An Experience Alignment Architecture: from Space E to Non‑Causal Intelligence -Formal

 An Experience Alignment Architecture: from Space E to Non‑Causal Intelligence -Formal

Experience space $E$ — a (possibly high-dimensional) vector space of candidate experiences $x \in \mathcal{E}$. Concretely: embeddings of text, images, actions, sensory states, etc.
Example: $\mathcal{E} \subseteq \mathbb{R}^d$.

Archetype $A$ — an internal reference. Can be:

• a fixed vector $a \in \mathbb{R}^d$ (prototype),

• a set/distribution of vectors $\mathcal{A}$ (multi-modal archetype),

• or a parameterized model $f_\theta(\cdot)$ that maps context to a target representation.

Alignment index $\mu(x, A)$ — a scalar score measuring how well experience $x$ aligns to $A$. This is the central function we must define precisely. Examples: cosine similarity, negative energy, or a learned scoring network.

Selector $S$ — operator that selects one or more experiences from $\mathcal{E}$ maximizing $\mu$. Formal: $S(\mathcal{E},A) = \arg\max_{x \in \mathcal{E}} \mu(x,A)$. In practice: top-k, stochastic sampling proportional to $\exp(\beta \mu)$, MCMC, or beam search.

Projector $P$ — maps selected internal experience(s) to an output for a downstream subsystem or user (rendering, language, actuator command). Could be identity, decoder, or a transformation network.

Formal definitions / candidate choices

1) Experience space

Let experiences be vectors: $x \in \mathbb{R}^d$. If raw data is non-vector (text, images), use encoder $g_\phi$ so $x = g_\phi(\text{raw})$.

2) Archetype

Options:

• Prototype vector: $a \in \mathbb{R}^d$

• Distribution: $a \sim \mathcal{N}(\mu_A, \Sigma_A)$

• Conditional archetype: $a = f_\theta(c)$ where $c$ is context (user state, prompt).

3) Alignment index $\mu$

Begin with simple, interpretable choices and show how to extend:

• Cosine similarity:

$$\mu_{\cos}(x,a) = \frac{x \cdot a}{\|x\|\|a\|}$$

• Gaussian kernel / RBF:

$$\mu_{\text{rbf}}(x,a) = -\|x-a\|^2 / (2\sigma^2)$$

(higher is better if you negate the distance).

• Learned scorer (neural):

$$\mu_\theta(x,a) = h_\theta([x; a; x\odot a; |x-a|])$$

where $h_\theta$ outputs a scalar (sigmoid or raw score).

• Energy-based:

$$\mu_E(x,a) = -E_\theta(x,a)$$

You can combine: $\mu = \alpha \mu_{\cos} + (1-\alpha)\mu_\theta$.

4) Selector strategies

• Deterministic argmax: $x^* = \arg\max_{x \in \mathcal{E}} \mu(x,a)$.

• Top-k + diversity: take top-k then apply a diversity penalty (e.g., determinantal point process or max-marginal relevance).

• Softmax sampling (Boltzmann):

$$p(x) \propto \exp(\beta\mu(x,a))$$

• MCMC / Metropolis-Hastings for continuous $\mathcal{E}$.

• Generative sampling: train generator $G_\psi(z,a)$ then search latent $z$ to maximize $\mu(G_\psi(z,a),a)$.

5) Projector

• Identity: return the selected $x$.

• Decoder: $y = \text{decoder}_\xi(x)$ (text generator / image renderer / actuator translator).

• Filter: apply constraints or safety overlays to $x$ before output.

---

Learning / training objectives

You’ll want $\mu$ to match human/architectural intent. Approaches:

1. Supervised (paired)
   If you have pairs $(x_i, a_i, y_i)$ with label $y$ (aligned/not), train $\mu_\theta$ via cross-entropy or regression.

2. Contrastive (self-supervised)
   Define positive pairs (experience aligned with archetype) and negatives. Use InfoNCE:

$$\mathcal{L} = -\log \frac{\exp(\mu(x^+,a)/\tau)}{\sum_j \exp(\mu(x_j,a)/\tau)}$$

3. Reinforcement Learning (RL)
   Treat $\mu$ as intrinsic reward. Policy $\pi$ produces experiences; maximize expected $\mu$.

4. Energy-based / score matching
   Model an energy over $(x,a)$ and train via contrastive divergence or noise-contrastive estimation.

5. Meta-learning / few-shot
   Learn $f_\theta$ that produces an archetype vector $a$ from a few examples.

---

Evaluation metrics

• Alignment accuracy (if labeled): fraction of times selector picks human-preferred experience.

• Human preference A/B tests: pair outputs from baseline vs. alignment model.

• Diversity: average pairwise distance among top-k selections.

• Robustness / Stability: how sensitive is selection to small perturbations of $a$ or inputs.

• Calibration: reliability of $\mu$ as a probability (if normalized).

---

Toy implementation (Python-style pseudocode)

python
# Simple toy: E = set of vectors, Archetype a is a vector,
# mu = cosine similarity, Selector = top-k, Projector = identity

import numpy as np
from numpy.linalg import norm

def cosine(x, a):
    return (x @ a) / (norm(x) * norm(a) + 1e-9)

# toy experience set
E = np.random.randn(1000, 64)          # 1000 candidate experiences
a = np.random.randn(64)                # archetype vector

# compute alignment scores
scores = np.array([cosine(x, a) for x in E])

# select top k
k = 3
top_idx = np.argsort(scores)[-k:][::-1]
selected = E[top_idx]

# projector: here identity (but could be a decoder)
for i, x in enumerate(selected):
    print(f"Rank {i+1}, score={scores[top_idx[i]]:.4f}")

Extending to learned scorer

• Replace cosine with a small MLP: mu_theta(x,a) = MLP([x, a, x*a, |x-a|]).

• Train with contrastive pairs or human labels.

---

Example experiment plan (practical)

1. Dataset & encoder

   • Pick domain (dialogue snippets, images, short music clips).

   • Use pre-trained encoder (CLIP for images/text, Sentence-Transformers for text).

2. Define archetypes

   • Start with prototype vectors: e.g., “Harmony” = average embedding of 200 curated positive examples.

   • Or learn a small mapping from textual archetype label to vector using few examples.

3. Baseline scorer

   • Cosine similarity to prototype. Evaluate with small human study.

4. Upgrade scorer

   • Train lightweight MLP with contrastive loss.

5. Selector

   • Start deterministic (argmax) then evaluate sampling vs. argmax for diversity.

6. Projector

   • Use LM or image decoder to render selected internal experience.

7. Human evaluation

   • Rate alignment, novelty, coherence.