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Interaction Network

Architectures AIMech:InteractionNetwork DRAFT

Aliases: Interaction Networks, IN (interaction network)

A graph-based neural architecture that applies a shared relation model to supplied directed attributed object relations, sums predicted effects for each receiver, and applies a shared object model to predict object outputs, with an optional aggregated global readout.

Identity Notes & Concept Scope Compared all 442 pinned AIO and 597 native IDs, names, aliases and scoped synonyms; no normalized identity match. Ignored- and hidden-inclusive fixed-string searches of the recovery, older discovery and original Documents checkouts returned 331, 176, 174 lines. All distinct match contents were inspected. Semantic matching covered 24 AIO and 50 native definitions, with every matched definition read. 4 full annotated AIO node/edge/generated contexts and 4 full native records were inspected. The named 2016 Interaction Network separately models supplied directed relation effects and object updates. It is distinct from VAIN learned-address communication and the maintained GAT, GIN and GraphSAGE constructions. The source matrix convention fixes receiver/sender ordering explicitly. The generic ANN target is a justified broad mapping; a shared graph vocabulary does not establish a named GCN identity.

Claims & Grounded Evidence

6 Claims

Mechanism #directed-relational-object-factorization

Given object states, explicit directed attributed relations and external effects, construct one interaction input for each supplied relation, apply the same learned relation function to every interaction, sum the resulting effects separately for each receiver, and apply the same object function to each object together with its external and pooled effects. The curated binary-relation construction allows parallel relations and excludes self-relations; it does not infer the input graph from observations.

supports Source: Interaction Networks for Learning about Objects, Relations and Physics · Locator: Section 2, Definition, PDF p. 3, Equations 1–2; Figure 1, p. 2

Scope #receiver-first-matrix-convention

This record follows the matrix implementation: concatenate receiver state, sender state and relation attributes as B=[O R_r; O R_s; R_a], compute relation effects E, and aggregate incoming effects as E R_r^T before concatenating them with O and X. R_r and R_s are receiver and sender incidence matrices. The matrix formula and Figure 1 specify receiver-first ordering more clearly than the inconsistent ordering language in the preceding definition; no author-code verification is claimed.

supports Source: Interaction Networks for Learning about Objects, Relations and Physics · Locator: Section 2, Implementation, PDF p. 4, lines 124–146; Figure 1, p. 2; contrasting Definition ordering, p. 3, lines 79–98

Scope #permutation-and-aggregation-boundaries

Shared edge/object functions and summation make the object-output map equivariant to consistent object relabeling and invariant to relation-list ordering. Object outputs reorder with the objects; they are not an unchanged ordered array. Sum aggregation counts repeated effects but is not generally injective over different effect multisets. These algebraic properties permit variable graph sizes without guaranteeing predictive accuracy on unseen sizes. Experimental invariance to absolute position additionally uses relative-state preprocessing and is not a property of arbitrary core MLPs.

supports Source: Interaction Networks for Learning about Objects, Relations and Physics · Locator: Section 2, PDF pp. 3–4, lines 109–113 and 137–150; experimental preprocessing, p. 7, lines 229–235; direct constructed routing and sum examples

Mechanism #edge-count-and-global-readout

One forward step applies the relation function once per supplied edge and the object function once per object. Complete directed graphs without self-edges have N(N-1) relations; sparse supplied graphs need not. This count does not certify runtime or optimal complexity for dense incidence-matrix implementations. An optional global-property variant sums object outputs and passes that aggregate to a separate abstraction model; this readout is distinct from the basic per-object predictor.

supports Source: Interaction Networks for Learning about Objects, Relations and Physics · Locator: Section 2, PDF pp. 3–4, Equations 1–2 and lines 105–108, 137–150; domain relation counts, p. 5

Scope #physical-experiment-scope

The main paper evaluates simulated two-dimensional n-body, bouncing-ball/wall and spring-string systems using supplied object states, physical attributes, relations and external effects. It trains on one-step velocity targets and rolls predictions forward with position updates. Training uses six n-body objects, six balls with four walls, or fifteen string masses; tests vary object counts and string pinning. These inputs are decomposed states, not raw images, and the surrounding learned model is not guaranteed to discover objects or relations.

supports Source: Interaction Networks for Learning about Objects, Relations and Physics · Locator: Section 3, PDF pp. 4–5; Figure 2, p. 6; Discussion, p. 8, lines 297–299

Limitation #evaluation-and-conservation-limits

Table 1 reports task-specific next-step mean squared errors of 0.25, 0.0020 and 0.0011 for n-body, balls and strings. The main paper samples separate training, validation and test data from simulated scenes and uses selected MLP widths, preprocessing, optimization and regularization. Its visually plausible long rollouts are not exact-trajectory guarantees; the text explicitly notes divergence of trajectories. Potential-energy estimation uses the optional global readout and does not impose or prove energy conservation. Supplementary details, trained models and author implementations were not inspected.

supports Source: Interaction Networks for Learning about Objects, Relations and Physics · Locator: Section 3, PDF pp. 5 and 7; Section 4, pp. 7–8, Figure 3 and Table 1; trajectory caveat, p. 7, lines 267–274

⚠️ Curated Limitations & Negative Results

The primary proceedings-hosted nine-page PDF retains anonymous submission placeholders and line numbers. Authors and NIPS 2016 identity come from the primary proceedings metadata; no unidentified PDF revision is equated with an inspected author implementation.
The matrix receiver-first convention is explicit. Earlier sender/receiver notation is inconsistent; the record does not silently claim all source expressions use the same order.
Supplied binary relations, shared functions and summation define the scoped neural architecture. Higher-order relations, perceptual front ends and probabilistic inference are discussed as future work.
All nine main-paper pages were read; supplementary material, other versions and author code were not inspected. Constructed algebra examples do not train a network, simulate the reported physics or replicate benchmarks. DRAFT remains.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:ArtificialNeuralNetwork` Artificial Neural Network	broad_match	Shared learned multilayer relation and object functions make this a particular artificial neural architecture. The target is broader. The graph-convolutional target references a distinct named GCN construction; graph use alone does not establish equivalence. Temporal recurrence and probabilistic graphical-model tasks are not required identities.

Evidence Sources & Primary Literature

1 Source

Source ID	Publication / Document	Type / Access	Reference & Checksum
`battaglia2016`	Interaction Networks for Learning about Objects, Relations and Physics Peter Battaglia, Razvan Pascanu, Matthew Lai, Danilo Jimenez Rezende, Koray Kavukcuoglu	primary paper full_text	ID: https://papers.nips.cc/paper_files/paper/2016/hash/3147da8ab4a0437c15ef51a5cc7f2dc4-Abstract.html sha256:942fe7e7e5f7…

Curation Provenance

Curator: Codex

Method: ai_assisted

Model: GPT-6

Created: 2026-10-13T09:29:34Z

Updated: 2026-10-13T09:29:34Z

Source File: data/curated/InteractionNetwork.yaml