LSTM Networks and Sequence Memory

Each sequence has a fixed length, often described as maxlen in the source.

Programming

One Character at a Time

Character-level generation asks a narrow question repeatedly: given the characters available so far, which character should come next? The model does not produce an entire word or sentence in one operation. It predicts one character, appends that character to the text, and uses the enlarged context for the next prediction.

Building Training Windows

Training begins by dividing the text into overlapping character sequences. Each sequence has a fixed length, often described as maxlen in the source. The character immediately following a sequence becomes that sequence's target. In other words, the input supplies the context and the target identifies what the model should learn to predict next.

Worked example

Aligning context and target

Suppose a toy text is divided into fixed-length windows of four characters. Show how overlapping windows are paired with the character that follows each window.

1
First window
The first four-character context is paired with the fifth character as its next-character target.
2
Advance one position
The next context begins one character later, so it overlaps most of the first context. Its target is the character immediately after this new window.
3
Repeat
Moving the window through the text creates many context-target pairs. Every pair preserves the same contract: the input is the context, and the target is the following character.

Result

Overlapping windows turn one text string into many supervised learning examples, each teaching the relationship between a fixed-length context and the character after it.

How does a text string become multiple fixed-length input windows, with each window aligned to the character that follows it?

The source describes the input array x as three-dimensional. Its dimensions correspond to the number of sequences, the sequence length maxlen, and the number of unique characters. The target array y contains the one-hot-encoded character that follows each input sequence. This alignment is the central data contract for the training data.

From Context to Probabilities

The generation model combines an LSTM layer with a Dense softmax classifier. The LSTM processes the character sequence and uses sequence memory to help represent information from earlier characters while considering the current sequence. The Dense softmax classifier converts the model's result into a probability distribution over possible next characters.

How does a fixed-length character sequence move through the LSTM and Dense softmax classifier to produce next-character probabilities?

The Dense softmax output must represent the full character vocabulary. If the vocabulary contains the unique characters used by the training text, the classifier needs one output position for each of those possible characters. The target's one-hot encoding and the classifier's output positions must therefore refer to the same character set.

How does the LSTM use earlier characters while processing the current sequence to help predict what comes next?

The Autoregressive Loop

After training, generation starts with a seed snippet. The routine sends the current fixed-length context through the model, obtains a distribution for the next character, adjusts that distribution using a temperature, and samples one character. The sampled character is appended to the generated text. The oldest character is then removed from the fixed-length context so that the next prediction uses the newest available window.

What happens at each step when the current context is sent through the model, a character is sampled, the context advances, and the new character is appended?

Worked example

Tracing one generation step

A seed snippet is already available as the current context. Describe one complete generation step without assuming a particular predicted character.

1
Read the context
The current fixed-length character window is presented to the trained model.
2
Predict
The LSTM and Dense softmax classifier produce a probability distribution over the character vocabulary.
3
Adjust and sample
The distribution is adjusted using the selected temperature, and one character is sampled from it.
4
Append
The sampled character is added to the generated text.
5
Advance
The oldest character is removed from the fixed-length context, leaving a new context for the next iteration.

Result

One iteration both extends the generated passage and prepares the next context. Repeating the iteration creates the passage character by character.

Temperature and Variety

Temperature changes the probability distribution used for sampling. A lower temperature makes the sampling distribution more concentrated, so choices tend to favor the model's more likely characters. A higher temperature makes the distribution more varied, allowing less likely characters to receive more opportunity during sampling. Temperature changes how the same model predictions are sampled; it does not create a separate model.

How does changing temperature reshape the probability distribution over possible next characters and affect generated text?

The source generation loop compares temperatures of 0.2, 0.5, 1.0, and 1.2 while training progresses. These values are alternative sampling choices applied to predictions from the same model, making it possible to compare more concentrated and more varied generated text.

Diagnosing Generation Failures

A poor-looking passage does not identify its own cause. Debug the system in stages: data preparation, model construction, and sampling. Checking these stages separately prevents a sampling adjustment from hiding a data or model problem.

How can symptoms of failed generation be traced to data preparation, model construction, or sampling?

Common mistake
Pairing a context with the wrong target character.
What it looks like
The input sequence is taken from one position, but the target is not the character immediately following that sequence.
Why it fails
The training example no longer teaches the intended next-character relationship.
Do this instead
Check that every input sequence is aligned with the character directly after it.
Common mistake
Using an output layer that does not cover the complete character vocabulary.
What it looks like
The classifier has fewer output positions than the number of unique characters used by the training text.
Why it fails
The model cannot represent a probability for every possible target character.
Do this instead
Check that the Dense softmax output size matches the character vocabulary.
Common mistake
Debugging only the temperature.
What it looks like
Changing temperature repeatedly when the sampled index is converted back to the wrong character.
Why it fails
Temperature changes sampling, but it does not correct a broken probability-to-character conversion.
Do this instead
Verify the conversion from predicted probabilities to a sampled index and then back to a character.

Practice the Trace

MEDIUM

Describe the next generation step after a model has received its current fixed-length context. Include the model prediction, temperature adjustment, character sampling, text append, and context update.

Hints

The model first produces a distribution over the character vocabulary.
The sampled character must be added to the generated text.
The next context removes the oldest character so the window remains fixed-length.

Your attempt (not saved)

MEDIUM

A generation result looks wrong. Explain which stage you would inspect first if the target is not the character immediately following each input sequence, and which stage you would inspect if the sampled probability index is converted back to the wrong character.