Concept-Level Memory

• Concept-level memory is a framework for storing, retrieving, and manipulating abstractions derived from experiences to enhance generalization and reasoning.
• Methodologies include autocatalytic network models, conceptors, and memory embeddings that enable structured abstraction and dynamic integration of information.
• Applications span continual learning, interpretable AI, and adaptive reasoning, addressing challenges like catastrophic forgetting and concept drift.

Concept-level memory refers to the organization, storage, retrieval, and manipulation of abstractions—generalized, reusable units derived from specific experiences or learned representations—within cognitive or artificial systems. Rather than treating memories as isolated instances, concept-level memory operates at the level of structured abstractions, enabling efficient generalization, robust reasoning, dynamic integration, and creative recombination. This approach underpins a range of cognitive phenomena, including abstraction, associative recall, continual learning, interpretability, and dynamic adaptation in both biological and artificial settings.

1. Emergence and Network Formation of Concept-Level Memory

Early models of concept-level memory draw inspiration from autocatalytic networks, suggesting that discrete episodic memories ("memes") become woven into a dense conceptual network through processes of abstraction (Gabora, 2013). In these models, individual episodes are initially stored as unconnected units—points in a high-dimensional conceptual space (e.g., the vertices of an n-dimensional hypercube). Reminding events, wherein one memory evokes another based on feature overlap, act analogously to catalytic reactions in biological networks. Over time, these events blend overlapping features, creating higher-order abstractions that "network" individual episodes.

As abstraction increases, the network reaches a percolation threshold: the set of memories achieves conceptual closure, such that any meme can be accessed via associative recall through the network of abstractions. This process is mathematically described by the distribution of Hamming distances among n-dimensional binary vectors: $C(n, d) = \frac{n!}{d! (n-d)!}$ for the number of memes at distance $d$, with the distribution approximating a Gaussian for large $n$.

The resulting conceptual memory is dynamic and continuously reorganized through ongoing streams of self-triggered thought, supporting the emergence of a self-organizing worldview that both structures and is structured by experience.

2. Neural and Symbolic Mechanisms for Concept Memory

At the neuro-computational level, mechanisms such as conceptors provide frameworks for dynamically extracting, storing, and manipulating concept-level representations in neural networks (Jaeger, 2014). Conceptors operate by capturing the characteristic geometry (e.g., an ellipsoidal envelope) of neural state clouds, functioning as filter matrices $C$ that can be combined using Boolean logic:

• OR ($\vee$): union of concept spaces
• AND ($\wedge$): intersection
• NOT ($\neg$): complement (free memory)

The learning of a conceptor typically involves solving a regularized projection problem: $C = X X^\top (X X^\top + \alpha^{-2} I)^{-1}$ where $X$ captures the neural states and $\alpha$ is an aperture (regularization) parameter.

Symbolic models extend these mechanisms to human-interpretable concepts by representing rules in explicit logical form. For instance, in interpretable concept bottleneck models (CBMs), task predictions are computed by symbolically evaluating learned logic rules over predicted concept values (Debot et al., 22 Jul 2024). At inference, the symbolic evaluation ensures transparency, formal verification, and direct rule interventions. The core evaluation is defined as: $$y = \bigwedge_{i=1}^{n_C} \left[ (r_i = I) \vee ((r_i = P) \Rightarrow c_i) \wedge ((r_i = N) \Rightarrow \neg c_i) \right]$$ where $r_i$ denotes the role of concept $c_i$ in the rule ($P$: positive, $N$: negative, $I$: irrelevant).

3. Memory Embeddings and Latent Factor Models

Memory embedding models, originating from knowledge graph reasoning, naturally encode concept-level memory through distributed real-valued vectors (latent representations) for entities, predicates, and even time points (Tresp et al., 2015). These embeddings serve as building blocks for diverse memory functions:

• Semantic (concept) memory: facts encoded as subject–predicate–object triples, with tensors modeled as

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

• Episodic memory: adds a time dimension to encode events
• Sensory working memory: stores short-term sensory buffers
• Prediction and simulation: recurrent or autoregressive models predict future concept states and decode them into likely events

These latent representations enable flexible inference, high capacity, and direct mapping to cognitive hypotheses (e.g., unique-representation or index neuron hypothesis). Models such as TransE combine entity and relation embeddings in additive fashion: $e_1 + r \approx e_2$ trained with margin-based ranking losses to ensure meaningful concept-level structure (Shi et al., 2015).

4. Continual Learning, Memory Consolidation, and Concept Drift

A central operational challenge for concept-level memory is maintaining stability (retaining past concepts) while enabling plasticity (learning new or evolving concepts). Lifelong and incremental learning settings require frameworks that mitigate catastrophic forgetting and accommodate concept drift.

• Pseudo-rehearsal approaches use generative models (e.g., LS-ACGAN) to synthesize pseudo-samples for previously learned concepts, supporting balanced online memory recall and joint training of old and new concepts (Li et al., 2019).
• Analytic frameworks such as CONCIL eliminate gradient-based updates in favor of recursive matrix operations, enabling efficient, scalable, and "absolute memory" retention in continual class- and concept-incremental learning by solving regularized least squares problems (Lai et al., 25 Nov 2024):

$$\hat{W}_c^{(t)} = (Z_{*t}^\top Z_{*t} + \lambda_1 I)^{-1} Z_{*t}^\top C_t$$

• Adaptive Memory Realignment (AMR) directly manages concept drift by statistically detecting distributional shifts (via Kolmogorov–Smirnov tests over predictive uncertainty/entropy) and actively realigning replay buffers with up-to-date samples, reducing the need for full retraining and significant annotation overhead (Ashrafee et al., 3 Jul 2025).

Such mechanisms ensure that concept-level memory systems remain adaptive in non-stationary environments while preserving prior knowledge.

5. Interpretability, Verification, and Security

Concept-level memory architectures are increasingly employed for transparency and robustness in high-stakes domains. Modern CBMs (Debot et al., 22 Jul 2024) and extended frameworks such as ConceptGuard (Lai et al., 25 Nov 2024) and Hierarchical Concept Memory Reasoner (H-CMR) (Debot et al., 26 Jun 2025) integrate explicit, human-interpretable memory stores—rulebooks, logic graphs, or rule DAGs—enabling:

• Full symbolic traceability from concept detection to prediction
• Formal predeployment verification of model properties using logic formulas (e.g., model checking)
• Rule or concept-level intervention (manual modification of rules or parent concepts by domain experts)
• Defense against concept-level backdoor attacks through concept clustering and ensemble majority voting, with provable robustness contingent on the fraction of corrupted concept groups

Rule memory and hierarchical reasoning extend interpretability to both intermediate concepts and final decisions, meeting requirements for certified reliability.

6. Abstraction, Retrieval, and Reasoning with Concept-Level Memory

Concept-level memory not only supports storage but also dynamic retrieval, recombination, and abstraction. ArcMemo (Ho et al., 4 Sep 2025) demonstrates that moving from instance-based to modular, abstract memory entries enables persistent, scalable, and continually improving reasoning for general intelligence tasks:

• Memory entries encode reusable "concepts" distilled from solution traces, formalized as minimally structured (situation, suggestion) pairs or parameterized program-like abstractions supporting higher-order reasoning.
• Retrieval is query-driven, leveraging both input transformation and reasoning about the compatibility (type and relevance cues) between current problems and stored concepts, thus facilitating prompt-time continual learning without weight modifications.
• Experiments show a 7.5% relative improvement over strong no-memory LLM baselines on the ARC-AGI benchmark, with dynamic memory updates enabling self-improvement.

Selective retrieval manages context overload, while abstraction ensures that memory can be reused, composed, and expanded as new domains or tasks are encountered.

7. Practical Applications and Future Directions

Concept-level memory is foundational in diverse applications:

• Distributed, multimodal AI in complex domains such as telecommunications leverages concept-level latent spaces (frequently hyperbolic for hierarchical relations) enabling cross-layer, cross-domain, and multilingual reasoning beyond the capacity of token-based LLMs (Kumarskandpriya et al., 27 Jun 2025).
• High-fidelity, selective unlearning and memory manipulation (e.g., in diffusion models) is facilitated via dynamic masking and concept-aware loss, ensuring that unwanted concepts can be erased, replaced, or restructured without substantial degradation to overall generative capability (Li et al., 12 Apr 2025).
• Adaptive dialog systems and intelligent agents (e.g., Aileen/Soar) harness analogical concept memory for interactive task learning, rapid generalization from few examples, and robust action planning grounded in dynamically abstracted relational knowledge (Mohan et al., 2020, Mohan et al., 2022).

Outstanding research challenges focus on more principled hierarchical abstraction, compositionality, consolidation of related concepts, formal metrics for abstraction-impact, and integration into real-time, lifelong learning architectures. The field continues to seek mechanisms that reliably balance granularity, efficiency, and adaptive reasoning in open-ended, continually evolving environments.