# The RNN used by `poet` (`RnnStack`)

This document explains how `RnnStack` — the model driving the `poet` character-generation
CLI — actually works. It is not an RNN in the LSTM/GRU sense: there is no shared weight matrix
applied repeatedly across time. Instead it's a **stack of independently-weighted RBMs, one per
"tap" in a fixed-size lookback window, chained together by feeding each layer's hidden
activations forward as extra "context" input to the next layer**. The recurrence is emulated by
re-running this same chain one step at a time during generation, sliding a window of the last N
characters through it.

Relevant sources: `source/RnnStack.{hpp,cpp}`, `source/Layer.{hpp,cpp}`, `source/AStack.cpp`,
`source/RnnTextHelper.{hpp,cpp}`, `source/matutils.hpp`, `source/poet.cpp`.

## The alphabet

`RnnTextHelper` encodes characters as one-hot vectors over `NUM_CODES = 37` symbols:

- index `0` = space (also the fallback for anything that isn't a letter or digit)
- indices `1..26` = `A`..`Z` (case is folded via `toupper` — **lowercase is not represented**)
- indices `27..36` = `0`..`9`

`ch2idx`/`idx2ch` do the conversion; `Matutils::char2vec`/`vec2char` wrap them as one-hot
`arma::mat` rows. Because case is discarded at encoding time, everything `poet` generates comes
out upper-case, regardless of the casing in the source text or seed string.

## Project geometry: `poet_2v_5s`

`poet.cpp` hardcodes the project name `poet_2v_5s`, loaded via `StackCreator::fromFile`. The name
encodes its shape: **2v** = 2 stacked visible character-frames per layer, **5s** = 5 layers deep
(the RBM "stack"). Concretely (`poet_2v_5s.prj`):

| layer id | visible (X×Y) | hidden | context |
|---|---|---|---|
| 0 | 37×2 = 74 | 128 | 0 |
| 1 | 37×2 = 74 | 128 | 128 |
| 2 | 37×2 = 74 | 128 | 128 |
| 3 | 37×2 = 74 | 128 | 128 |
| 4 | 37×2 = 74 | 128 | 128 |

Each `Layer` is a plain `Rbm` (`Layer.hpp:29` → `Rbm(numVisibleX*numVisibleY + numContext,
numHidden)`), so layers 1–4 are actually 202-visible-unit RBMs (74 character bits + 128 context
bits inherited from the previous layer); layer 0 has no context and is a plain 74-unit RBM.
`RnnStack::getSeqLen()` returns `numLayers()` (5) — the "depth" of the stack doubles as the length
of the character lookback window used during generation.

## Training data: character bigrams

`RnnTextHelper::createTraining(file, seq_len=2)` turns a text file into a training batch:

- keeps a rolling 2-row window (`pattern`) of one-hot vectors: `row0` = current character,
  `row1` = previous character (each new character shifts the window and overwrites row 0).
- collapses runs of whitespace/unknown characters down to a single space (skips a char if both it
  and the previous character map to index 0).
- for every accepted character, flattens `pattern` row-major (`as_row()`, confirmed block order:
  `[current(37) | previous(37)]`) and appends it as one training row.

So the batch has one 74-wide row per character in the source text: `[char_t | char_t-1]`. This
matches every layer's 74-wide visible geometry — every layer is trained on the *same* stream of
character bigrams, just offset in time from each other (next section).

## Training: `RnnStack::train`

```cpp
padding      = zeros(numLayers - 1, batch.n_cols)     // 4 zero rows
batch_padded = [batch ; padding]                       // append padding at the end
c            = zeros(N, layer[0].numContext())         // starts as an N×0 matrix (no columns)

for i in 0..numLayers-1:
    layer          = getLayer(i)
    batch_shifted  = batch_padded.rows(i, N+i-1)        // batch, shifted forward by i rows
    vc             = join_rows(batch_shifted, c)        // attach inherited context
    layer.train(vc, listener)                           // contrastive divergence on this layer
    layer.gibbs_vh(vc, c)                                // c ← toHiddenProbs(vc); vc ← reconstruction (vc discarded)
```

The subtlety is `c`: it starts as a zero-column matrix (matching layer 0, which has no context),
and is **mutated in place** by `gibbs_vh` on every iteration — `gibbs_vh(v_probs, h_probs)` sets
`h_probs = toHiddenProbs(v_probs)`, so after layer *i* trains, `c` becomes layer *i*'s hidden-unit
probabilities, which is exactly what layer *i+1* expects as its context input. This is the whole
recurrence mechanism: **each layer's hidden activations become the next layer's extra visible
input**, propagated forward once per training step.

`batch_shifted` is `batch_padded` windowed with an offset of `i` rows, i.e. layer `i` is trained on
training-row `j+i` while the loop index is conceptually `j`. So for a given alignment index `j`,
layer 0 sees the bigram at `j`, layer 1 sees the bigram at `j+1`, ..., layer 4 sees the bigram at
`j+4` (the most recent). In other words: **layer 0 is the "oldest" tap, layer 4 the "newest"**, and
by the time training reaches layer 4, its context input already encodes information recursively
folded in from characters `j..j+3`. This is a 5-character lookback window, unrolled across depth
(distinct weights per tap) rather than across time (shared weights) as a true RNN would.

## Generation: `RnnStack::step_forward`

`state` is a rolling `numLayers × NUM_CODES` matrix of single-character one-hot rows: row 0 is the
newest character, row `numLayers-1` the oldest of the last 5. Each call:

```cpp
state = shift(state, 1, 0);   // age every row down by one
state.row(0) = v_curr;        // newest known character goes in at row 0

for j in 0..numLayers-1:
    k      = numLayers - j - 1              // j=0 → k=4 (oldest); j=4 → k=0 (newest/current)
    layer  = getLayer(j)
    v      = [zeros(37) | state.row(k)]     // "unknown target" bigram: only the lagged half is known
    vc     = join_rows(v, c)                // attach context inherited from layer j-1
    layer.gibbs_vh(vc, c)                   // c ← this layer's hidden probs (context for next layer)
    r      = vc_to_v(vc, layer.numContext())// strip context columns back off
return r   // == the last layer's (j=4, k=0) reconstruction
```

Each layer is asked "given only the known previous character (`state.row(k)`) plus context
inherited from older taps, reconstruct the full bigram" — the zeroed first half is what the RBM's
one round of Gibbs sampling (`toHiddenProbs` then `toVisibleProbs`) has to fill in. Only the
**last** layer's reconstruction (built from the newest character, `k=0`, with all four older
layers' context folded in) is returned; `to_next()` (`RnnStack.cpp:121`) takes the first 37 columns
of that as the network's guess for the *next* character.

## Decoding: `poet.cpp` / `RbmListener::forward`

`forward()` takes an optional `temperature` (default `0.0`):

```cpp
auto pickNext = [temperature](arma::mat &next) {
    if (temperature > 0.0) stack->sample_one_hot(next, temperature);
    else                   stack->clamp_one_hot(next);
};

// priming: feed the seed string character-by-character to populate `state`
for each char in seed:
    r    = step_forward(state, char2vec(char))
    next = to_next(r); pickNext(next)          // result unused except to keep looping

// generation: feed each predicted character back in as the next input
for i in seqLen..len:
    curr = next
    r    = step_forward(state, curr)
    next = to_next(r); pickNext(next)
```

`temperature <= 0` keeps the original behavior: `clamp_one_hot` is a hard argmax (`index_max()` →
one-hot), fully deterministic given a trained model and a seed. `temperature > 0` instead calls
`sample_one_hot` (`RnnStack.cpp`), which now does proper categorical sampling: the 37 independent
sigmoid activations in `next` are raised to `1/temperature` and renormalized into a distribution
(`temperature < 1` sharpens it towards argmax, `temperature > 1` flattens it towards uniform), then
one code is drawn from that distribution via a cumulative-sum draw. This replaced an older
implementation that sampled each code as an independent Bernoulli and only patched the result back
into a proper one-hot vector when *more than one* bit happened to fire — leaving `srcDst` as a
non-one-hot probability vector whenever exactly zero or one bits fired.

`main()` exposes this as a third CLI argument: `poet f <seed> [temperature]`, e.g. `poet f "the "
0.7`. Sampling only produces different output across process runs because `main()` now seeds
Armadillo's RNG (`arma::arma_rng::set_seed_random()`) — Armadillo otherwise defaults to a fixed
seed, which would have made every run's "random" draws identical.

`RnnStack::to_curr()` is also computed once per generation step but its result is immediately
discarded (overwritten by `curr = next` at the top of the next iteration) — dead code kept from
development/debugging.

Two consequences worth knowing when reading `poet` output:

- **Greedy argmax decoding (`temperature <= 0`, the default) is why generated text degenerates into
  short repeating loops** (e.g. `...MURPURSE AN MURPURSE AN...`) once the rolling 5-character state
  re-enters a cycle it has visited before — there's no randomness to break out. Passing a
  `temperature > 0` avoids this by sampling instead.
- If the seed string is shorter than `numLayers` (5) characters, the oldest rows of `state` are
  still zero (not a space one-hot) when generation begins — the model briefly sees "blank" rather
  than real history for the first few generated characters.

## Summary picture

```
Text file --collapse whitespace, bigram window--> training batch [char_t | char_t-1]  (74-wide rows)
                                                          │
                    ┌─────────────────────────────────────┴─────────────────────────────────────┐
                    │  Layer 0 (oldest tap, no context)                                            │
                    │     CD train on batch                                                        │
                    │     context₀ = hidden_probs(batch)          ──► fed into Layer 1              │
                    │  Layer 1 (context=128)                                                        │
                    │     CD train on [batch shifted +1 | context₀]                                 │
                    │     context₁ = hidden_probs(...)            ──► fed into Layer 2              │
                    │  ...                                                                            │
                    │  Layer 4 (newest tap)                                                          │
                    │     CD train on [batch shifted +4 | context₃]                                  │
                    └───────────────────────────────────────────────────────────────────────────────┘

Generation: same 5-layer chain, run once per output character, consuming a sliding 5-character
window of state (oldest → layer 0 ... newest → layer 4), context threaded the same way; only
layer 4's reconstruction is decoded (argmax) into the next character.
```