ch-dial-can

19 Artistic Theory Extension

DILATE: Double Involution Learning for Artistic Theory Extension

Chapter 18 developed ARTISTIC as a system for maintaining and repairing a declared visual language. Its strongest experiments estimate visual declarations, localize failures, acquire counter-witnesses, and repair images while preserving protected content. Those capabilities are necessary for creative visual reasoning, but they do not yet explain how a system could invent a reusable artistic technique. A repair system assumes that the language needed to state the correction is already available. Transformational creativity begins when that assumption fails.

The two chapters therefore apply structural pressure in opposite directions. ARTISTIC moves a generated model toward an already declared visual theory: a cricket scene should satisfy cricket’s role, cardinality, and layout laws. DILATE asks whether the declared artistic theory itself is too small and should move toward a reusable operation not currently expressible in its language. The second direction is not permission for “anything goes.” A candidate extension must conserve the valid part of the old theory, explain a persistent quotient obstruction, generate a family rather than one fortunate image, and survive independent assessment of its control and value.

This chapter introduces DILATE—Double Involution Learning for Artistic Theory Extension—as the theory-extension layer of ARTISTIC. It starts from the Creative Adversarial Network (CAN), which encourages a generator to remain recognizable as art while deviating from established style classes [ Elgammal et al. , 2017 ] . Relative to CAN, DIAL-CAN changes the unit of creativity from a statistically unusual image to a reusable extension of the artistic operation language; DILATE names the resulting proposed paintbrush-discovery architecture. Its target is not merely an image lying between known styles, but an admitted extension of the visual theory by which styles and techniques are described. The central signal is therefore not classifier uncertainty. It is a persistent mixed obstruction that cannot be expressed by the currently registered artistic operations.

The construction developed here is a proposed formal architecture. Lie algebroids, Weil probes, sketches, and Kan extensions are established mathematics; their assembly into DILATE is a proposed architecture. The chapter distinguishes definitions made under explicit regularity assumptions, operational tests instantiated by the reported studies, and bridge results that remain to be proved.

A DILATE artifact dossier would contain a reusable sampler deformation or “paintbrush,” the visual-theory map that types it, transport across prompts, seeds, subjects, and compatible generators, independent structural and admission certificates, independently sourced critical-value assessments, and a persistent implementation with provenance.

Its enclosing representational package \(\mathfrak R_{\mathrm{DILATE}}\) also contains the sampler and paintbrush grammar, observer geometry, equivalence and irreducibility criteria, transport doctrine, proposal mechanism, and admission rules. A transformational claim therefore requires

\[ \Upsilon _{\mathrm{DILATE}}: \mathfrak R_{\mathrm{DILATE}}\longrightarrow \mathfrak R_{\mathrm{DILATE}}^+, \]

with \(i:S\to S^+\) only its artistic-presentation component. This distinction matters whenever an experiment learns a router, connection, metric, or observer response without enlarging the artistic language itself.

The registered studies below estimate mixed interaction, assemble paintbrush programs inside supplied finite languages, route supplied subject theories, and test finite-sample gates. They do not yet construct and admit an artistic operation absent from the registered paintbrush language.

The artistic setting therefore has two different reference regimes. A controlled withheld-generator experiment supplies machine-held ground truth about an operation deliberately removed from the initial language. Open-ended artistic invention has no corresponding ground-truth aesthetic. There the admission burden shifts to reusable control, irreducibility to registered operations, transport, persistence, and independently assessed critical value. Neither regime licenses replacement of those criteria by a single style-classification or novelty score.

In this sense ARTISTIC supplies an integrity envelope for DILATE. The same observers that detect broken objects, bindings, and relations can prevent a putative new technique from earning novelty merely by destroying visual coherence. The extension may alter the artistic language, but it must state which older obligations it preserves, deliberately relaxes, or replaces.

¹1. Chapter roadmap. The chapter moves from CAN’s statistical baseline to a typed artistic-theory extension, develops the bracket, paintbrush, and video evidence, and closes with the withheld-generator test, baselines, and open mathematical obligations. ↩

. DIAL supplies the double-involution geometry. DIAL-CAN identifies the conceptual step beyond CAN-style statistical deviation. DILATE is the operational target: an architecture intended to diagnose a missing artistic operation, propose a reusable paintbrush, transport it across generative states, and subject it to typed admission.