinformation about other cortical areas than they should“by right” by tangling informationalrelationships into concepts and modes.
Mentions: Figure 13A shows a systemcomprising 4 input elements (sensors) and 1 output element (detector), whichimplements a COPY of one input element. In doing so, theCOPY element generates 1 bit of information, whether it fires or not, andspecifies a single informational relationship (q-arrow), corresponding tothe simplest possible concept: that things are one way rather than anotherway, just like the photodiode in Fig. 1. If the input is pure noise (themaximum entropy distribution on24 = 16 possible inputpatterns), then extracting 1 bit of information is indeed the best a singleelement can do. By contrast, the “BAR”element in Fig. 13B“integrates” information from 4 sensors. If the input is1100, 0110, or 0011, the BAR element fires, and generates 2.4 bits ofinformation, more than the COPY element. It can do so because theconnections it receives from the 4 sensors are tangled, meaning that jointlythey generate more information than the sum of the information generated byeach connection independently (0.08 bits each). The corresponding tangledinformational relationship(γ = 0.25 bits) corresponds to theconcept BAR. By contrast, when the input pattern is not a bar (13 patternsout of 16), the element generates 0.3 bits. On average, then, the BARelement performs worse than the COPY element on pure noise, but can dobetter, thanks to entanglement, if bars are a common statistical feature ofthe input, i.e. more common than other patterns. In general,“integrating” information through entanglement and theformation of concepts is an effective strategy to extract more informationfrom an input under the constraint of dimensionality reduction (here from 4inputs to 1 output), as long as the input has some statistical structure.Neurons are certainly well-suited to extracting information from their input[26], and they must perform extreme dimensionalityreduction, as they receive thousands of inputs but emit a single output.Indeed, it is frequently stated that neurons are wired to“integrate information.” The notion of entanglementprovides a precise formulation of this function.

Bottom Line: Both active and inactive elements specify a quale, but elements that are inactivated do not.In principle, different aspects of experience may be classified as different shapes in Q, and the similarity between experiences reduces to similarities between shapes.Finally, specific qualities, such as the "redness" of red, while generated by a local mechanism, cannot be reduced to it, but require considering the entire quale.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychiatry, University of Wisconsin, Madison, WI, USA.

ABSTRACT
According to the integrated information theory, the quantity of consciousness is the amount of integrated information generated by a complex of elements, and the quality of experience is specified by the informational relationships it generates. This paper outlines a framework for characterizing the informational relationships generated by such systems. Qualia space (Q) is a space having an axis for each possible state (activity pattern) of a complex. Within Q, each submechanism specifies a point corresponding to a repertoire of system states. Arrows between repertoires in Q define informational relationships. Together, these arrows specify a quale -- a shape that completely and univocally characterizes the quality of a conscious experience. Phi -- the height of this shape -- is the quantity of consciousness associated with the experience. Entanglement measures how irreducible informational relationships are to their component relationships, specifying concepts and modes. Several corollaries follow from these premises. The quale is determined by both the mechanism and state of the system. Thus, two different systems having identical activity patterns may generate different qualia. Conversely, the same quale may be generated by two systems that differ in both activity and connectivity. Both active and inactive elements specify a quale, but elements that are inactivated do not. Also, the activation of an element affects experience by changing the shape of the quale. The subdivision of experience into modalities and submodalities corresponds to subshapes in Q. In principle, different aspects of experience may be classified as different shapes in Q, and the similarity between experiences reduces to similarities between shapes. Finally, specific qualities, such as the "redness" of red, while generated by a local mechanism, cannot be reduced to it, but require considering the entire quale. Ultimately, the present framework may offer a principled way for translating qualitative properties of experience into mathematics.

Show MeSH
Related in: MedlinePlus