The phenomenon known as model collapse provides an illuminating case for VGF analysis. Research on generative AI has shown that, under particular training regimes, models repeatedly trained on data generated by earlier models can progressively lose information about the distribution represented in the original training data. Rare structures may disappear, common structures may become disproportionately reinforced, and distortions introduced by one generation can become part of the apparent training reality of the next.

In VGF terms, there is a natural reason why such a process should occur. If an artificial system is recursively trained only on its own stabilised outputs, the recursion progressively loses access to the wider possibility spaces from which those outputs were originally generated. Stabilisation begins to outrun reopening.

1. Human cultural output is already a stabilised projection

The starting point is the distinction between human conceptualisation space and its externally expressed symbolic products.

A human conceptual state contains a much richer network of associations, memories, embodied contexts, uncertainties, affective relations and possible interpretations than can normally be expressed in a single sentence or document.

In VGF notation, the movement from human conceptualisation into symbolic expression can be represented schematically as:

Here, β_H represents the comparatively open relational domain of human conceptualisation, while γ_H represents its more stable linguistic or symbolic expression.

Human cultural artefacts — language, books, articles, mathematical notation, images, software, recorded conversations and other symbolic products — can therefore be regarded, in the generalised VGF sense, as gamma stabilisations produced from much richer human possibility spaces.

A large AI training corpus consequently contains enormous numbers of such stabilisations:

Behind those expressions, however, lie enormous numbers of partially independent human conceptualisation spaces:

This distinction is important. Although the training corpus itself consists predominantly of stabilised symbolic products, those products were generated by systems whose possibility spaces extend far beyond the corpus itself.

2. AI learns a further transformation of those gamma products

Training an AI model does not reproduce the original human conceptualisation spaces. Nor does the resulting model simply contain a literal copy of its training corpus.

Instead, training produces a parameterised model of regularities occurring within the training distribution:

where Γ_H denotes the large collection of human symbolic outputs and M₀ denotes the resulting trained model.

When the model generates new material, it produces another symbolic stabilisation:

The overall transformation is therefore approximately:

The generated AI output is not a fresh sample directly from the human conceptualisation spaces that originally produced the training culture. It is generated from the model's learned approximation to regularities within their externalised products.

That difference becomes crucial when AI-generated output itself is made the exclusive source of subsequent training.

3. An image of an image becomes the new source

Consider a model M₀ whose generated outputs are used to train a second model M₁:

If M₁ then supplies the training material for M₂, the recursion becomes:

What has disappeared from this sequence is the independent human beta domain.

The new generation is no longer being continually supplied with distinctions generated by wider human conceptualisation spaces. Instead, it is being trained upon stabilised products generated by its artificial predecessors.

In VGF terminology the process resembles:

but without a sufficiently independent possibility space continually reopening the recursion from outside itself.

4. Why the tails of the distribution are vulnerable

The empirical model-collapse literature places particular emphasis on the progressive loss of relatively rare structures in the original distribution.

Suppose the original cultural dataset is described by some distribution:

A trained model constructs an approximation:

The approximation cannot be perfect. Structures occurring very frequently in the original distribution will generally be easier to reproduce reliably than extremely unusual or low-frequency structures.

Once the next training corpus is sampled from P_M0 rather than from the original distribution, underrepresented possibilities have another opportunity to disappear.

The recursion becomes:

Low-probability distinctions are particularly vulnerable because they possess comparatively little redundancy within the generated corpus.

In VGF terminology:

Low-redundancy regions of the possibility distribution are progressively vulnerable to elimination because each gamma stabilisation preferentially reproduces structures that were already sufficiently stable to survive the preceding reduction.

5. Model collapse as recursive over-stabilisation

This suggests a particularly simple VGF interpretation of model collapse.

Highly represented structures are repeatedly regenerated:

A rare structure has a greater probability of dropping out:

The effective represented possibility space therefore tends to contract:

This notation should not be interpreted as requiring a strict mathematical subset relation at every generation. It represents the broader tendency for successive recursive reductions to lose faithful representation of some modes of the original distribution.

Meanwhile, dominant attractors become increasingly reinforced.

Model collapse can therefore be interpreted as an instance of the VGF Stability–Fidelity relation.

6. Model-generated distortion becomes training reality

There is a second recursive problem.

Suppose the first model introduces a small distortion ε₀:

If output from that model is subsequently treated as training data, the next model has no intrinsic way of knowing that ε₀ was a departure from the original distribution.

For the next training process it is simply part of the available data:

The second model may then add another distortion ε₁:

The recursive system is consequently capable not merely of becoming less diverse, but also of drifting away from the distribution from which it originally learned.

A closure generated by the system is recursively being treated as evidence concerning the possibility space from which the system itself should subsequently generate.

The distinction between the representation and the source of the representation begins to disappear.

7. Why the human–AI loop is different

This provides an important contrast with the recursive human–AI interaction considered elsewhere in VGF analysis.

The human–AI loop can be represented as:

Something important occurs at the final transition.

The AI output encounters an independent human conceptual system whose possibility space is not exhausted by the AI's own preceding output.

A human may:

• reject the AI's conclusion;
• reinterpret it;
• connect it with embodied or experiential knowledge;
• compare it with empirical evidence;
• bring in memories or contexts absent from the AI interaction;
• recognise an unstated assumption;
• or generate a new question not previously represented in the loop.

Thus:

can constitute genuine reopening because β_H′ possesses degrees of freedom that were not generated solely by the preceding AI output.

The next human contribution can consequently introduce material from outside the AI's own recursive trajectory:

8. Open recursion and closed self-recursion

VGF analysis therefore permits a useful distinction between two types of recursive system.

Open recursion

Here each system can perturb the other from a possibility space that is not entirely generated by the other's immediately preceding output.

The characteristic process is:

Closed self-recursion

Here each generation is increasingly dependent upon the stabilised outputs of preceding artificial generations.

The tendency becomes:

In the VGF interpretation, this represents a regime in which stabilisation progressively outruns reopening.

9. Synthetic data does not inevitably cause collapse

An important scientific qualification is required.

Model-collapse research does not justify the general claim that all use of synthetic data inevitably damages AI models.

The outcome depends strongly upon the training regime. Preserving original real data, mixing synthetic and non-synthetic material, accumulating rather than replacing high-quality source data, filtering generated material, and otherwise maintaining access to a sufficiently rich reference distribution can substantially change the result.

This qualification actually strengthens the VGF interpretation.

The central question is not simply:

It is:

If such access is maintained, reopening remains possible.

If it is progressively removed, recursive stabilisation increasingly dominates.

10. Model collapse and the Stability–Fidelity Law

Model collapse therefore provides a particularly useful computational illustration of the VGF Stability–Fidelity Law.

Recursive generation can increase the redundancy of already dominant structures. Those structures consequently become increasingly stable within the generated distribution.

But the same process may progressively eliminate weakly represented alternatives.

Thus increasing stability within the recursively generated distribution can coincide with decreasing fidelity to the richer possibility distribution from which the recursion originally arose.

In this interpretation, the problem is not recursion itself. Recursion is generative when it includes reopening.

Collapse occurs when recursive stabilisation ceases to be adequately counterbalanced by renewed access to degrees of freedom outside the system's own previously stabilised outputs.

11. The human as a source of external reopening

This leads to an important interpretation of the human role in human–AI interaction.

The human does not merely supply additional tokens to the AI system. Human conceptualisation space provides an external source of reopening.

The human receives:

and reopens it within:

The result may then be transformed into a new human gamma output:

That new output returns material to the AI loop that is not simply a reproduction of the AI's preceding probability distribution.

Human and AI systems can therefore participate in a recursive relation capable, at least in principle, of continuing to reopen rather than merely progressively restabilise their previous outputs.

12. The VGF proposition

From this perspective, model collapse is not an anomalous failure of recursion. It illustrates a general property of recursive systems: iteration becomes generative only insofar as previously stabilised structures remain capable of being reopened into a sufficiently rich possibility space.

This also clarifies the potential significance of recursive human–AI coupling. Human conceptualisation can supply precisely the kind of external reopening that is absent from a completely self-consuming artificial loop.

The crucial distinction is therefore between a system recursively consuming only its own closures and a coupled system in which each closure can encounter a possibility domain not exhausted by the preceding iteration.