RSPA: Recursive Sub-word Pruning Algorithm

A high-performance C++ tokenizer engine that uses Branching Entropy to outperform BPE in morphological segmentation speed and accuracy.

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The Breakthrough: Speed & Intelligence

RSPA is a departure from standard frequency-based tokenization methods such as BPE and WordPiece. Instead of greedily merging frequent character pairs, RSPA analyzes the information entropy of character transitions to discover statistically meaningful cut points in text.

Performance Benchmarks (Single Core)

Metric	GPT-4 (TikToken)	RSPA (C++ Engine)	Difference
Initialization (Cold Start)	~14.6 ms	~0.15 ms	97x Faster
Inference Time (per word)	~0.02 ms	~0.008 ms	2.5x Faster
Training Throughput	~20 MB/s	~400 MB/s	20x Faster
Memory Architecture	HashMap / Trees	Flat Arrays (LCP)	Low RAM Usage

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The Algorithm: Branching Entropy vs. BPE

Most modern language models rely on Byte Pair Encoding (BPE). BPE operates by merging the most frequent adjacent character pairs. While effective, this approach is blind to linguistic structure and often breaks morphological roots.

Example:

unremarkable → unr + emark + able   (BPE-style)
un + remark + able                 (Linguistically correct)

How RSPA Works

RSPA (Recursive Sub-word Pruning Algorithm) treats tokenization as a signal processing problem, using Shannon Entropy to identify semantic boundaries.

1. Trie Construction (O(N))

The corpus is streamed into a specialized C++ trie built on flat memory buffers. This enables processing of gigabytes of text with near-constant RAM usage.

2. Branching Entropy (H)

At each trie node, the entropy of outgoing character transitions is computed.

• Low Entropy: If a prefix is almost always followed by the same continuation, uncertainty is minimal. The prefix should be merged.
• High Entropy: If a prefix is followed by many different continuations, uncertainty spikes. This indicates a semantic boundary and triggers a cut.

Example:

• semi → conductor (low entropy → merge)
• semi → automatic, final, circle, colon (high entropy → cut)

3. Viterbi Inference (Dynamic Programming)

Unlike greedy tokenizers, RSPA uses a Viterbi pathfinding algorithm during inference.

Each candidate token is assigned a cost:

Cost = -log(P(token))

The tokenizer selects the sequence of tokens that minimizes the total cost across the sentence.

Result:

unhappiness → un + happiness   (optimal path)
unh + app + iness              (greedy failure)

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Build & Installation

The engine is implemented in pure C++17 with pybind11 bindings for seamless Python integration.

Prerequisites

• Python 3.x
• C++ compiler (GCC, Clang, or MSVC)
• pybind11

Compilation

RSPA compiles directly into a Python shared library (.so or .pyd).

# 1. Install dependencies
pip install pybind11

# 2. Compile the high-performance extensions
python3 setup.py build_ext --inplace

This produces two binaries:

• rspa_builder — the training engine with streaming I/O
• rspa_inference — the Viterbi tokenizer

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Usage

1. Training (Builder)

Train a vocabulary on large datasets (e.g., WikiText-103) without exhausting system memory.

import rspa_builder

trainer = rspa_builder.RPSA_Builder()

# Stream text directly from disk
trainer.train_from_file("wikitext-103/wiki.train.tokens")

# Export the optimized vocabulary
trainer.saveVocabulary("vocab_wiki.json")

2. Inference (Tokenizer)

Load the trained vocabulary and tokenize text using the Viterbi engine.

import rspa_inference

tokenizer = rspa_inference.RPSA_Inference("vocab_wiki.json")

text = "Unremarkable disagreements in the semiconductor industry."

tokens = tokenizer.tokenize(text)
print(tokens)

Output:

['Un', 'remarkable', ' ', 'disagreement', 's', ' ', 'in', ' ', 'the', ' ', 'semiconductor', ' ', 'industry', '.']

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Experimental Results (WikiText-103)

All experiments were conducted on the WikiText-103 dataset using a single CPU core. Training and inference were executed through the C++ engine with Python bindings, ensuring no Python-side loops during critical paths.

Training Performance

• Dataset Size: 515.59 MB (train.csv)
• Total Lines Processed: ~1.8 million
• Training Time: 6.56 seconds
• Throughput: 78.64 MB/s
• Vocabulary Size: 701,006 trie nodes
• Export Format: JSON (vocab_wiki.json)

The training pipeline streams data directly from disk into a flat-memory trie, avoiding full corpus loading and maintaining stable memory usage throughout.

Tokenization Quality Comparison

Comparison between RSPA (Viterbi-based inference) and GPT-4 tokenizer (TikToken-style BPE) using a high-vocabulary setting.

Example Outputs

Input: The semiconductor industry relies on photolithography.

• RSPA (13 tokens):

  ['The', ' ', 'semiconductor', ' ', 'industry', ' ', 'relies', ' ', 'on', ' ', 'photo', 'lithography', '.']
  

• GPT-4 (9 tokens):

  ['The', ' semiconductor', ' industry', ' relies', ' on', ' phot', 'olith', 'ography', '.']
  

Input: Hyperactive hypervisors virtualize the infrastructure.

• RSPA (13 tokens):

  ['Hyper', 'active', ' ', 'hyper', 'visors', ' ', 'virtualiz', 'e', ' ', 'the', ' ', 'infrastructure', '.']
  

• GPT-4 (10 tokens):

  ['Hyper', 'active', ' hyp', 'erv', 'isors', ' virtual', 'ize', ' the', ' infrastructure', '.']
  

Input: Artificial intelligence revolutionizes data processing.

• RSPA (11 tokens):

  ['Artificial', ' ', 'intelligence', ' ', 'revolutionize', 's', ' ', 'data', ' ', 'processing', '.']
  

• GPT-4 (8 tokens):

  ['Art', 'ificial', ' intelligence', ' revolution', 'izes', ' data', ' processing', '.']
  

Input: The electromagnetic spectrum contains ultraviolet light.

• RSPA (12 tokens):

  ['The', ' ', 'electromagnetic', ' ', 'spectrum', ' ', 'contains', ' ', 'ultraviolet', ' ', 'light', '.']
  

• GPT-4 (8 tokens):

  ['The', ' electromagnetic', ' spectrum', ' contains', ' ultr', 'aviolet', ' light', '.']
  

Input: Microservices architecture improves scalability.

• RSPA (9 tokens):

  ['Micro', 'services', ' ', 'architecture', ' ', 'improves', ' ', 'scalability', '.']
  

• GPT-4 (6 tokens):

  ['Micro', 'services', ' architecture', ' improves', ' scalability', '.']
  

Aggregate Results

• Total Tokens (RSPA): 58
• Total Tokens (GPT-4): 41
• Token Difference: +17 tokens (RSPA produces finer-grained morphological splits)

Inference Time (Total)

• RSPA: 1.0055 ms
• GPT-4: 8.9405 ms

Despite producing more linguistically meaningful tokens, RSPA achieves significantly lower total inference time due to flat-memory traversal and optimized Viterbi decoding.

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Contributing

RSPA is an open research project. Contributions are welcome in the following areas:

• Rust Port: Porting the inference engine to Rust for safety and parallelism
• GPU Acceleration: CUDA kernels for batched tokenization
• HuggingFace Integration: Wrapping RSPA as a custom PreTrainedTokenizer

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License

MIT Open Source