FlexCartesian

Explore real systems as functions of parameters.

Build a holistic digital twin in four steps: describe parameters, model system behaviour, capture real data, and derive insights. From bottlenecks to best practices - and beyond. Any question, answered in one line of code.

Fragmented knowledge.

Real systems are defined by multiple independent parameters. Each configuration is just one observation in a much larger space. Yet exploration is typically performed through isolated runs: ad-hoc benchmarks, biased experiments, manual comparisons, and fragmented logs. These observations are never integrated into a coherent model. What we get is not understanding - but a collection of disconnected observations. The system is never seen as a whole - rather built upon assumptions.

Parametric Behaviour Blueprinting.

What if we stopped running blind experiments and started exploring the system itself? FlexCartesian introduces a paradigm shift: Parametric Behaviour Blueprinting (PBB). It treats a system not as a set of scattered measurements, but as a holistic function over a space with dimensions defined by its parameters. This shift allows us to move from fragmented data points to a structured, mathematically proven understanding of system behaviour.

01

Define parameters

Build a parameter space with independent dimensions reflecting the system's degrees of freedom, including conditional constraints.

02

Express behavioural functions

Express system properties strictly as functions, abandoning ad-hoc notes and isolated benchmarking scripts.

03

Extract the blueprint

These functions obtain live data from the real system via APIs or infrastructure—allowing the behavioural blueprint to evolve while remaining continuously linked to reality.

04

Derive insights

Visualize the full behavioural blueprint. Apply built-in analyzers to identify bottlenecks and sweet spots, moving from reactive troubleshooting to proactive optimization.

Concise for human, precise for insight.

Let’s ground this in a real-world scenario. LLMs tend to answer the same question differently each time. For scientific topics, inconsistency is unacceptable. Using FlexCartesian, we can extract a complete behavioural blueprint of the LLM and reveal its optimal operating mode to ensure response stability.

# test prompt; we'll use ChatGPT as an example LLM
msg = [ { role: "system", content: "You are a precise and consistent assistant." },
        { role: "user", content: "Explain quantum mechanics in one sentence." } ]

# first response from LLM, from which we'll be measuring semantic shift
anchor = nil

# behavioural space for LLM
space = FlexCartesian.new({ temperature: [0.0, 0.2, 0.4, 0.6, 0.8, 1.0], tokens: [20, 50, 100, 200, 400] })

# behavioural functions for LLM
space.func(:add, :response) { |v| llm(temperature: v.temperature, max_tokens: v.tokens, messages: msg ) }
space.func(:add, :embedding) { |v| anchor ||= embed(v.response); embed(v.response) }
space.func(:add, :semantic_shift) { |v| (1.0 - cosine(v.embedding, anchor)).round(2) }
space.func(:run, progress: true, title: "Extracting behavioural blueprint")

# visualize behavioural blueprint as a 2D-heatmap
space.visualize(x: :temperature, y: :tokens, func: :semantic_shift)

# quantify influence of the parameters in the blueprint
space.analyzer(:morris, trajectories: 10, step: 0.1, seed: 42).output(func: :semantic_shift)

Complete behavioural blueprint.

Instead of relying on isolated runs, FlexCartesian builds a comprehensive digital blueprint of the system across its entire parameter space. It reveals exactly where optimal configurations emerge, and where limits, bottlenecks, and trade-offs dictate the system's nature. This makes optimization systematic rather than experimental, exposes non-obvious interactions, and makes system behaviour fully reproducible and explainable. The system is no longer sampled. It is understood.

Heatmap Insights

"LLM responses are stable if the temperature does not exceed 0.4, including longer context lengths. This is the optimal operating mode for answering scientific questions."

Parameter Influence Deviation Probes Category Linearity Recommendation
tokens 0.15 0.29 10 strong highly non-linear critical parameter with complex interactions; prioritize for variance-based analysis (e.g. Sobol)
temperature 0.13 0.2 10 strong highly non-linear critical parameter with complex interactions; prioritize for variance-based analysis (e.g. Sobol)

Sensitivity Insights

"Temperature and tokens have comparably strong, non-linear influence on the semantics. This requires finding an area of stability, mathematically confirmed by the heatmap insight."

Why FlexCartesian.

Parametric Behaviour Blueprinting

A new way to model systems: not as isolated experiments, but as holistic functions over comprehensive parameter spaces.

  • Systems as parametric models
  • High-level, human-readable DSL
  • Synthesize models with real world

Enterprise AI & Predictable ROI

Move from hype-driven adoption to a rigorous methodology. Extract the exact operational sweet spots for your AI workloads.

  • Slash Proof-of-Concept cycles
  • Pinpoint optimal operating modes
  • Predict ROI and eliminate cloud waste

Sovereign & Critical Systems

Bridge the gap between strict data isolation (air-gapping) and the need for continuous performance telemetry.

  • Blueprint air-gapped systems
  • Optimize with zero data exposure
  • Validate decision-making