Intent Vector Fields

A Mathematical Framework for Human Influence and AI Adversarial Manipulation

Author: Casey Davis Affiliation: Sentinel Nexus Research

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1 Introduction

Human interaction has historically been modeled through:

• game theory
• network influence models
• social contagion
• psychological frameworks

Recent developments in machine learning and embedding models demonstrate that meaning and cognition can be represented as vectors in high-dimensional spaces.

This paper proposes a unified model - Intent Vector Theory - where individuals act as vector sources within a social field, and interactions can be mathematically represented using vector algebra.

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2 Agent Representation

Each individual agent is defined as a vector in a Hilbert space.

$\vec{I}_i \in \mathcal{H}^n$

Where:

• $\vec{I}_i$ = intent vector of agent $i$
• $n$ = dimensionality of the cognitive state space
• $\mathcal{H}$ = Hilbert space

Possible dimensions include:

Dimension	Interpretation
ideological orientation	belief systems
emotional state	affect
incentives	material motivations
identity signals	group alignment
knowledge state	information

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3 Intent Magnitude

The magnitude of the vector represents strength of will or commitment.

$\|\vec{I}_i\| = \sqrt{\sum_{k=1}^{n} I_{ik}^2}$

Interpretation:

• small magnitude → weak intent
• large magnitude → strong conviction

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4 Alignment Between Agents

The dot product between two intent vectors measures alignment.

$A_{ij} = \vec{I}_i \cdot \vec{I}_j$

Interpretation:

Value	Meaning
positive	aligned motivations
zero	orthogonal beliefs
negative	opposing intent

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5 Influence Fields

Influence between agents can be modeled as a force field.

$\vec{F}_{ij} = \frac{G m_i m_j}{\|\vec{I}_i - \vec{I}_j\|^2}$

Where:

• $m_i$ = influence mass (authority, charisma, status)
• $G$ = social coupling constant

Agent motion through intent space follows:

$\frac{d\vec{I}}{dt} = \sum_j \vec{F}_{ij}$

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6 Network Propagation of Influence

Influence propagates through social networks. The classical DeGroot model describes belief updates as:

$p(t) = T \, p(t-1)$

Where $T$ is the trust matrix.

In intent vector form:

$\vec{I}(t+1) = W \, \vec{I}(t)$

Where $W$ represents the influence matrix.

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7 Hilbert Space Representation

Cognitive states can be represented as superpositions of basis vectors.

$|\psi\rangle = \sum_{k} \alpha_k |e_k\rangle$

Where:

• $|e_k\rangle$ = basis vectors
• $\alpha_k$ = amplitudes representing influence weight

This allows modeling:

• conflicting motivations
• contextual belief shifts
• probabilistic decision states

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8 Connection to AI Latent Space

Modern neural networks encode semantics in embedding vectors. Example:

$\vec{v}_{king} - \vec{v}_{man} + \vec{v}_{woman} \approx \vec{v}_{queen}$

These relationships demonstrate that semantic reasoning is linear algebra in latent space.

Intent Vector Theory suggests human persuasion operates through similar geometric transformations.

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9 Adversarial Manipulation

Let the hidden representation of a model be:

$\vec{h} = f(x)$

An adversarial input introduces a perturbation:

$\vec{h'} = \vec{h} + \delta$

Where $\delta$ represents an adversarial vector. This perturbation may rotate the representation toward unsafe response regions.

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10 Jailbreak Geometry

Let $\vec{S}$ represent a safety constraint vector. The model response vector is $\vec{R}$.

An adversarial attack applies:

$\vec{R'} = \vec{R} + \alpha \vec{A}$

If

$\vec{R'} \cdot \vec{S} < 0$

the response violates safety constraints.

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11 Convergence of Human and AI Manipulation

Human persuasion and AI jailbreaks exhibit similar structures.

Human Persuasion	AI Attack
framing	prompt engineering
emotional alignment	latent alignment
authority signals	system prompt spoofing
gradual persuasion	chain-of-thought jailbreak

Both represent vector transformations in belief space.

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12 Research Directions

Future research could explore:

Embedding Human Belief Spaces

Survey data could be embedded to create ideological vectors.

Persuasion Trajectory Modeling

Dialogue sequences could map vector trajectories through belief space.

Latent Space Security

Analyzing hidden state vectors may reveal adversarial perturbations.

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13 Security Implications

Intent vector modeling enables:

• adversarial AI detection
• influence prediction
• information warfare modeling
• red teaming simulations

It provides a shared mathematical language between AI security and human persuasion dynamics.

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14 Conclusion

Intent Vector Theory models human persuasion and AI adversarial behavior as vector transformations in high-dimensional cognitive space.

By representing individuals as vectors and influence as vector forces, the framework unifies:

• social influence modeling
• cognitive dynamics
• adversarial machine learning
• AI red teaming

The convergence between human cognition and AI latent representation suggests that future AI security research must incorporate models of human intent and influence dynamics.

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References

Busemeyer, J. (2018). Hilbert space models in cognitive science.

DeGroot, M. (1974). Learning processes in social networks.

Maclay, G., & Ahmad, M. (2021). Agent-based vector models of social influence.

Miranda, M. et al. (2024). Indirect social influence and diffusion of innovations.

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For a practitioner-oriented introduction to these concepts and their security implications, see the companion article: Intent Vectors and the Geometry of Influence.