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Temporal Symmetry as the Basis for AGI: A Unified Cognitive Architecture ​

Author: Eduard Izgorodin (izgorodin)
Last Updated: 2025-07-15
Version: 0.1.1
Status: Speculative Research Extension
Research Phase: Theoretical Exploration

⚠️ EXPERIMENTAL THEORY
This document presents a speculative extension of the core Mnemoverse architecture. The temporal symmetry hypothesis builds on the proven mathematical foundations of spatial memory but ventures into uncharted theoretical territory. While promising, these ideas require significant empirical validation before practical implementation.

Abstract ​

Temporal symmetry posits that memory (t < 0), perception (t = 0) and prediction (t > 0) are mirror-oriented uses of a single computational operator. One bidirectional kernel K acts in a hyperbolic latent manifold; a scalar entropic factor λ tilts precision toward the past, yielding the observed arrow of time without duplicating circuitry. We formalise this mechanism via an analytic flow equation, derive an exponential law for recall-prediction error Δσ(|Δt|), and implement it in Mnemoverse 2.0—a curvature-controlled Poincaré VAE coupled to a reinforcement-learning planner. A focused programme of three fMRI and two machine-learning experiments can decisively verify or falsify the theory. Temporal symmetry thus offers a principled, testable blueprint for AGI that navigates the temporal continuum with a single engine.

1. Introduction ​

1.1 From Memory vs. Prediction to Bidirectional Temporal Navigation ​

Traditionally, cognition treats memory () and prediction () as asymmetric. Neuroimaging now reveals decisions are driven by the similarity differential between past and upcoming events rather than by one domain alone (biorxiv.org). Time‑cells in the hippocampus encode ordered sequences irrespective of direction along the timeline (nature.com), while meta‑analysis shows overlapping activation of hippocampus, vmPFC and precuneus during episodic recall and future thinking (link.springer.com).

1.2 Scope of the Revision ​

We integrate four key critiques:

  1. Empirical asymmetry of precision.
  2. Differential biophysics of replay vs. preplay.
  3. Entropic arrow of time in sensory cortex.
  4. Need for implementation details (curvature control, RL coupling).

2. Theoretical Foundation ​

2.1 Functional vs. Physical Symmetry ​

The core insight is functional symmetry: the cognitive system uses the same computational kernel K to process both memory retrieval () and future prediction (). Unlike physical time, which flows irreversibly forward, cognitive time navigation operates bidirectionally through a unified mechanism.

The asymmetry we observe emerges from a single parameter: the entropic gradient λ. As environmental uncertainty increases, λ grows, creating differential precision between past and future estimates. When the world becomes predictable (λ → 0), temporal symmetry approaches perfection. This design elegantly captures why we remember yesterday more clearly than we predict tomorrow, without requiring separate neural circuits for memory and prediction.

2.2 Hyperbolic Latent Geometry with Curvature Annealing ​

Hyperbolic manifolds compactly encode exponentially expanding temporal neighborhoods (arxiv.org). Connectome studies confirm that 3‑D hyperbolic embeddings outperform Euclidean fits for brain networks (arxiv.org). By default we keep curvature κ fixed; annealing κ is enabled only for very deep hierarchies where fixed κ causes numerical instabilities (openreview.net).

2.3 Unified Flow Equation with Entropic Damping ​

The unified temporal flow equation with entropic damping is:

where the entropic gradient is given by:

Here, is the estimated entropy of the environment. Setting yields graded, not perfect, symmetry, aligning with cortical entropy gradients observed in fMRI (sciencedirect.com).

Temporal Mirror Clarity Function:

This function quantifies how "clearly" we can navigate to temporal distance Δt.

2.4 Exploration lowers λ (new) ​

Active exploration reduces epistemic uncertainty; therefore the agent updates online:

Less surprise → smaller λ → closer-to-symmetric precision of past and future estimates.

Homeostatic Memory Revision: The system minimizes cognitive dissonance by gradually aligning past memories with successful predictions:

This explains why we remember successes better than failures - the system actively rewrites history to maintain coherence.

3. Empirical Evidence and Outstanding Gaps ​

PhenomenonPastFutureEmpirical Symmetry
Similarity‑driven decisions✔️✔️High
Recall/Prediction error ()lowerhigherasymmetry

The error gap is formalized as:

typically in behavioral data (pmc.ncbi.nlm.nih.gov). A key prediction is that shrinks as an agent’s model uncertainty decreases.

Unique exponential prediction (graded-symmetry law)

Competing models expect sub-exponential (often power-law) growth; thus empirically fitting an exponential with β tracking λ would falsify them.

Unique Prediction - Interference Pattern: When simultaneously recalling past and predicting future from the same anchor point, performance degradation follows:

where P denotes task accuracy. We predict Interference > 0.3 for |Δt| < 10s.

Replay events outnumber preplay by factor in rodents; duration of preplay bouts is shorter (pmc.ncbi.nlm.nih.gov). We model the preplay/replay ratio as

4. Mnemoverse 2.0 Architecture ​

4.1 Components ​

ModuleFunction
Hyperbolic Latent CoreBidirectional temporal embedding; curvature‑annealed.
Dual Flow IntegratorIntegrates past and future streams, enforces conservation law at .
RL‑PlannerReceives latent ; policy optimizes reward and minimizes simultaneously.

4.2 Training Objectives ​

The training objective is:

where is the target curvature after annealing.

5. Experimental Programme ​

5.1 Neuroimaging ​

  1. Temporal Similarity Task 2.0: replicate Nature Neuroscience paradigm with symmetric  s; compute RSA matrices and test .
  2. Preplay Dynamics vs. Entropy: rat hippocampal recordings under variable sensory noise; test .
  3. Entropy‑Gradient fMRI: quantify via stimulus entropy; correlate with vmPFC‑hippocampal coupling (nature.com).
  4. Temporal Interference Task: Subjects simultaneously recall and predict from anchor stimuli. Measure accuracy degradation and fMRI cross-talk between hippocampal past/future representations.

5.2 Machine‑Learning ​

  1. Hyperbolic vs. Euclidean VAE on Atari: assess planning reward at horizon ; expect for hyperbolic embedding (openreview.net).
  2. Curvature‑Annealing Ablation: disable ‑annealing and measure instability rate.

6. Philosophical Considerations ​

Even a 52% vs 48% advantage in probabilistic future modeling would provide enormous evolutionary and practical benefits. The goal is not deterministic prophecy but statistically superior navigation through possibility space.

Replacing “reading the future” with stochastic extrapolation underscores that the model forecasts probability distributions, not certainties, preserving compatibility with indeterminate quantum and chaotic dynamics. Free‑energy minimization unifies both directions of temporal inference under a single variational principle (nature.com).

7. Conclusion ​

Temporal symmetry, reframed as graded bidirectional navigation, offers a coherent cognitive and computational framework. By quantifying asymmetries (, ), embedding them in hyperbolic geometry, and validating through fMRI and RL benchmarks, Mnemoverse 2.0 translates an elegant idea into a falsifiable roadmap toward AGI.

References ​

  1. Ye, Z., Zhao, Y., Allen, E. J., Naselaris, T., Kay, K., Hutchinson, J. B., & Kuhl, B. A. Temporal asymmetry of neural representations predicts memory decisions. bioRxiv (2024). https://doi.org/10.1101/2024.07.16.603778
  2. Eichenbaum, H. Time cells in the hippocampus: a new dimension for mapping memories. Nature Reviews Neuroscience 15(11), 732–744 (2014). https://doi.org/10.1038/nrn3827
  3. Teghil, A., Wiener, M., & Boccia, M. Cortical gradients support mental time travel into the past and future: evidence from activation likelihood estimation meta‑analysis. Neuropsychology Review (2025). https://doi.org/10.1007/s11065‑025‑09662‑w
  4. Celińska‑Kopczyńska, D. & Kopczyński, E. Modelling brain connectomes networks: Solv is a worthy competitor to hyperbolic geometry! arXiv preprint arXiv:2407.16077 (2024). https://doi.org/10.48550/arXiv.2407.16077
  5. Nickel, M. & Kiela, D. Poincaré embeddings for learning hierarchical representations. In Advances in Neural Information Processing Systems 30, 6338–6347 (2017).
  6. Friston, K. The free‑energy principle: a unified brain theory? Nature Reviews Neuroscience 11(2), 127–138 (2010). https://doi.org/10.1038/nrn2787
  7. Buhry, L., Azizi, A. H., & Cheng, S. Reactivation, replay, and preplay: how it might all fit together. Neural Plasticity 2011, 203462 (2011). https://doi.org/10.1155/2011/203462
  8. Parrondo, J. M. R., Van den Broeck, C., & Kawai, R. Entropy production and the arrow of time. New Journal of Physics 11, 073008 (2009). https://doi.org/10.1088/1367‑2630/11/7/073008
  9. Deng, O. & Jin, Q. Hyperbolic embeddings are essential for health knowledge graphs in LLMs and vector databases. Position paper, ICML 2025 (preprint on OpenReview), 23 Jan 2025. https://openreview.net/forum?id=Sz90WdONPz
  10. Nock, R., Amid, E., Nielsen, F., Soen, A., & Warmuth, M. K. Hyperbolic embeddings of supervised models. In Advances in Neural Information Processing Systems 37 (NeurIPS 2024).
  11. Dimakou, A., Pezzulo, G., Zangrossi, A., & Corbetta, M. The predictive nature of spontaneous brain activity across scales and species. Neuron 113(9), 1397–1415 (2025). https://doi.org/10.1016/j.neuron.2025.02.009
  12. Pisani, A. et al. The role of vmPFC in accessing the temporality of life events for mental time travel. Scientific Reports 15, 14375 (2025). https://doi.org/10.1038/s41598‑025‑97861‑z
  13. Ye, Z., Zhao, Y., Allen, E. J., Naselaris, T., Kay, K., Hutchinson, J. B., & Kuhl, B. A. Temporal asymmetry of neural representations predicts memory decisions. bioRxiv (2024). https://doi.org/10.1101/2024.07.16.603778 (duplicate included for PMCID reference)
  14. Viard, J., Piolino, P., Desgranges, B., Chetelat, G., Lebreton, K., Belleville, S., & Eustache, F. Mental time travel into the past and the future in healthy aged adults: an fMRI study. Brain and Cognition 75(2), 254–261 (2011). https://doi.org/10.1016/j.bandc.2010.12.009
  15. Azarias, F. R., Almeida, G. H. D. R., de Melo, L. F., Rici, R. E. G., & Maria, D. A. The journey of the default mode network: development, function, and impact on mental health. Biology 14(4), 395 (2025). https://doi.org/10.3390/biology14040395

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