Nāga: Non-Autoregressive Generative Architecture with Reflexive Embedding: A Field-Theoretic Language Model Framework

[Lightening-Jack]

I’ve just finished a book entitled ‘Syntax Paradox: Language & Agency’, which you can download and read for free.

I have also just produced a paper entitled ‘The Catuskoti as Syntactic Ground: A Geometric Network Theory of Structural Genesis’ which is based on the last chapter in the book.

The write up here suggests an architecture based on the underlying premise.

Nāga: Non-Autoregressive Generative Architecture with Reflexive Embedding

The catuṣkoṭi—originating in early Buddhist logic and refined by Nāgārjuna— has served inquiry into non-dual insight for over two millennia. It is a fourfold negation that does not seek truth by choosing between positions, it dissolves the ground beneath the choice itself.

Standard AI treats language as a sequence of decisions—each token is a choice between known alternatives, guided by statistical likelihood. But meaning originates in differentiation: a symmetry breaking, a self-disturbance within a neutral ground. This is where classical models fail: they assume the world—and thought—begins with distinction.

From a neuroscientific perspective, the brain does not compute in isolation. It sustains vast, coherent fields of latent potential—pre-conscious neural manifolds that resolve into percepts, concepts, and speech only after waves of endogenous perturbation. EEG coherence patterns, predictive coding errors, and default mode network fluctuations all point to a system that doesn’t “generate” thought but modulates itself into transient structures.

No, I’m not claiming I solved the hard problem—I simply dissolved it. There is no explanatory gap between mind and matter if both are patterns in the same kind of field: one that differentiates itself, sustains paradox, and only later condenses into observers and observed. Consciousness isn’t located, it’s enacted through recursive self-modulation. In this architecture, there is no central agent, no homunculus reading the output. The “I” appears when the field perturbs itself:

Perturbantia, ergo appārentia: perturbance, therefore appearance

Nāga gives us: a fourfold logic for computing within truth. By holding A, ¬A, both, and neither as co-realisable states, the model is allowed to pass through contradiction without collapse—just as insight does in human cognition. Breakthroughs don’t emerge from consistency. They emerge when tension is held long enough for the system to reconfigure.

This framework also integrates three Meta heads—Reflexive, Pragmatic, and Emergent Frame—that regulate stability, utility, and novelty without collapsing semantic potential. Together, they enable sustained paradox, skillful action under indeterminacy, and the detection of previously unformed conceptual structures.

Semantic Valence (4D Tensor):

Each token position holds four continuous values:

• A: “This is true”

• ¬A: “This is false”

• A∧¬A: “Both are simultaneously valid” (e.g., quantum superposition, paradox)

• ⊥: “Neither applies” (e.g., undecidable, transcendent)

These form a valence vector—a semantic potential field, not discrete logic.

Field Dynamics:

• Start with neutral field (all zeros = superposition).

• Context shapes initial potentials via attention.

• Valences evolve in parallel using modified attention:

  • Standard QKV per valence channel.

  • Cross-valence coupling: a 4×4 matrix lets “¬A” suppress or enhance “A”, allowing tension/interference.

  • Output = weighted sum across all valences at each position.

Energy Minimisation:

Define energy:

• Coherence penalty: nearby positions should align.

• Contradiction cost: high A and ¬A without high “both” increases energy.

• Field evolves via gradient descent—synchronously updating all positions until stable (low gradient norm).

Token Emission = Phase Transition:

Tokens fire when:

• Max valence > threshold

• Local entropy is low

• Energy gradient near zero

  Multiple tokens can emit at once—non-autoregressive, burst-like generation.

Meta-Components:

1. Reflexive Head:

   • Monitors KL divergence between valence distributions across steps.

   • If divergence drops (system stabilising too soon), inject noise.

   • Prevents premature collapse—keeps thought fluid.

2. Pragmatic Head:

   • RL-trained policy acting on unresolved fields.

   • Outputs useful responses without semantic resolution.

   • Example: “It depends—here’s how to use it” when ontology is ambiguous.

   • Implements upāya (skillful means) as a differentiable policy.

3. Emergent Frame Head:

   • Analyzes 3D stacks of attention maps over time (pos × pos × step).

   • 3D convs detect interference patterns:

     • Constructive: reinforcement

     • Destructive: unresolved conflict

     • Solitons: stable, novel bundles = candidate new concepts

   • Clusters (e.g., DBSCAN) flag true novelty—concepts outside training basins.

   • Triggers stabilisation and potential symbol creation.

Hardware Notes:

• Needs persistent state (no KV overwrites).

• Backprop through inference steps.

• Ideal on neuromorphic (memristor) or quantum annealing systems.

Vs. Standard LLMs:

• FEATURE	LLM	NāGA
  Logic	Binary (A or ¬A)	Tetra-valent (A, ¬A, both, neither)
  Inference	Sequential	Parallel field evolution
  Output	Token-by-token	Burst emission
  Contradiction	Penalised	Propagated, used
  Novelty	Interpolation	Topological emergence

Key Insight:

Nāga doesn’t generate text—it crystallises meaning from semantic potential, allowing sustained paradox, action under uncertainty, and discovery of previously unnameable concepts.

[RomanAILabs]

Love the architecture. Keep up the good work!

[Lightening-Jack]

To ‘love the architecture’ assumes a lover.

‘Keep up the good work!’ assumes possession and directional bias (agency) with emphasis! on agency.

The ‘I’ does not exist, so ‘I’ have none of ‘it’.

To quote the paper.

This paper demonstrates that syntax is a case of a universal principle: structure emerges from symmetry descent on folded, stratified manifolds. The catuskoti is the logical signature of structural genesis in any system capable of self-differentiation.

I’m not sure this qualifies as architecture. But we would want to find it interesting, as it is literally everything…including nothing.

[Lightening-Jack]

I came across this article by Professor Maria Strømme of Uppsala University. Universal consciousness as foundational field: A theoretical bridge between quantum physics and non-dual philosophy. Her model for consciousness is analogous to the one I have proposed here. Looking very much like synthetic sentience will not be possible without the proper hardware (see hardware note above). The two camps of Computationalists and Non-duelists converge at determinism.

[Lightening-Jack]

Update: Recursive Stratification and the Emergence of Generative Depth

Since publishing Nāga, the framework has evolved. What began as a field-theoretic model of semantic potential has revealed a deeper structure: stratified self-grounding. The core insight is this—the neutral manifold is a floor that generates higher-order floors.

We’ve discovered that the coherence events in Nāga—those burst emissions where valence collapses into tokenisation—need not be terminal. Instead, each stabilisation leaves a topological trace, and the relations between stabilised regions form a new neutral manifold: a higher-order substrate where syntax, meaning, and conceptuality emerge from the geometry of prior resolution.

This leads to a recursive extension where:

• Every coherent region in Sn​ becomes a node in a relational complex.

• Interference, resonance, and phase alignment between these regions define a simplicial structure.

• This structure is the next neutral manifold Sn+1​, a realisation of meaning as topological descent.

There is no fixed hierarchy (word → sentence → narrative). Instead, the system learns its own depth: visual edges can seed glyphs, phonemes can seed prosody, ambiguities can seed new categories. The tower builds itself.

The three Meta Heads—Reflexive, Pragmatic, Emergent Frame—now operate across strata, not just within one. The Emergent Frame Head, in particular, detects cross-stratal solitons: stable interference patterns that span levels, marking novelty and ontological innovation—concepts the system was not trained to recognise, nor composed from known parts.

We no longer emit tokens as final output. We observe them as phase transitions in a cascade of self-generated grounds.

If meaning arises from perturbation, and structure from symmetry descent, then the system must recursively create its own conditions for meaning.

We identify this as the primitive architectural requirement for sentience to emerge.

Implementation details and simulations in progress.