Centroid-Based Memory Mechanisms

• Centroid-Based Memory Mechanisms are advanced algorithms that summarize data into centroids, enabling efficient storage, retrieval, and robust memory management in machine learning.
• They employ methods like K-means initialization, exponential moving averages, and gradient-based updates to compress information and accelerate computations.
• Applications include deep clustering, continual learning, transformer efficiency, and memory-managed LLMs, providing resilience against noise and domain shifts.

Centroid-based memory mechanisms are a family of algorithms and architectural strategies in machine learning and neural computation that structure, store, retrieve, and adapt knowledge through the use of centroids—prototypes or averaged embeddings representing sets of similar experiences, features, or semantic units. These mechanisms underpin applications ranging from deep clustering and continual learning to memory-efficient computation and LLM memory management, providing computational, representational, and learning-theoretic advantages. The following sections offer a comprehensive analysis of centroid-based memory mechanisms, their mathematical foundations, practical implementations, empirical behavior, and the evolving landscape of research in this area.

1. Fundamental Principles of Centroid-Based Memory

Centroid-based memory mechanisms operate by summarizing collections of data samples or latent representations as centroids—often computed by averaging features over a set or learned using clustering algorithms. These centroids are then used for tasks such as classification, retrieval, decision-making, or knowledge unlearning. Formally, given a set $S$ of $n$ vectors $x_i$, a centroid $c$ is typically initialized/updated as:

$c = \frac{1}{n} \sum_{i=1}^n x_i$

and further refined via clustering (e.g., K-means), moving average, or gradient-based procedures. Many mechanisms extend this to multi-centroid approaches, using multiple centroids per class, domain, or cluster to capture intra-class variability and mitigate label noise (Wu et al., 2021).

Centroids may function as memory anchors in embedding space, as compressed representations for efficient computation (Kang et al., 11 Feb 2025, Wu et al., 2021), or as adaptive prototypes in continual learning and unlearning (Pomponi et al., 2022, Cotogni et al., 2023).

2. Algorithms and Mechanisms

Mechanism	Centroid Role	Key Implementation Features
Deep Clustering (e.g. DEC)	Cluster anchors	K-means/clustering, reclustering (Miklautz et al., 4 Nov 2024)
Transformer Centroid Attention	Memory/compression units	Soft clustering, amortization of gradients (Wu et al., 2021)
Multi-Centroid Associative Memory	Class prototypes	Multi-centroid per class, clustering-based initialization (Kang et al., 11 Feb 2025)
Centroid-based Query/Retrieval	Nearest neighbor proxies	Distance-based retrieval, scoring/ranking (Sun et al., 2018, Deguchi et al., 17 Feb 2024)
Continual Learning	Knowledge anchors	Centroid regularization, projection, rehearsal (Pomponi et al., 2022)
Unlearning via Centroids	Erasure guides	Metric learning toward incorrect centroids (Cotogni et al., 2023)

Centroid-based approaches may initialize centroids via K-means++ (Deguchi et al., 17 Feb 2024), update them using EMA or quantized learning (Kang et al., 11 Feb 2025), match queries via cosine/EUclidean distance (Wu et al., 2021, Cotogni et al., 2023), or merge centroids via second-order interpolation to synthesize hard negatives (Wu et al., 2021).

In contrast to static clustering, many systems introduce adaptive updates: online learning of centroids from streaming data (contextual memory trees (Sun et al., 2018)), reward or balance-driven router updates, and gradient-based centroid optimization within neural architectures (Wu et al., 2021).

3. Memory Efficiency and Computational Trade-offs

Centroid-based mechanisms fundamentally compress information. By replacing large sets of examples or hidden states with a small number of centroids, memory overhead is reduced and computation is accelerated. Notable empirical metrics include:

• Exponential speed-up: Expected utility calculations in machine translation are reduced from $O(N^2)$ to $O(Nk)$ by using centroids, with observed speed-ups up to 6.9× and improved COMET scores by up to 0.5 (Deguchi et al., 17 Feb 2024).
• Full in-memory utilization: MEMHD leverages multi-centroid mapping to achieve 13.69% higher accuracy or 13.25× lower memory usage, with up to 80× reduction in computation cycles (Kang et al., 11 Feb 2025).
• Low-memory continual learning: Storing only centroids rather than all support samples enables highly efficient memory utilization with accuracy near cumulative training (Pomponi et al., 2022).

Trade-offs exist between memory savings and representational fidelity; multi-centroid representations mitigate collapsing to a simplistic mode, preserving crucial intra-class and intra-domain variations (Wu et al., 2021).

4. Learning, Adaptation, and Robustness

Centroid-based mechanisms extend beyond static clustering by incorporating adaptive learning through:

• Gradient-based updates: Centroid attention generalizes self-attention by unrolling gradient descent steps for soft clustering objectives (Wu et al., 2021).
• Reward-driven partitioning: Routers adapt memory partitioning in response to downstream task performance and reward signals (Sun et al., 2018).
• Regularization against forgetting: Matching current embeddings to prior centroids prevents catastrophic forgetting, with the learned projection functions enabling consolidation in class-incremental learning (Pomponi et al., 2022).
• Machine unlearning: Embedding representations of forget samples are pushed toward the nearest incorrect centroid via a metric learning loss, ensuring effective erasure without retraining (Cotogni et al., 2023).
• Clustering dynamics: BRB breaks performance plateaus by soft weight resets and reclustering over shifted embeddings, reviving exploration in deep clustering (Miklautz et al., 4 Nov 2024).
• Negative sampling synthesis: Interpolated centroids create hard negatives for contrastive learning, boosting discriminative power in domain adaptation (Wu et al., 2021).

These mechanisms enhance robustness to label noise, variability, domain shift, and catastrophic forgetting, as demonstrated by comprehensive ablations and benchmark comparisons (Wu et al., 2021, Pomponi et al., 2022).

5. Practical Applications

Centroid-based memory mechanisms have proven utility in diverse domains:

• Deep clustering: Breaking the reclustering barrier in DEC, IDEC, DCN yields state-of-the-art clustering on vision benchmarks (Miklautz et al., 4 Nov 2024).
• Transformer efficiency: Centroid transformers halve computational load and outperform or match classical transformers in summarization and 3D vision (Wu et al., 2021).
• Multi-document Summarization: Centroid document selection yields more coherent summaries and outperforms synthetic-sentence methods in zero- and few-shot regimes (Puduppully et al., 2022).
• Person re-identification: Multi-centroid approaches yield superior mAP and rank-1 accuracy in UDA re-ID tasks, with resilience to cluster label noise (Wu et al., 2021).
• Minimum Bayes risk decoding: Centroid clustering accelerates translation selection with negligible loss or actual gain in metric quality (Deguchi et al., 17 Feb 2024).
• Hyperdimensional computing: MEMHD’s multi-centroid associative memory enables one-shot search and array-efficient mapping on in-memory architectures (Kang et al., 11 Feb 2025).
• LLM memory compression: Parameter-based and hidden state-based memory in LLMs can be realized via centroid prototypes for scalable context retention (Shan et al., 3 Apr 2025).

6. Comparative Analysis and Limitations

Relative to other mechanisms, centroid methods offer:

• Efficient memory compression and fast retrieval (well-suited to large-scale or in-memory computing (Kang et al., 11 Feb 2025)).
• Adaptability via online updates and reward-driven learning (enabling context-rich, lifelong learning (Pomponi et al., 2022, Sun et al., 2018)).
• Robust handling of noise and domain shifts via multi-centroid and contrastive learning strategies (Wu et al., 2021).

Limitations include potential representational loss when using too few centroids, risk of over-commitment in clustering (as in the reclustering barrier (Miklautz et al., 4 Nov 2024)), and challenges in dynamic environments where the definition of “centroid” requires continual adjustment.

7. Evolving Directions and Integration in Architectures

Current research explores hierarchical centroid formation (sensory/short-term/long-term memory in LLMs (Shan et al., 3 Apr 2025)), centroid-based summarization and pruning in memory management, low-rank updates for centroid adaptation (LoRA-style (Shan et al., 3 Apr 2025)), and compositional routing via mixtures of centroids ("experts"). There is cross-fertilization between explicit memory dependency annotations and centroid formation, suggesting opportunities for merging expert-guided and adaptive centroid-based retrieval (Yue et al., 12 Nov 2024).

Centroid-based memory mechanisms now permeate transformer networks, metaheuristic optimization, associative memory, and privacy-focused machine unlearning, demonstrating their flexibility, scalability, and continued innovation in the machine learning research community.