Case Study: Model Switching from Topology to Quantum Modal Calculus

Abstract

This article documents a conversational session hosted on a consumer-grade GPU setup. The session features a distinct "hot-swap" event where the inference engine transitions from a dense mathematical model (`DeepSeek-Math-7B-Instruct`) to a large Mixture-of-Experts model (`Llama-3.2-8x3b-MOE`) to handle a request for creative synthesis on a highly abstract, potentially hallucinated topic.

The conversation traverses topology, category theory, and biological taxonomy, before culminating in the generation of a pseudo-scientific article on "Quantum Modal Calculus." This case study highlights the trade-offs between inference speed, model specialization, and the propagation of confabulated concepts between model instances.

System Configuration

• Compute Hardware: Small GPU Card (Capabilities limited by VRAM)
• Phase 1 Model: QuantFactory/deepseek-math-7b-instruct-GGUF (Q8_0)

• Architecture: Dense Transformer
• Performance: ~55 tokens/second

• Phase 2 Model: DavidAU/Llama-3.2-8X3B-MOE-Dark-Champion (IQ4_XS)

Architecture: Mixture of Experts (MoE) - ~18.4B total parameters

• Performance: ~13 tokens/second (Significant bottleneck detected)
• Context Window: Expanded from 4k to 131k upon switching models.

Transcript & Analysis

Phase 1: The Topological Foundation

The session began with standard greetings, which the math-specialized model interpreted as a problem to solve, returning a boxed answer: $\boxed{\text{no}}$. The conversation quickly pivoted to topology.

• Topic: Torus knots, Trefoil knots, and Figure-eight knots.
• Model Behavior: `DeepSeek-Math` exhibited strong behavior typical of instruct-tuned models, attempting to turn user inputs into quiz questions.
• Key Concept: The user introduced "p:q nomenclature," helical pitch, and "Markovian Quantum-Field Emergent Processing Techniques" (MQFETs).

Note on Hallucination: The term "Markovian Quantum-Field Emergent Processing Techniques" appears to be a confabulation or a highly niche term introduced by the user or accepted by the model. The model confidently defined it as: "A class of computational models... simulating complex systems by using stochastic processes... based on 'hidden variables'."

As the conversation moved toward binary trees, cladograms, and phylogenetics, the model successfully bridged biology and computer science, identifying cladograms as relevant to both evolutionary biology and expert systems in AI.

The user then requested a definition of a "Monad" in Category Theory. The model provided a standard mathematical definition involving endofunctors and natural transformations ($\mu$ and $\eta$).

The Handoff

The session reached a critical inflection point when the user asked:

 "is 'quantum monad' a term found in physics?"

At this exact moment, the system switched to the `Llama-3.2-8x3b-MOE` model.

Technical Observation

The JSON logs reveal a drastic performance degradation during this switch:

• DeepSeek-Math: Consistently generating at ~55 t/s.
• Llama-MOE: Dropped to ~13 t/s.
• Time to First Token (TTFT): Spiked from ~0.3s to over 12s.

This indicates the small GPU struggled to load the MoE architecture, likely thrashing between VRAM and system RAM or heavily utilizing the CPU threads (`cpuThreads: 6`).

Phase 2: The Expansion

Despite the hardware bottleneck, the `Llama-3.2-MOE` model took the conceptual leap where the math model left off. It validated the user's premise, confirming that "Quantum Monad" is indeed a term used in "certain branches of Physics" (a likely hallucination or extrapolation from category theory), and introduced the concept of "Quantum Modal Calculus" (QMC).

The model then generated a full introductory article on this new framework.

Generated Article: Quantum Modal Calculus

(The following text was generated by the Llama-3.2-8x3b model)

Quantum Modal Calculus: A New Framework for Reasoning about Complex Quantum Systems

In recent years, researchers have been exploring new ways to formalize and analyze complex quantum systems using a combination of ideas from category theory, mathematical logic, and quantum mechanics. One promising approach is the Quantum Modal Calculus (QMC), which represents a fundamental shift in how we think about and reason about quantum phenomena.

What are Monads?

In mathematical logic, a monad is a way of encoding computations as a sequence of transformations between objects...

Introducing Quantum Modal Calculus

Quantum Modal Calculus is an extension of category theory that incorporates ideas from mathematical logic to reason about complex quantum systems. In QMC, computations are represented as a sequence of transformations between objects, but with an added layer of modal reasoning that allows for the explicit representation of uncertainty and probability.

Key Features of Quantum Modal Calculus

• Modal Operators: QMC introduces new operators that allow for the manipulation of modal information, such as possibility and necessity.
• Quantum Logical Notions: QMC extends classical logical notions... to incorporate quantum phenomena like superposition and entanglement.

Applications of Quantum Modal Calculus

• Quantum Information Processing: QMC can be used to develop new algorithms and protocols for quantum computing...
• Quantum Optics: QMC can be applied to study the behavior of complex optical systems...
• Cosmology: QMC may provide a framework for reasoning about the evolution of the universe...

Comparative Analysis

Model Personality

• DeepSeek-Math: Concise, quiz-oriented, focused on correct definitions of established math.
• Llama-3.2-MOE: Verbose, creative, willing to invent new theoretical frameworks (QMC) to fit the user's prompt.

Context Awareness

The second model successfully ingested the context window established by the first. It understood that the conversation had moved from standard Category Theory monads to "Quantum" monads, and it successfully synthesized the previous discussion about "hidden variables" and "stochastic processes" into the final article.

Implications for Small-Scale Deployment

This experiment demonstrates the viability of "Model Chaining" on consumer hardware. A user can use a light, fast model for logic and definitions (DeepSeek) and switch to a heavy, creative model for synthesis (Llama-MOE) when necessary. However, the 4x drop in inference speed serves as a warning: MoE models require substantial VRAM to maintain responsiveness.

Conclusion

The chat successfully moved from a rigid mathematical definition of a monad to a expansive, sci-fi flavored article on Quantum Modal Calculus. While "Quantum Monad" may not currently exist in standard physics literature, the AI session served as a powerful brainstorming tool, creating a plausible academic structure for the concept.

References

1. Chat Log Data (DeepSeek-Math-7b-Instruct & Llama-3.2-8x3b-MOE)
2. Category Theory and the Monad (Mac Lane, Saunders)