// Adaptive State from Partially Observed Streams

Most artificial-intelligence systems are evaluated as static functions: provide an input, obtain an output, and compare it with a defined target. Real environments are less orderly. Evidence arrives incrementally, observations are incomplete, labels are delayed, and old regularities can recur after long absences. The same action may be useful in one context and harmful in another. Retention also demands discrimination: some events deserve durable storage, while others should remain provisional or eventually disappear.

ADAPT makes that changing state a primitive: a first-class computational object.

ADAPT is neither a language model nor a database. It is an adaptive intelligence-state system that accepts text, structured events, feedback, and perceptual results; converts them into interacting memory representations; and exposes retrieval, explanation, prediction, and policy-selection surfaces.

The central research question is simple to state and difficult to satisfy:

ADAPT approaches this question through a collection of defined and auditable mechanisms. It retrieves episodic evidence through associative memory, strengthens repeated co-retrievals, induces typed rules, learns relation-specific policies from feedback, predicts declared transitions, detects recurrent numeric intervals, maintains latent regimes, and abstains when support is insufficient. A later installment reports the controlled intrinsic evaluation and its comparisons with ablations and stream-learning baselines.

Before examining the architecture, two terms need precise meanings.

Reasoning is the evidence-conditioned transformation of a cue into retrieved support, relational paths, hypotheses, counterevidence, and either a selection or an abstention.

Learning occurs when an eligible observation or measured outcome produces a persistent state change capable of altering a future result.

Reasoning can occur without changing state. Learning must be attributable to evidence. This distinction separates a system that merely emits a new trace from one whose future behavior has actually changed.

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1. From Stateless Inference to Adaptive State

A conventional model call can be written as the function

where the model parameters theta are fixed during inference. A retrieval-augmented system (RAG) adds an external collection M:

The collection may grow, but retrieval is often the only adaptive operation. The system remembers more documents without necessarily learning how observations relate, which actions work in which contexts, when a concept has changed or whether an inferred structure has been falsified.

ADAPT instead maintains a composite state

where:

• E_t is episodic memory — the stored events and their metadata;
• A_t is associative state — attractor patterns and Hebbian links;
• G_t is relational state — concepts, typed edges and hyperedges;
• R_t is executable structural state — hypotheses and induced rules;
• P_t is policy state — context-dependent reward beliefs;
• T_t is transition state — learned mappings from current observations and actions to future values;
• L_t is latent state — regimes, recurrent sets and interval structures that are not directly observed.

Each incoming event e_t updates only the mechanisms for which it is eligible:

with D denoting an optional Domain declaration that defines the measurable variables, candidate hypotheses, reward semantics, target paths, and support thresholds required by the relevant learning mechanisms.

Why partial observability changes the design

In a fully observed supervised dataset, the learner receives (x_t, y_t) pairs. In a real stream, the state that generated an observation is often hidden:

while the system sees only o_t, perhaps an action a_t, and delayed or incomplete feedback. To operate under that uncertainty, ADAPT implements bounded approximations to hidden state:

• associative completion reconstructs a query from nearby stored patterns;
• latent regimes partition contexts with different reward behavior;
• structural induction creates compact predicates that explain labels or set membership;
• interval recurrence reconstructs persistent numeric regions from intermittent scans;
• transition learning estimates what follows from nearby observed states;
• missing-evidence and abstention states prevent unsupported predictions from being presented as facts.

The premise is that an adaptive system benefits from separating fast episode capture, slow structural learning, uncertainty-aware decisions, and explicit revision. This division is related to complementary learning systems theory, in which rapid episodic acquisition and slower extraction of statistical regularity address different parts of the stability-plasticity problem [1, 2]. The comparison is computational rather than a claim of biological equivalence.

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2. The Life and Death of an Observation

An observation follows two different processes: one when it is written and another when it is queried.

At write time, the system normalizes content, extracts concepts, computes a vector representation, assigns novelty and importance estimates, tests whether a near-duplicate should be reconsolidated, and then fans the accepted record into several indexes. A Domain event may additionally update policy, transition, structural or interval learners.

At query time, the system parses the information need, creates a query representation, retrieves candidate episodes, applies associative completion, traverses learned relations, evaluates symbolic and domain-specific evidence, and fuses compatible results. Adaptive reads can update bounded access, consolidation and association state; frozen reads disable those mutations. Query-plan parameters never learn from retrieval diagnostics alone in either mode.

2.1 Hybrid Representation

Data representation combines a pinned compact semantic encoder with a deterministic lexical tail. The normalized vector is approximately

where s is the semantic component and h is a hashed lexical component. The lexical term uses term frequency and an online inverse-document-frequency estimate. Query and passage roles add small retrieval cues for informational categories such as location, time, cause, quantity and so on.

This hybrid has pragmatic advantages: semantic similarity helps bridge paraphrases, while lexical hashing preserves identifiers and unusual tokens. Backend identity is preserved with exported state because different embedding backends define different retrieval geometries.

2.2 Concepts are sparse handles for structure

Concept extraction produces normalized handles that support inverted lookup, overlap scoring and graph construction. These handles are not intended to be a complete ontology, rather they are lossy anchors between raw records and structural memory.

That distinction is important. A concept node can mean that a term recurred, that two records co-mentioned it, or that a learned relation connects it to another concept. None of those facts alone establishes causal dependence. ADAPT therefore preserves edge type, confidence and supporting memories so that downstream explanations can distinguish a direct observation from an induced connection.

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3. Relational Hopfield Memory

The core retrieval subsystem is called Relational Hopfield Memory. It combines direct similarity, a modern Hopfield update, sparse concept overlap, one-hop structural information, Hebbian co-retrieval, novelty and surprise.

The name does not imply that the entire system is a neural associative memory. Relational Hopfield Memory is one component in a larger retrieval stack. It stores normalized memory vectors as patterns, selects a bounded candidate set, performs one continuous attractor update, and then reranks candidates.

3.1 Associative completion

Let M = [m_1, ..., m_n] contain normalized candidate memories and let q be a normalized query. The attention over memories is

with inverse temperature beta = 4 in the current implementation. The reconstructed state is

and candidates are ranked by M^T z. This update is closely related to the continuous modern Hopfield formulation and its equivalence to attention [3].

The attractor is intentionally mixed with direct query similarity:

This prevents a dense cluster from pulling the query so strongly that a directly relevant but less common memory disappears before fusion. In other words, the attractor can complete a cue, but it is not allowed to replace the cue.

3.2 Candidate fusion

For candidate i, the implemented relational-memory score is

Each term serves a different purpose:

• Direct plus attractor similarity is the main relevance signal.
• Concept overlap rewards sparse symbolic agreement.
• Structure rewards support from the candidate's local relational neighborhood.
• Hebbian association recalls memories that repeatedly appeared together in successful support sets.
• Novelty prevents unusual but relevant memories from being erased by dense repetition.
• Surprise penalizes mismatch between the current cue and the retrieved trace.

The coefficients are explicit engineering priors. ADAPT keeps this base ranking surface constrained and inspectable, while traversal adaptation, outcome-trained channel reliability and optional trainable rerankers provide learning around it.

3.3 Approximate search

The candidate index identifies its backend as deterministic multi-table random-hyperplane locality-sensitive hashing [4], where each vector is assigned binary signatures from seeded hyperplanes. Search probes the exact bucket first, then bounded Hamming-distance neighbors and exactly reranks the resulting candidates against the original query. Deletion and session-level candidate filtering remain supported.

For small corpora, the system deliberately uses exact search because approximation overhead is unnecessary. At scale, candidate generation is bounded rather than scanning every eligible vector. The backend reports its identity and search diagnostics directly, so deployment traces state which retrieval geometry produced a result.

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The ADAPT series will continue across the architecture's other pillars, with later parts reporting task-level behavior and results from controlled experiments.

References

1. McClelland, J. L., McNaughton, B. L. & O'Reilly, R. C. "Why There Are Complementary Learning Systems in the Hippocampus and Neocortex: Insights From the Successes and Failures of Connectionist Models of Learning and Memory." Psychological Review 102, 419-457 (1995). Author-hosted paper
2. Kumaran, D., Hassabis, D. & McClelland, J. L. "What Learning Systems Do Intelligent Agents Need? Complementary Learning Systems Theory Updated." Trends in Cognitive Sciences 20, 512-534 (2016). PubMed Central
3. Ramsauer, H. et al. "Hopfield Networks is All You Need." ICLR (2021). arXiv
4. Charikar, M. S. "Similarity Estimation Techniques from Rounding Algorithms." STOC (2002). DOI