Multi-Level Embedding Memory Engine

• Multi-Level Embedding Memory Engine is a framework that organizes memory representations as high-dimensional embeddings across multiple abstraction levels for efficient data retrieval and learning.
• It integrates semantic, episodic, and sensory memory functions using tensor decompositions to capture time, hierarchy, and dynamic query answering in large-scale systems.
• Its design supports scalable implementations in knowledge graphs, intelligent agents, and cognitive architectures, bridging advanced representation learning with biological memory theories.

A multi-level embedding memory engine is a computational framework or system in which memory organization, storage, retrieval, and learning are mediated by embeddings—high-dimensional, dense vector representations—structured or operated upon at multiple levels of abstraction, hierarchy, or semantic granularity. This concept appears across diverse domains, including knowledge graph modeling, neural memory architectures, hardware implementations, and agent memory systems, with foundational work presented in “Learning with Memory Embeddings” (Tresp et al., 2015) and extended in both algorithmic and engineering contexts.

1. Embedding-Based Memory Functions and Cognitive Analogues

The central theoretical underpinning is the mapping of memory subsystems directly onto embedding models. Each generalized entity—objects, predicates, sensory channels, or even time points—is assigned a unique high-dimensional latent vector, $a_{e_k} \in \mathbb{R}^{\tilde{r}}$. These embeddings are reused across various memory functions:

• Semantic Memory is formalized as a (subject, predicate, object) tensor, with the indicator mapping:

$$\theta^{(\text{semantic})}_{s,p,o} = f^{(\text{semantic})}(a_{e_s}, a_{e_p}, a_{e_o})$$

• Episodic Memory extends this format by introducing a time axis, modeling events and sequences within a four-way tensor:

$$\theta^{(\text{episodic})}_{s,p,o,t} = f^{(\text{episodic})}(a_{e_s}, a_{e_p}, a_{e_o}, a_{e_t})$$

where $a_{e_t}$ captures the latent representation of system state at time $t$.

• Sensory Memory is represented with a three-way tensor, capturing low-level sensory buffer states:

$$\theta^{(\text{sensory})}_{q,\gamma,t} = f^{(\text{sensory})}(a_{e_q}, a_{e_\gamma}, a_{e_t})$$

with $q$ indexing channels and $\gamma$ buffer positions.

• Working Memory and Prediction are realized as operations directly over shared latent vectors, enabling short-term reasoning, prediction, and decision support.

This model provides a structural and mathematical basis for relating technical approaches in knowledge graph representation learning to established neurocognitive memory functions, exploiting tensor decompositions (e.g., PARAFAC, Tucker, RESCAL) for scalable and expressive knowledge encoding (Tresp et al., 2015).

2. Temporal and Hierarchical Organization in Memory Engines

Multi-level embedding memory engines inherently model time and structure. Temporal extensions involve representing event quadruples—incorporating time as an explicit axis—and allow not only static fact storage but also modeling of event evolutions and patterns across time:

$\mathcal{Z}(s,p,o,t) \text{ (episodic tensor)}$

Temporal knowledge graphs admit inductive inference; queries such as "When did event $e$ occur?" correspond to maximizing over time indices based on the learned mapping function.

Hierarchy emerges in both storage (e.g., query-result-key tri-level arrangements in dialog systems (Reddy et al., 2018), or tree-structured memory schemas (Rezazadeh et al., 17 Oct 2024)) and retrieval (e.g., memory modules for part, instance, and domain-level cues in person re-identification (Zhang et al., 2020)).

Such structuring supports flexible memory capacity, efficient indexing, and dynamic composition of facts, events, or experiences.

3. Learning Procedures and Memory-Driven Query Answering

Learning in a multi-level embedding memory engine is fundamentally “global” because latent representations are shared across all memory functions. The system minimizes a total cost, the sum of negative log-likelihoods (and regularization), each corresponding to a different memory subsystem:

$$\text{cost}^{(\text{semantic})} = -\sum_{(s,p,o) \in \tilde{\tau}} \log P\left( x_{s,p,o} \mid \theta^{(\text{semantic})}_{s,p,o} \right)$$

Similar expressions are defined for episodic, sensory, and predictive models. Key practical learning mechanisms include function approximators (multi-way neural networks predicting over the embedding space), and (multi)linear approaches (enabling marginalization, conditional probabilities, and simulation-based sampling for queries).

Efficient query answering involves:

• Predicting missing entities (e.g., $(s, p, ?)$) through inner products or energy-based sampling,
• Simulated annealing or Boltzmann sampling over the embedding-defined energy surface,
• Tensor decomposition techniques allowing for scalable marginalization and conditioning.

4. Human Memory Hypotheses Inferred from Mathematical Embedding Models

Several cognitive hypotheses arise from the embedding framework (Tresp et al., 2015):

• Triple Hypothesis: Semantic memory is best represented as $<$subject, predicate, object$>$ triples, while episodic memory extends this to include temporal information.
• Unique-Representation Hypothesis (Tensor Memory): Every entity (subject, object, predicate, time) is represented via a singular latent vector, enabling integration and propagation across memory types.
• Semantic Decoding and Association: Sensory inputs (subsymbolic buffer) are decoded into symbolic triples through sampling in latent space, enabling both immediate and retrospective interpretation.
• Consolidation and Mutual Dependence: There is overlap but partial independence between episodic and semantic memory, allowing for plausible dissociation as seen in cognitive neuroscience.
• Working Memory as Active Latent Manipulation: Prediction, decision support, and dynamic recall operate directly on these shared latent spaces, realized as recurrent transformations or autoregressive models.

5. Sensory-to-Semantic Processing Pipeline

A key operational sequence is described for entity and event formation:

• Low-Level Encoding: Sensory data streams are captured in short-term buffer tensors.
• Latent Representation Induction: Vectorized sensory input for time $t$ is transformed to a latent code $h_t^{(\text{time})}$ via a modular mapping function.
• Time Indexing and Episodic Memory Creation: If the new latent is novel or significant, a new temporal index is instantiated in the system’s memory, linking it to $h_t^{(\text{time})}$.
• Semantic Decoding: Latent time representations are mapped to symbolic interpretations (triples) using the semantic indicator mapping, often via tensor contraction with the core tensor (e.g., Tucker core).
• Predictive Feedback: Separate predictive models can forecast future latent states, providing a basis for simulation, anticipation, and downstream semantic decoding.

This pipeline underpins agentive and intelligent behaviors, from perception to high-level reasoning.

6. Model Extensions, Computational Aspects, and Applications

Embedding-memory engines are designed with extensibility and scalability in mind:

• Tensor Decomposition Models (e.g., RESCAL, Tucker): Provide computational efficiency and structured parameterization for large, sparse knowledge graphs.
• Memory Sharing and Latent Propagation: Entities, events, predicates, and temporal markers reuse shared vectors, facilitating compactness and efficient querying.
• Integration with Neural and Cognitive Architectures: The approach is compatible with architectures for working memory, attention, and learning sequences, reflecting functional neuroanatomy (e.g., hippocampal formation for rapid episodic coding) (Tresp et al., 2015).

Applications include:

• Large-scale semantic knowledge graph modeling,
• Temporal reasoning in intelligent agents,
• Scene understanding from sensory data,
• Unified architectures for prediction, recall, and associative learning.

7. Implications and Theoretical Significance

Multi-level embedding memory engines provide a rigorous bridge between representation learning and theories of cognitive memory. They offer explanatory power for operations such as semantic–episodic consolidation, context-dependent recall, and rapid formation of new memories. Mathematically, the shared latent vector framework yields tensor parameterizations that are both scalable and biologically plausible.

Functionally, these models are foundational for high-throughput knowledge management, flexible query answering, and predictive intelligence in artificial agents. They support the synthesis of high-dimensional input into actionable, structured representations, enabling both inductive and deductive reasoning over dynamic knowledge bases.