A Theory of Relation Learning and Cross-domain Generalization

TL;DR

This paper proposes that human cross-domain generalization emerges from analogical inference over structured relational representations learned from non-relational inputs. It introduces a unified model that extends LISA and DORA, enabling discovery of relational invariants, learning of predicate structure, and reinforcement-learning-guided model construction. Through simulations, the authors demonstrate zero-shot transfer between video games, cross-domain generalization from shape images to games, and developmental-like trajectories that echo human analogy development. The work argues that explicit, binding-capable relational representations confer greater generalization flexibility than purely statistical approaches, offering a path toward general intelligence.

Abstract

People readily generalize knowledge to novel domains and stimuli. We present a theory, instantiated in a computational model, based on the idea that cross-domain generalization in humans is a case of analogical inference over structured (i.e., symbolic) relational representations. The model is an extension of the LISA and DORA models of relational inference and learning. The resulting model learns both the content and format (i.e., structure) of relational representations from non-relational inputs without supervision, when augmented with the capacity for reinforcement learning, leverages these representations to learn individual domains, and then generalizes to new domains on the first exposure (i.e., zero-shot learning) via analogical inference. We demonstrate the capacity of the model to learn structured relational representations from a variety of simple visual stimuli, and to perform cross-domain generalization between video games (Breakout and Pong) and between several psychological tasks. We demonstrate that the model's trajectory closely mirrors the trajectory of children as they learn about relations, accounting for phenomena from the literature on the development of children's reasoning and analogy making. The model's ability to generalize between domains demonstrates the flexibility afforded by representing domains in terms of their underlying relational structure, rather than simply in terms of the statistical relations between their inputs and outputs.

Figures (19)

• Figure 1: Knowledge representation and temporal binding in DORA. (a) Representation of a single proposition (above (ball, paddle)) in DORA. Feature units represent properties of objects and relational roles in a distributed manner. Token units in T1 represent objects and roles in a localist fashion; token units in T2 conjunctively bind roles to their arguments (e.g., objects); token units in T3 conjunctively link role-argument pairs into multi-place relations. (b) A time-series illustration of the activation of the units illustrated in (a). Each graph corresponds to one unit in (a) (i.e., the unit with the same name as the graph). The abscissa of the graph represents time, and the ordinate represents the corresponding unit's activation. (c) Time-based binding illustrated as a sequence of discrete frames (i$\ldots$iv). (i) Units encoding higher-than-something fire. (ii) Units encoding ball fire. (iii) Units encoding lower-than-something fire. (iv) Units encoding paddle fire. Labels in units indicate what the unit encodes (see key); the labels on the units are provided for clarity and are meaningless to DORA.
• Figure 2: DORA's Macrostructure. (a) DORA’s long-term-memory (LTM), consisting of layers of token units (T1-T3; black rectangles), and the feature units connected to the bottom layer of LTM. During processing, some units in LTM enter active memory (AM). (b) Expanded view of AM. AM is composed of two sets, the driver (the current focus of attention) and the recipient (the content of working memory available for immediate processing). Black lines indicate bidirectional excitatory connections.
• Figure 3: Representation learning in DORA. (a) Learning a single-place predicate representation by comparing two objects. (i) A representation of a ball in the driver is mapped (grey double-headed arrow) to a representation of a paddle in the recipient. (ii) The representation of the ball in the driver activates the mapped unit in the recipient (through shared features and mapping connection); as units pass activation to their features, shared features become more active (dark grey units) than unshared features (light grey units). (iii) Units in T1 and T2 are recruited (activation clamped to 1; dark grey units with white squiggle) in the recipient, and weighted connections are learned via Hebbian learning (i.e., stronger connections between more active units). (iv) The result is an explicit representation of the featural overlap of the ball and paddle—in this case the property of being higher-than-something (see main text)—that can be bound to an argument (as in Figure \ref{['fig:1']}). (b) Learning a multi-place relational representation by linking a co-occurring set of role-argument pairs. (i) a representation of a ball that is higher-than-something and a paddle that is lower-than-something is mapped to a different representation of a paddle that is higher-than-something, and a ball that is lower-than-something (e.g., from a different game screen). (ii) (Mapping connections, grey doubled-headed arrows, have been lightened to make the rest of the figure clearer.) When the representation of higher-than-something (ball) becomes active in the driver it activates mapped units in the recipient; a T3 unit is recruited (activation clamped to 1; dark grey unit with white squiggle) in the recipient and learns weighted connections to units in T2 via Hebbian learning (iii) When the representation of lower-than-something (paddle) becomes active in the driver, it activates corresponding mapped units in the recipient; the active T3 unit learns weighted connections to T2 units. (iv) The result of learning is a LISAese representation of the relational proposition above (ball, paddle) (see Figure \ref{['fig:1']}). Labels in units indicate what the unit encodes (see key). The labels on the units are provided for clarity and are meaningless to DORA.
• Figure 4: (a) The relational invariance circuit. (b) (i) Activation flows from clamped feature units encoding a dimension or property to T1 units (dark grey units indicate more active units).(ii) T1 units compete via lateral inhibition to respond to the active feature units (light grey units indicate less active units). (iii) T1 units activate proxy units, which feed activation to E units. E units pass activation to a subset of feature units non-m and connections between active feature units non-m and T1 units are updated via Hebbian learning. (iv) The active T1 unit is inhibited to inactivity by its inhibitor (black square). (v-vi) The process repeats for the second active T1 unit.
• Figure 5: Analogical inference in DORA. (a) The representation of the right-of (ball, paddle1), and right-of (paddle2, paddle1) in the driver maps to the representation of above (paddle2, paddle1) in the recipient (grey double-arrowed lines indicate mappings). (b) As the representation of right-of (ball, paddle1) becomes active in the driver, some active units have nothing to map to in recipient (the units representing ball, more-x+ball, less-x+paddle1, and right-of (ball, paddle1)). DORA recruits and activates units to match the unmapped driver units (black units indicate recruited units; black double-arrowed lines indicate inference relationships). DORA learns connections between co-active token units in the recipient (heavy black lines). The result is a representation of the situation: above (ball, paddle1) $\&$above (paddle2, paddle1) in the recipient.