Limits...
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.

Show MeSH
Tangled concepts can generate more information about their inputs                                than their atomic subconcepts.(A): An element extracts information from a set of four sensors. If                                the input received by the sensor layer is pure noise (the maximum                                entropy distribution on                                24 = 16 possible firing                                patterns) then the best a single element can do, on average, is to                                extract 1 bit of information. An efficient strategy is to                                    COPY the output of one of the sensors, so that                                the 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 connections                                together generate 2.4 bits of information, whereas the individual                                connections generate 0.08 bits independently. For the 4 connections                                to generate more information as a whole than separately they must be                                tangled: γ = 0.25 bits. If                                the input pattern is not a bar, the element generates 0.3 bits, so                                that it performs worse than the COPY, on average,                                on maxent noise. However, if bars are sufficiently common in the                                input, then the element generates more information than a                                    COPY element. (C): Two elements                                COPY their inputs. This produces the maximum                                possible average effective information (2 bits for 2 binary                                elements) assuming the inputs are maxent distributed. The elements                                are not tangled, γ = 0, and                                so the whole generates information equal to the sum of the parts.                                (D): A cartoon cortical area: a subsystem that receives more inputs                                than there are elements. If there is some statistical structure to                                the inputs (certain patterns are more common than others), the                                system can form concepts specific to the input structure. The 2                                binary elements shown generate 4 bits of information about the input                                pattern, more than the elements taken individually (2.7 bits). On                                average, using maxent, the 2 elements generate 1.8 bits, less than                                the COPY elements. However, if the inputs are                                structured and so not maxent, the elements can generate more                                information about other cortical areas than they should                                “by right” by tangling informational                                relationships into concepts and modes.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2713405&req=5

pcbi-1000462-g013: Tangled concepts can generate more information about their inputs than their atomic subconcepts.(A): An element extracts information from a set of four sensors. If the input received by the sensor layer is pure noise (the maximum entropy distribution on 24 = 16 possible firing patterns) then the best a single element can do, on average, is to extract 1 bit of information. An efficient strategy is to COPY the output of one of the sensors, so that the 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 connections together generate 2.4 bits of information, whereas the individual connections generate 0.08 bits independently. For the 4 connections to generate more information as a whole than separately they must be tangled: γ = 0.25 bits. If the input pattern is not a bar, the element generates 0.3 bits, so that it performs worse than the COPY, on average, on maxent noise. However, if bars are sufficiently common in the input, then the element generates more information than a COPY element. (C): Two elements COPY their inputs. This produces the maximum possible average effective information (2 bits for 2 binary elements) assuming the inputs are maxent distributed. The elements are not tangled, γ = 0, and so the whole generates information equal to the sum of the parts. (D): A cartoon cortical area: a subsystem that receives more inputs than there are elements. If there is some statistical structure to the inputs (certain patterns are more common than others), the system can form concepts specific to the input structure. The 2 binary elements shown generate 4 bits of information about the input pattern, more than the elements taken individually (2.7 bits). On average, using maxent, the 2 elements generate 1.8 bits, less than the COPY elements. However, if the inputs are structured and so not maxent, the elements can generate more information about other cortical areas than they should “by right” by tangling informational relationships into concepts and modes.

Mentions: Figure 13A shows a system comprising 4 input elements (sensors) and 1 output element (detector), which implements a COPY of one input element. In doing so, the COPY element generates 1 bit of information, whether it fires or not, and specifies a single informational relationship (q-arrow), corresponding to the simplest possible concept: that things are one way rather than another way, just like the photodiode in Fig. 1. If the input is pure noise (the maximum entropy distribution on 24 = 16 possible input patterns), then extracting 1 bit of information is indeed the best a single element can do. By contrast, the “BAR” element in Fig. 13B “integrates” information from 4 sensors. If the input is 1100, 0110, or 0011, the BAR element fires, and generates 2.4 bits of information, more than the COPY element. It can do so because the connections it receives from the 4 sensors are tangled, meaning that jointly they generate more information than the sum of the information generated by each connection independently (0.08 bits each). The corresponding tangled informational relationship (γ = 0.25 bits) corresponds to the concept BAR. By contrast, when the input pattern is not a bar (13 patterns out of 16), the element generates 0.3 bits. On average, then, the BAR element performs worse than the COPY element on pure noise, but can do better, thanks to entanglement, if bars are a common statistical feature of the input, i.e. more common than other patterns. In general, “integrating” information through entanglement and the formation of concepts is an effective strategy to extract more information from an input under the constraint of dimensionality reduction (here from 4 inputs 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 dimensionality reduction, 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 entanglement provides 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 inputs                                than their atomic subconcepts.(A): An element extracts information from a set of four sensors. If                                the input received by the sensor layer is pure noise (the maximum                                entropy distribution on                                24 = 16 possible firing                                patterns) then the best a single element can do, on average, is to                                extract 1 bit of information. An efficient strategy is to                                    COPY the output of one of the sensors, so that                                the 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 connections                                together generate 2.4 bits of information, whereas the individual                                connections generate 0.08 bits independently. For the 4 connections                                to generate more information as a whole than separately they must be                                tangled: γ = 0.25 bits. If                                the input pattern is not a bar, the element generates 0.3 bits, so                                that it performs worse than the COPY, on average,                                on maxent noise. However, if bars are sufficiently common in the                                input, then the element generates more information than a                                    COPY element. (C): Two elements                                COPY their inputs. This produces the maximum                                possible average effective information (2 bits for 2 binary                                elements) assuming the inputs are maxent distributed. The elements                                are not tangled, γ = 0, and                                so the whole generates information equal to the sum of the parts.                                (D): A cartoon cortical area: a subsystem that receives more inputs                                than there are elements. If there is some statistical structure to                                the inputs (certain patterns are more common than others), the                                system can form concepts specific to the input structure. The 2                                binary elements shown generate 4 bits of information about the input                                pattern, more than the elements taken individually (2.7 bits). On                                average, using maxent, the 2 elements generate 1.8 bits, less than                                the COPY elements. However, if the inputs are                                structured and so not maxent, the elements can generate more                                information about other cortical areas than they should                                “by right” by tangling informational                                relationships into concepts and modes.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000462-g013: Tangled concepts can generate more information about their inputs than their atomic subconcepts.(A): An element extracts information from a set of four sensors. If the input received by the sensor layer is pure noise (the maximum entropy distribution on 24 = 16 possible firing patterns) then the best a single element can do, on average, is to extract 1 bit of information. An efficient strategy is to COPY the output of one of the sensors, so that the 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 connections together generate 2.4 bits of information, whereas the individual connections generate 0.08 bits independently. For the 4 connections to generate more information as a whole than separately they must be tangled: γ = 0.25 bits. If the input pattern is not a bar, the element generates 0.3 bits, so that it performs worse than the COPY, on average, on maxent noise. However, if bars are sufficiently common in the input, then the element generates more information than a COPY element. (C): Two elements COPY their inputs. This produces the maximum possible average effective information (2 bits for 2 binary elements) assuming the inputs are maxent distributed. The elements are not tangled, γ = 0, and so the whole generates information equal to the sum of the parts. (D): A cartoon cortical area: a subsystem that receives more inputs than there are elements. If there is some statistical structure to the inputs (certain patterns are more common than others), the system can form concepts specific to the input structure. The 2 binary elements shown generate 4 bits of information about the input pattern, more than the elements taken individually (2.7 bits). On average, using maxent, the 2 elements generate 1.8 bits, less than the COPY elements. However, if the inputs are structured and so not maxent, the elements can generate more information about other cortical areas than they should “by right” by tangling informational relationships into concepts and modes.
Mentions: Figure 13A shows a system comprising 4 input elements (sensors) and 1 output element (detector), which implements a COPY of one input element. In doing so, the COPY element generates 1 bit of information, whether it fires or not, and specifies a single informational relationship (q-arrow), corresponding to the simplest possible concept: that things are one way rather than another way, just like the photodiode in Fig. 1. If the input is pure noise (the maximum entropy distribution on 24 = 16 possible input patterns), then extracting 1 bit of information is indeed the best a single element can do. By contrast, the “BAR” element in Fig. 13B “integrates” information from 4 sensors. If the input is 1100, 0110, or 0011, the BAR element fires, and generates 2.4 bits of information, more than the COPY element. It can do so because the connections it receives from the 4 sensors are tangled, meaning that jointly they generate more information than the sum of the information generated by each connection independently (0.08 bits each). The corresponding tangled informational relationship (γ = 0.25 bits) corresponds to the concept BAR. By contrast, when the input pattern is not a bar (13 patterns out of 16), the element generates 0.3 bits. On average, then, the BAR element performs worse than the COPY element on pure noise, but can do better, thanks to entanglement, if bars are a common statistical feature of the input, i.e. more common than other patterns. In general, “integrating” information through entanglement and the formation of concepts is an effective strategy to extract more information from an input under the constraint of dimensionality reduction (here from 4 inputs 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 dimensionality reduction, 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 entanglement provides 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