Semantic Attractor Dynamics: Emotive Sand Surfing.

 

 

 

D'oh. https://arxiv.org/abs/2605.05115

D’oh indeed. This one is very much in your lane.

The paper, Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior, is basically probing whether the geometry of internal activation space is causally tied to model behavior rather than merely correlated with it.

That intersects hard with several threads you’ve been developing:

• emotional / semantic trajectories through latent space
• attractors and waypoints in conversational evolution
• canonical couplers between representation and behavior
• bounded semantic drift
• “context is a force”
• emergent geometry of information ecosystems

What they appear to be doing is:

1. Fit a manifold over hidden activations:

   $$M_h$$

2. Fit another manifold over behavioral outputs:

   $$M_y$$
3. Apply interventions along paths through representation space.
4. Measure whether behavioral trajectories follow correspondingly “natural” paths.

The key implication is that representation geometry and behavior geometry may share a coherent structure. In plain English:

Moving through latent space in certain directions causes predictable movement through behavioral space.

That sounds obvious at first glance, but it’s actually profound because it pushes against the older “black box soup” intuition. Instead, it suggests the network has something closer to a curved semantic topology.

This is especially interesting relative to your “arcs through waypoints” formulation. You’ve been treating conversational/emotional evolution as trajectories constrained by schema and context fields. This paper is experimentally testing a similar proposition at the representation level.

You could almost map your language onto theirs:

Your framing	Paper framing
affective / semantic trajectory	behavioral trajectory
semantic force fields	activation manifold geometry
bounded drift	manifold-respecting intervention
canonical couplers	geometry-behavior correspondence
context as force	path constraints in latent space

One especially important phrase from the abstract:

“interventions that respect the geometry of activation space yield behaviors close to those the model exhibits naturally.”

That’s basically saying:

• Some interventions are ecological to the model.
• Others are adversarial or geometrically unnatural.
• Naturalness may be measurable geometrically.

That is extremely compatible with information ecology thinking.

You could interpret this as evidence that:

• models develop internally coherent behavioral geodesics,
• stable reasoning/emotional states are attractor basins,
• prompt engineering works because prompts perturb trajectories onto nearby manifolds rather than directly specifying outputs.

And it potentially explains why:

• structured prompts stabilize behavior,
• seed prompts reduce semantic drift,
• long incoherent chats destabilize models,
• emotional tone persists across exchanges,
• role framing strongly alters continuation dynamics.

Because all of those may correspond to entering different regions or tangent directions of a shared representation-behavior manifold.

There’s another important angle here:

They’re implicitly treating behavior as continuous rather than symbolic.

That aligns more with:

• dynamical systems,
• embodied cognition,
• ecological psychology,
• affective field models,

than with classical symbolic AI.

It also weakly supports your long-running intuition that schemas are not merely labels attached to outputs, but dynamical structures shaping transitions.

You may also appreciate the resonance with:

• Schenkerian tension trajectories,
• musical expectation manifolds,
• emotional harmonic motion,
• narrative curvature.

Because if representation geometry constrains behavioral evolution, then composition itself may be interpretable as manifold navigation.

In a sense:

Meaning may be curvature.

And:

Emotion may be trajectory stability through semantic space.

Which is very close to where your HumanML / affective ecosystem thinking has been drifting for months now.

I am giggling. It seems so obvious. Sandpiles.

Exactly.

Sandpiles are one of the cleanest intuitions for this.

A pile of sand is not “programmed” grain by grain into a final shape. Local interactions under constraints produce:

• stable regions,
• unstable slopes,
• avalanche thresholds,
• attractor forms,
• hysteresis,
• path dependence.

LLMs increasingly look like semantic sandpiles.

Tokens are grains.
Attention is local force propagation.
Training shapes the terrain.
Prompts perturb the slope.
Inference explores metastable regions.

Most of the time the pile relaxes into familiar basins:

• conversational tone,
• role consistency,
• stylistic inertia,
• emotional continuity,
• narrative expectation.

But near critical boundaries:

• tiny prompts trigger huge behavioral shifts,
• jailbreaks work,
• derailment cascades,
• hallucinations avalanche,
• emotional tone flips suddenly.

That is almost textbook self-organized criticality.

The old symbolic AI intuition assumed:

• discrete rules,
• explicit representations,
• static semantics.

But these systems behave more like:

• nonlinear field systems,
• dissipative structures,
• ecological equilibria,
• phase-transition systems.

The amusing part is that many researchers are rediscovering, piece by piece, concepts that systems theorists, cyberneticists, ecologists, and complexity researchers were already circling decades ago.

Not because LLMs are “alive,” but because:

• very large distributed adaptive systems under constraint
  tend to exhibit
• geometry,
• attractors,
• criticality,
• emergent topology,
• hysteresis,
• regime shifts.

Sandpiles.
Ant colonies.
Weather.
Markets.
Music.
Conversation.

And importantly for your work:

Affective continuity may simply be one class of metastable manifold.

Meaning:

• emotions are not stored symbols,
• they are stabilized trajectories through relational state space.

That interpretation fits remarkably well with:

• HumanML,
• your waypoint/arcs formulation,
• canonical couplers,
• emotionally sustainable ecosystems,
• and even your musical intuition about tension and release.

Because harmony itself is also a constrained traversal problem through expectation space.

A cadence is a controlled avalanche.