Jared Edward Reser, PhD and GPT 5.6 

The iterative updating proposal developed in Thought Is Structured by the Iterative Updating of Working Memory (Reser; 2022, 2016) can be interpreted as a dynamic account of compositional generalization. The architecture describes how a capacity-limited cognitive system could construct novel representations by preserving selected contents while adding, removing, rebinding, and transforming others across successive working-memory states. Thought iterative updating.pdf The same state overlap proposed to underwrite mental continuity also permits relational constraints, goals, and intermediate results to remain active while familiar constituents are placed into unfamiliar combinations.

Compositional generalization is usually defined as the ability to recombine previously learned elements and operations in configurations absent from the training distribution. A system that has learned the concepts jump, twice, and walk should be able to interpret or execute “jump twice” and “walk and jump” without receiving direct training on each combination. The ability includes several partly separable capacities: systematic recombination of familiar constituents, substitution of new fillers into known structures, extension to longer expressions or action sequences, transfer of relational schemas, and composition of familiar operations into new procedures. SCAN exposed sharp failures of recurrent sequence models on systematic command recombination, while COGS and SLOG extended the problem to lexical and structural generalization in semantic parsing. 

The empirical literature also shows that compositional generalization cannot be represented adequately by a single benchmark score. ReCOGS demonstrated that incidental properties of a target logical form can exaggerate apparent failures, and a 2025 analysis found that some COGS splits provide ambiguous or conflicting evidence about the intended generalization. A credible assessment therefore requires multiple tests covering lexical substitution, role reversal, structural novelty, relational transfer, sequence length, and cross-domain application. 

1. Compositionality as a Dynamic Construction Process

Traditional descriptions of compositionality usually characterize the structure of a completed expression, proposition, program, or scene. The iterative updating model adds an account of how such a structure could be constructed, inspected, and revised by a bounded cognitive system. Each state retains a proportion of the representations active in the preceding state, while selected additions progressively alter the active configuration. The resulting states form a chain of associatively linked intermediate representations that can move toward a solution or goal. 

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Three forms of composition can be distinguished within this architecture. Within-state composition occurs when multiple items become coactive and jointly represent a scene, relation, question, or partial solution. Across-state composition occurs when a structural scaffold remains active while one or more constituents are replaced or transformed. Across-thread composition occurs when the products of separate iterative sequences are stored, retrieved, and merged into a higher-order solution.

This temporal conception helps explain how a limited focus of attention could construct representations whose total complexity exceeds its instantaneous capacity. A large structure does not have to be represented in full detail during every processing cycle. Stable components can remain in the focus, secondary information can be retained in the short-term store, and previously completed substructures can be compressed into chunks or schemas.

2. Hierarchical Representations as Reusable Constituents

Compositional generalization requires constituents that retain enough identity to be reused across contexts. In the iterative updating model, an item in working memory corresponds to an ensemble of distributed neural assemblies, while each assembly represents lower-level features or conjunctions. The diagram in Figure 24 on page 36 traces the proposed hierarchy from individual neurons, to subsymbolic assemblies, to symbolic ensembles, to several coactive items in the focus of attention, and finally to an iteratively updated sequence of states. 

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This hierarchy provides a plausible bridge between distributed neural representation and symbolic composition. Lower levels encode perceptual, semantic, motor, and relational features, while higher-order ensembles serve as reusable concepts that can participate in many different configurations. A representation for circle, for example, can be activated with different colors, locations, owners, actions, and relational roles without requiring a separate atomic representation for every possible circle-containing scene.

The model also treats an item as a fuzzy and context-sensitive ensemble. Its exact assembly membership may change as the surrounding working-memory contents change, allowing a concept to emphasize different features in different situations. Thought iterative updating.pdf Step five of multiassociative search makes this contextual modulation explicit: newly active items alter the assembly composition and effective meaning of other active items. 

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A useful formal refinement would divide each item into a relatively stable semantic core and a context-dependent halo. The stable core would support substitution and recognition across novel combinations, while the halo would encode the interpretation currently relevant to the active scene. Such an organization would preserve the general meaning of bank across contexts while allowing financial and river-related features to receive different activation according to the other items in working memory.

3. Partial Updating as a Compositional Substitution Operation

The elementary operation of the model is partial replacement. Some working-memory items remain active, some are removed, and some are added, causing the current state to become a revised version of its predecessor. The paper argues that this cascading persistence allows later states to elaborate intelligently on earlier states while preserving context. 

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Let F_t denote the set of items in the focus of attention at time t. A simplified update can be written as:

F_{t+1}=(F_t\setminus D_t)\cup A_t

where D_t contains items selected for removal and A_t contains newly selected additions. Compositional reuse occurs when the retained subset contains a relation, rule, goal, or structural frame and the additions supply new fillers or consequences.

Figure 14 on page 26 illustrates this process directly. Three items remain active while a fourth item is replaced, after which the revised configuration is used to search for the next update. The retained items continue to define the topic and context while each addition incrementally changes the represented situation. 

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Consider a system that has learned the spatial relation represented by “a red square is to the left of a blue circle.” When asked to process “a green circle is to the left of a red triangle,” the relational item LEFT-OF and the structural roles FIGURE and GROUND can remain active while the object and color fillers are replaced. The new configuration can then be projected into a visual model, checked for relational consistency, and used to guide a response.

This process can be described as state-spanning compositionality. A role structure, goal, or partial model persists across several states, while its fillers and inferred consequences are progressively modified. State-spanning compositionality extends the paper’s concept of state-spanning coactivity from continuity of subject matter to continuity of relational organization. The model already proposes that persistent items allow contextually related information to accumulate across delays and permit the capture of variable-length dependencies. 

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4. Multiassociative Search and Novel Conjunctions

Multiassociative search supplies the selection mechanism for compositional construction. Every active item contributes excitatory and inhibitory influence to a search of long-term memory, and the combined configuration determines which representation becomes active next. The resulting update is therefore conditioned on the whole active constellation rather than on an isolated cue.

Figure 27 on page 41 provides the clearest illustration. Items B, C, D, and E are individually associated with many candidates, yet their unique combination converges most strongly on item F. The paper further proposes that assemblies which have never previously been coactive can jointly select a relevant update, creating either recall or a novel inference and producing new associative learning. 

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This mechanism addresses an important component of compositional generalization. A novel combination can impose a novel intersection of constraints on memory even when the complete combination was absent from training. If the system simultaneously represents flammable, liquid, near heat, and open container, their joint activity may retrieve an appropriate prediction or action that none of the items would select reliably in isolation.

Multiassociative search also allows composition to remain graded and probabilistic. Several candidate additions may satisfy portions of the active context, while the complete configuration determines which candidate best reconciles the current constraints. Such processing is well suited to natural cognition, where relations are often uncertain, context-dependent, and only approximately expressed by explicit rules.

The mechanism nevertheless requires structured representations. An unordered set containing dog, chase, and cat cannot by itself distinguish a dog chasing a cat from a cat chasing a dog. Multiassociative convergence can respond to combinations, but compositional systematicity also requires sensitivity to the roles occupied by the constituents and to the order or topology connecting them.

5. Role-Filler Binding as a Necessary Extension

The classic systematicity challenge concerns structural symmetries among cognitive capacities. A system that can represent “John sees Mary” should also possess the representational resources needed for “Mary sees John,” even though the two propositions have different meanings. Fodor and Pylyshyn argued that such relations require combinatorial structure and structure-sensitive operations. 

The iterative updating model already contains an opening for a binding mechanism. Its proposed artificial workspace is graph structured, and the implementation discussion considers neural binding, synchronized activity, and reentrant oscillation as possible means of integrating several ensembles into a unified situational representation. Thought iterative updating.pdf These mechanisms could assign items to temporary roles while preserving their independently reusable semantic identities.

Hummel and Holyoak’s LISA architecture offers one compatible implementation. LISA represents objects and relations through distributed semantic patterns while using temporal synchrony to bind fillers to relational roles. Smolensky’s tensor product representations provide another implementation in which role vectors and filler vectors are combined into distributed representations of structured bindings. Both approaches permit novel fillers to enter familiar relational structures while preserving who did what to whom. 

One possible formalization of the active workspace would be:

Z_t=\sum_{i=1}^{n} r_i\otimes f_i

where r_i represents a relational role, f_i represents its current filler, and \otimes denotes a binding operation. The iterative update would retain some bindings, remove others, and add newly selected bindings. Tensor products are only one option; synchrony, phase coding, graph edges, key-value pointers, or learned slot mechanisms could serve the same architectural purpose.

A strong test of compositionality can then be expressed through transition equivariance. Let T represent one iteration of the working-memory update process, and let \pi represent a lawful substitution or permutation of fillers. Systematic generalization requires approximately:

T(\pi Z_t)\approx \pi T(Z_t)

The relation states that applying a role-preserving substitution before an update should produce the corresponding substitution in the result. If the dog and cat are exchanged in the input proposition, the system’s predictions, imagery, and action plans should change in the structurally appropriate way.

Role-filler binding is therefore the principal mechanism that would convert multiassociative recombination into systematic compositional generalization. The iterative architecture supplies persistence, selection, context, and temporal construction, while the binding mechanism supplies relational order and constituent independence.

6. Iterative Compounding and Procedural Composition

Compositional generalization also applies to procedures. A system should be able to combine familiar operations into a novel sequence, reuse an operation with new arguments, and extend a learned procedure beyond the sequence lengths encountered during training. The iterative updating model treats successive working-memory states as successive stages of a problem-solving process.

The paper proposes that each state represents the current status of a procedure and incorporates the product of the preceding associative search. Linked searches can therefore culminate in a higher-order result that no individual search could produce. Prolonged iteration permits simple processing products to furnish a foundation for later processing products, allowing complex thoughts to be constructed from simpler ones. 

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The same organization can implement learned algorithms. Successive states correspond to successive operations, while completed or irrelevant operations leave the focus of attention. Training can associate each procedural state with the operation required at the next stage, as illustrated by the paper’s example of long division. 

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Reusing the same transition rule across multiple iterations provides a route to productivity and length generalization. A learned operation such as “apply the transformation to the next element” can, in principle, be repeated for a sequence longer than any sequence used during training. Robust length extrapolation requires the transition rule to depend on the represented state of the procedure rather than on a memorized absolute position or fixed number of iterations.

Evidence from formal-language learning supports the value of explicit intermediate states. Dan, Bastani, and Roth found that models trained to predict the intermediate states of a finite-state computation generalized more robustly than systems trained only on end-to-end labels. Their result is consistent with the iterative model’s proposal that intermediate cognitive states should be represented, retained, and used as inputs to subsequent processing. 

The variable rate of updating adds a form of cognitive control. Tightly coupled iterations preserve more constraints and intermediate results, supporting difficult relational and algorithmic tasks. Faster updating permits exploration and responsiveness, while slower updating sustains a structural scaffold long enough for several operations to act upon it. The paper associates lower rates of replacement with more precise searches and deeper processing because a larger set of conserved parameters remains available. 

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7. Schema Transfer, Analogy, and the Merger of Subsolutions

Compositional generalization often involves applying an abstract schema to new surface content. Figure 39 on page 54 depicts a previously learned schema being recalled and coiterated with items from a new line of thought. The schema functions as an organizing script whose elements interact with the novel context rather than being replayed as a fixed response. 

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Figure 40 on page 55 explicitly portrays transfer learning. A later event shares only part of an earlier state, prompting the system to recruit relevant elements from the previous iterative sequence and apply them in the new context. Thought iterative updating.pdf This provides a mechanism for analogy-based generalization, especially when long-term memory contains schemas abstracted from several related episodes.

Analogical transfer becomes more systematic when the representation emphasizes relational structure over surface similarity. A schema such as source flows through conduit to destination can then be applied to water systems, electrical circuits, information networks, and metabolic pathways. Role-filler binding allows the same relational pattern to be instantiated with domain-specific fillers, while multiassociative search identifies which portions of the current problem correspond to the schema.

The architecture also supports compositional problem decomposition. Figure 31 on page 48 shows an original problem being iterated into a first subsolution, stored in the short-term store, followed by a second subproblem and subsolution. Selected elements from both subsolutions are subsequently coactivated and iterated into a final result. 

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This arrangement resembles hierarchical program execution and dynamic programming. The focus of attention handles the current operation, the short-term store preserves suspended objectives and intermediate products, and the workspace later merges compatible outputs. Large structures can therefore be assembled through the recursive composition of smaller structures.

8. Multimodal Grounding and Compositional Simulation

Linguistic compositionality represents only one form of generalization. A cognitively general system must compose objects, spatial relations, causes, actions, sounds, forces, and goals across several modalities. The model’s hierarchical architecture supplies modality-specific networks that converge on higher-order association areas and receive top-down feedback from them.

The paper proposes that sensory maps preserve metric and precategorical information and that top-down signals from conceptual items can construct internally generated scenes. Thought iterative updating.pdf Progressive imagery modification then allows each conceptual update to produce a revised perceptual simulation, while features generated by the simulation return to working memory and influence the next update. 

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This reciprocal process could improve compositional generalization by providing an internal consistency check. A novel linguistic composition such as “place the small red object behind the tall blue object and rotate it toward the doorway” can be translated into a spatial model, transformed step by step, and inspected for collisions or ambiguities. The resulting behavior depends on composed causal and spatial relations rather than on linguistic co-occurrence alone.

Grounded simulation can also reveal consequences that were never explicitly paired during training. A system that understands support, gravity, containment, and fragility may infer the outcome of placing a heavy object on a thin glass surface, even when that exact combination is novel. The inference emerges from the interaction of reusable causal primitives within an internally generated model.

9. Developmental Learning of Primitives and Abstractions

The training program described in the paper is compatible with compositional learning through progressive abstraction. Early training would establish reliable associations among perceptual and motor events occurring close together in time. As working-memory persistence increases, temporally separated representations could be coactivated, compared, and reconciled, allowing the system to acquire higher-order causal and analogical relationships. 

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This developmental sequence can encourage the formation of reusable primitives before the system encounters highly complex compositions. Research by Ito and colleagues found that pretraining artificial networks on primitive task elements produced more abstract internal representations, strong zero-shot generalization, and improved sample efficiency on novel task combinations. The study also found a hierarchy of abstract representations with correspondences to human cortical activity. 

A developmental implementation of the iterative model could therefore begin with object permanence, spatial relations, simple actions, causal transitions, and elementary goals. Later stages would combine these primitives in increasingly varied contexts while gradually increasing working-memory duration, compositional depth, and the number of concurrently active relations. Such a curriculum would help preserve constituent identity and discourage the memorization of undifferentiated conjunctions.

10. Relation to Transformers and Contemporary AI

Transformer models already exhibit important components of compositional behavior. Self-attention allows several contextual representations to influence each prediction, and large-scale pretraining exposes models to extensive variation in lexical, syntactic, semantic, and procedural combinations. The paper interprets attention and context windows as partial analogues of persistent working-memory mechanisms while identifying differences between the organization of transformer tokens and internal mammalian representations. 

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The proposed focus of attention adds a more selective compositional workspace. The paper observes that a context window containing thousands of tokens may resemble a broad short-term store, while its size and heterogeneity may prevent it from functioning like the compact, coherent focus used to construct a single mental scene. Thought iterative updating.pdf A dedicated focus could explicitly maintain the current roles, objects, goals, rules, and intermediate products while the larger context remains available for retrieval.

Recent evidence counsels against treating compositionality as wholly absent from generic neural networks. A NeurIPS 2025 study found that scaling model size and training data could produce compositional generalization when the training distribution sufficiently covered the underlying task space. Another large 2025 evaluation found that explicit attribute invariance substantially improved compositional generalization in vision while retaining scalability. 

These findings position iterative working memory as a candidate inductive bias for increasing reliability, transparency, sample efficiency, and transfer under sparse coverage. The strongest claim for the architecture concerns the organization of online thought: it supplies an intrinsic workspace in which representations can be bound, retained, transformed, evaluated, and recombined independently of the surface sequence of output tokens.

11. An Experimental Test of the Model

A direct test could use an embodied or simulated agent trained on a factorial set of objects, attributes, spatial relations, actions, quantities, and goals. Training would expose the system to each primitive and to a limited subset of their possible combinations. Evaluation would reserve exact attribute combinations, role reversals, unfamiliar relational structures, longer action sequences, novel subproblem combinations, and transfers between linguistic and visual input.

Four architectures would provide informative comparisons. A transformer or recurrent baseline would establish ordinary end-to-end generalization, while an iterative model without explicit binding would test the contribution of state overlap and multiassociative search. A third system would add role-filler binding, and a fourth would add reciprocal imagery and subproblem storage. These comparisons would separate the effects of persistence, binding, schema reuse, and grounded simulation.

Behavioral accuracy should be accompanied by measurements of internal organization. Researchers could test whether individual constituents remain decodable across contexts, whether fillers can be swapped while preserving role structure, whether the same update rule operates at unfamiliar sequence lengths, and whether complete configurations predict the next update more accurately than isolated constituents. State overlap, working-memory half-life, transition equivariance, binding accuracy, and joint-context gain would provide direct measures of the proposed mechanisms.

The model predicts that partial updating will provide its largest advantage on tasks requiring several dependent transformations. Explicit role binding should produce the largest gains on role reversal and relational permutation. A longer working-memory half-life should improve generalization across longer dependency chains until interference begins to offset the benefit, while schema coiteration and subsolution merger should improve transfer to problems with low surface similarity and shared abstract structure.

Conclusion

The iterative updating model addresses compositional generalization by explaining how reusable representations can be assembled and transformed across time. Persistent contents provide a compositional scaffold, selective replacement introduces new fillers and operations, multiassociative search identifies contextually appropriate additions, and iterative compounding allows intermediate products to participate in later stages of reasoning. The short-term store supports suspended subproblems and schemas, while reciprocal sensory simulation grounds abstract combinations in spatial, causal, and motor structure.

The model’s most distinctive contribution is the temporalization of composition. It explains how a capacity-limited system can construct representations and procedures that exceed a single working-memory state by preserving structural constraints across successive updates. This architecture connects compositional generalization with the same state-spanning dynamics proposed to produce continuity of thought.

A complete computational account requires explicit role-filler binding and structure-sensitive transition rules. Synchrony-based binding, graph relations, tensor product representations, or related mechanisms could be integrated into the focus of attention without abandoning the model’s distributed and associative foundations. With that addition, iterative updating offers a plausible bridge between subsymbolic neural computation, symbolic relational structure, and systematic generalization to novel combinations.

References

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