Transformational Equivalence: Learning to Preserve Meaning Across Representational Layers

Research Objective

To explore and implement a learnable system that can transform an agent state through various representational forms—structured, binary, latent, compressed—and reconstruct it while preserving its semantic meaning, not just its raw structure.

Hypothesis

An intelligent agent does not store complete representations of experience or state. Instead, it realizes relevance through compression, preserving only those features most useful for future inference, planning, or meaning reconstruction. The fidelity of these reconstructions is not measured by accuracy to the original state, but by retention of semantic intent and behavioral utility.

Implications

If we can measure semantic preservation even weakly, and show it emerges from compression-aware models, then we have evidence that meaning is not only representable but also resilient—emerging naturally from efficient encoding processes rather than needing to be explicitly defined.

Key Questions:

• How can we define, observe, and measure "meaning" in the context of agent states and their transformations?
• How can we train a Variational Autoencoder (VAE) (or similar model) to understand a state well enough to reconstruct its meaning from a compressed representation?
• What types of transformations occur between layers of representation?
• How is meaning preserved, altered, or lost as data moves through different forms?

For a comprehensive list of research questions we've explored and answered through our experiments, see Questions.md.

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2. Theoretical Framing

Core Concepts:

• Meaning as invariance through transformation
  The idea that what constitutes "meaning" is precisely what remains constant when information undergoes various transformations. If the essential properties persist across different forms of representation, those properties constitute meaning. Read more

• Latent space as structured essence
  The compressed representation in latent space captures not just data patterns but the underlying semantic structure that gives rise to those patterns. This essence is what allows reconstruction of behaviorally equivalent states. Read more

• Compression as semantic distillation
  The process of compression forces a system to prioritize what's most important, naturally separating signal from noise. This distillation process naturally preserves semantic content over superficial details. Read more

• Intuition as learned, reversible mapping across modalities
  Intuition emerges from the ability to translate between different representational forms without losing critical information. This mapping becomes more efficient and accurate as the system learns which features matter most. Read more

• Understanding as regenerative compression
  True understanding emerges when an agent can distill something to its essential properties and then expand it back in a way that preserves behavioral and perceptual equivalence. Understanding isn't about perfect recall of details, but about extracting patterns that allow meaningful reconstruction. We "understand" when we can compress to essence and regenerate equivalence. Read more

Relevant Fields:

• Representation Learning: Implement contrastive learning objectives that focus on preserving relationships between agent states rather than exact reconstruction. Consider using techniques like SimCLR or BYOL adapted to structured state data.

• Information Theory: Apply mutual information estimation between original and reconstructed states to quantify semantic preservation. Use techniques like MINE or InfoNCE to create loss functions that maximize mutual information across transformations.

• Neural Compression: Adapt neural compression architectures like Ballé et al.'s hyperprior models to handle structured agent states. Implement entropy models that can adapt to the distribution of agent state features.

• Symbolic ↔ Subsymbolic Translation: Create hybrid architectures that maintain symbolic interpretability while leveraging neural networks for generalization. Consider neuro-symbolic approaches like Logic Tensor Networks or Neural Theorem Provers.

• Philosophy of Meaning / Semiotics: Design evaluation metrics that test for preservation of relationships rather than exact structures. Create "meaning benchmarks" where models must demonstrate semantic equivalence in downstream tasks despite representational differences.

Foundational Works:

• Ballé et al. (Entropy bottleneck): Their neural compression framework demonstrates how variational models can learn to prioritize information through a bottleneck, similar to how we want to preserve semantic meaning. We can adapt their end-to-end optimizable compression system to prioritize semantic rather than perceptual loss.

• VQ-VAEs (van den Oord et al.): Vector Quantized VAEs provide discrete latent representations that could help capture symbolic aspects of agent states. Their ability to represent complex distributions through codebook vectors aligns with our goal of finding compressed but meaningful representations.

• Kolmogorov Complexity: This theoretical framework defines the complexity of information as the length of the shortest program that produces it. We can use this concept to measure how efficiently our models capture the "essence" of an agent state—lower complexity representations that preserve functionality indicate better semantic compression.

• Information Bottleneck Principle: Tishby's work on the tradeoff between accuracy and compression provides a mathematical framework for our hypothesis. By gradually restricting the information flow while maintaining task performance, we can identify which features constitute "meaning" in the context of agent behavior.

• Vervaeke's 4P Model of Knowing: John Vervaeke's framework distinguishes between propositional, procedural, perspectival, and participatory knowing. This can guide our evaluation of semantic preservation - true meaning retention should preserve not just facts (propositional) but also skills (procedural), viewpoints (perspectival), and relational aspects (participatory).

• Relevance Realization Theory: Vervaeke's work on how cognitive agents determine what's relevant provides theoretical grounding for our compression approach. Our system's ability to selectively preserve meaning mirrors the human mind's capacity to extract and maintain what matters across contexts.

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3. System Architecture Overview

Simplified Representational Pipeline:

[Agent State (dict)] 
      ↓ serialize
[Binary Representation]
      ↓ encoder (VAE)
[Latent Space]
      ↓ entropy model / quantization
[Compressed Code]
      ↑ decode & reconstruct
[Reconstructed State (as dict)]

Each stage is invertible (lossless or learned), and the focus is on preserving semantic intent across the pipeline.

For a detailed diagram of the pipeline with example data at each stage, see PipelineDiagram.md.

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4. Evaluation

Technical Metrics:

• Compression ratio and latent space entropy
• Reconstruction fidelity (L2, RMSE)
• Feature-specific accuracy (binary, categorical, continuous features)

Semantic Preservation:

• Weighted semantic equivalence scores
• Behavioral similarity between original and reconstructed agents
• Role and attribute preservation accuracy
• Semantic drift tracking over time and compression levels

Visualization & Analysis:

• Latent space projections (t-SNE, UMAP)
• Feature importance and sensitivity analysis
• Reconstruction deltas at various compression levels

For detailed definitions of our standardized metrics framework, evaluation methods, and validation approach, see StandardizedMetrics.md and Validation.md.

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5. Implementation Details

• AgentMemory Perspective
• Reconstruction Process