Dual Layer Lexical Transformations

• Dual layer lexical transformations are mechanisms mapping lexical data across distinct layers in computational models and social networks to enhance interpretability and facilitate multilingual transfer.
• They employ linear and affine mappings—such as relational extraction in transformers and targeted lexical injection—to decode morphological rules and improve cross-lingual alignment.
• These methods also simulate language evolution by modeling interactions between social and media layers, shedding light on semantic drift and the emergence of polysemy.

Dual layer lexical transformations encompass a class of mechanisms and methodologies by which lexical information—such as word forms, meanings, and alignments—is mapped, modified, or propagated across distinct representational layers in both computational LLMs and networked language communities. The term encompasses explicit cross-layer mappings within transformer architectures, coordinated interventions in multi-layer neural finetuning, and dynamic interactions between structurally distinct layers (such as “social” and “media” strata) in evolutionary LLMs. Contemporary interest in this paradigm has expanded due to its relevance for interpretability, efficiency in multilingual transfer, language change modeling, and the manipulation of internal lexical structure in LLMs.

1. Definition and Theoretical Foundations

Dual layer lexical transformations are formally defined as explicit mappings or interaction protocols that translate lexical representations from one layer or substrate to another. In computational models, this corresponds to a transformation $F_r: x^\ell_s \mapsto x^L_o$ where $x^\ell_s \in \mathbb{R}^d$ is the hidden state associated with a “subject” token at a source (typically earlier) layer $\ell$, and $x^L_o \in \mathbb{R}^d$ is the corresponding “object” token state at a destination (usually final) layer $L$ (Xia et al., 19 Jul 2025). In social-dynamical models, dual-layer structures may partition transmission routes or innovation flows between, for example, an agent-based “social” layer and an information-dispersing “media” layer (Javarone, 2013).

The appeal of dual-layer approaches derives from the observation that certain relational, morphological, or cross-lingual properties are more linearly or sparsely encoded at intermediate layers, but may become enmeshed or attenuated at deeper layers due to non-linear transformations, motivational regularization, or aggregation effects. Consequently, targeting, extracting, or modifying lexical structure at multiple layers enables both a mechanistic understanding and practical manipulation of model behaviors.

2. Linear and Affine Cross-Layer Decoding in Transformer LMs

In neural LMs, especially transformer architectures, dual-layer lexical transformation is operationalized via cross-layer relational extraction (LRE). Here, the aim is to recover or enforce a relationship (e.g., morphological or semantic) connecting two tokens by learning an explicit linear or affine mapping between their respective hidden states. Given $s = x^\ell_s$ (subject layer) and $o = x^L_o$ (object layer), the transformation is:

• Affine LRE:

$\hat{o} = \beta W_r s + b_r$

• Linear LRE (single-matrix):

$\hat{o} = W_r s$

where $W_r$ is a $d \times d$ Jacobian estimated by averaging $\frac{\partial o_i}{\partial s_i}$ across in-context demonstration pairs, $b_r$ is a bias accounting for layer norm and residual mismatches, and $\beta$ is a scale to compensate for norm compression (Xia et al., 19 Jul 2025).

Xia & Kalita demonstrate that for a diverse set of morphological relations (“[noun → plural]”, “[adj → comparative]”, etc.), the linear LRE achieves ≈90% token-level faithfulness, with the affine variant reaching ≈95%. The mapping $W_r$ is empirically sparse—only a low-dimensional subspace of directions is actively modulated—suggesting that morphological rules correspond to localized multiplicative circuits in residual stream space. Application of this approach to multiple models (GPT-J, Llama-7B) and languages (DE, FR, HU, PT) confirms the robustness of the dual-layer linear mechanism.

3. Dual-Layer Interventions for Cross-Lingual Lexical Alignment

Beyond static mapping, dual-layer structure enables parameter-efficient propagation and anchoring of lexical alignments in large LMs. In Targeted Lexical Injection (TLI), an empirically optimal “alignment layer” is identified—Layer 2 in Lugha-Llama’s case, with cosine similarity ≈0.99998 for Swahili–English translation pairs (Ngugi, 18 Jun 2025). LoRA-based adapters are then inserted into this early layer and fine-tuned with a contrastive objective. The update rule:

$W' = W + \Delta W, \quad \Delta W = BA,$

with $A, B$ of low rank, restricts modifications to a subspace, ensuring efficiency.

The fine-tuning maximizes cosine similarity for correct translation pairs and pushes negatives apart via hardest-in-batch triplet penalties. The dual-layer propagation effect is that small corrections at the optimal alignment layer are preserved and amplified through the deeper network, with final output similarity improving by 28% (from ≈0.32 to ≈0.41) for both trained and unseen control word pairs—demonstrating strong generalization and validating the dual-layer propagation hypothesis (Ngugi, 18 Jun 2025).

4. Dual-Layer Models in Lexical Innovation and Language Evolution

Outside neural architectures, dual-layer constructs arise in agent-based models of lexical innovation, where population-level dynamics are mediated by interactions between two structurally distinct network layers—typically, a “social” network (undirected, dense acquaintances) and a “media” network (directed, sparse, mass-broadcast) (Javarone, 2013).

In Javarone’s framework, lexical innovations (signifiers) are diffused and negotiated through dual layers, with social links propagating both form and meaning (driving negotiation and consensus), whereas media links introduce signifiers without meaning (seeding misunderstanding and polysemy). The formalism leverages:

• A population $S$ of agents and a set $M$ of media nodes.
• Transient, directed edges transmitting innovations between and within layers.
• State transitions characterized by negotiation rules (success probabilities $W_i$, $W_j$ based on confirmation counts $\sigma_{i,k}$ and fitness $\nu_k$).

Simulation results reveal that fully connected and scale-free social layers drive rapid consensus on the most “fit” meaning, while small-world, locally connected layers support long-lived polysemy and spatial domains of meaning. The dual-layer interplay modulates the balance between semantic drift, translation, and conventionalization.

5. Methodologies for Estimation and Evaluation

Cross-layer mappings in auto-regressive LMs are estimated using a first-order Taylor approximation. For a relation $r$, $k$ in-context demonstration pairs $(s_i, o_i)$ are sampled, and the Jacobian $W_r$ is computed by backpropagating from final-layer object states to middle-layer subject states:

$$W_r = \frac{1}{k} \sum_i \frac{\partial o_i}{\partial s_i}, \quad b_r = \frac{1}{k} \sum_i [o_i - W_r s_i].$$

No additional loss minimization is applied. Faithfulness is evaluated by checking whether the decoded token from $\hat{o}$ matches the LM’s own output for $o$ (Xia et al., 19 Jul 2025). In the TLI framework, layer-scanning identifies latent alignment maxima, and LoRA adaptation is restricted to low-rank bases, tuned by hardest-in-batch contrastive or InfoNCE losses. Evaluation relies on cosine similarity across aligned pairs and rigorous significance testing over held-out control sets (Ngugi, 18 Jun 2025).

In network models, empirical density curves, scaling with agent number $N$, and time-to-consensus $T_s$ are measured, with power-law decay exponents $\gamma$ varying with layer topology (Javarone, 2013).

6. Applications, Implications, and Limitations

Dual-layer lexical transformation supports the following:

• Model interpretability: Linear LREs reveal interpretable, sparse circuits in neural LMs for regular morphological rules.
• Parameter-efficient transfer: TLI demonstrates that targeted, early-layer adaptation can improve multilingual lexical alignment with minimal risk of catastrophic forgetting.
• Model editing: Dual-layer maps enable imposed or modified lexical relations by directly replacing $W_r$.
• Language evolution simulation: Agent-based dual-layer frameworks explain how media-driven transmission interfaces with community negotiation to shape polysemy, lexical replacement, and language change.

Limitations include restriction of experimental evidence to moderate-size models (GPT-J, Llama-7B, Lugha-Llama-8B-wura), and—especially in LREs—a lack of causal evidence for $W_r$ driving token selection during generation, as opposed to post hoc matching. Fine-tuning and innovation models are currently limited to word-level relations; extension to phrase- or discourse-level structure remains an open challenge.

7. Comparative Summary of Key Results

Approach	Domain	Layer Role	Metric/Result
Linear/Affine LRE (Xia et al., 19 Jul 2025)	Transformer LM	Middle → Final hidden	Morph. faithfulness ≈90–95%
TLI (Ngugi, 18 Jun 2025)	LLM, cross-lingual	Early alignment → output	Cosine sim. Δ ≈+28% (output)
Dual-layer network (Javarone, 2013)	Language evolution	Social ↔ Media diffusion	Polysemy/convergence regime

Each methodology leverages dual-layer structure to either decode, align, or propagate lexical information, revealing interpretable geometry or emergent population-level outcomes. The mechanisms are robust to language, model architecture, and in the case of agent-based networks, network topology.

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Dual-layer lexical transformations constitute a foundational analytical and practical paradigm for both interpreting and intervening in the lexical properties of artificial language systems and, by analogy, understanding the co-evolution of form and meaning in social communication.