Generalized Mathematical Music Neural Network Architecture Specification

Neural Architecture Instructions for Generating the Musical Artwork

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Let me break down each section and explain how they work together:

1. Input Processing:

Tokenizer --> |Embeddings| Transformer[Math Understanding Transformer]
Mathinput[Mathematical Formula/Concept] --> Tokenizer[Custom Math Tokenizer]
GenreInput[Genre Specification] --> StyleEncoder[Style Embedding Layer]

This section handles two parallel inputs:

• Mathematical Input: Say we input "T(H) function composition". The Custom Math Tokenizer would break this into meaningful tokens like ["T(", "H", ")", "function", "composition"], similar to how GPT tokenizes text, but specialized for mathematical notation.
• Genre Input: When we specify "Mathematical Hip-Hop", the Style Embedding Layer converts this into a vector representation that captures musical characteristics of hip-hop.

2. Core Architecture:

StyleEncoder --> |Style Vectors| StyleMixer[Style Conditioning Layer]
Transformer --> |Encoded Patterns| LSTM1[LSTM Pattern Generator]

This is where the magic happens:

• The Transformer (similar to GPT architecture) takes those math tokens and generates a deep understanding of the mathematical patterns
• The LSTM Pattern Generator takes these patterns and starts generating basic musical structures
• The StyleMixer combines these with the genre characteristics

3. Musical Elements Generator:

LSTM1 --> |Contours| RNN3[Melody RNN]
LSTM1 --> |Base Patterns| RNN1[Rhythm RNN]
LSTM1 --> |Progressions| RNN2[Harmony RNN]

This splits the musical generation into three parallel streams:

• Rhythm RNN: Generates rhythmic patterns that reflect the mathematical transformations
• Harmony RNN: Creates chord progressions that represent state spaces
• Melody RNN: Develops melodic lines that embody the mathematical processes

4. Generation Pipeline:

Quantizer --> MidiGen[MIDI Generator]
EventSeq --> |MIDI Events| Quantizer[Musical Quantizer]
StyleMixer --> |Styled Patterns| EventSeq[Musical Event Sequence]

This converts the abstract musical patterns into actual music:

• Musical Event Sequence: Combines rhythm, harmony, and melody into a single timeline
• Quantizer: Ensures everything aligns to musical time (like snapping to a grid)
• MIDI Generator: Produces playable MIDI files

5. Validation:

Backprop --> |Adjustments| LSTM1
MidiGen --> |Generated MIDI| RuleCheck[Rule-Based Validator]
RuleCheck --> |Validation Score| Backprop[Backpropagation Loop]

This ensures quality and accuracy:

• Rule-Based Validator: Checks both musical rules (like proper harmony) and mathematical validity
• Backpropagation Loop: Feeds errors back to improve generation

6. Training Data:

Rules[(Validation Rules DB)] --> RuleCheck
MathCorpus[(Mathematical Corpus)] --> Transformer
MusicDataset[(Genre-Labeled MIDI)] --> StyleEncoder

The knowledge bases:

• Mathematical Corpus: Repository of mathematical concepts and their relationships
• Genre-Labeled MIDI: Database of music in different styles
• Validation Rules: Both musical theory rules and mathematical validity checks

[^1]: graph TD