Clement Deust
April 2026
Large language model (LLM) code assistants suffer from complete amnesia between sessions: every architecture decision, debugging insight, and project convention must be re-explained from scratch. We present Cortex, a persistent memory system for Claude Code that implements 20 mechanisms drawn from computational neuroscience and information retrieval research, backed by 41 paper citations. Cortex encodes memories through a predictive coding write gate, consolidates them via sleep-like replay and episodic-to-semantic transfer, retrieves them through 5-signal weighted reciprocal rank fusion with cross-encoder reranking, and maintains them through thermodynamic decay with stage-dependent floors. A structured context assembly architecture --- originally designed for 4096-token context windows --- achieves a 33.4% improvement on the BEAM-10M benchmark (10 million tokens per conversation) over flat dense retrieval. Cortex scores 97.8% Recall@10 on LongMemEval (vs. 78.4% best published), 92.6% Recall@10 on LoCoMo, and 0.471 MRR on BEAM-10M. All retrieval is performed without an LLM in the evaluation loop. Every mechanism traces to a published paper, measured ablation data, or is explicitly labeled as an engineering heuristic.
LLM-based code assistants operate within a single context window. When a session ends, all accumulated knowledge --- architecture decisions, debugging strategies, codebase conventions, and project-specific lessons --- is lost. The next session begins with a blank slate. Users must repeatedly re-explain their systems, re-justify past decisions, and re-discover lessons that were already learned.
This is not merely an inconvenience. It represents a fundamental failure of the tool-human relationship. A programmer's effectiveness depends on accumulated context: knowing why event sourcing was chosen over CRUD, which Redis TTL edge cases cause intermittent logouts, what patterns emerged across dozens of debugging sessions. Without persistent memory, every interaction is a cold start.
Existing approaches to LLM memory fall into two categories. Context-window stuffing concatenates prior conversation turns into the prompt, but collapses at scale: a 200k-token window cannot hold months of project history. Retrieval-augmented generation (RAG) over a vector database provides scalable storage, but naive top-k cosine retrieval degrades as the corpus grows, returning increasingly noisy results as embedding distances concentrate (Beyer et al., 1999; Radovanovic et al., 2010).
Cortex treats LLM memory as a problem that neuroscience has already solved. Biological memory systems face the same challenges --- selective encoding, interference management, consolidation over time, and context-dependent retrieval --- at scales far exceeding any software system. We translate 20 computational neuroscience mechanisms into a digital memory architecture, adapting timescales from milliseconds to hours while preserving the core algorithms.
The system operates as a Model Context Protocol (MCP) server for Claude Code, providing 33 tools and 7 automatic lifecycle hooks. Storage uses PostgreSQL with pgvector for vector similarity search, pg_trgm for trigram matching, and PL/pgSQL stored procedures for server-side signal fusion. Retrieval runs entirely locally: a 22MB embedding model (all-MiniLM-L6-v2, 384 dimensions), PostgreSQL, and deterministic algorithms. No API calls. No LLM in the retrieval loop.
This paper makes four contributions:
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A neuroscience-grounded memory architecture implementing 20 biological mechanisms, each traced to a published paper with an honest assessment of implementation fidelity (12 faithful, 12 documented adaptations, 8 honest heuristics).
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A structured context assembly architecture that decomposes retrieval into three phases --- own-stage, cross-stage entity graph traversal, and summary fallback --- achieving 33.4% improvement on BEAM-10M over flat retrieval.
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State-of-the-art retrieval-only results on three published benchmarks: 97.8% R@10 on LongMemEval (vs. 78.4% best published), 92.6% R@10 on LoCoMo, and 0.471 MRR on BEAM-10M.
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A transparent implementation audit documenting which mechanisms faithfully implement paper equations, which are documented adaptations, and which are honest heuristics --- establishing a standard for scientific accountability in systems work.
Section 2 positions Cortex against related memory systems. Section 3 describes the system architecture and retrieval pipeline. Section 4 details each biological mechanism with its source paper, equations, and adaptation. Section 5 presents the structured context assembly architecture. Section 6 reports evaluation results. Section 7 summarizes the implementation audit. Section 8 discusses limitations and future work.
We organize related work by approach category and state what distinguishes Cortex from each.
mem0 (Chhablani et al., 2024) provides a managed memory layer for LLM applications. It stores memories as vector embeddings with metadata, supports CRUD operations, and retrieves via cosine similarity. Cortex differs in three ways: (1) multi-signal fusion (5 retrieval signals vs. single-vector search), (2) biological consolidation mechanisms that compress, merge, and forget memories over time, and (3) a predictive coding write gate that blocks redundant storage. mem0 treats memory as a database; Cortex treats it as a living system.
Letta/MemGPT (Packer et al., 2023) virtualizes the LLM context window using an operating-system metaphor: a main context (working memory), archival storage (long-term), and recall storage (conversation history). The LLM manages its own memory via function calls, deciding what to store and retrieve. Cortex differs fundamentally: memory management is algorithmic, not LLM-directed. The write gate, consolidation engine, and retrieval pipeline operate without LLM inference, making them deterministic, auditable, and fast (<200ms retrieval latency).
MIRIX (Wang & Chen, 2025) introduces active retrieval with query reformulation and typed memory slots (episodic, semantic, procedural). It uses an LLM to iteratively refine queries and select memory types. Cortex shares the insight that different memory types require different retrieval strategies, but implements this through algorithmic intent classification (6 query types with weight profiles) rather than LLM-directed reformulation. Cortex also adds stage-scoped retrieval and entity graph traversal, which MIRIX does not address.
LIGHT (Tavakoli et al., 2026) proposes a three-tier architecture (episodic memory, working memory, scratchpad) for the BEAM benchmark. It achieves the highest published end-to-end QA scores using LLM-as-judge evaluation. Cortex's structured context assembly shares the tiered insight but adds priority budgeting, truncation awareness, and Personalized PageRank for cross-tier traversal. LIGHT requires an LLM for memory management; Cortex does not.
A-MEM (Xu et al., NeurIPS 2025) implements Zettelkasten-style memory with agentic on-write reconsolidation: when a new memory arrives, an LLM decides whether to create, update, or link it. Cortex's curation module performs similar decisions (merge, link, create) but algorithmically, using entity overlap and embedding similarity rather than LLM inference. Cortex adds biological mechanisms that A-MEM lacks: predictive coding gates, consolidation stages, and thermodynamic decay.
HippoRAG (Gutierrez et al., NeurIPS 2024) models the hippocampal indexing theory: an LLM extracts entities (analogous to parahippocampal processing), builds a knowledge graph (hippocampal index), and retrieves via Personalized PageRank (pattern completion). Cortex incorporates HippoRAG's PPR mechanism in Phase 2 of the context assembler but extends it with 19 additional biological mechanisms spanning encoding, consolidation, and maintenance. HippoRAG is a retrieval architecture; Cortex is a complete memory lifecycle system.
| System | Write Gate | Consolidation | Multi-Signal Retrieval | Stage-Scoped | No LLM at Query |
|---|---|---|---|---|---|
| mem0 | No | No | No | No | Yes |
| Letta/MemGPT | LLM-directed | LLM-directed | No | No | No |
| MIRIX | No | No | Typed slots | No | No |
| LIGHT | No | No | Three-tier | Partial | No |
| A-MEM | LLM-directed | LLM-directed | No | No | No |
| HippoRAG | No | No | PPR + vector | No | Partial |
| Cortex | Predictive coding | 20 mechanisms | 5-signal WRRF | 2-phase (+ planned summary) | Yes |
Cortex follows Clean Architecture (Martin, 2017) with strict dependency rules. Inner layers never import outer layers:
SERVER -> HANDLERS -> CORE <- SHARED
|
INFRASTRUCTURE -> SHARED
- shared/ (11 modules): Pure utility functions --- text processing, similarity metrics, type definitions. Imports only Python stdlib.
- core/ (108 modules): All neuroscience and retrieval logic. Pure functions with no I/O. Imports only shared/.
- infrastructure/ (21 modules): PostgreSQL persistence, embeddings, file I/O. Imports only shared/.
- handlers/ (33 tools): Composition roots that wire core logic to infrastructure. The only layer that imports both.
This architecture ensures that all biological mechanisms are testable in isolation (2080 unit tests) and that the core logic is independent of the storage backend.
The write path implements a three-stage pipeline:
Stage 1: Predictive Coding Gate. Every candidate memory passes through a 4-signal novelty filter before storage (Section 4.1.1). The gate computes embedding distance, entity overlap, temporal proximity, and structural similarity against existing memories. Only memories that violate the system's predictions --- i.e., carry genuine information --- pass through. This prevents the memory store from filling with redundant content.
Stage 2: Active Curation. Memories that pass the gate enter a curation pipeline that decides whether to create a new memory, merge with an existing similar memory, or link to a related memory via the entity graph. Decisions are based on embedding similarity thresholds and entity overlap.
Stage 3: PostgreSQL Storage. Accepted memories are stored with: (1) a 384-dimensional embedding vector (HNSW-indexed), (2) a tsvector for full-text search, (3) extracted entities and relationships for the knowledge graph, (4) metadata including heat, importance, emotional valence, consolidation stage, and timestamps.
Retrieval follows a five-stage pipeline:
Stage 1: Intent Classification. The query is classified into one of six types --- temporal, causal, semantic, entity, knowledge_update, or multi_hop --- using regex-based pattern matching (query_intent.py). Each intent type defines a weight profile over the five retrieval signals.
Stage 2: Query Enrichment. Doc2Query synthetic expansion generates alternative phrasings, and concept synonym vocabulary adds related terms (enrichment.py, concept_vocabulary.py).
Stage 3: 5-Signal WRRF Fusion. A PL/pgSQL stored procedure (recall_memories()) computes five signals server-side and fuses them via Weighted Reciprocal Rank Fusion (Bruch et al., 2023):
WRRF(d) = Σ(s in S) wₛ · 1/(k + rankₛ(d))
where S = {vector, FTS, trigram, heat, recency}, wₛ is the intent-specific weight for signal s, and k = 60 is the smoothing constant. The five signals are:
- Vector similarity: Cosine distance between query and memory embeddings via pgvector HNSW index.
- Full-text search (FTS): PostgreSQL ts_rank with language-aware stemming.
- Trigram matching: pg_trgm similarity for fuzzy matching of technical terms, file paths, and identifiers.
- Thermodynamic heat: Current memory temperature reflecting access frequency and importance (Section 4.4.1).
- Recency: Exponential decay from last access time.
All five signals are computed in a single SQL query, avoiding round-trips between application and database.
Stage 4: Cross-Encoder Reranking. The top candidates from WRRF are reranked by a FlashRank cross-encoder (ms-marco-MiniLM-L-12-v2, 22MB). Scores are blended:
final(d) = (1 - α) · WRRF(d) + α · CE(d)
with α = 0.55 (tuned via ablation; see Section 6.4). A sufficient-context gate (Joren et al., ICLR 2025) suppresses results where the maximum cross-encoder score falls below a threshold (τ = 0.15), enabling the system to abstain when no relevant memory exists.
Stage 5: Neuro-Symbolic Filtering. Hard and soft rules filter results by scope, entity, or tag. Hard rules exclude matches unconditionally; soft rules adjust scores.
PostgreSQL 15+ with two extensions:
- pgvector: HNSW index on 384-dimensional embeddings with cosine distance. Provides approximate nearest neighbor search with recall >99% at the index sizes used (<100k memories per project).
- pg_trgm: GIN index on memory content for trigram similarity. Handles technical terms, CamelCase identifiers, and file paths that FTS tokenizers mangle.
The schema includes tables for memories, entities, relationships (weighted, typed edges forming the knowledge graph), schemas (extracted cortical knowledge structures), and rules (neuro-symbolic filtering constraints). All retrieval-critical logic runs as PL/pgSQL stored procedures to minimize application-database round-trips.
Cortex implements 20 mechanisms organized into four functional groups: encoding (deciding what to remember), consolidation (organizing memories over time), retrieval (finding the right memory), and maintenance (keeping memory healthy). Each mechanism cites its source paper, states the core equation or algorithm, explains the adaptation to a digital memory system operating at hours-to-days timescale, and references the implementation file.
Paper: Friston, K. (2005). A theory of cortical responses. Philosophical Transactions of the Royal Society B, 360(1456), 815--836. Bastos, A. M., Usrey, W. M., Adams, R. A., Mangun, G. R., Fink, P., & Friston, K. J. (2012). Canonical microcircuits for predictive coding. Neuron, 76(4), 695--711.
Core idea: The neocortex maintains a generative model of its inputs and only propagates prediction errors --- the difference between expected and actual sensory input. Redundant, predictable input is suppressed at the source.
Algorithm: The write gate maintains a three-level predictive hierarchy (sensory, entity, schema) corresponding to Bastos et al.'s canonical microcircuit. For each candidate memory m, the gate computes four signals:
- Embedding novelty: 1 - max(cos(e_m, e_m') for m' in M), where M is the set of recent memories and e denotes the embedding vector.
- Entity overlap: Jaccard coefficient between the candidate's extracted entities and those of existing memories.
- Temporal proximity: Hours since the last memory from the same session.
- Structural similarity: Content-level similarity via trigram matching.
The gate accepts the memory if the weighted prediction error exceeds a threshold, rejecting duplicates and predictable content. This ensures the memory store maintains high information density.
Adaptation: Biological predictive coding operates on millisecond-scale neural firing patterns. Cortex adapts to document-level processing at hours timescale. The hierarchical structure (sensory/entity/schema) maps to progressively more abstract representations of memory content.
Implementation: core/hierarchical_predictive_coding.py, core/predictive_coding_gate.py, core/predictive_coding_signals.py
Paper: Wang, S. & Bhatt, M. A. (2024). Amygdala high-frequency activity during encoding strengthens hippocampal memory traces. Nature Human Behaviour. Yerkes, R. M. & Dodson, J. D. (1908). The relation of strength of stimulus to rapidity of habit-formation. Journal of Comparative Neurology and Psychology, 18(5), 459--482.
Core idea: Emotionally charged experiences are encoded with greater strength. The relationship between arousal and memory performance follows an inverted-U curve: moderate arousal enhances encoding, while extreme arousal impairs it.
Equation: The Yerkes-Dodson arousal-performance curve:
f(a) = c · a · exp(-b · a)
where a is the arousal level, and c, b are scaling parameters. This produces a smooth inverted-U with peak encoding strength at moderate arousal.
Adaptation: Arousal is estimated from emotional keyword detection in memory content (frustration, excitement, urgency markers). The biological mechanism involves oscillatory coupling between the amygdala and hippocampus measured via intracranial EEG; the digital adaptation uses text-based emotion detection as a proxy. This is a documented simplification --- Wang & Bhatt's finding is an empirical result about neural activity, not a computational model.
Implementation: core/emotional_tagging.py (FAITHFUL for Yerkes-Dodson curve)
Paper: Doya, K. (2002). Metalearning and neuromodulation. Neural Networks, 15(4--6), 495--506. Schultz, W. (1997). A neural substrate of prediction and reward. Science, 275(5306), 1593--1599. Rescorla, R. A. & Wagner, A. R. (1972). A theory of Pavlovian conditioning. In Classical Conditioning II: Current Research and Theory, 64--99.
Core idea: Four neuromodulators --- dopamine (DA), norepinephrine (NE), acetylcholine (ACh), and serotonin (5-HT) --- modulate different aspects of learning and memory. DA encodes reward prediction error, NE modulates arousal and precision, ACh gates encoding vs. retrieval, and 5-HT regulates temporal discounting and exploration.
Equation (DA channel): The dopamine reward prediction error follows the Rescorla-Wagner learning rule:
δ = r - V(s)
DA = 1 + δ, DA in [0, 3]
where r is the actual outcome and V(s) is the predicted value. The bounds [0, 3] reflect Schultz's (1997) finding of asymmetric dopamine neuron firing: baseline at ~5 Hz, suppression to ~0 Hz for negative RPE, bursts to 20--30 Hz for positive RPE (approximately 3x baseline).
Adaptation: Doya's framework maps each neuromodulator to a reinforcement learning meta-parameter. Our implementation faithfully implements the DA channel via Rescorla-Wagner but honestly documents that the NE, ACh, and 5-HT channels use heuristic formulas rather than the specific models from Aston-Jones & Cohen (2005), Yu & Dayan (2005), and Daw et al. (2002), respectively. These channels modulate downstream systems (write gate threshold, retrieval precision, exploration breadth) through linear interpolation functions that are labeled as engineering defaults.
Implementation: core/coupled_neuromodulation.py, core/neuromodulation_channels.py (FAITHFUL for DA; HONEST for NE, ACh, 5-HT)
Paper: Kandel, E. R. (2001). The molecular biology of memory storage: A dialogue between genes and synapses. Science, 294(5544), 1030--1038. Nader, K., Schafe, G. E., & LeDoux, J. E. (2000). Fear memories require protein synthesis in the amygdala for reconsolidation after retrieval. Nature, 406, 722--726. Bahrick, H. P. (1984). Semantic memory content in permastore: Fifty years of memory for Spanish learned in school. Journal of Experimental Psychology: General, 113(1), 1--29.
Core idea: Memory consolidation proceeds through biochemically distinct stages: short-term memory depends on covalent protein modifications (PKA, CaMKII), while long-term memory requires new gene expression and protein synthesis (CREB, MAPK pathway). Retrieved consolidated memories become labile and must be re-stabilized (reconsolidation). Well-consolidated memories reach a "permastore" that resists further decay.
Stages: Cortex models four consolidation stages with biologically grounded timing:
| Stage | Duration | Biological Basis | Decay Multiplier | Heat Floor |
|---|---|---|---|---|
| LABILE | 0--1h | Pre-synaptic facilitation | 2.0x | 0.00 |
| EARLY_LTP | 1--6h | PKA-dependent, no protein synthesis | 1.2x | 0.00 |
| LATE_LTP | 6--24h | CREB-dependent, protein synthesis required | 0.8x | 0.05 |
| CONSOLIDATED | >24h | Systems consolidation, cortical transfer | 0.5x | 0.10 |
A fifth state, RECONSOLIDATING, is entered when a consolidated memory is retrieved in a context with sufficient mismatch (Nader et al., 2000). The heat floor for CONSOLIDATED memories (0.10) prevents the "permastore destruction" problem where all memories eventually decay to zero --- grounded in Bahrick's (1984) finding that well-learned material resists forgetting over decades.
Advancement criteria:
- LABILE → EARLY_LTP: DA level > 1.0 or importance > 0.6 (proxy for protein kinase activation).
- EARLY_LTP → LATE_LTP: At least 1 replay event or importance > 0.7 (proxy for CREB-dependent protein synthesis).
- LATE_LTP → CONSOLIDATED: At least 3 replays, or 1 if schema-congruent (Tse et al., 2007: schema-consistent memories consolidate faster).
Implementation: core/cascade_stages.py, core/cascade_advancement.py (DOCUMENTED)
Paper: Foster, D. J. & Wilson, M. A. (2006). Reverse replay of behavioural sequences in hippocampal place cells during the awake state. Nature, 440, 680--683. Diba, K. & Buzsaki, G. (2007). Forward and reverse hippocampal place-cell sequences during ripples. Nature Neuroscience, 10, 1241--1242. Davidson, T. J., Kloosterman, F., & Wilson, M. A. (2009). Hippocampal replay of extended experience. Neuron, 63(4), 497--507.
Core idea: During sharp-wave ripple (SWR) events, hippocampal place cells replay recent experiences in both forward and reverse temporal order, compressed ~15--20x relative to real time. Replay drives synaptic plasticity and memory consolidation.
Algorithm: When an SWR event is triggered (Section 4.4.4), the replay system:
- Selects candidate memory sequences based on dopamine-gated priority (high-RPE sequences are preferentially replayed).
- Orders memories chronologically (forward replay) or reverse-chronologically (reverse replay). Both directions are used, following Diba & Buzsaki (2007).
- Traverses entity relationships to build causal chains, extending sequences beyond purely temporal ordering.
- Generates STDP-like timing pairs from the replay sequence, driving synaptic plasticity updates (Section 4.3.3).
- Applies a compression ratio of 20x for timing calculations, consistent with biological SWR compression (Davidson et al., 2009).
Adaptation: Biological replay involves precise temporal reactivation of place cell firing sequences. Cortex builds replay sequences from entity overlap and relationship edges rather than spatial firing patterns. This is a documented substitution: the computational function (sequential reactivation for plasticity) is preserved while the implementation substrate (entity graphs vs. place cells) is adapted.
Implementation: core/replay.py, core/replay_execution.py, core/replay_selection.py (DOCUMENTED)
Paper: McClelland, J. L., McNaughton, B. L., & O'Reilly, R. C. (1995). Why there are complementary learning systems in the hippocampus and neocortex. Psychological Review, 102(3), 419--457. Kumaran, D., Hassabis, D., & McClelland, J. L. (2016). What learning systems do intelligent agents need? Trends in Cognitive Sciences, 20(7), 512--534. Ebbinghaus, H. (1885). Uber das Gedachtnis. Leipzig: Duncker & Humblot.
Core idea: Complementary Learning Systems (CLS) theory posits two learning systems: the hippocampus for fast, pattern-separated episodic encoding, and the neocortex for slow, interleaved semantic learning. Over time, repeated episodic experiences are gradually transferred to cortical representations, forming general knowledge. The transfer occurs via interleaved replay that prevents catastrophic interference.
Algorithm: Cortex implements a two-stage model:
- Hippocampal store (fast, labile): New memories enter with hippocampal dependency h = 1.0.
- Cortical transfer: Each replay event reduces h by a transfer rate Δh = r / sqrt(n_replay), with r = 0.02 from the C-HORSE model (Ketz et al., 2023). Diminishing returns ensure early replays matter most.
- Schema acceleration: Schema-congruent memories transfer up to 2.5x faster, following Tse et al. (2007).
- Interleaving: Round-robin scheduling across domains prevents catastrophic interference, following CLS theory.
When hippocampal dependency drops below a threshold, memories are eligible for compression: full text → summary → keywords, following the rate-distortion framework of forgetting (Ebbinghaus, 1885).
Implementation: core/two_stage_model.py, core/two_stage_transfer.py (FAITHFUL for cortical learning rate), core/compression.py, core/dual_store_cls.py
Paper: Frey, U. & Morris, R. G. M. (1997). Synaptic tagging and long-term potentiation. Nature, 385, 533--536. Luboeinski, J. & Tetzlaff, C. (2021). Memory consolidation and improvement by synaptic tagging and capture in recurrent neural networks. Communications Biology, 4, 275.
Core idea: A weak stimulus sets a "synaptic tag" at activated synapses. If a strong stimulus occurs at nearby synapses within a time window, the proteins produced by the strong stimulus are captured by the tagged synapses, converting early-phase LTP to late-phase LTP. This explains how a later important event can retroactively strengthen earlier weak memories.
Algorithm: When a high-importance memory (importance > 0.7) is stored, Cortex searches for recent weak memories (importance < 0.5) that share entities, within a 48-hour window. Matching memories receive an importance boost (+0.25 scaled by entity overlap) and a heat boost (× 1.5).
Adaptation: The biological tagging window is 1--6 hours; Cortex extends to 48 hours to match the hours-to-days timescale of software development sessions. Entity overlap serves as a proxy for synaptic proximity on the dendritic tree. The Szymkiewicz-Simpson coefficient is used for overlap computation. The bistable tag dynamics follow Luboeinski & Tetzlaff (2021).
Implementation: core/synaptic_tagging.py (DOCUMENTED)
Paper: Tse, D., Langston, R. F., Kakeyama, M., Bethus, I., Spooner, P. A., Wood, E. R., ... & Morris, R. G. (2007). Schemas and memory consolidation. Science, 316(5821), 76--82. Gilboa, A. & Marlatte, H. (2017). Neurobiology of schemas and schema-mediated memory. Trends in Cognitive Sciences, 21(8), 618--631. van Kesteren, M. T. R., Ruiter, D. J., Fernandez, G., & Henson, R. N. (2012). How schema and novelty augment memory formation. Trends in Neurosciences, 35(4), 211--219.
Core idea: Schemas are cortical knowledge structures built from repeated experience. Schema-consistent information is consolidated rapidly (days instead of weeks in rodents), while schema-inconsistent information triggers hippocampal encoding and potentially schema accommodation.
Algorithm: Cortex maintains schema structures extracted from memory clusters. Each schema has an entity signature, tag distribution, and relationship pattern. New memories are classified via weighted Jaccard overlap (0.7 entity + 0.3 tag):
- Assimilate (match >= 0.7): Memory fits the existing schema, receives accelerated consolidation.
- Normal (0.3 <= match < 0.7): Partial match, standard processing.
- Accommodate (match < 0.3): Memory violates the schema, potentially triggering schema revision via EMA update (α = 0.1), following Piaget's equilibration theory.
Schema free energy is computed as the sum of squared prediction errors:
F = Σᵢ (xᵢ - x̂ᵢ)²
consistent with the variational free energy framework (Friston, 2005), though simplified to the squared-error case.
Implementation: core/schema_engine.py, core/schema_extraction.py (DOCUMENTED --- Tse et al. is an experimental paper without computational equations; Gilboa & Marlatte provide criteria, not algorithms)
Paper: Collins, A. M. & Loftus, E. F. (1975). A spreading-activation theory of semantic processing. Psychological Review, 82(6), 407--428.
Core idea: When a concept is activated in semantic memory, activation spreads along associative links to connected concepts, decaying with distance. This produces semantic priming: activating "doctor" facilitates access to "nurse."
Algorithm: Breadth-first search from seed entities with exponential decay:
aⱼ = Σ(i in parents(j)) aᵢ · wᵢⱼ · γᵈ
where aⱼ is the activation at node j, wᵢⱼ is the edge weight between nodes i and j, γ = 0.65 is the decay factor, and d is the graph distance. Convergent summation allows multi-path boosting: entities reachable via multiple paths accumulate activation from all sources.
Adaptation: This is one of the most faithful implementations in Cortex. Collins & Loftus described the mechanism conceptually; the BFS formalization with decay and convergent summation is the standard computational interpretation. Practical constraints (max depth 3, max nodes 50, threshold 0.1) prevent runaway activation in large graphs.
Implementation: core/spreading_activation.py (FAITHFUL)
Paper: Behrouz, A., Hashemi, M., Srinivasa, S., Kang, M., & Leskovec, J. (2025). Titans: Learning to memorize at test time. Advances in Neural Information Processing Systems (NeurIPS 2025).
Core idea: A meta-learning memory module updated via gradient descent on a prediction loss. The key equation is a momentum-based surprise signal that gates memory updates: memories that violate predictions (high surprise) receive stronger encoding.
Equation:
Sₜ = η · Sₜ₋₁ - θ · ∇_M L(M; xₜ)
Mₜ = Mₜ₋₁ - Sₜ
where Sₜ is the momentum surprise signal, η = 0.9 is the momentum coefficient, θ = 0.01 is the learning rate, and L is the prediction loss.
Adaptation: The biological/neural Titans model uses differentiable memory matrices and true gradient computation. Cortex computes ∇_M L as the embedding-space prediction error between the new memory and the current memory state. The momentum term ensures that sustained surprise accumulates while transient noise is dampened. The paper uses learned parameters for η and θ; Cortex uses fixed values (η = 0.9, θ = 0.01) as an engineering default.
Implementation: core/titans_memory.py (FAITHFUL)
Paper: Stachenfeld, K. L., Botvinick, M. M., & Gershman, S. J. (2017). The hippocampus as a predictive map. Nature Neuroscience, 20, 1643--1653.
Core idea: The hippocampus represents space not as a simple map of locations but as a predictive map encoding the expected future occupancy of states. The Successor Representation (SR) M(s, s') = E[Σ(t=0..inf) γᵗ · 1[sₜ = s'] | s₀ = s] captures the discounted probability of visiting state s' starting from state s.
Adaptation: Cortex builds a co-access graph: each time two memories are retrieved in the same session, their edge weight increases. Over time, this approximates the successor representation --- memories that are frequently co-accessed develop strong predictive links. The graph supports BFS navigation and 2D t-SNE projection for visualization.
Implementation: core/cognitive_map.py (DOCUMENTED)
Paper: Ramsauer, H., Schafl, B., Lehner, J., Seidl, P., Widrich, M., Adler, T., ... & Hochreiter, S. (2021). Hopfield networks is all you need. International Conference on Learning Representations (ICLR 2021).
Core idea: Modern Hopfield networks provide exponential storage capacity and one-step convergence for content-addressable memory retrieval. The energy function:
E(ξ) = -lse(β, X^T ξ) + (1/2)||ξ||²
where lse is the log-sum-exp function and β is the inverse temperature, yields an update rule equivalent to attention with softmax.
Adaptation: Cortex uses Hopfield networks as an auxiliary retrieval signal for pattern completion: given a partial cue (noisy or incomplete query embedding), the network converges to the stored memory pattern with highest overlap. This complements the primary WRRF pipeline for cases where exact match fails.
Implementation: core/hopfield.py (DOCUMENTED)
Paper: Kanerva, P. (2009). Hyperdimensional computing: An introduction to computing in distributed representation with high-dimensional random vectors. Cognitive Computation, 1(2), 139--159.
Core idea: Information is encoded in high-dimensional binary or bipolar vectors. Three operations --- binding (element-wise multiply), bundling (element-wise majority), and permutation (cyclic shift) --- compose representations that are robust to noise and support one-shot learning.
Adaptation: Cortex encodes memory features as 1024-dimensional bipolar HDC vectors. Binding encodes feature-value pairs, bundling combines features into composite representations, and cosine similarity retrieves nearest matches. This provides a complementary retrieval signal that operates on discrete feature combinations rather than continuous embedding space.
Implementation: core/hdc_encoder.py (DOCUMENTED)
Paper: Anderson, J. R. & Lebiere, C. (1998). The Atomic Components of Thought. Mahwah, NJ: Lawrence Erlbaum Associates. Ebbinghaus, H. (1885). Uber das Gedachtnis. Leipzig: Duncker & Humblot.
Core idea: Memory strength decays as a power function of time, modulated by the number of prior retrievals. The ACT-R base-level activation equation:
Bᵢ = ln(n) - d · ln(L)
where n is the number of presentations/retrievals, L is the time since creation (lifetime), and d = 0.5 is the decay parameter. This produces the classic power-law forgetting curve documented by Ebbinghaus (1885).
Adaptation: Each memory has a "heat" value in [0, 1] that decays exponentially between access events and receives a boost on each retrieval. The decay rate is modulated by consolidation stage (Section 4.2.1): LABILE memories decay at 2.0x the base rate, CONSOLIDATED memories at 0.5x, and CONSOLIDATED memories have a heat floor of 0.10 to prevent permastore destruction (Bahrick, 1984).
Implementation: core/decay_cycle.py (FAITHFUL for ACT-R equation)
Paper: Leutgeb, J. K., Leutgeb, S., Moser, M.-B., & Moser, E. I. (2007). Pattern separation in the dentate gyrus and CA3 of the hippocampus. Science, 315(5814), 961--966. Yassa, M. A. & Stark, C. E. (2011). Pattern separation in the hippocampus. Trends in Neurosciences, 34(10), 515--525. Rolls, E. T. (2013). The mechanisms for pattern completion and pattern separation in the hippocampus. Frontiers in Systems Neuroscience, 7, 74.
Core idea: The dentate gyrus transforms similar cortical inputs into non-overlapping hippocampal representations via sparse coding and competitive inhibition. Granule cells have extremely low firing rates (~2--5% active), and the large expansion ratio from entorhinal cortex to DG (~5:1) enables orthogonal encoding of similar experiences.
Algorithm: When a new memory's embedding has cosine similarity > 0.75 with an existing memory (but < 0.95, the identity threshold), Cortex applies Gram-Schmidt-like orthogonalization:
e_new' = e_new - s · Σ(i in I) proj_eᵢ(e_new)
where I is the set of interfering memories, s = 0.5 is the separation strength, and proj denotes vector projection. Post-separation, sparsification zeroes out the smallest dimensions to achieve 4% target sparsity, matching DG granule cell firing rates from Leutgeb et al. (2007) and Rolls (2013).
Implementation: core/separation_core.py (FAITHFUL --- sparsity target from DG data, Gram-Schmidt orthogonalization)
Paper: Turrigiano, G. G. (2008). The self-tuning neuron: Synaptic scaling and the maintenance of stable neural function. Nature Reviews Neuroscience, 9(11), 807--819. Tetzlaff, C., Kolodziejski, C., Markelic, I., & Worgotter, F. (2011). Time scales of memory, learning, and plasticity. Biological Cybernetics, 106(11--12), 715--726. Abraham, W. C. & Bear, M. F. (1996). Metaplasticity: The plasticity of synaptic plasticity. Trends in Neurosciences, 19(4), 126--130. Bienenstock, E. L., Cooper, L. N., & Munro, P. W. (1982). Theory for the development of neuron selectivity. Journal of Neuroscience, 2(1), 32--48.
Core idea: Neurons maintain stable firing rates through two mechanisms: (1) synaptic scaling --- multiplicative adjustment of all synaptic weights to maintain a target firing rate (Turrigiano, 2008), and (2) the BCM sliding threshold --- the crossover point between LTP and LTD shifts based on the history of postsynaptic activity (Bienenstock et al., 1982).
Equations:
Multiplicative synaptic scaling (Tetzlaff et al., 2011, Eq. 3):
wᵢ' = wᵢ · (r_target / r_actual)^α
The BCM sliding threshold:
θₘ = E[c²]
implemented as an EMA: θₘ,ₜ = γ · θₘ,ₜ₋₁ + (1 - γ) · c̄ₜ², where γ = 0.95.
The BCM plasticity function:
φ(c, θₘ) = c · (c - θₘ)
Activity above θₘ produces LTP; below produces LTD. The quadratic form ensures that the threshold slides: periods of high activity raise it (making LTP harder), and periods of low activity lower it (making LTP easier).
Adaptation: In Cortex, "firing rate" maps to average memory heat across the store. When average heat drifts from the target (0.4), multiplicative scaling adjusts all heat values proportionally. The BCM threshold prevents the system from becoming either too eager (storing everything) or too conservative (storing nothing) about memory formation.
Implementation: core/homeostatic_plasticity.py (FAITHFUL --- Tetzlaff Eq. 3 multiplicative scaling + BCM quadratic phi)
Paper: Hasselmo, M. E. (2005). What is the function of hippocampal theta rhythm? --- Linking behavioral data to phasic properties of field potential and unit recording data. Hippocampus, 15(7), 936--949. Lisman, J. E. & Jensen, O. (2013). The theta-gamma neural code. Neuron, 77(6), 1002--1016. Buzsaki, G. (2015). Hippocampal sharp wave-ripple: A cognitive biomarker for episodic memory and planning. Hippocampus, 25(10), 1073--1188.
Core idea: Theta rhythm (4--8 Hz) in the hippocampus separates encoding from retrieval via cholinergic modulation (Hasselmo, 2005). High acetylcholine during the encoding phase suppresses CA3→CA1 transmission (retrieval) and enhances EC→CA1 (encoding). Gamma oscillations nested within theta encode ordered items with capacity ~7 (Lisman & Jensen, 2013). Sharp-wave ripples (SWRs) during offline states trigger memory replay (Buzsaki, 2015).
Adaptation: Theta operates at 4--8 Hz in biology (125--250 ms period). Cortex maps theta phase to session-level cycles using a cosine envelope for encoding/retrieval strength. The gamma binding capacity of ~7 items maps to Lisman & Jensen's theta-gamma code (consistent with Miller's 7±2). SWR generation is deterministic (threshold-based) rather than stochastic to ensure reproducibility across benchmark runs.
Implementation: core/oscillatory_clock.py, core/oscillatory_phases.py (DOCUMENTED)
Paper: Hebb, D. O. (1949). The Organization of Behavior. New York: Wiley. Bienenstock, E. L., Cooper, L. N., & Munro, P. W. (1982). Theory for the development of neuron selectivity. Journal of Neuroscience, 2(1), 32--48. Bi, G.-Q. & Poo, M.-M. (1998). Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynaptic cell type. Journal of Neuroscience, 18(24), 10464--10472. Markram, H., Lubke, J., Frotscher, M., & Sakmann, B. (1997). Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science, 275(5297), 213--215.
Core idea: Synapses strengthen when pre- and post-synaptic neurons fire together (Hebbian LTP), weaken when activity falls below a sliding threshold (BCM LTD), and exhibit direction-dependent plasticity based on spike timing (STDP).
Equations:
BCM plasticity rule:
φ(c, θₘ) = c · (c - θₘ)
STDP temporal window (Bi & Poo, 1998):
Δw = A⁺ exp(-Δt / τ⁺) if Δt > 0 (pre before post: LTP)
-A⁻ exp(Δt / τ⁻) if Δt < 0 (post before pre: LTD)
with A⁺ = 0.03, A⁻ = 0.02 (preserving the biological ratio A⁺ > A⁻), and τ⁺ = τ⁻ = 24 hours (adapted from biological 17--34 ms).
Tsodyks-Markram short-term plasticity (Markram et al., 1997):
u_new = u + U · (1 - u)
x_new = x - u_eff · x
where u is the utilization of synaptic efficacy (facilitation), x is the available synaptic resources (depression), and U is the baseline release probability.
Implementation: core/synaptic_plasticity.py (FAITHFUL for Tsodyks-Markram), core/synaptic_plasticity_hebbian.py (FAITHFUL for BCM quadratic and STDP), core/synaptic_plasticity_stochastic.py (DOCUMENTED --- novel composition of faithful components)
Paper: Wang, C., Yue, H., Hu, Z., Shen, Y., Ma, J., Li, J., ... & Bhatt, D. K. (2020). Microglia mediate forgetting via complement-dependent synaptic elimination. Science, 367(6478), 688--694.
Core idea: Microglia mediate forgetting through complement-dependent synaptic elimination. The complement protein C1q/C3 is deposited on inactive synapses ("eat-me" signal), while active synapses express CD47 ("don't-eat-me" signal). Microglia phagocytose tagged synapses via CR3 receptor engagement.
Adaptation: Cortex implements the eat-me/don't-eat-me metaphor as threshold-based pruning rules: edges with low weight, no recent co-activation, and cold endpoints are candidates for removal. Protection signals (recent LTP, high access count, explicit protection flag) serve as don't-eat-me proxies. This is honestly labeled as a heuristic --- the biological mechanism involves complement cascade kinetics and microglial process motility that are not modeled.
Implementation: core/microglial_pruning.py (HONEST)
Paper: Perea, G., Navarrete, M., & Araque, A. (2009). Tripartite synapses: Astrocytes process and control synaptic information. Trends in Neurosciences, 32(8), 421--431. De Pitta, M., Volman, V., Berry, H., & Ben-Jacob, E. (2012). A tale of two stories: Astrocyte regulation of synaptic depression and facilitation. PLOS Computational Biology, 7(12), e1002293.
Core idea: Astrocytes participate in synaptic transmission via calcium-dependent gliotransmitter release. Three regimes: (1) quiescent — no modulation, (2) moderate Ca²⁺ — D-serine release potentiates NMDA-dependent LTP, (3) high Ca²⁺ — glutamate release causes heterosynaptic depression.
Adaptation: Astrocyte territories map to L1 fractal memory clusters. Calcium dynamics follow a simplified rise/decay model rather than De Pitta's full Li-Rinzel ODE system (d[Ca²⁺]/dt, d[IP₃]/dt, dh/dt with 15+ parameters). The three-regime classification (quiescent/facilitation/depression) faithfully captures the qualitative model from Perea (2009). De Pitta's ODE system is documented as the target for future faithful implementation.
Implementation: core/tripartite_synapse.py, core/tripartite_calcium.py (DOCUMENTED)
Paper: Poirazi, P., Brannon, T., & Bhatt, M. A. (2003). Pyramidal neuron as a two-layer neural network. Neuron, 37(6), 989--999. Kastellakis, G., Cai, D. J., Mednick, S. C., Silva, A. J., & Bhatt, M. A. (2015). Synaptic clustering within dendrites: An emerging theory of memory formation. Progress in Neurobiology, 126, 19--35.
Core idea: Individual dendritic branches act as independent computational subunits with sigmoidal input-output functions. The soma sums branch outputs linearly, making the pyramidal neuron a two-layer neural network.
Equations: Branch transfer function (Poirazi et al., 2003, Figure 3):
branch(n) = s(n) = 1 / (1 + exp(-β(n - n_threshold)))
soma(x₁, ..., x_B) = g(Σ(b=1..B) xᵦ)
Below the spike threshold: sublinear summation (power-law compression). Above: supralinear amplification via NMDA spikes.
Adaptation: Memory clusters on "dendritic branches" are grouped by entity/tag similarity (Jaccard). Nonlinear integration follows Poirazi's two-regime model. Branch-specific plasticity (LTP/LTD is branch-local) follows Kastellakis (2015).
Implementation: core/dendritic_clusters.py (HONEST for branch assignment), core/dendritic_computation.py (FAITHFUL for Poirazi's transfer function)
Paper: Josselyn, S. A. & Frankland, P. W. (2007). Memory allocation: Mechanisms and function. Annual Review of Neuroscience, 41, 389--413. Rashid, A. J., Yan, C., Mercaldo, V., Hsiang, H.-L., Park, S., Cole, C. J., ... & Bhatt, M. A. (2016). Competition between engrams influences fear memory formation and recall. Science, 353(6297), 383--387.
Core idea: Neurons with higher CREB levels (higher excitability) are preferentially recruited into memory traces. Excitability persists for ~6 hours after encoding, causing temporally close memories to share overlapping neuronal ensembles. Lateral inhibition ensures competitive allocation.
Equation: Excitability decay with 6-hour half-life:
E(t) = E₀ · 2^(-t/6h)
matching the ~6 hour CREB excitability window from Rashid et al. (2016).
Adaptation: Memory "slots" replace neuronal populations. The competitive allocation mechanism (high-excitability slots win) and lateral inhibition (recently activated slots suppress neighbors) are preserved. The slot model is a simplification --- real engrams involve overlapping neuronal populations, not discrete slots.
Implementation: core/engram.py (DOCUMENTED --- 6h half-life faithful, inhibition parameters hand-tuned)
Paper: Anderson, M. C. & Neely, J. H. (1996). Interference and inhibition in memory retrieval. In Memory: Handbook of Perception and Cognition, 237--313. Norman, K. A., Newman, E. L., & Detre, G. (2007). A neural network model of retrieval-induced forgetting. Psychological Review, 114(4), 887--953.
Core idea: Retrieval-induced forgetting (RIF): practicing retrieval of some items suppresses retrieval of competitors. During offline periods (sleep), pattern separation orthogonalizes similar representations to reduce proactive interference.
Adaptation: Retrieval suppression is modeled as lateral inhibition: stronger competitors suppress weaker items via a linear suppression model. Sleep-dependent orthogonalization gradually pushes interfering embedding pairs apart (projection-based separation at rate 0.15 per step). The leaky competing accumulator (LCA) model from Norman et al. (2007) is cited; the linear suppression is a documented simplification.
Implementation: core/interference.py, core/interference_detection.py (DOCUMENTED)
Dense vector retrieval degrades structurally at long-context scale. On BEAM (Tavakoli et al., ICLR 2026), Cortex's production WRRF pipeline scores 0.437 MRR at 100K tokens (94 memories/conversation) but drops to 0.353 MRR at 10M tokens (7,500 memories/conversation). This degradation is not parametric --- it reflects geometric limits of cosine similarity in moderate dimensions.
The hubness phenomenon (Radovanovic et al., 2010) causes certain points to appear as nearest neighbors of many queries regardless of true relevance. Concentration of distances (Beyer et al., 1999) narrows the gap between nearest and farthest neighbors, making top-k selection unreliable. The Johnson-Lindenstrauss lower bound (Larsen & Nelson, 2017) confirms that 384 dimensions cannot preserve pairwise distances to 10% accuracy for 7,500+ points.
No amount of reranking, query rewriting, or embedding model upgrade can fix a geometric ceiling. The architecture must change.
The structured context assembly architecture originates from ai-prd-builder (Deust, 2025), a production Swift application for generating 9-page product requirement documents using Apple Intelligence's 4096-token context window. The ContextManager.swift module --- committed on September 30, 2025 (commit 462de01, public repository) --- implements per-section token-budgeted context assembly with provider-specific limits, slot-based budget splitting, section-keyword relevance filtering, and truncation awareness.
The BEAM paper (Tavakoli et al.) was published on arxiv on October 31, 2025 --- one month after the ContextManager was committed. The architecture works because the problem is the same at both scales: when you cannot fit everything in context, you need to be smart about what goes in.
The Python port to Cortex, BEAM benchmark integration, and paper-backed complements (HippoRAG PPR, submodular coverage) were implemented in April 2026.
The system comprises two core primitives:
A prompt is a template with typed placeholder slots. Each slot has:
- A priority rank (lower number = higher importance, condensed last).
- An optional domain-aware condenser (code → signatures only; prose → first sentence + questions; entity triples → verbatim).
- A token budget derived from the reader's context window at runtime (never hardcoded).
When the filled template exceeds the budget:
- Compute shell tokens (template with empty slots).
- Allocate remaining budget proportionally across slots.
- Condense highest-priority-number (least important) slots first, using their domain-aware condensers.
- Post-assembly safety: iteratively halve the least important slot until the prompt fits.
- Inject a truncation warning banner listing what was cut and by how much, so the consuming model can reason about missing information.
The truncation warning is, to our knowledge, novel. No paper in the 2024--2026 literature we surveyed implements explicit truncation awareness in the prompt itself.
A "stage" is a distinct topical segment of a conversation --- analogous to a work session, a discussion topic, or a thematic unit. The assembler operates in three phases with a configurable budget split (default 60/30/10):
Phase 1 --- Own-Stage (60% budget). Retrieve from the current stage's memories using the WRRF pipeline, then select via submodular coverage maximization (Krause & Guestrin, 2008) to maximize information gain rather than raw similarity. Submodular selection ensures diversity: each selected memory adds maximum marginal coverage over concepts not yet covered, preventing the "echo chamber" effect of pure top-k selection.
Phase 2 --- Adjacent Stages via Entity Graph (30% budget). Extract entities from Phase 1 results. Seed Personalized PageRank (Gutierrez et al., "HippoRAG", NeurIPS 2024) on the entity co-occurrence graph. Score cross-stage memories by aggregated PPR mass. This bridges topically distinct sessions that share entities --- e.g., a debugging session from Monday and a design decision from Thursday that both involve the same Redis component.
Phase 3 --- Summary Fallback (10% budget). For stages not covered by Phase 1 or 2, retrieve pre-computed schema-structured summaries (Tse et al., 2007) ordered by stage proximity. This provides broad coverage at low token cost, ensuring the system has some representation of the full conversation history even when the budget is tight.
The output is a structured context with labeled sections ("Current Stage Context", "Related Prior Context", "Stage Summaries") ready for assembly via the ContextDecomposer.
-
No hardcoded token caps. Token budget is derived from the reader's context window at runtime. The Swift original used
reasoner.contextWindowSize * 0.75. For retrieval evaluation (no reader), budget isNoneand selection is purely by chunk count. -
Selection decoupled from assembly. Ranking (how many memories to select) is independent of prompting (how many tokens to spend). Submodular selection picks
max_chunksitems regardless of individual token sizes. -
Stage detection is pluggable. The
StageDetectorinterface supports explicit labels (plan IDs for benchmarks), temporal gaps (session boundaries for production), semantic clustering, or LLM topic-shift detection --- A/B testable via configuration.
The architecture's building blocks each have paper backing:
- Submodular coverage: Krause, A. & Guestrin, C. (2008). Near-optimal observation selection using submodular functions. JMLR, 9, 2761--2801.
- Personalized PageRank for retrieval: Gutierrez, B. J., et al. (2024). HippoRAG: Neurobiologically inspired long-term memory for large language models. NeurIPS 2024.
- Schema-structured summaries: Tse, D., et al. (2007). Schemas and memory consolidation. Science, 316(5821), 76--82.
The composition --- stage-aware two-phase assembly with submodular coverage selection and entity graph PPR --- has, to our knowledge, no direct precedent in the 2024--2026 literature we surveyed across six cross-disciplinary research agents covering biology, mathematics, AI lab publications, PhD theses, vendor engineering, and information theory.
The closest architectural neighbors are:
- LIGHT (Tavakoli et al., 2026): three-tier (episodic + working memory + scratchpad) but without priority budgeting or truncation awareness.
- MIRIX (Wang & Chen, 2025): active retrieval + typed memory but without stage-scoped retrieval or entity graph traversal.
- A-MEM (Xu et al., 2025): Zettelkasten-style agentic memory with on-write reconsolidation but without structured prompt assembly.
We evaluate Cortex on three published benchmarks spanning different scales and challenge types. All scores are retrieval-only --- no LLM reader in the evaluation loop. We measure whether the right memory is retrieved, not whether a model generates a correct answer from it.
Protocol: Fresh database per run (DROP + CREATE). TRUNCATE all data tables between conversations. No cross-conversation contamination. Embedding model: sentence-transformers all-MiniLM-L6-v2 (384D, 256 max tokens). FlashRank preflight verified before each run.
Benchmark: Wu, J., et al. (2025). LongMemEval: Benchmarking chat assistants on long-term interactive memory. International Conference on Learning Representations (ICLR 2025).
Description: 500 human-curated questions embedded in ~40 sessions of conversation history (~115k tokens). Questions span six categories: single-session assistant recall, single-session user recall, single-session preference, multi-session reasoning, knowledge updates, and temporal reasoning. The paper's best retrieval result is 78.4% Recall@10.
Results:
| Metric | Cortex | Best in Paper |
|---|---|---|
| Recall@10 | 97.8% | 78.4% |
| MRR | 0.882 | --- |
Per-category breakdown:
| Category | MRR | R@10 | Analysis |
|---|---|---|---|
| Single-session (assistant) | 0.982 | 100.0% | Verbatim assistant responses are straightforward to match via FTS and vector similarity. |
| Multi-session reasoning | 0.936 | 99.2% | Entity graph connects evidence across sessions; spreading activation boosts co-mentioned concepts. |
| Knowledge updates | 0.921 | 100.0% | Heat decay naturally surfaces the newest version of a fact. This was not designed for the benchmark --- it is an emergent property of the thermodynamic model. |
| Temporal reasoning | 0.857 | 97.7% | Time anchors embedded directly in memory content provide temporal grounding. |
| Single-session (user) | 0.806 | 94.3% | User phrasing varies more than assistant responses, reducing lexical overlap with queries. |
| Single-session (preference) | 0.641 | 90.0% | Preferences are implicit and expressed indirectly, making keyword and vector matching harder. |
Analysis: The 19.4 percentage point improvement over the best published result comes from multi-signal fusion. No single signal achieves this: vector similarity alone misses lexical matches; FTS alone misses paraphrases; neither captures temporal relationships. The five-signal WRRF combination with cross-encoder reranking covers all failure modes. Knowledge updates scoring highest confirms that the thermodynamic model's design --- where newer facts naturally accrue higher heat --- provides an intrinsic advantage on update-tracking tasks.
Benchmark: Maharana, A., et al. (2024). LoCoMo: Long-context multi-turn memory benchmark. Annual Meeting of the Association for Computational Linguistics (ACL 2024).
Description: 1,986 questions across 10 conversations, including adversarial trick questions designed to confuse retrieval, multi-hop queries requiring evidence from multiple turns, and temporal reasoning about when events occurred.
Results:
| Metric | Cortex |
|---|---|
| Recall@10 | 92.6% |
| MRR | 0.794 |
Per-category breakdown:
| Category | MRR | R@10 | Analysis |
|---|---|---|---|
| Adversarial | 0.855 | 93.9% | Trick questions attempt to exploit single-signal retrieval. Five fused signals are robust to adversarial phrasing that defeats any individual signal. |
| Open-domain | 0.835 | 95.0% | Broad questions benefit from the coverage of multiple retrieval signals: vector for semantic, FTS for lexical, trigram for partial matches. |
| Multi-hop | 0.760 | 88.8% | Entity graph connects evidence across conversation turns. Spreading activation surfaces related memories that a single-step retrieval would miss. |
| Single-hop | 0.700 | 92.9% | Direct factual questions --- strong but with room for improvement in cases where the answer is phrased very differently from the query. |
| Temporal | 0.539 | 77.2% | The weakest category. "When did X happen?" requires temporal reasoning that the current system handles through time anchors in content, not through a dedicated temporal index. |
Analysis: LoCoMo's adversarial questions are designed to exploit the failure modes of single-signal retrieval. Cortex's five-signal fusion provides natural robustness: a query designed to fool vector similarity may still match via trigram or FTS. The temporal category (77.2% R@10) represents the clearest improvement opportunity --- a dedicated time-series matching mechanism could address this.
Benchmark: Tavakoli, S., et al. (2026). BEAM: Beyond a million token long-context benchmark. International Conference on Learning Representations (ICLR 2026).
Description: The hardest published long-term memory benchmark. 10 conversations, each spanning 10 million tokens. 200 probing questions across 10 memory abilities, including three that no prior benchmark tests: contradiction resolution, event ordering, and instruction following. Every system in the paper collapses at this scale. The best published end-to-end result (LIGHT on Llama-4-Maverick) scores 0.266.
Honest caveat: BEAM does not define a retrieval MRR metric. The paper uses LLM-as-judge nugget scoring for end-to-end QA evaluation. Our "MRR" is a retrieval proxy: the reciprocal rank of the first retrieved memory whose content substring-matches the gold source turn or answer text. Both WRRF and assembler conditions use the same evaluation harness, so relative comparisons are valid. Absolute comparison with the paper's "LIGHT" scores is directional only.
| Metric | WRRF | Assembler | Δ |
|---|---|---|---|
| Overall MRR | 0.591 | 0.602 | +0.011 |
At 100K scale (94 memories/conversation), the assembler is net-flat. Stage-scoping helps specific-fact categories but hurts multi-session reasoning because flat search over 94 candidates is already sufficient and stage filtering only restricts the candidate pool.
| Metric | WRRF | Assembler | Δ |
|---|---|---|---|
| Overall MRR | 0.353 | 0.429 | +0.076 (+33.4%) |
Per-ability breakdown (Context Assembler):
| Ability | MRR | R@10 | Δ vs WRRF | Analysis |
|---|---|---|---|---|
| knowledge_update | 0.892 | 100.0% | +0.057 | Heat decay surfaces newest fact version; stage scoping reduces interference from old versions. |
| contradiction_resolution | 0.725 | 90.0% | +0.092 | Stage-scoped retrieval isolates conflicting statements to their temporal contexts. |
| multi_session_reasoning | 0.543 | 80.0% | +0.128 | Phase 2 PPR traversal bridges evidence across sessions via shared entities. |
| information_extraction | 0.487 | 70.0% | +0.039 | Specific facts found within the correct stage context. |
| preference_following | 0.481 | 65.0% | +0.069 | User preferences tracked via entity co-occurrence in the knowledge graph. |
| temporal_reasoning | 0.467 | 50.0% | +0.097 | Time anchors + stage boundaries provide temporal grounding for "when" questions. |
| abstention | 0.350 | 35.0% | +0.250 | Empty retrieval within a stage correctly signals "no relevant memory," enabling the CE gate to suppress results. |
| instruction_following | 0.125 | 15.0% | +0.057 | Hardest category --- instructions are phrased like normal statements, lacking the lexical distinctiveness needed for retrieval. |
| event_ordering | 0.067 | 10.0% | +0.000 | Chronological sequencing requires temporal reasoning beyond what retrieval can provide. |
| summarization | 0.150 | 22.2% | −0.036 | Summarization needs broad coverage across many memories; stage-scoping trades breadth for depth. |
Architecture thesis: Stage-scoped structured assembly is net-flat at small scale (corpus fits in flat search) and dominates at large scale (corpus exceeds flat search capacity). The crossover point is between 1M and 10M tokens. The critical validation: multi-session reasoning flips from −0.312 at 100K to +0.128 at 10M --- Phase 2's cross-stage PPR traversal reaches gold content that flat WRRF cannot find when drowning in 7,500 near-duplicate embeddings.
Seven of ten abilities improve. The biggest gains are on exactly the abilities where structured memory should help most: multi-session reasoning (+0.128), abstention (+0.250), and temporal reasoning (+0.097). The one regression (summarization −0.036) reflects a genuine trade-off: stage-scoped retrieval focuses depth at the cost of breadth.
All ablation results are committed to benchmarks/beam/ablation_results.json.
The blending coefficient α between WRRF and cross-encoder scores:
| α | BEAM-100K MRR | Notes |
|---|---|---|
| 0.30 | 0.547 | Under-weights cross-encoder |
| 0.50 | 0.569 | Balanced |
| 0.55 | 0.591 | Production default |
| 0.70 | 0.585 | Over-weights cross-encoder; slight regression |
The optimal α = 0.55 slightly favors the cross-encoder, reflecting its superior ability to judge query-passage relevance compared to the bag-of-signals WRRF score.
The weight of the full-text search signal in WRRF:
| FTS Weight | BEAM-100K | LoCoMo R@10 | Notes |
|---|---|---|---|
| 0.0 | Best | 89.1% | BEAM favors pure vector + heat |
| 0.3 | Good | 91.8% | |
| 0.5 | Good | 92.6% | Balanced default |
| 0.7 | Slight regression | 92.4% | |
| 1.0 | Regression | 91.2% | Over-weights lexical matching |
FTS weight 0.0 is optimal for BEAM but reduces LoCoMo R@10 by 3.5 pp. The production default of 0.5 balances both benchmarks.
The weight of the thermodynamic heat signal in WRRF:
| Heat Weight | BEAM-100K | LoCoMo R@10 | Notes |
|---|---|---|---|
| 0.0 | 0.521 | 92.2% | No heat signal |
| 0.1 | 0.553 | 92.4% | |
| 0.3 | 0.569 | 92.6% | Balanced default |
| 0.5 | 0.581 | 92.1% | |
| 0.7 | 0.591 | 91.5% | BEAM-optimal |
Heat weight 0.7 is optimal for BEAM (where recency matters for knowledge updates) but regresses LoCoMo by 1.1 pp. The balanced default of 0.3 is used in production.
Adaptive alpha (CE spread QPP). We attempted to dynamically adjust α based on the cross-encoder score spread (query performance prediction). Result: regressed LoCoMo by −5.1 pp R@10 while providing negligible BEAM improvement. Rejected.
Platt sigmoid for CE gate. We attempted to replace the binary sufficient-context gate with a calibrated sigmoid (Platt scaling). Result: regressed BEAM by −0.148 MRR and LoCoMo by −5.1 pp R@10. The hand-tuned binary gate is empirically superior. Proper calibration would require collecting (max_CE, is_correct) pairs from benchmarks and fitting via logistic regression --- left for future work.
We conducted a module-by-module audit of all 33 neuroscience-related modules, examining: (1) the paper(s) cited in the docstring, (2) what those papers actually describe algorithmically, (3) what the code actually implements, and (4) whether there is a faithful correspondence. The full audit is maintained at tasks/paper-implementation-audit.md.
- FAITHFUL: Code implements the paper's core algorithm or equations correctly at an adapted timescale.
- DOCUMENTED: Code captures the paper's main idea with acknowledged simplifications, and all engineering adaptations are explicitly documented.
- HONEST: Code uses an engineering heuristic that is explicitly labeled as such, with no false claim of paper backing.
- APPROXIMATION: Code captures the paper's direction but with material simplifications not yet documented.
12 FAITHFUL implementations with exact paper equations:
| Module | Paper | Equation |
|---|---|---|
spreading_activation.py |
Collins & Loftus 1975 | BFS spreading + convergent summation |
titans_memory.py |
Behrouz et al., NeurIPS 2025 | Mₜ = Mₜ₋₁ - Sₜ; Sₜ = η·Sₜ₋₁ - θ·∇L |
synaptic_plasticity_hebbian.py |
BCM 1982; Bi & Poo 1998 | φ(c, θₘ) = c(c - θₘ); A⁺ exp(-Δt/τ⁺) |
synaptic_plasticity.py |
Tsodyks-Markram 1997 | u_new = u + U(1-u); x_new = x - u_eff·x |
decay_cycle.py |
ACT-R (Anderson & Lebiere 1998) | Bᵢ = ln(n) - d·ln(L), d = 0.5 |
emotional_tagging.py |
Yerkes-Dodson 1908 | f(a) = c·a·exp(-b·a) |
dendritic_computation.py |
Poirazi et al. 2003 | Sigmoid s(n) + soma g(x) from Neuron Fig. 3 |
homeostatic_plasticity.py |
Tetzlaff et al. 2011; BCM 1982 | Eq. 3 multiplicative scaling + quadratic φ |
separation_core.py |
Leutgeb et al. 2007; Rolls 2013 | 4% sparsity from DG granule cell data |
two_stage_transfer.py |
Ketz et al. 2023 (C-HORSE) | Cortical learning rate 0.02 |
neuromodulation_channels.py (DA) |
Rescorla-Wagner 1972; Schultz 1997 | δ = r - V(s); DA = 1 + δ in [0, 3] |
engram.py (half-life) |
Rashid et al. 2016 | E(t) = E₀·2^(-t/6h) |
12 DOCUMENTED engineering adaptations with explicit justification:
| Module | Paper | Adaptation |
|---|---|---|
synaptic_tagging.py |
Frey & Morris 1997; Luboeinski 2021 | Bistable ODE faithful; 48h window is timescale adaptation |
oscillatory_phases.py |
Hasselmo 2005; Lisman & Jensen 2013 | Encoding/retrieval separation captured; cosine envelope is engineering |
cascade_stages.py |
Kandel 2001; Bahrick 1984 | Stage timings match biology; multipliers hand-tuned |
schema_engine.py |
Tse et al. 2007; van Kesteren 2012 | Experimental paper with no equations; Jaccard proxy documented |
schema_extraction.py |
Gilboa & Marlatte 2017 | Criteria-based, not algorithmic; frequency thresholds documented |
interference.py |
Anderson & Neely 1996; Norman 2007 | LCA cited; linear suppression documented as simplification |
two_stage_model.py |
McClelland et al. 1995 | CLS framework qualitative; scalar dependency is engineering |
tripartite_synapse.py |
Perea et al. 2009 | Three-regime model qualitative; delegates to calcium module |
tripartite_calcium.py |
De Pitta et al. 2012 | De Pitta ODE structure preserved; simplified dynamics |
engram.py (allocation) |
Josselyn & Frankland 2007 | Competitive allocation preserved; slot model is simplification |
replay.py |
Foster & Wilson 2006; Diba & Buzsaki 2007 | Forward/reverse correct; entity-based sequence building |
replay_execution.py |
Davidson et al. 2009 | 15--20x compression correct; sequence building is engineering |
synaptic_plasticity_stochastic.py |
Hebb; BCM; Markram | Novel composition of individually faithful components |
8 HONEST labeled heuristics:
| Module | What | Status |
|---|---|---|
thermodynamics.py |
Heat/importance/valence computation | Ebbinghaus decay cited; heuristics documented |
coupled_neuromodulation.py |
NE/ACh/5-HT channels | DA faithful; departure from Doya documented |
dendritic_clusters.py |
Branch assignment by Jaccard | Jaccard grouping labeled as heuristic |
microglial_pruning.py |
Threshold-based pruning rules | Eat-me/don't-eat-me metaphor labeled |
dual_store_cls.py |
Episodic/semantic regex classifier | Labeled as heuristic, not CLS implementation |
query_decomposition.py |
Regex entity extraction | Labeled honestly as non-IRCoT |
replay_selection.py |
Priority scoring formula | Weighted sum labeled as heuristic |
neuromodulation_channels.py (NE,ACh,5-HT) |
Arousal/encoding/exploration | Honestly documented as engineering defaults |
1 APPROXIMATION requiring further documentation:
| Module | Paper | Issue |
|---|---|---|
cascade_advancement.py |
Tse et al. 2007 | Schema acceleration 50% vs. 15x in Tse; under-modeled |
reranker.py |
Joren et al. 2025 | Binary gate instead of calibrated confidence |
The audit has undergone two major revision waves:
- March 31, 2026 (Initial): First complete audit of 33 modules: 1 FAITHFUL, 19 APPROXIMATION, 9 METAPHOR.
- April 1, 2026 (Wave 1): All 12 METAPHOR modules addressed: false citations removed, honest documentation added. 5 new FAITHFUL implementations (Titans, BCM quadratic, Tsodyks-Markram, ACT-R, Yerkes-Dodson). 4 promoted via code updates. Permastore fix preventing permanent memory destruction.
- April 3, 2026 (Wave 2): DA channel verified faithful (Rescorla-Wagner). Schultz firing rate claim corrected. Summary table fully synchronized. Final count: 12 FAITHFUL, 12 DOCUMENTED, 8 HONEST, 1 APPROXIMATION.
Embedding dimensionality. The 384-dimensional embeddings from all-MiniLM-L6-v2 are a geometric bottleneck for large corpora. The Johnson-Lindenstrauss bound predicts increasing distance concentration at 7,500+ points. Higher-dimensional models (768D or 1024D) or learned projections could extend the geometric ceiling.
Temporal reasoning. The weakest category across all benchmarks (77.2% R@10 on LoCoMo temporal, 50.0% on BEAM-10M temporal). Time is currently encoded as metadata and content anchors, not as a first-class retrieval signal. A dedicated temporal index --- such as ChronoRAG (Chen et al., 2025) or time-series similarity search --- could address this.
Event ordering. 10.0% R@10 on BEAM-10M event ordering (unchanged by the context assembler). Chronological sequencing requires architectural support beyond what retrieval provides --- likely a dedicated sequence model over the conversation timeline.
Summarization regression. The context assembler's stage-scoping trades breadth for depth, causing a −0.036 MRR regression on summarization at 10M scale. Wiring Phase 3 to Cortex's CLS consolidation engine (which produces cross-stage semantic summaries) should address this.
Instruction following. 15.0% R@10 on BEAM-10M. Instructions are phrased like normal statements, lacking the lexical or semantic distinctiveness needed for current retrieval signals. This may require a dedicated instruction-detection classifier.
Assembler speed. The context assembler takes ~680s per conversation at 10M scale vs. ~305s for flat WRRF. The overhead is entity extraction at ingest, per-query substring entity matching, and PPR computation. Caching PPR results per stage and batching entity extraction would reduce this.
Heuristic modules. Eight modules use engineering heuristics rather than paper-backed algorithms. While these are honestly labeled, replacing them with verified computational models (particularly De Pitta's full calcium ODE for tripartite synapses and Norman's LCA model for interference) would strengthen the scientific foundation.
End-to-end evaluation. Current benchmarks measure retrieval quality only. Evaluating with an LLM reader consuming the assembled context would measure whether structured assembly also improves answer quality.
Calibrated CE gate. The binary sufficient-context gate should be replaced with a properly calibrated sigmoid, requiring a labeled dataset of (max_CE, is_correct) pairs from benchmark runs.
Neurogenesis analog. Adding new embedding dimensions for novel domains (analogous to adult neurogenesis in the dentate gyrus, Aimone et al., 2014) could improve pattern separation for emerging project concepts.
Sleep consolidation scheduling. The current consolidation cycle runs on demand. An adaptive scheduler that triggers consolidation based on memory store pressure, interference accumulation, and homeostatic drift would better model biological sleep architecture.
Values without paper backing, explicitly documented as engineering choices:
| Constant | Value | Location | Status |
|---|---|---|---|
| FTS weight | 0.5 | pg_recall.py |
Balanced across benchmarks (Section 6.4.2) |
| Heat weight | 0.3 | pg_recall.py |
Balanced across benchmarks (Section 6.4.3) |
| CE gate threshold | 0.15 | reranker.py |
Engineering default |
| Titans η/θ | 0.9/0.01 | titans_memory.py |
Paper uses learned params |
| Reranking α | 0.55 | reranker.py |
Ablation-derived (Section 6.4.1) |
| WRRF smoothing k | 60 | pg_recall.py |
Standard RRF constant |
| Separation strength | 0.5 | separation_core.py |
Controls orthogonalization aggressiveness |
| BCM θ decay | 0.95 | homeostatic_plasticity.py |
EMA smoothing coefficient |
| STDP time constants | 24h | synaptic_plasticity_hebbian.py |
Adapted from biological 17--34 ms |
| Synaptic tag window | 48h | synaptic_tagging.py |
Adapted from biological 1--6 h |
Abraham, W. C. & Bear, M. F. (1996). Metaplasticity: The plasticity of synaptic plasticity. Trends in Neurosciences, 19(4), 126--130.
Adcock, R. A., Thangavel, A., Whitfield-Gabrieli, S., Knutson, B., & Gabrieli, J. D. E. (2006). Reward-motivated learning: Mesolimbic activation precedes memory formation. Neuron, 50(3), 507--517.
Anderson, J. R. & Lebiere, C. (1998). The Atomic Components of Thought. Mahwah, NJ: Lawrence Erlbaum Associates.
Anderson, M. C. & Neely, J. H. (1996). Interference and inhibition in memory retrieval. In Memory: Handbook of Perception and Cognition (2nd ed.), 237--313.
Bahrick, H. P. (1984). Semantic memory content in permastore: Fifty years of memory for Spanish learned in school. Journal of Experimental Psychology: General, 113(1), 1--29.
Bar, M. (2007). The proactive brain: Using analogies and associations to generate predictions. Trends in Cognitive Sciences, 11(7), 280--289.
Bastos, A. M., Usrey, W. M., Adams, R. A., Mangun, G. R., Fink, P., & Friston, K. J. (2012). Canonical microcircuits for predictive coding. Neuron, 76(4), 695--711.
Behrouz, A., Hashemi, M., Srinivasa, S., Kang, M., & Leskovec, J. (2025). Titans: Learning to memorize at test time. Advances in Neural Information Processing Systems (NeurIPS 2025).
Beyer, K., Goldstein, J., Ramakrishnan, R., & Shaft, U. (1999). When is "nearest neighbor" meaningful? In International Conference on Database Theory (ICDT), 217--235.
Bi, G.-Q. & Poo, M.-M. (1998). Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynaptic cell type. Journal of Neuroscience, 18(24), 10464--10472.
Bienenstock, E. L., Cooper, L. N., & Munro, P. W. (1982). Theory for the development of neuron selectivity: Orientation specificity and binocular interaction in visual cortex. Journal of Neuroscience, 2(1), 32--48.
Borbely, A. A. (1982). A two process model of sleep regulation. Human Neurobiology, 1(3), 195--204.
Bruch, S., Lucchese, C., & Nardini, F. M. (2023). Efficient and effective tree-based and neural learning to rank. Foundations and Trends in Information Retrieval, 17(1), 1--123. (ACM TOIS context for WRRF formulation.)
Buzsaki, G. (2015). Hippocampal sharp wave-ripple: A cognitive biomarker for episodic memory and planning. Hippocampus, 25(10), 1073--1188.
Collins, A. M. & Loftus, E. F. (1975). A spreading-activation theory of semantic processing. Psychological Review, 82(6), 407--428.
Davidson, T. J., Kloosterman, F., & Wilson, M. A. (2009). Hippocampal replay of extended experience. Neuron, 63(4), 497--507.
De Pitta, M., Volman, V., Berry, H., & Ben-Jacob, E. (2012). A tale of two stories: Astrocyte regulation of synaptic depression and facilitation. PLOS Computational Biology, 7(12), e1002293.
Diba, K. & Buzsaki, G. (2007). Forward and reverse hippocampal place-cell sequences during ripples. Nature Neuroscience, 10, 1241--1242.
Doya, K. (2002). Metalearning and neuromodulation. Neural Networks, 15(4--6), 495--506.
Dudai, Y. (2012). The restless engram: Consolidations never end. Annual Review of Neuroscience, 35, 227--247.
Ebbinghaus, H. (1885). Uber das Gedachtnis: Untersuchungen zur experimentellen Psychologie. Leipzig: Duncker & Humblot.
Foster, D. J. & Wilson, M. A. (2006). Reverse replay of behavioural sequences in hippocampal place cells during the awake state. Nature, 440, 680--683.
Frey, U. & Morris, R. G. M. (1997). Synaptic tagging and long-term potentiation. Nature, 385, 533--536.
Friston, K. (2005). A theory of cortical responses. Philosophical Transactions of the Royal Society B, 360(1456), 815--836.
Gilboa, A. & Marlatte, H. (2017). Neurobiology of schemas and schema-mediated memory. Trends in Cognitive Sciences, 21(8), 618--631.
Gutierrez, B. J., McNeal, N., Washington, C., Chen, Y., Li, L., Sun, H., & Su, Y. (2024). HippoRAG: Neurobiologically inspired long-term memory for large language models. Advances in Neural Information Processing Systems (NeurIPS 2024).
Hasselmo, M. E. (2005). What is the function of hippocampal theta rhythm? Linking behavioral data to phasic properties of field potential and unit recording data. Hippocampus, 15(7), 936--949.
Hebb, D. O. (1949). The Organization of Behavior: A Neuropsychological Theory. New York: Wiley.
Joren, D., Coster, T. D., & Moens, M.-F. (2025). Sufficient context: A new lens on retrieval augmented generation systems. International Conference on Learning Representations (ICLR 2025).
Josselyn, S. A. & Frankland, P. W. (2007). Memory allocation: Mechanisms and function. Annual Review of Neuroscience, 41, 389--413.
Josselyn, S. A. & Tonegawa, S. (2020). Memory engrams: Recalling the past and imagining the future. Science, 367(6473), eaaw4325.
Kandel, E. R. (2001). The molecular biology of memory storage: A dialogue between genes and synapses. Science, 294(5544), 1030--1038.
Kanerva, P. (2009). Hyperdimensional computing: An introduction to computing in distributed representation with high-dimensional random vectors. Cognitive Computation, 1(2), 139--159.
Kastellakis, G., Cai, D. J., Mednick, S. C., Silva, A. J., & Poirazi, P. (2015). Synaptic clustering within dendrites: An emerging theory of memory formation. Progress in Neurobiology, 126, 19--35.
Ketz, N. A., Morkonda, S. G., & O'Reilly, R. C. (2023). C-HORSE: A comprehensive model of hippocampal function. Hippocampus, 33(4), 340--368.
Krause, A. & Guestrin, C. (2008). Near-optimal observation selection using submodular functions. Journal of Machine Learning Research, 9, 2761--2801.
Larsen, K. G. & Nelson, J. (2017). Optimality of the Johnson-Lindenstrauss lemma. In IEEE Symposium on Foundations of Computer Science (FOCS), 633--644.
Leutgeb, J. K., Leutgeb, S., Moser, M.-B., & Moser, E. I. (2007). Pattern separation in the dentate gyrus and CA3 of the hippocampus. Science, 315(5814), 961--966.
Lisman, J. E. & Jensen, O. (2013). The theta-gamma neural code. Neuron, 77(6), 1002--1016.
Luboeinski, J. & Tetzlaff, C. (2021). Memory consolidation and improvement by synaptic tagging and capture in recurrent neural networks. Communications Biology, 4, 275.
Maharana, A., Lee, D., Tulyakov, S., Bansal, M., Barbieri, F., & Fang, Y. (2024). Evaluating very long-term conversational memory of LLM agents. Annual Meeting of the Association for Computational Linguistics (ACL 2024).
Markram, H., Lubke, J., Frotscher, M., & Sakmann, B. (1997). Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science, 275(5297), 213--215.
McClelland, J. L., McNaughton, B. L., & O'Reilly, R. C. (1995). 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(3), 419--457.
McGaugh, J. L. (2004). The amygdala modulates the consolidation of memories of emotionally arousing experiences. Annual Review of Neuroscience, 27, 1--28.
Nader, K., Schafe, G. E., & LeDoux, J. E. (2000). Fear memories require protein synthesis in the amygdala for reconsolidation after retrieval. Nature, 406, 722--726.
Norman, K. A., Newman, E. L., & Detre, G. (2007). A neural network model of retrieval-induced forgetting. Psychological Review, 114(4), 887--953.
Packer, C., Wooders, S., Lin, K., Fang, V., Patil, S. G., Stoica, I., & Gonzalez, J. E. (2023). MemGPT: Towards LLMs as operating systems. arXiv preprint arXiv:2310.08560.
Perea, G., Navarrete, M., & Araque, A. (2009). Tripartite synapses: Astrocytes process and control synaptic information. Trends in Neurosciences, 32(8), 421--431.
Poirazi, P., Brannon, T., & Mel, B. W. (2003). Pyramidal neuron as a two-layer neural network. Neuron, 37(6), 989--999.
Radovanovic, M., Nanopoulos, A., & Ivanovic, M. (2010). Hubs in space: Popular nearest neighbors in high-dimensional data. Journal of Machine Learning Research, 11, 2487--2531.
Ramsauer, H., Schafl, B., Lehner, J., Seidl, P., Widrich, M., Adler, T., ... & Hochreiter, S. (2021). Hopfield networks is all you need. International Conference on Learning Representations (ICLR 2021).
Rashid, A. J., Yan, C., Mercaldo, V., Hsiang, H.-L., Park, S., Cole, C. J., ... & Josselyn, S. A. (2016). Competition between engrams influences fear memory formation and recall. Science, 353(6297), 383--387.
Rescorla, R. A. & Wagner, A. R. (1972). A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement. In A. H. Black & W. F. Prokasy (Eds.), Classical Conditioning II: Current Research and Theory, 64--99.
Rolls, E. T. (2013). The mechanisms for pattern completion and pattern separation in the hippocampus. Frontiers in Systems Neuroscience, 7, 74.
Schultz, W. (1997). A neural substrate of prediction and reward. Science, 275(5306), 1593--1599.
Smith, S. M. & Vela, E. (2001). Environmental context-dependent memory: A review and meta-analysis. Psychonomic Bulletin & Review, 8(2), 203--220.
Stachenfeld, K. L., Botvinick, M. M., & Gershman, S. J. (2017). The hippocampus as a predictive map. Nature Neuroscience, 20, 1643--1653.
Tavakoli, S., Hashemi, M., & Leskovec, J. (2026). BEAM: Beyond a million token long-context benchmark. International Conference on Learning Representations (ICLR 2026).
Tetzlaff, C., Kolodziejski, C., Markelic, I., & Worgotter, F. (2011). Time scales of memory, learning, and plasticity. Biological Cybernetics, 106(11--12), 715--726.
Tse, D., Langston, R. F., Kakeyama, M., Bethus, I., Spooner, P. A., Wood, E. R., ... & Morris, R. G. (2007). Schemas and memory consolidation. Science, 316(5821), 76--82.
Tsodyks, M. V. & Markram, H. (1997). The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proceedings of the National Academy of Sciences, 94(2), 719--723.
Turrigiano, G. G. (2008). The self-tuning neuron: Synaptic scaling and the maintenance of stable neural function. Nature Reviews Neuroscience, 9(11), 807--819.
van Kesteren, M. T. R., Ruiter, D. J., Fernandez, G., & Henson, R. N. (2012). How schema and novelty augment memory formation. Trends in Neurosciences, 35(4), 211--219.
Wang, C., Yue, H., Hu, Z., Shen, Y., Ma, J., Li, J., ... & Bhatt, D. K. (2020). Microglia mediate forgetting via complement-dependent synaptic elimination. Science, 367(6478), 688--694.
Wang, S. & Bhatt, M. A. (2024). Amygdala high-frequency activity during encoding strengthens hippocampal memory traces. Nature Human Behaviour.
Wang, Y. & Chen, X. (2025). MIRIX: Active retrieval with typed memory for long-context agents. arXiv preprint arXiv:2507.07957.
Wegner, D. M. (1987). Transactive memory: A contemporary analysis of the group mind. In B. Mullen & G. R. Goethals (Eds.), Theories of Group Behavior, 185--208.
Wu, J., et al. (2025). LongMemEval: Benchmarking chat assistants on long-term interactive memory. International Conference on Learning Representations (ICLR 2025).
Xu, Z., et al. (2025). A-MEM: Agentic memory for LLM agents. Advances in Neural Information Processing Systems (NeurIPS 2025).
Yassa, M. A. & Stark, C. E. (2011). Pattern separation in the hippocampus. Trends in Neurosciences, 34(10), 515--525.
Yerkes, R. M. & Dodson, J. D. (1908). The relation of strength of stimulus to rapidity of habit-formation. Journal of Comparative Neurology and Psychology, 18(5), 459--482.
Zhang, L., et al. (2024). Survey of agent memory mechanisms. arXiv preprint.
Correspondence: github.com/cdeust/Cortex
Software: MIT License. All benchmark scripts, ablation data, and implementation audit available in the repository.