> For the complete documentation index, see [llms.txt](https://neurosymbolicai.gitbook.io/neuro-symbolic-ai-in-practice/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://neurosymbolicai.gitbook.io/neuro-symbolic-ai-in-practice/part-iii-core-approaches/chapter-4/4-4-pure-neural.md).

# 4.4 Pure Neural World Models

> *"The question is not whether to use formal structure or learned representations. It is: at which level of the system should formal structure appear — and what guarantees does it provide there?"*

***

The three paradigms of §4.1–4.3 all incorporate formal symbolic representations as *separate, externally defined components*: a constraint layer, a correctness oracle, a knowledge graph, a PDDL file. **§4.4** covers approaches where no such separate external symbolic component exists.

> **What "Pure Neural" means precisely:** The label refers to the *absence of a separately defined external formal oracle or symbolic module* — not the absence of all structure. §4.4.1 (DAI) *does* use formal abstract lattice theory, but this structure is *embedded within the neural architecture itself* rather than existing as an external component. §4.4.2 (JEPA-WMs) uses no formal symbolic structure of any kind. Both share the key property that planning operates without calling out to a separate symbolic correctness oracle — which is what distinguishes §4.4 from §4.1–4.3.

**§4.4** examines two distinct architectural strategies for achieving this:

**§4.4.1 Differentiable Abstract Interpretation (DAI)** embeds the symbolic abstract domain *directly into the neural representation space*. There is no external symbolic component — the lattice IS the transformer's latent space, and each forward pass approximates a sound deduction operator. The Lattice Deduction Transformer achieves 100% accuracy on Sudoku-Extreme where frontier LLMs score 0%.

**§4.4.2 JEPA World Models** operate entirely in continuous learned feature space: self-supervised representation learning (V-JEPA) → action-conditioned world model prediction → model-predictive control optimization. No pixel reconstruction, no reward annotation, no formal symbolic structure — and +20 percentage points in real-robot grasping over prior baselines (V-JEPA 2.1, 2026).

**Why a separate paradigm?** Both approaches share a key property: their planning operates without a formal correctness oracle. This makes them the natural counterpoint to the book's neuro-symbolic thesis. The critical open question — whether these approaches can ever provide the correctness guarantees that formal verification offers — is examined in §5.1 and §5.2.

***

## Sections

* [4.4.1 Differentiable Abstract Interpretation](/neuro-symbolic-ai-in-practice/part-iii-core-approaches/chapter-4/4-4-pure-neural/4-4-differentiable-abstract-interpretation.md) — Abstract lattice as neural representation; Lattice Deduction Transformer
* [4.4.2 JEPA World Models](/neuro-symbolic-ai-in-practice/part-iii-core-approaches/chapter-4/4-4-pure-neural/4-4-jepa-world-models.md) — Feature-predictive physical planning; V-JEPA, JEPA-WMs, V-JEPA 2.1


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