Ask HN: How are Markov chains so different from tiny LLMs?

📝 Discussion Summary (Click to expand)

The Hacker News discussion primarily revolves around comparing and contrasting Large Language Models (LLMs) with traditional Markov chains for text generation.

Here are the three most prevalent themes:

1. LLMs as Sophisticated/High-Order Markov Chains (or not)

There is significant debate over whether LLMs fundamentally differ from Markov chains, or if they are simply very high-order, continuous-space versions of them. Some argue that any autoregressive system using a context window satisfies the Markov property, regardless of underlying implementation (neural network vs. lookup table). Others contend that the continuous latent space and mechanisms like attention fundamentally break the discrete, fixed-context limitations of traditional N-gram Markov models, making the analogy unhelpful for practical comparison.

Quote: "An LLM inference system with a loop is trivially Turing complete if you use the context as an IO channel, use numerically stable inferencing code, and set temperature to 0... If you want to make a universal Turing machine out of an LLM only requires a loop and the ability to make a model that will look up a 2x3 matrix of operations based on context and output operations to the context on the basis of them (the smallest Turing machine has 2 states and 3 symbols or the inverse)." - @vrighter

Quote: "Both LLMs and n-gram models satisfy the markov property, and you could in principle go through and compute explicit transition matrices... But LLMs aren't trained as n-gram models, so besides giving you autoregressive-ness, there's not really much you can learn by viewing it as a markov model" - @krackers

2. Creativity, Novelty, and Generation Outside of Training Data

A core tension in the discussion is whether LLMs can genuinely create or solve problems "not in their training data," in contrast to Markov chains, which are often asserted to only output sequences seen in the corpus. Users debate whether LLM outputs that deviate from the training material—like the simulated Trump speech—are true creativity or merely "hallucinations" resulting from exploiting the density of the learned probability distribution.

Quote: "LLMs will generate token sequences that didn't exist in the source material, whereas Markov Chains will ONLY generate sequences that existed in the source." - @Sohcahtoa82

Quote: "Hallucinations are not novel ideas. They are novel combinations of tokens constrained by learned probability distributions." - @johnisgood

3. The Importance of Attention and Latent Space over Discrete States

Commenters highlight that the key differentiator, aside from sheer scale, is how LLMs utilize continuous representations. Attention mechanisms allow LLMs to dynamically weigh long-range dependencies, whereas traditional Markov chains struggle with context lengths that quickly become prohibitively large (the curse of dimensionality). This capability allows LLMs to handle semantic relationships that are impossible for simple N-gram models to capture.

Quote: "The main reason here is that sometimes, the last N words (or tokens, whatever) simply do not have sufficient info about what the next word should be. Often times some fragment of context way back at the beginning was much more relevant. ... Attention solves this problem." - @ComplexSystems

Quote: "With NN-based LLMs, you don't have that exact same issue: even if you have never seen that n-word sequence in training, it will get mapped into your high-dimensional space. And from there you'll get a distribution that tells you which words are good follow-ups." - @kleiba

🚀 Project Ideas

Tokenized Markov Chain (TMC) Search Indexer

Summary

A tool that addresses the failure mode of traditional Markov Chain text generators when presented with sequences unseen in the training corpus (resulting in zero probability for the next token).
This tool would augment a standard N-gram Markov Chain indexer by integrating a lightweight, pre-initialized word embedding layer (like a small BERT model) to handle out-of-vocabulary (OOV) or unseen context sequences by finding the nearest semantic neighbors in the embedding space.
Core value proposition: Making handcrafted, constrained text generation systems (like those for specific domain mimicry) robust to novel inputs by introducing semantic interpolation instead of discrete lookup failure.

Details

Key	Value
Target Audience	Users wanting to deploy lightweight, fast, and highly constrained text generators capable of handling user input variation (e.g., custom chatbots for legacy data, stylized writing tools).
Core Feature	Semantic fallback mechanism: When an N-gram context fails a lookup, the system converts the context tokens into embeddings, finds the nearest seen N-grams semantically, and uses the transition probability associated with those similar (but seen) states.
Tech Stack	Python, NLTK/spaCy for tokenization, a very small pre-trained self-supervised model (e.g., DistilBERT or a custom-trained 2-layer MLP over GloVe/fastText embeddings) for semantic mapping.
Difficulty	Medium (Integrating the embedding lookup and state mapping efficiently requires careful balancing to maintain the speed benefit of Markov Chains).
Monetization	Hobby

Notes

Users discussed how Markov chains "fall apart when the source material is very large" due to incoherent results, but also how they fail completely on unseen sequences ("the list of possible next tokens is an empty set" - Sohcahtoa82). This tool bridges that gap by allowing semantic generalization in the face of discrete failure.
It directly addresses the observed weakness that Markov chains "will ONLY generate sequences that existed in the source" (Sohcahtoa82) while retaining performance benefits over full LLMs for specific tasks.

Deterministic, Verifiable AI Sandbox

Summary

A service/tool designed to allow users to perfectly replicate LLM output by controlling for (and optionally disabling) the sources of non-determinism discussed in the thread.
Addresses confusion around output consistency ("even with temperature 0, decoding on a GPU is not guaranteed to be bit identical every run").
Core value proposition: Providing a computing environment where users can execute an LLM inference run and explicitly verify that the lack of determinism is due to configurable parameters (like floating-point ordering) rather than inherent model structure.

Details

Key	Value
Target Audience	Researchers, auditors, and developers needing provable reproducibility for small/medium models (e.g., benchmarking, debugging specific failure modes).
Core Feature	Environment configuration enforcing strict determinism: Disable GPU non-associative math (forcing CPU execution or specific CUDA flags), set fixed seed/temperature=0, and use highly stable tokenization/decoding libraries.
Tech Stack	Docker/Containerization, Python, dedicated libraries for deterministic float arithmetic (if running on GPU is required, otherwise CPU execution is primary), integration with popular inference frameworks (Hugging Face Transformers).
Difficulty	Medium (Achieving true bit-identical results across all hardware/software stacks, especially GPU, requires deep systems knowledge, but enforcing a CPU-only deterministic path is easier).
Monetization	Hobby

Notes

This solves the frustration mentioned by czl: "To make it fully deterministic you often have to disable some GPU optimizations or run on CPU only, which has a performance cost." This tool packages that complexity.
It directly engages with the concept of "best quality output" (otabdeveloper4: "turning off 'temperature' entirely makes sense") by creating the ideal environment where that quality can be consistently achieved and analyzed for loops or errors without external noise.

Schema-Oriented Reasoning Benchmark Generator

Summary

A service that automates the creation of structured, abstract logic puzzles (like the "wizards and warriors" example where the LLM failed to follow all rules) based on user-defined constraints, focusing on testing rule adherence and conceptual combination rather than rote memorization.
Solves the problem raised by wadadadad and Ardren regarding judging creativity/problem-solving correctness: LLMs often fail complex constraint satisfaction, even if the concepts are in the training data.
Core value proposition: Provides a clear, quantifiable, and repeatable way to test an LLM's ability to synthesize new procedural knowledge by assembling known components according to arbitrary, novel rules.

Details

Key	Value
Target Audience	AI researchers, prompt engineers, and developers building agents that require strict adherence to procedural instructions (e.g., agent simulation, complex data validation).
Core Feature	Procedural Graph Generator: User inputs a set of entities (e.g., 'Wizard', 'Witch', 'Pig', 'Dragon') and a list of abstract operations/rules ('Summon', 'Teleport', 'Combine'). The system generates sequences of turns/prompts that test the system's ability to maintain state and follow rules that result in a composition the model has likely never seen.
Tech Stack	Python, Pydantic for defining structured operations/states, possibly using a fine-tuned model optimized for schema/JSON output to generate the problem sequence/expected state tracking.
Difficulty	High (Requires defining a robust abstract state machine parser to verify correctness, which is harder than simple text comparison).
Monetization	Hobby

Notes

This directly addresses the discussion around the wizards puzzle failure: "Wizzard1 cannot summon," "Wizard2 has already teleported" (Ardren). This tool generates thousands of such scenarios automatically to test generalizable reasoning vs. pattern matching.
It leverages the Humean concept of combining known ideas ('pig' + 'dragon head') but formalizes it into testable procedural steps, satisfying shagie's interest in seeing how the model handles new problems.