Abstract

This article proposes a model of rule/policy discovery based on examining experienced sequences. Fluid intelligence, as measured by intelligence tests, can be viewed as the ability to discover policies for solving problems from one or a small number of examples. Agents with fluid intelligence examine a small number of experienced time series to discover common rules. If the sequence is not present, memory recall (replay) would be used. The proposed model ”goes over” experienced sequences and extracts elements such as attributes, relationships among the input elements, and agent actions, to generate hypothetical policies.

1. Introduction

AGI as engineering is an attempt to give artifacts a general problem-solving capability beyond design. General intelligence was originally postulated as a factor of one or a few general problem-solving capabilities in the measurement of human intelligence [1]. Fluid intelligence was postulated as one of the factors that make up general intelligence. While the original definition of fluid intelligence [2] was "the ability to recognize relationships," the definitions in the community vary. Kievit et al. summarize fluid intelligence as "the ability to solve novel, abstract problems that do not depend on task-specific knowledge" [3]. More generally, Hernández-Orallo [4](Chapter 12) addresses fluid intelligence as a policy-generating capability. In an intelligence test, the subject is required to find a policy for solving the problem from one or a few examples. This requires the ability to conduct an internal search, generate multiple hypotheses, and find a solution, and it would be the central ability of fluid intelligence. In the following, fluid intelligence is regarded as the ability to discover policies for problem solving from one or a few examples. Note that while there are attempts to solve fluid intelligence tasks such as Raven’s Progressive Matrices (see Appendix) with deep learning methods [5], if they have learned with ample task data similar to the task to be tested, they are using crystallized intelligence rather than fluid intelligence to solve it.

In intelligence test-like tasks (see "Appendix: Assessment Tasks"), abstraction is necessary, for the same situation is not normally repeated. The abstract elements of the solution include the attributes of the input elements, the relationships between the attributes, and the actions of the agent. Policy discovery, including abstraction, is a process of induction. While machine learning is also inductive, a difference lies in the number of samples. Fluid intelligence in intelligence testing requires finding common structures from a small number of samples. This ability is useful in devising solutions to problems encountered in a variety of situations. In the following, a model of rule (policy) discovery based on examining experienced time series is proposed.

2. Model of the Discovery Process

Discovery of rules (policies) from experienced series is done by "going over" the the series:

If the entire problem is not presented to the agent at once, a replay is performed, otherwise the agent goes over the presented scene.
Elements (attributes of input elements, relations among the attributes, and actions of agents) are extracted from the success series to form a hypothetical policy series.
Various heuristics can be used to determine which elements are prioritized in the hypothetical policy. (e.g., Emphasis is placed on elements in close temporal and spatial proximity and the relationships associated with them.)
Elements in the failed series are discounted.
The hypothetical policy is verified with one or more series.
Hypothetical policies that fail verification are stored as rejected policies so that they will not be tested/used again.

3. Required Mechanisms

Mechanism to go over spatial scenes by gaze (eye) movement for problems presented visually
Mechanism to go over a temporal sequence – replay mechanism which recalls memorized sequences for policy generation and validation
Mechanism to generate policy elements; e.g., attribute extraction (abstraction) and discovery of relationships between elements
Mechanism to give preference: preferences are useful for the search process to select policy elements.
Mechanism to create a hypothetical policy series by adopting policy elements
Mechanism to store hypothetical policies
Mechanism to determine whether a hypothetical policy can be applied to a spatial scene or temporal (replayed) series
Mechanism not to use rejected series
Working memory – required for various tasks
Mechanism to control the process as a whole

4. Policy Generation, Verification, and Application

Based on the required mechanisms, the process of policy generation, verification, and application can be summarized as follows:

Policy generation

Go over the successful series and create a series that reproduces the input elements.
Attention is given preferentially to a specific attribute or relation in the sequence.
Generate a hypothetical policy series from the sequence of attributes or relations extracted with the given attention.

Policy Verification

A series may be made by trial runs or by memory recall (replay).
Recall the hypothetical policy from the (trial or recalled) series, and try to apply it (see below).
If a (trial or recalled) success series matches the policy, retain it for further validation with other success series.
If a (trial or recalled) failure series matches the policy, reject the policy.

Applying policy to a series

Apply the policy to the sequence, starting with the first element in the sequence and checking for a match to each recalled policy sequence element in turn.
If the application of a policy element fails, then the policy fails.

5. Implementation with (Artificial) Neural Networks

If the elements (attributes and relations) are entirely symbolized and provided, the mechanism above could be implemented by a symbolic (GOFAI) algorithm. If the elements are not clearly defined, it should be difficult to create a symbolic algorithm, and implementation would require fuzzy pattern matching and learning functions as found in (artificial) neural networks. Note that problems must be solved without having been exposed to similar tasks even when learning is required. In the following, hints for implementation with (artificial) neural networks are presented in line with the Required Mechanisms.

Mechanism to go over spatial scenes
The mechanism of saccade control by the brain can be imitated.
Mechanism to go over temporal sequences
Experienced sequences are recalled from other sequences and used for policy generation and validation. Since no generalization is needed in the memory of series, a simple non-learning storage device could be used.
Since replay is believed to occur in the hippocampus in the brain, the hippocampal mechanism can be imitated. Meanwhile, as the phonological loop (working memory for speech) [6] is assumed to be located in the cortex, extra-hippocampal cortical circuits may also have replay-like functions.
Mechanism for generate policy elements

Attribute extraction (Abstraction)
It is known that abstraction occurs in artificial neural networks through learning.
Discovery of relations between elements
Relations (e.g., co-occurrence of attributes) among elements can be extracted with artificial neural networks. In order for a neural network to recognize transformation (such as rotation) of a figure, it must have learned the transformation.
When policy elements are created during replay, it would be better to have a mechanism to control the timing of replay to create a time margin for processing. [Note]

Mechanism to give preferences
Preferences such as for spatial proximity can be incorporated into the structure of a neural network.
Mechanism to create a hypothetical policy series by adopting policy elements/Mechanism to store hypothetical policies

Policy elements are recalled and adopted by attention. A certain mechanism (e.g., winner-takes-all) would be needed to select an element for attention.
The series formed in the system can be stored in a mechanism similar to replay.
Policy elements are pairs of attributes or relations to be selected and attention.

Mechanism to determine whether a hypothetical policy can be applied to a spatial scene or replayed temporal series / Mechanism not to use rejected series

Matching a hypothetical policy with memorized series could be implemented with the pattern matching function of a neural network.
Policies that match the failed series are classified as rejected, and will not be used.

Working memory – networks such as a bi-stable network could be used.
Mechanism to control the process as a whole
The process is repeated until a policy consistent with all the presented series is generated.

Note: Policy elements become the object of attention (i.e., made aware) when they are added to the policy. In this sense, policy generation involves System 2 in dual-process theory [7], which also makes policy verbalization possible. However, other processes are not necessarily brought to attention.

6. Conclusion

This article has only suggested a model. Future work would include its psychological validation and/or software implementation. A literature survey on brain regions and functions corresponding to the model will be necessary to support it from the neuroscientific viewpoint. Since policies discovered by the model include the actions (operations) of the agent, the mechanism is to discover at least one class of algorithms. By examining how general the class of algorithms it discovers, it will be possible to evaluate it as a model of general intelligence.

References

[1] Spearman, C.: General Intelligence, Objectively Determined and Measured, The American Journal of Psychology, Vol.15, No.2, pp.201--292. doi:10.2307/1412107 (1904).

[2] Cattell, R.B.: The measurement of adult intelligence, Psychol. Bull., Vol.40, pp.153-–193. doi:10.1037/h0059973 (1943)

[3] Kievit, R.A., et al.: A watershed model of individual differences in fluid intelligence, Neuropsychologia, Vol.91, pp.186–198 (2016)
doi:10.1016/j.neuropsychologia.2016.08.008

[4] Hernández-Orallo, J.: The Measure of All Minds: Evaluating Natural and Artificial Intelligence, The Cambridge University Press (2017)

[5] Małkiński, M., et al.: Deep Learning Methods for Abstract Visual Reasoning: A Survey on Raven’s Progressive Matrices, arXiv, doi:10.48550/arXiv.2201.12382 (2022)

[6] Baddeley, A.D., Hitch, G.J.: Working Memory, In G.A. Bower (Ed.), Recent advances in learning and motivation (Vol. 8, pp. 47-90), New York: Academic Press (1974)

[7] Kahneman, D.: A perspective on judgement and choice, American Psychologist, Vol.58, No.9, pp.697-–720. doi:10.1037/0003-066x.58.9.697 (2003)

[8] Joyner, A., et al.: Using Human Computation to Acquire Novel Methods for Addressing Visual Analogy Problems on Intelligence Tests, ICCC (2015) [PDF]

[9] Carpenter, A., Just, A., Shell, P.: What one intelligence test measures: A theoretical account of the processing in the Raven Progressive Matrices Test, Psychological Review, 97(3) doi: 10.1037/ 0033-295X.97.3.404 (1990)

Appendix: Assessment Tasks

In this appendix, visual tasks that require fluid intelligence are introduced. Since visual pattern recognition is not an essential part of fluid intelligence, the attributes of the figure may be used as input in the tasks.

A.1 Delayed Matching Task

The task to determine if two figures appearing in the different times have the ‘same’ shape.

A.1.1 Mechanisms required

Visual attribute extraction
Short-term memory to retain shape attributes
Mechanism to apply policy and determine output based on the short-term memory and current input
Recognition mechanism to determine a figure is the ‘same’ as presented before
Mechanism to discover policy hypotheses (⇒ main text)

A.1.2 Policy to be found

[start, figure t₁, blank, f(figure t1) = f(figure t2) ⇒ reaction]

t1 refers to the time when the figure appears immediately after the start, and t2 the time when the figure appears after the blank.
f refers to the attribute set of the figure stored at t1.

A.1.3 Policy Discovery Process

With the proximity of {blank, figure, reaction}, create a policy: [blank, figure ⇒ reaction].
The policy is rejected as it does not always succeed in subsequent trials.
[start, figure t1, f(figure t1) = f(figure t2)] is detected in the replay of a successful sequence, to be adopted as a hypothetical policy.

Judgment of whether attributes are the same is done by a required mechanism.
The attribute f is retained until the recognition (working memory).

A.2 Simultaneous Matching Task

The task to determine whether two shapes appearing simultaneously in different locations are the ‘same’ while performing gaze movement (this requires working memory even for simultaneous judgment).

A.2.1 Mechanisms Required

Mechanisms required for the delayed matching task
Mechanism to control gaze movement

A.2.2 Policy to be found

[f(figure l1), l1 ⇒ l2, f(figure l1) = f(figure l2) ⇒ reaction]

l1 ⇒ l2 is a gaze movement.

A.2.3 Process of Policy Discovery

If f(figure l1) = f(figure l2) is detected in the success sequence, it is adopted as a policy hypothesis element. (It is necessary to retain the attributes of the shape l1 until recognition in working memory.)
The gaze movement that appears in the success sequence is adopted as a policy hypothesis element.

A.3 Cued {Delayed|Simultaneous} Matching Task

In this task, after a cue is presented, the subject has to determine if two shapes that appear {at the same location at different times|simultaneously at different locations} are the same in terms of a specific attribute (shape, color, etc.) according to the cue.

The cue should be remembered.
The correspondence between the cue and the attribute to be retained should be learned.

A.3.1 Mechanisms Required

Mechanisms required for the {Delayed|Simultaneous} Matching Task

A.3.2 Policy to be found

Delayed: [cue x, fx (figure t1), blank, fx(figure t1) = fx(figure t2) ⇒ reaction]
Simultaneous: [cue x at l0, l0 ⇒ l1, fx(figure l1), l1 ⇒ l2,
fx(figure l1) = fx(figure l2) ⇒ reaction]

l0 ⇒ l1 and l1 ⇒ l2 stand for gaze movements.
fx depends on the cue.

A.3.3 Process of Policy Discovery (Delayed)

Since (blank, figure, reaction) occur successively, make the policy
[blank, figure ⇒ reaction].

This policy is rejected as it does not always succeed in subsequent trials.
...
[cue x, fx(figure t1) = fx(figure t2)] is found in the success sequence and incorporated into a policy hypothesis.

The attribute types and values of fx(figure t1) should be retained until the judgment fx(figure t1) = fx(figure t2) in working memory.
More than one element is added to the policy at once.
Prior knowledge or learning of the usefulness of attribute equivalence judgment would be necessary.

A.3.3 Process of Policy Discovery (Simultaneous)

Omitted

A.4 {Delayed|Simultaneous} Transformational Matching Task

The task is to judge whether a figure appearing at {while after|a different location from} another figure is obtained by applying one of the given transformations to the latter, and to return a reaction corresponding to the transformation. (See Visual Analogy Task 1 below)

A.4.1 Mechanisms Required

The mechanisms required for the {Delayed|Simultaneous} Matching Task
List of graphic transformations
Mechanism for applying transformations
Output of transformation types

A.4.2 Policy to be found

Delay: [f(figure t1), blank, f(ax(figure t1)) = f(figure t2) ⇒ reaction]
Simultaneous: [f(figure l1), l1 ⇒ l2, f(ax(figure l1)) = f(figure l2) ⇒ reaction]

l1 ⇒ l2 stands for gaze movement.
ax is a graphic transformation.

A.4.3 Process of Policy Discovery (Delayed)

Since (blank, figure, reaction) occur successively, generate the policy
[blank, figure ⇒ reaction].
The policy is rejected as it does not always succeed in subsequent trials.
Find [start, figure t1, blank, f(ax(figure t1)) = f(figure t2)] is true in successful trials to adopt it in a policy hypothesis.

ax is recalled from figure t1 and figure t2.
The judgment f(ax(figure t1)) = f(figure t2) requires working memory.
More than one element is added to the policy at once.

A.4.3 Process of Policy Discovery (Simultaneous)

Omitted

A.5 Visual Analogy Task 1

With a 2x2 matrix, the subject has to infer the lower right frame from the shapes in other frames (see Fig.1).

Fig.1 an example of Visual Analogy Task 1 [8]

A.5.1 Mechanisms Required

The mechanisms required for the Simultaneous Transformational Matching Task
Mechanism to generate transformed figures (for a multiple choice task, figure recognition)

A.5.2 Policy/Rule to be found

For each row: [ax(figure l1) = figure l2]
l1 and l2 denote the locations of the figures.
ax stands for a figure transformation.
ax(figure l1) is the correct answer for the lower right frame.

A.5.3 Process of Policy Discovery

Discover a policy hypothesis at once from the first row.

ax is either discovered by trial and error, or is recalled from the figures at l1 and l2.
More than one element is added to the policy at once.

The discovered rule is applied to the second row to produce ax(figure l1).

A.6 Raven’s Progressive Matrices

A Raven’s Progressive Matrix (RPM hereafter) is a task in which typically a 3 x 3 matrix is presented, and the subject is required to discover the relationship between the shapes in the cell in the top two rows and apply it to the bottom row to infer the shape of the blank cell on the bottom right (Fig. 2). RPM is said to be central to the measurement of fluid intelligence, in that it requires functions required by other types of tasks [9].

Fig. 2 Raven’s Progressive Matrices

CC BY-SA 3.0 Life of Riley @Wikimedia

A.6.1 Mechanisms Required

The mechanisms required for Visual Analogy Task 1

A.6.2 Policy/Rule to be found

In each row: [ l1 ⇒ l2, ax(figure l1) = figure l2, l2 ⇒ l3, ax(figure l2) = figure l3]

Only shape transformations are used as RPM rules.
(Tasks with rules such that a row always contains a certain set of figures, are not dealt with here.)
l1, l2, l3 stand for the locations of the figures.
ln ⇒ lm stands for gaze movement.
ax stands for a figure transformation.

A.6.3 Process of Policy Discovery

The subject is required to discover rules that can be applied to all rows, with the first two rows as the sample series.

Generate a policy hypothesis from the first row.

ax is recalled from figures at l1 and l2 and figures at l2 and l3.
The figures are memorized before the gaze movement.

Apply the policy hypothesis found in the first row to the second row.

If successful, apply the policy hypothesis to the third row.

If successful, generate ax(figure l2) ⇒ End
If not, generate another policy hypothesis ⇒ Go to 1.

If not, reject the first policy hypothesis and look for another one
⇒ Go to 1.

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Monday, November 21, 2022

A Model of Fluid Intelligence based on Examining Experienced Sequences