Project 16: Markov Chain Text Generator

A text generator that learns from a corpus (e.g., Shakespeare) and generates new text that mimics the style. Uses Markov chains: the next word depends only on the previous n words.

Quick Reference

Attribute Value
Difficulty Level 2: Intermediate (The Developer)
Main Programming Language Python
Alternative Programming Languages C, JavaScript, Rust
Coolness Level Level 4: Hardcore Tech Flex
Business Potential 2. The “Micro-SaaS / Pro Tool” (Solo-Preneur Potential)
Knowledge Area Probability / Markov Chains
Software or Tool Text Generator
Main Book “Speech and Language Processing” by Jurafsky & Martin

1. Learning Objectives

By completing this project, you will:

  1. Translate math definitions into deterministic implementation steps.
  2. Build validation checks that make correctness observable.
  3. Diagnose numerical, logical, and data-shape failures early.
  4. Explain tradeoffs in interviews using evidence from your own build.

2. All Theory Needed (Per-Concept Breakdown)

This project applies the following theory clusters:

  • Symbolic-to-numeric translation (expressions, data shapes, invariants)
  • Stability constraints (precision, scaling, stopping criteria)
  • Optimization or inference logic (depending on project objective)
  • Evaluation discipline (error analysis, test coverage, reproducibility)

Concept A: Mathematical Representation Discipline

Fundamentals A math expression is not executable until you define representation, ordering, and domain constraints. The same equation can be represented as a token stream, tree, matrix pipeline, or probability graph. Choosing representation determines what bugs you can catch early.

Deep Dive into the concept Most project failures begin before algorithm selection: they start with ambiguous representation. If your parser cannot distinguish unary minus from subtraction, your calculator fails. If your matrix dimensions are implicit rather than validated, your linear algebra pipeline fails silently. If your probabilistic assumptions (independence, stationarity, or class priors) are not explicit, your inference can look accurate on one split and collapse on another. The core implementation move is to treat representation as a contract. Define each object with shape, domain, and semantic intent. Then enforce invariants at boundaries: input parser, preprocessing, training loop, evaluation stage. This makes debugging local instead of global.

How this fits this project You will encode each operation with explicit contracts and invariant checks.

Definitions & key terms

  • Invariant: Property that must hold before and after each operation.
  • Shape contract: Expected dimensional structure of vectors/matrices/tensors.
  • Domain constraint: Allowed value range (for example log input > 0).

Mental model diagram

User Input -> Representation Layer -> Validated Operation -> Observable Output
              (tokens/shapes)        (invariants pass)       (tests/plots/logs)

How it works

  1. Parse/ingest data into typed structures.
  2. Validate shape/domain invariants.
  3. Execute operation.
  4. Compare observed output with expected behavior.
  5. Record failure signature if mismatch appears.

Minimal concrete example

PSEUDOCODE
read expression
tokenize with precedence rules
if token sequence invalid -> return syntax error
evaluate tree
if domain violation -> return bounded diagnostic
print value and confidence check

Common misconceptions

  • “If it runs once, representation is correct.” -> false.
  • “Type checks are enough without shape checks.” -> false.

Check-your-understanding questions

  1. Which invariant catches division-by-zero earliest?
  2. Why does shape validation belong at boundaries rather than only in core logic?
  3. Predict failure if tokenization ignores unary minus.

Check-your-understanding answers

  1. Domain check on denominator before operation execution.
  2. Boundary validation keeps errors local and diagnostic.
  3. Expressions like -2^2 get misinterpreted and produce wrong precedence behavior.

Real-world applications Feature preprocessing, model-serving input validation, and experiment-tracking schema enforcement.

Where you’ll apply it This project and every downstream project in the sprint.

References

  • CSAPP (Bryant & O’Hallaron), floating-point chapter
  • Math for Programmers (Paul Orland), representation-oriented chapters

Key insight Correct representation reduces the complexity of every later decision.

Summary Stable ML math implementations start with explicit contracts, not implicit assumptions.

Homework/Exercises

  1. Write five invariants for your project.
  2. Build a failing test input for each invariant.

Solutions

  1. Include at least one shape, one domain, one convergence, one reproducibility, and one output-range invariant.
  2. Each failing input should trigger exactly one diagnostic to keep root-cause analysis clean.

3. Build Blueprint

  1. Scope the smallest end-to-end slice that produces visible output.
  2. Add deterministic tests and edge-case probes.
  3. Layer complexity only after baseline behavior is stable.
  4. Add metrics logging before optimization.
  5. Run failure drills: perturb inputs, scale values, and check stability.

4. Real-World Outcome (Target)

$ python markov.py train shakespeare.txt --order=2

Training on Shakespeare's complete works...
Vocabulary: 29,066 unique words
Bigram transitions: 287,432

$ python markov.py generate --words=50

Generated text (order-2 Markov chain):
"To be or not to be, that is the question. Whether 'tis nobler
in the mind to suffer the slings and arrows of outrageous fortune,
or to take arms against a sea of troubles and by opposing end them."

$ python markov.py generate --order=1 --words=50

Generated text (order-1, less coherent):
"The to a of and in that is not be for it with as his this
but have from or one all were her they..."

[Shows transition table for common words]
P(next="be" | current="to") = 0.15
P(next="the" | current="to") = 0.12

Implementation Hints: Build a dictionary: transitions[context] = {word: count, ...}

For bigrams (order-1): context is single previous word. For trigrams (order-2): context is tuple of two previous words.

To generate:

context = start_token
while True:
    candidates = transitions[context]
    next_word = weighted_random_choice(candidates)
    if next_word == end_token:
        break
    output.append(next_word)
    context = update_context(context, next_word)

Higher order = more coherent but less creative (starts copying source).

Learning milestones:

  1. Generated text is grammatical-ish → You understand transition probabilities
  2. Higher order = more coherent → You understand model complexity trade-offs
  3. You see this as a simple language model → You’re ready for RNNs/transformers

5. Core Design Notes from Main Guide

Core Question

“How much of the past do you need to remember to predict the future?”

This is one of the deepest questions in sequence modeling. Markov chains give a precise answer: you only need the last n states. This “memoryless” property seems limiting, but it is remarkably powerful. Language has patterns–“to be” is often followed by “or”–and these patterns are captured by conditional probabilities. The philosophical insight: most sequential data has structure, and that structure can be exploited even with limited memory. Modern transformers use attention to look at ALL previous states, but Markov chains teach you why that is valuable by showing you what is lost when you cannot.

Concepts You Must Understand First

Stop and research these before coding:

  1. **Conditional Probability P(A B)**
    • What does “probability of A given B” actually mean?
    • How is it different from P(A and B)?
    • Why does P(next_word current_word) define the whole Markov chain?
    • Book Reference: “Think Bayes” Chapter 1 - Allen Downey
  2. The Markov Property (Memorylessness)
    • What does it mean that “the future depends only on the present”?
    • Why is this assumption both a simplification and a feature?
    • How do n-gram models extend this to “n states” of memory?
    • Book Reference: “All of Statistics” Chapter 21 - Larry Wasserman
  3. Transition Probability Matrices
    • How do you represent all P(next current) in a matrix?
    • What do the rows and columns mean?
    • Why must each row sum to 1?
    • Book Reference: “Speech and Language Processing” Chapter 3 - Jurafsky & Martin
  4. N-gram Language Models
    • What is the difference between unigrams, bigrams, trigrams?
    • How does increasing n affect model behavior?
    • What is the tradeoff between memory and generalization?
    • Book Reference: “Natural Language Processing” Chapter 4 - Eisenstein
  5. Sampling from Discrete Distributions
    • How do you pick a random word according to probabilities?
    • What is the weighted random choice algorithm?
    • Why is this fundamental to generative models?
    • Book Reference: “Grokking Algorithms” Chapter 10 - Aditya Bhargava

Questions to Guide Your Design

Before implementing, think through these:

  1. Data structure for transitions: How will you store P(next context) efficiently? A dictionary of dictionaries? What happens when context has not been seen?

  2. Handling sentence boundaries: How do you know when to start a new sentence? Do you need special START and END tokens?

  3. Smoothing unseen transitions: What if your model encounters a context it never saw during training? Should probability be 0, or should you “smooth” it somehow?

  4. Order selection: How do you let users choose bigrams vs trigrams vs higher? How does your data structure change?

  5. Memory vs creativity tradeoff: With high n, the model starts copying the source verbatim. How do you measure this? What is the “right” n?

  6. Evaluation: How do you measure if generated text is “good”? Perplexity? Human evaluation?

Thinking Exercise

Before coding, trace through this by hand:

Given this tiny corpus: “the cat sat. the cat ran. the dog sat.”

Build the bigram (order-1) transition table:

P(next | "the") = ?
P(next | "cat") = ?
P(next | "dog") = ?
P(next | "sat") = ?
P(next | "ran") = ?

Now generate text starting from “the”:

  1. Look up P(next “the”). What are the options?
  2. Randomly choose according to probabilities
  3. Repeat until you hit a sentence end

Questions to answer:

  • What is P(“cat” “the”)? What is P(“dog” “the”)?
  • Why can you not generate “the dog ran” even though all words exist?
  • What would happen with a trigram model on this tiny corpus?

Interview Questions

  1. “What is the Markov property and why is it useful?”
    • Expected answer: Future depends only on present state, not full history. Useful because it makes computation tractable–you only need to track current state.
  2. “How do Markov chains relate to modern language models like GPT?”
    • Expected answer: Markov chains are a simple language model. GPT uses attention to consider ALL previous tokens (not just the last n), with learned representations instead of raw counts.
  3. “What is the time and space complexity of training an n-gram model?”
    • Expected answer: O(total_words) time to scan corpus. Space is O(vocab^n) in worst case but typically sparse–actual unique n-grams seen.
  4. “How would you handle words not seen during training?”
    • Expected answer: Smoothing techniques like Laplace (add-1), Kneser-Ney, or backoff to lower-order models.
  5. “What is perplexity and how does it relate to Markov chains?”
    • Expected answer: Perplexity measures how “surprised” the model is by test data. Lower is better. For Markov chains, perplexity = 2^(cross-entropy).
  6. “Why do higher-order Markov models eventually just memorize the training data?”
    • Expected answer: With high n, each context becomes unique, so there is only one possible next word–the exact word from training. Model loses ability to generalize.

Hints in Layers (Treat as pseudocode guidance)

Hint 1: Start by just counting. Build a dictionary where keys are contexts (single words for bigrams, tuples for higher) and values are dictionaries mapping next_word to count.

Hint 2: To sample from counts, convert to probabilities by dividing each count by the total for that context. Use random.choices() with weights, or implement weighted random choice yourself.

Hint 3: For sentence boundaries, add special tokens like <START> and <END>. When training, each sentence becomes: <START> word1 word2 ... wordN <END>. When generating, start from <START> and stop when you hit <END>.

Hint 4: For higher-order models (trigrams, etc.), use tuples as dictionary keys: transitions[("the", "cat")] = {"sat": 1, "ran": 1}. The tuple represents the context.

Hint 5: If you want the model to be more “creative,” add temperature scaling: instead of sampling from raw probabilities, raise them to power 1/T and renormalize. T > 1 makes output more random; T < 1 makes it more deterministic.

Books That Will Help

Topic Book Chapter
Markov Chains Theory “All of Statistics” by Larry Wasserman Chapter 21: Markov Chain Monte Carlo
N-gram Language Models “Speech and Language Processing” by Jurafsky & Martin Chapter 3: N-gram Language Models
Conditional Probability “Think Bayes” by Allen Downey Chapter 1-2: Probability Basics
Smoothing Techniques “Foundations of Statistical NLP” by Manning & Schutze Chapter 6: Statistical Estimation
Language Model Evaluation “Natural Language Processing” by Eisenstein Chapter 6: Language Models
Practical Implementation “Natural Language Processing with Python” by Bird et al. Chapter 2: Accessing Text

Part 5: Optimization

Optimization is how machines “learn.” Every ML algorithm boils down to: define a loss function, then minimize it.

6. Validation, Pitfalls, and Completion

Common Pitfalls and Debugging

Problem 1: “Outputs drift after a few iterations”

  • Why: Hidden numerical instability (unscaled features, aggressive step size, or repeated subtraction of nearly equal values).
  • Fix: Normalize inputs, reduce step size, and track relative error rather than only absolute error.
  • Quick test: Run the same task with two scales of input (for example x and 10x) and compare normalized error curves.

Problem 2: “Results are inconsistent across runs”

  • Why: Random seeds, data split randomness, or non-deterministic ordering are uncontrolled.
  • Fix: Set seeds, log configuration, and store split indices and hyperparameters with each run.
  • Quick test: Re-run three times with the same seed and confirm metrics remain inside a tight tolerance band.

Problem 3: “The project works on the demo case but fails on edge cases”

  • Why: Tests only cover happy-path inputs.
  • Fix: Add adversarial inputs (empty values, extreme ranges, near-singular matrices, rare classes).
  • Quick test: Build an edge-case test matrix and ensure every scenario reports expected behavior.

Definition of Done

  • Core functionality works on reference inputs
  • Edge cases are tested and documented
  • Results are reproducible (seeded and versioned configuration)
  • Performance or convergence behavior is measured and explained
  • A short retrospective explains what failed first and how you fixed it

7. Extension Ideas

  1. Add a stress-test mode with adversarial inputs.
  2. Add a short benchmark report (runtime + memory + error trend).
  3. Add a reproducibility bundle (seed, config, and fixed test corpus).

8. Why This Project Matters

Not specified

This project is valuable because it creates observable evidence of mathematical reasoning under real implementation constraints.