Knowledge Evolution Layer (KEL) Explained

• Knowledge Evolution Layer (KEL) is a modular abstraction that dynamically tracks and updates internal knowledge representations across neural or cognitive system layers.
• It employs local entropy minimization and adaptive chunk management to align knowledge states with decision shifts, enhancing interpretability and memory efficiency.
• KEL formalizations integrate mathematical models and algorithmic routines to drive layerwise learning, supporting practical advances in neural dynamics and multi-agent systems.

A Knowledge Evolution Layer (KEL) is a modular architectural or functional abstraction, applied in neural models and multi-agent cognitive systems, in which knowledge representations are dynamically tracked, evolved, and operationalized at the level of individual layers or storage units. Across recent literature, KEL constructions formalize both the mathematical evolution of internal knowledge states via local optimization (as in neural layer stacks) and the adaptive management of externalized, chunked knowledge stores (as in knowledge-intensive educational multi-agent systems). Consistently, a KEL seeks to capture, at each system layer or stage, the dynamic interplay between knowledge representation, activation, and temporal adaptation, providing a substrate for local learning, interpretability, or efficient memory management (Quantiota, 18 Mar 2025, Wu et al., 29 Nov 2025, Bronzini et al., 4 Apr 2024).

1. Mathematical Formulations and Core Principles

The defining property of KELs is the explicit formulation and update of a knowledge state at each layer or chunk, using task-relevant signals to drive its evolution.

Structured Knowledge Accumulation: In feedforward neural architectures, the SKA framework introduces a per-layer knowledge vector $z_k^{(\ell)}$ (logits of neurons in layer $\ell$ at step $k$) and defines a local entropy

$$H^{(\ell)} = -\frac{1}{\ln 2} \sum_{k=1}^K z_k^{(\ell)} \cdot \Delta D_k^{(\ell)}$$

where $\Delta D_k^{(\ell)}=D_k^{(\ell)}-D_{k-1}^{(\ell)}$ is the change in decision probabilities (entry-wise sigmoid applied to $z_k^{(\ell)}$). KELs minimize this local entropy using forward-only, layer-local updates derived from

$$\frac{\partial H^{(\ell)}}{\partial z^{(\ell)}_k} = -\frac{1}{\ln 2}[z^{(\ell)}_k \odot (D^{(\ell)}_k \odot (1 - D^{(\ell)}_k)) + \Delta D^{(\ell)}_k]$$

Knowledge vectors evolve autonomously, driving their alignment with local decision shifts without error backpropagation (Quantiota, 18 Mar 2025).

Knowledge Base Evolution: In multi-agent knowledge systems, such as CogEvo-Edu, KELs formalize a per-chunk value function

$$V(c_i) = \alpha \frac{f(c_i)}{\max_j f(c_j)} + \beta \exp\left(-\frac{\Delta t_i}{\tau_{\text{decay}}}\right) + \gamma \mathcal{D}_{\text{sem}}(c_i)$$

with $f(c_i)$ as interaction frequency, $\Delta t_i$ as recency, and $\mathcal{D}_{\text{sem}}(c_i)$ as semantic centrality in the knowledge embedding graph. This value steers chunk activation, semantic compression, or deletion via threshold partitioning (Wu et al., 29 Nov 2025).

Interpretability in LLMs: As a latent concept, a KEL can also be formalized as

$\mathrm{KEL}_\ell := (\bar h^{(\ell)}, G^{(\ell)})$

where $\bar h^{(\ell)} = \sum_{i \in I} w_i h_i^{(\ell)}$ (summary vector over tokens) and $G^{(\ell)}$ is a fact graph decoded from this representation. This yields a layerwise mapping from vector encodings to predicate graphs for granular interpretability (Bronzini et al., 4 Apr 2024).

2. Architectural Components and Workflow

SKA-Style Neural Layers:

• Each neural layer is augmented with a KEL tracking its own $z^{(\ell)}$ and $D^{(\ell)}$.
• The KEL module mediates stepwise entropy reduction, aligning $z^{(\ell)}$ with $\Delta D^{(\ell)}$ via local, forward-only updates.
• Standard activation functions like the sigmoid arise naturally from the minimization condition on the continuous entropy functional (Quantiota, 18 Mar 2025).

CogEvo-Edu Knowledge Base Management:

• The KEL is composed of four interacting submodules: spatiotemporal valuation (tracking $f(c_i)$, $\Delta t_i$, $\mathcal{D}_{\text{sem}}$), an activation mechanism (partitioning into active/condensed/deletable chunks), a semantic compression module (LLM-based summarization), and a forgetting process (removal of low-value chunks).
• Upon each system turn, all knowledge chunks in $\mathcal{K}$ are revalued, repartitioned, and the active store is exposed for downstream action selection (Wu et al., 29 Nov 2025).

Layer-wise LLM Reasoning:

• In LLMs, each KEL summarizes the knowledge embedded at a particular hidden layer as $(\bar h^{(\ell)}, G^{(\ell)})$.
• Patching $\bar h^{(\ell)}$ into a scaffold prompt and decoding the resulting output enables empirical recovery and analysis of the evolving internal knowledge graph (Bronzini et al., 4 Apr 2024).

3. Algorithmic Realizations and Pseudocode

SKA/KEL Forward Pass:

for k=1…K: for ℓ=1…L: z^(ℓ) = W^(ℓ)·X^(ℓ) + b^(ℓ) D^(ℓ) = sigmoid(z^(ℓ)) ΔD^(ℓ) = D^(ℓ) - D_prev^(ℓ) H_grad = −(1/ln 2)[ z^(ℓ) * (D^(ℓ)*(1−D^(ℓ))) + ΔD^(ℓ) ] ∂H/∂W = H_grad · (X^(ℓ))ᵀ W^(ℓ) = W^(ℓ) − η ∂H/∂W b^(ℓ) = b^(ℓ) − η ∂H/∂z X^(ℓ+1) = D^(ℓ) D_prev^(ℓ) = D^(ℓ)

This forward-only local update stands in contrast to backpropagation, requiring only signals local to each layer (Quantiota, 18 Mar 2025).

CogEvo-Edu KEL Routine:

for each chunk c_i in 𝒦: f_i ← retrieval count Δt_i ← recency D_sem(c_i) via average cosine over k-NN V_i = α·(f_i/max_j f_j) + β·exp(–Δt_i/τ_decay) + γ·D_sem(c_i) Partition: 𝒦_act = {c_i | V_i ≥ θ_solid} 𝒦_sol = {c_i | θ_forget ≤ V_i < θ_solid} 𝒦_del = {c_i | V_i < θ_forget} Delete all c_i in 𝒦_del; compress all c_i in 𝒦_sol with LLM_summ(c_i) Return 𝒦_act

This algorithm ensures the knowledge base dynamically adapts to interaction patterns and semantic structure (Wu et al., 29 Nov 2025).

4. Empirical Validation, Metrics, and Signatures

SKA KELs:

• Layerwise entropy $H^{(\ell)}_k$ decreases to equilibrium, with deeper layers converging faster (Fig. 2, (Quantiota, 18 Mar 2025)).
• Cosine alignment $\cos\theta^{(\ell)}_k$ between $z^{(\ell)}_k$ and $\Delta D^{(\ell)}_k$ rises steadily, indicating effective alignment of knowledge and decision evolution (Fig. 3).
• Clear separation in decision probabilities and layer-specific Frobenius norm dynamics confirm the hierarchical knowledge structuring predicted by the KEL formalism.

CogEvo-Edu:

• Dynamic KEL valuation and chunk management yield significant gains in factual correctness (+0.9) and contextual relevance (+2.2) versus static RAG on DSP-EduBench, highlighting improved knowledge precision and reduced “retrieval piling” ((Wu et al., 29 Nov 2025), Table 1).
• The active set of knowledge chunks prioritizes recent/high-value information; low-value or stale chunks are compressed or deleted, with temporal dynamics controlled by tunable decay constants and semantic density metrics.
• Hyperparameter adaptation orchestrated by the Meta-Control Layer (MCL) further optimizes retention-coverage trade-offs.

LLM Layerwise Evolution:

• KEL decoding reveals multi-phase knowledge flows, from entity resolution (early layers) through claim-level factual construction (mid-layers) to reasoning failures (late layers), as quantified by dynamic graph similarity metrics (Eq. (8)) and cluster analysis.
• Case studies (e.g., claim verification in FEVER) demonstrate direct mapping from hidden layer KELs to claim graph structures and error patterns (Bronzini et al., 4 Apr 2024).

5. Comparative Analysis and Theoretical Implications

A unifying feature of KELs across domains is the emphasis on local, temporally or structurally grounded optimization of knowledge representations:

• In SKA, this induces emergent activation functions (sigmoid) as a direct result of entropy minimization,
• Enables biologically plausible, massively parallel learning unattainable by global backpropagation,
• And organizes representation learning around local alignment between knowledge vectors and observed decision changes (Quantiota, 18 Mar 2025).
• In knowledge systems, KELs couple retrieval dynamics to spatiotemporal and semantic signals, transforming static retrieval-augmented generation into adaptive, compact knowledge processes (Wu et al., 29 Nov 2025).
• In LLM interpretability, KELs formalize the transition of hidden representations to explicit, layerwise predicate graphs, allowing detailed view of factual reasoning and reasoning failures at every processing step (Bronzini et al., 4 Apr 2024).

A plausible implication is that KELs provide a generic prescription for enhancing interpretability, parallelism, and adaptability in both connectionist and symbolic-AI regimes.

6. Variants, Hyperparameters, and Adaptive Control

Across reported frameworks, KELs expose critical hyperparameters for robust operation:

• SKA KELs primarily tune learning rates and initialization for per-layer knowledge vectors; the local entropy landscape structures learning trajectories (Quantiota, 18 Mar 2025).
• CogEvo-Edu KELs depend on $\alpha, \beta, \gamma$ (frequency/recency/semantic), thresholds $\theta_\text{solid}$, $\theta_\text{forget}$, temporal constant $\tau_\text{decay}$, and neighborhood size $k$. MCL modules adapt these using batch interaction metrics to maximize reward $J(\theta, \lambda) = \mathbb{E}[\sum_t r_t]$ (Wu et al., 29 Nov 2025).
• In the LLM KEL analysis, vector aggregation weights and predicate-decoder embeddings affect decoding sensitivity and specificity; clustering and similarity analyses tune the granularity of graph evolution metrics (Bronzini et al., 4 Apr 2024).

7. Contextual Significance and Applications

KELs operate as pivotal modules in:

• Autonomous neural learning with transparent, entropy-minimizing layers (SKA),
• Multi-agent cognitive systems for adaptive educational tutoring—dynamically evolving, pruning, compressing, or forgetting knowledge based on spatiotemporal relevance (CogEvo-Edu),
• Layerwise interpretability of LLMs, enabling direct inspection of factual knowledge and reasoning evolution via dynamic knowledge graphs.

KELs thus underpin advances in scalable, biologically plausible, and explainable learning across deep neural networks, symbolic representation systems, and emergent multi-agent platforms (Quantiota, 18 Mar 2025, Wu et al., 29 Nov 2025, Bronzini et al., 4 Apr 2024).