AI_ML_DL’s diary


Defining intelligence: a formal synthesis

Ⅱ.2  Defining intelligence: a formal synthesis


これは、F. Chollet氏のThe Measure of Intelligenceの、27ページから43ページまで続く記事である。



この節の直前に、”four core knowledge systems" が示されている。



2番目のagentnessのagentは、強化学習reinforcement learningの説明の際に初めて出くわした単語だったと思う。代理人という意味しか思い浮かばず、なぜこんな用語が使われるのか理解できなかった。今は、勝手な解釈かもしれないが、そもそも強化学習はコンピュータゲームから派生しており、ゲームの主人公を、ゲーマーの代理人と言うことで、agentと呼ぶことにしたのだろうと思っている。


1番目の物体の概念、3番目の数の概念、4番目の幾何学的・トポロジカル的概念については、core knowledgeそのものだろうと思う。







ステップ1:np.tile(x, (3, 3))で、x(3x3)を9x9のグリッドに張り付け、aに代入する。

ステップ2:x(3x3)を元の分布を維持したまま拡大:b=x.repeat(3, axis=0).repeat(3, axis=1)

ステップ3:a & bにより、タイルの分布を、3x3が持っていた分布に変更する。


ステップ1:タイルかどうかの判定:入力と出力のグリッドサイズが整数倍か否かの判定を行う:グリッドサイズをSin、Soutとして、mod = Sout % Sinで、modがゼロかどうか調べる



ed98d772:3x3 ⇒ 6x6、左上コピー、左下180度回転、右上90度、右上90度左回転、右下90度右回転

d4b1c2b1:3x3 ⇒ 3nx3n、nは、色の種類の数、分割数は増えるが、模様は変わらず。

ccd554ac:nxn ⇒ n^nxn^n、2x2 ⇒ 4x4、3x3 ⇒ 9x9、4x4 ⇒ 16x16、5x5 ⇒ 25x25、ただし、trainは4までで、testのみ5となっている。

cad67732:説明が難しいので画像を張り付けた。タイルに分類しても良いのかな。こういうパターンを判定するには どうすれば良いのだろうか。グリッドサイズは4倍で単純だが、このパターンを生成するコーディング能力が、別途必要になる。






回転はnp.rot90( )、上下入れ替えは、np.flipud( )、左右入れ替えは、np.fliplr( )。




F. Chollet氏が言われているように、手作業で条件文とか従来のプロギラミング手法を駆使して10個か20個ぐらいのパターンに対応できるだけの技術を身に着けて、そこから徐々に汎用性を考えていくという地道な作戦でいくしかないんだろうな。





Objectness and elementary physics: humans assume that their environment should
be parsed into “objects” characterized by principles of cohesion (objects move as
continuous, connected, bounded wholes), persistence (objects do not suddenly cease
to exist and do not suddenly materialize), and contact (objects do not act at a distance
and cannot interpenetrate).

Agentness and goal-directedness: humans assume that, while some objects in their
environment are inanimate, some other objects are “agents”, possessing intentions of
their own, acting so as to achieve goals (e.g. if we witness an object A following
another moving object B, we may infer that A is pursuing B and that B is fleeing
A), and showing efficiency in their goal-directed actions. We expect that these agents
may act contingently and reciprocally.
Natural numbers and elementary arithmetic: humans possess innate, abstract number
representations for small numbers, which can be applied to entities observed through
any sensory modality. These number representations may be added or subtracted, and
may be compared to each other, or sorted.
Elementary geometry and topology: this core knowledge system captures notions
of distance, orientation, in/out relationships for objects in our environment and for
ourselves. It underlies humans’ innate facility for orienting themselves with respect
to their surroundings and navigating 2D and 3D environments.



The Core Knowledge priors assumed by ARC are as follows:

 a. Objectness priors:
Object cohesion: Ability to parse grids into “objects” based on continuity criteria including color continuity or spatial contiguity (figure 5), ability to parse grids into zones, partitions.

Object persistence: Objects are assumed to persist despite the presence of noise (figure
6) or occlusion by other objects. In many cases (but not all) objects from the input persist
on the output grid, often in a transformed form. Common geometric transformations of
objects are covered in category 4, “basic geometry and topology priors”.

Object influence via contact: Many tasks feature physical contact between objects (e.g.
one object being translated until it is in contact with another (figure 7), or a line “growing” until it “rebounds” against another object (figure 8).

b. Goal-directedness prior:
While ARC does not feature the concept of time, many of the input/output grids can be
effectively modeled by humans as being the starting and end states of a process that involves intentionality (e.g. figure 9). As such, the goal-directedness prior may not be strictly necessary to solve ARC, but it is likely to be useful.

c. Numbers and Counting priors:
Many ARC tasks involve counting or sorting objects (e.g. sorting by size), comparing
numbers (e.g. which shape or symbol appears the most (e.g. figure 10)? The least? The
same number of times? Which is the largest object? The smallest? Which objects are the
same size?), or repeating a pattern for a fixed number of time. The notions of addition and subtraction are also featured (as they are part of the Core Knowledge number system as per [85]). All quantities featured in ARC are smaller than approximately 10.

d. Basic Geometry and Topology priors:
ARC tasks feature a range of elementary geometry and topology concepts, in particular:
• Lines, rectangular shapes (regular shapes are more likely to appear than complex
• Symmetries (e.g. figure 11), rotations, translations.
• Shape upscaling or downscaling, elastic distortions.
• Containing / being contained / being inside or outside of a perimeter.
• Drawing lines, connecting points, orthogonal projections.
• Copying, repeating objects. 


Ⅱ.2.1  Intelligence as skill-acquisition efficiency


It is marked by flexibility and adaptability (i.e. skill-acquisition and generalization).

Unlimited priors or experience can produce systems with little-to-no generalization power (or intelligence) that exibit high skill at any number of tasks.

General AI should be benchmarked against human intelligence and should be founded on a similar set of knowledge priors.


これから、intelligenceとその測定の正式な定義を確立するために必要な主要な概念の一連の定義を、 アルゴリズム情報理論のツールを用いて示す、ということのようだ。


central idea:

The intelligence of a system is a measure of its skill-acquisition efficiency over a scope of tasks, with respect to priors, experience, and generalization difficulty.


Position of the problem

We consider the interaction between a "task" and an "intelligent system". This interaction is mediated by a "skill program" (generated by the intelligent system) and a "scoring function" (part of the task)







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