Entity-Centric Memory Graph

• Entity-Centric Memory Graph is a computational framework that organizes and reasons over knowledge using unique high-dimensional latent entity embeddings.
• It maps structured knowledge graphs to tensor representations, linking semantic, episodic, sensory, and working memory functions via models like Tucker and RESCAL.
• The framework supports inductive inference, temporal reasoning, and sensory-to-semantic translation, bridging biological memory with AI systems.

An Entity-Centric Memory Graph is a representational and computational framework that organizes, stores, and enables reasoning over structured knowledge using unique distributed embeddings for generalized entities and their interactions—extending this paradigm to incorporate temporal, episodic, sensory, and working memory functions. This approach leverages high-dimensional tensor models and probabilistic sampling to unify cognitive memory tasks, supporting the inductive inference, semantic decoding, and time-sensitive reasoning found in both artificial and biological memory systems.

1. Representation of Knowledge Graphs as Tensors with Latent Entity Embeddings

The foundational principle is the mapping of large-scale semantic knowledge graphs (KGs) to tensor representations, where each fact or assertion is expressed as a tuple and associated with a learnable score that depends on its constituent entities’ latent vectors. For a semantic KG, facts are encoded as triples (eₛ, eₚ, eₒ) for subject, predicate, and object. These are organized into a 3-way adjacency tensor $\mathcal{X}$, where each entry $x_{s,p,o}$ holds the value (typically a Boolean or real) describing the fact’s validity.

Each generalized entity—subject, predicate, or object—is assigned a unique high-dimensional latent vector ($\mathbf{a}_e \in \mathbb{R}^{\tilde{r}}$), leading to the “unique-representation hypothesis,” which asserts that all entities and relations are characterized by their own vector representations throughout all roles and contexts.

The score or “natural parameter” $\theta_{s,p,o}^{\text{semantic}}$ of a triple is determined as: $$\theta_{s,p,o}^{\text{semantic}} = f^{\text{semantic}}(\mathbf{a}_{e_s},\mathbf{a}_{e_p},\mathbf{a}_{e_o}),$$ where $f^{\text{semantic}}$ is instantiated by various tensor factorization models, such as Tucker, PARAFAC, or RESCAL. For example, the Tucker model: $$f^{\text{semantic}}(\mathbf{a}_{e_s},\mathbf{a}_{e_p},\mathbf{a}_{e_o}) = \sum_{r_1, r_2, r_3} a_{e_s}[r_1] \cdot a_{e_p}[r_2] \cdot a_{e_o}[r_3] \cdot g(r_1, r_2, r_3),$$ with $g(r_1, r_2, r_3)$ the entries of a core tensor $\mathcal{G}$, ensuring expressiveness in capturing multirelational association patterns and supporting generalization through shared latent representations.

2. Mapping Embedding Models to Cognitive Memory Functions

The entity-centric memory graph framework maps embedding models developed for KGs onto multiple cognitive memory modules:

• Semantic Memory is realized via the KG tensors (triples), with latent codes encoding world knowledge.
• Episodic Memory introduces an explicit time dimension, forming a four-way tensor $\mathcal{Z}$ indexed by (eₛ, eₚ, eₒ, eₜ), with a latent time vector $\mathbf{a}_{e_t}$. Episodic events thus become quadruples, allowing representations such as “(Jack, met, Mary, last week).”
• Sensory Memory is represented by a separate tensor $\mathcal{U}$ over subsymbolic sensory channels (e.g., image pixels), with a mapping function $f^{\mathcal{M}}$ that translates sensory input into a structured, latent time representation.
• Short-Term and Working Memory are modeled as mediation layers utilizing the shared latent entity representations to support prediction, planning, and decision-making.

This structure is conceptualized as the “tensor memory hypothesis”—posited as a mathematical principle connecting biological and artificial memory: entity-centric latent variables orchestrate all memory functions via shared codes across semantic, episodic, sensory, and working modules.

3. Temporal Extension and Encoding of Episodic Memory

Temporal evolution is incorporated into the entity-centric memory graph by extending triple-based tensors to higher-order tensors, enabling explicit modeling of knowledge and event dynamics. The episodic memory tensor $\mathcal{Z}$ is indexed by time as: $$\theta_{s,p,o,t}^{\text{episodic}} = f^{\text{episodic}}(\mathbf{a}_{e_s}, \mathbf{a}_{e_p}, \mathbf{a}_{e_o}, \mathbf{a}_{e_t}),$$ binding time representations ($\mathbf{a}_{e_t}$) directly to event facts. This mechanism links raw time-stamped sensor data and higher-level semantic knowledge, facilitating recall (“what happened at time $t$?”) and supporting queries that trace the semantic evolution of entities across temporal contexts.

Latent time representations not only serve as event “indices” but also act as bridges from short-term sensory input to longer-term semantic and episodic store—structurally supporting both learning from sequence data and memory consolidation.

4. Learning Paradigm and Querying Mechanisms

Training occurs by optimizing a global cost function that combines the negative log-likelihood terms over all memory modules (semantic, episodic, sensory, prediction), for example: $$\text{cost}^{\text{semantic}} = -\sum \log P(x_{s,p,o}\mid \theta_{s,p,o}^{\text{semantic}}(\mathbf{A}, W)),$$ where $\mathbf{A}$ denotes latent representations and $W$ the model parameters for the mapping function.

Query answering leverages the continuous latent representations. For incomplete queries (e.g., $(e_s, e_p, ?)$), the system defines an energy function: $$E(s,p,o) = -f^{\text{semantic}}(\mathbf{a}_{e_s}, \mathbf{a}_{e_p}, \mathbf{a}_{e_o}),$$ and samples predictions or completes queries using a Boltzmann distribution: $$P(s,p,o) \propto \exp[\beta f^{\text{semantic}}(\mathbf{a}_{e_s}, \mathbf{a}_{e_p}, \mathbf{a}_{e_o})].$$ Sampling methods (e.g., Gibbs sampling, simulated annealing) are used to generate likely completions. Because each entity has a single latent code, retrieval integrates across the full representational graph—enabling both semantic knowledge recovery and episodic recall.

5. Sensory-to-Semantic Information Pipeline

A central operational feature is the pathway from raw sensory input to semantic memory. Sensory data, organized as tensor $\mathcal{U}$ over channels, is processed through a mapping function $f^{\mathcal{M}}$ to generate a latent time code: $$h_t^{(\text{time})} = f^{\mathcal{M}}(\text{vec}(u_{:,:,t}))$$ If the input is “important” (e.g., novel or emotionally salient), a new time neuron $e_t$ is instantiated with $\mathbf{a}_{e_t} := h_t^{(\text{time})}$. This representation is then incorporated as the temporal component in episodic memory.

Semantic decoding proceeds by feeding the latent time code into the semantic tensor model, synthesizing probable $(s, p, o)$ triples for that moment: $$\theta_{s,p,o}^{(\text{decoded})} = f^{\text{semantic}}(\mathbf{a}_{e_s},\mathbf{a}_{e_p},\mathbf{a}_{e_o}, h_t^{(\text{time})})$$ These decoded triples reflect the system’s semantic interpretation of sensory information at time $t$, closing the loop between perception and knowledge graph update.

6. Inductive Inference, Generalization, and Unified Representations

The entity-centric memory graph framework enables inductive inference and generalization due to the sharing and reuse of latent entity codes across multiple memory roles and tensor dimensions. Information flows via shared representations—structurally facilitating imagery (“mental simulation” by triggering latent codes), prediction (via the propagation of future event patterns), and knowledge integration across sensory and symbolic modalities.

A salient aspect is the architecture’s support for both online and offline consolidation: recurrent/auto-regressive models enable real-time updating, while batch/model-based recall mimics biological consolidation from episodic to semantic memory. The framework supports not only static knowledge representation but also the integration of new knowledge, temporal progression, and semantic interpretation, tightly binding perception, memory, and reasoning in a mathematically coherent system.

7. Implications and Extensions

The entity-centric memory graph, as formalized in the “tensor memory hypothesis,” offers a unified view of memory and reasoning where all information about entities—be it semantic, episodic, sensory, or anticipatory—is encoded in shared, high-dimensional representations. This provides a tractable mechanism for integrating heterogeneous information and supports flexible, scalable AI systems that can achieve both symbolic reasoning and adaptive learning over time.

Empirically, this paradigm has enabled efficient modeling of large-scale, sparse knowledge graphs and serves as a foundation for subsequent advances in, for example, neural-symbolic architectures, memory-augmented neural networks, and models that bridge low-level perception with high-level knowledge representation (Tresp et al., 2015). The model’s design and mathematical underpinnings facilitate cross-disciplinary exploration between computational neuroscience, machine learning, and cognitive systems.