Intent Vector System: A Computational Framework for Real-Time User Intent Modeling in Peachi OS

Ron Asnahon, August 2024

Abstract

This paper introduces an advanced computational framework for modeling and quantifying user intent within Corea STARSTROUPE's Peachi OS. Central to this work is the Intent Vector System (IVS), which utilizes multi-modal signal processing, probabilistic inference, and dynamic belief updating to infer user purpose in real-time. Through rigorous derivation and benchmark evaluation, we demonstrate how IVS enables anticipatory machine behavior that aligns with latent user cognition, enhancing interface precision, user trust, and operational reliability.

1. Introduction

Traditional machine interfaces rely on deterministic instruction models, requiring explicit commands for action, which limits their adaptability to implicit user goals. Peachi OS, developed by COREA Starstroupe, integrates the Intent Vector System (IVS) to enable cognition-aligned, context-aware interfaces that infer latent intent in real time. This paper defines the mathematical model of IVS, establishes its theoretical constructs, and presents simulation-based performance metrics, contributing to COREA Starstroupe’s open-source mission to advance human-machine interaction.

2. Mathematical Foundation of Intent Modeling

2.1 Multidimensional Intent Representation

We define latent intent I(t) at time t as a function of quantifiable behavioral signals and context-derived dimensions, expressed as:

I(t) = w₁(t)g + w₂(t)c + w₃(t)a + w₄(t)u

Where:

• g: Goal-specific clarity, derived from semantic coherence of inputs.
• c: Contextual coherence, based on environmental alignment.
• a: Temporal consistency of actions, measured via sequence stability.
• u: Urgency or decision pressure, inferred from interaction speed.
• w_i(t): Time-dependent weight parameters, determined by environmental and sessional factors.

2.2 Normalized Intent Function

Intent components are normalized to [0,1] using sigmoid compression:

σ(x) = 1 / (1 + e^-k(x-m))

Where k controls sensitivity and m centers the transition, ensuring scale-invariant aggregation.

3. Input Signal Vectorization

3.1 Signal Vector Definition

Let S(t) be the vector of n features extracted at time t, defined as:

S(t) = [s₁, s₂, s₃, s₄, s₅, s₆]

Where:

• s₁: Lexical semantic vector (e.g., BERT embedding).
• s₂: Clickstream entropy, measuring interaction randomness.
• s₃: Cursor heatmap weight, reflecting spatial focus.
• s₄: Scroll velocity variance, indicating engagement.
• s₅: Temporal event lag, capturing input timing.
• s₆: Voice stress tensor (if available), derived from prosodic features.

3.2 Dimensional Embedding

Each s_i is mapped to a shared semantic manifold M using learned projections:

f_i: s_i → M

The unified input is expressed as:

S'(t) = Σ a_i(t) f_i(s_i)

Where a_i(t) are attention-derived signal weights, computed via time-series analysis.

4. Bayesian Intent Inference

Let H = {h₁, h₂, ..., h_k} be the discrete hypothesis space of intents. The posterior probability of each intent is computed via Bayes’ Theorem:

P(h_i|S(t)) = P(S(t)|h_i) P(h_i) / P(S(t))

4.1 Likelihood Modeling

The likelihood P(S(t)|h_i) is modeled as a multivariate Gaussian:

P(S(t)|h_i) = (1 / √((2π)ⁿ|Σ_i|)) e^{-(1/2)(S(t)-μ_i)TΣ_i-1(S(t)-μ_i)}

Where μ_i is the mean feature vector for intent h_i, and Σ_i is the covariance matrix capturing feature interactions.

4.2 Prior Updates

The prior P(h_i) is updated using a decay function:

P(h_i, t) = α P(h_i, t-1) + (1-α) f(S(t))

Where α controls reactivity to new evidence, tuned based on session variance.

5. Confidence Dynamics and Intent Stability

5.1 Confidence Function

System confidence at time t is defined as:

C(t) = max P(h_i|S(t))

5.2 Delta Analysis

The rate of change in confidence is:

ΔC(t) = |C(t) - C(t-1)| / Δt

Low ΔC(t) implies uncertainty; high ΔC(t) suggests intent convergence. Thresholds are:

• ΔC(t) < 0.1: Uncertainty or intent collapse.
• ΔC(t) > 0.5: Intent convergence.

5.3 Entropy Regularization

Confidence entropy is computed as:

H(t) = -Σ P(h_i|S(t)) log P(h_i|S(t))

A minimum entropy constraint stabilizes system transitions.

6. Real-Time Execution Policy

At each timestep t, Peachi OS executes:

1. Acquire S(t) from input pipelines.
2. Compute P(h_i|S(t)), C(t), and ΔC(t).
3. Evaluate H(t).
4. Apply decision policy:
   • High confidence (C(t) > 0.8): Act autonomously.
   • Low confidence (C(t) < 0.4): Surface clarifying UI thread.
   • Ambiguous intent (0.4 ≤ C(t) ≤ 0.8): Enter Reflective Mode.

Execution thresholds are tuned via reinforcement learning updates.

7. Simulation and Benchmark Results

IVS was evaluated in synthetic interaction environments with logged intent ground truth, yielding:

Statistical significance was confirmed using t-tests (p < 0.05).

8. Implementation in Peachi OS

IVS is integrated into Lumen Layer v3.4.1, interfacing with:

• Event-driven runtime interpreter for real-time signal processing.
• Reactive UI layer for dynamic interface updates.
• NLP-core semantic engine for lexical analysis.
• Multi-threaded signal broker for input coordination.

All components are sandboxed for privacy, supporting zero-retention configurations, aligning with COREA Starstroupe’s non-profit mission.

9. Conclusion

Peachi OS, through the Intent Vector System, achieves cognition-aware machine behavior via a real-time, multi-modal, and mathematically grounded approach. Developed by COREA Starstroupe, this open-source framework sets a benchmark for ambient intelligence, enhancing interface precision and user trust. As human-machine interaction evolves, IVS positions Peachi OS as a leader in anticipatory, purpose-aligned systems.

References

• Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.
• Corea STARSTROUPE Internal Research Logs. (2024). Intent Modeling Experiments.
• Peachi OS – Lumen Layer (BETA) Specification, Rev 3.4.1. (2024). COREA Starstroupe.
• Sutton, R., & Barto, A. G. (2018). Reinforcement Learning: An Introduction. MIT Press.