The Markovian Ceiling: Coherence ≠ Relevance — A Clean Empirical Proof
Posted by: Chetan Sharma
Date: 15 May 2026
Location: Kolkata, India
You can teach a language model to speak perfectly. It can write grammatically flawless sentences. It can mimic your style, your vocabulary, your cadence. It can be coherent.
But can it mean what it says?
This morning, at approximately 5:30 AM IST, I ran a simulation that answered this question definitively.
The Setup
Three models. All trained on the same 20,000 sentences.
UniLSTM — a standard Markovian language model. It predicts the next word based on the previous words. It never sees a goal.
Bidirectional Seq2Seq LSTM — reads the goal with a bidirectional encoder, then generates the sentence. Non-Markovian.
Multidirectional Transformer — full self-attention across the goal, then generates. Non-Markovian.
The task: given a three-word goal like [fox, under, sofa], generate a sentence that contains those elements in the correct order. The test goals are novel combinations — never seen during training.
The Result
Model Relevance
UniLSTM (Markovian) 0.0%
Bidirectional Seq2Seq 100.0%
Multidirectional Transformer 100.0%
The unidirectional model didn't just score low. It didn't fail gracefully. It collapsed entirely. For every single test goal — all 1,000 of them — it spat out the exact same sentence:
"bear and the park jumped"
Coherent? Yes. Grammatically correct, statistically fluent.
Relevant? Absolutely not. It had no idea what it was supposed to be talking about. It couldn't. Its architecture makes it blind to any goal outside its forward-looking probability chain.
Meanwhile, the non-Markovian models composed novel sentences perfectly. For [fox, near, mat], they generated "a fox slept near a mat." For [bird, beside, rug], "a bird slept beside the rug." They didn't just copy training data. They composed.
What This Proves
Coherence and relevance are fundamentally different dimensions of text quality.
A Markovian model — no matter how well-trained, no matter how rich the data — can achieve coherence. It cannot achieve relevance. Relevance requires something outside the forward chain: a goal representation that pulls generation toward meaning. Bidirectionality is not a luxury. It's the minimum requirement.
This isn't a metaphor. It's an empirical boundary.
Why This Matters for C.H.E.T.A.N (Coherent Human Engine for Trusted Autonomy and Networking .)
The digital twin project isn't about making a model that sounds like me. It's about making a model that can pursue what I would pursue. That requires non-Markovian conditioning — a self-model, a constitutional anchor, a persistent identity that exerts a pull on every generated word.
The Markovian ceiling is real. Today I proved it with code. Tomorrow I build above it.
Paper & Code
The full paper, Relevance Requires Non‑Markovian Conditioning, is available on Zenodo (DOI - SUBMISSION HERE - https://zenodo.org/records/20201889).
The simulation code runs on a single Colab cell with a free T4 GPU.
If you're building goal-directed AI, digital twins, or any system that needs to mean what it says — this boundary matters. Reach out.
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