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uuugi/gclm-constrained-decoding

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Goal-Conditioned Reachability Logit Masker (GCLM)

![GitHub Repo](https://github.com/uuuugi/Goal-Conditioned-Reachability-Logit-Masker) ![Paper PDF](paper.pdf) ![Hugging Face](https://huggingface.co/uuugi/gclm-constrained-decoding) ![Python 3.9+](https://www.python.org/downloads/) ![PyTorch 2.0+](https://pytorch.org/) ![License: MIT](LICENSE)

An ultra-fast, strictly O(1) runtime Goal-Conditioned Reachability Logit Masking Engine for Large Language Models. GCLM mathematically guarantees that an LLM will strictly reach designated goal/accepting states within a fixed token budget (T_max), fundamentally preventing dead-end traps and truncated syntax failures.

๐Ÿ“„ Paper: **Read / Download `paper.pdf`**  |  ๐Ÿ’ป GitHub: **uuuugi/Goal-Conditioned-Reachability-Logit-Masker**


๐Ÿ’ก Key Differences: GCLM vs. Forward DFA Maskers (Outlines / SGLang)

[Traditional Forward DFA (Outlines / SGLang)]
  Start (A) โ”€โ”€โ”€ Token X โ”€โ”€โ”€โ–ถ [Valid Branch D] โ”€โ”€โ”€ Token Y โ”€โ”€โ”€โ–ถ [Dead-End / Truncated Trap โŒ]
  (Only checks if transition exists from current state)

[GCLM: Time-Bounded Backward Reachability (Ours)]
  Start (A) โ”€โ”€โ”€ Token X (Masked to -inf โ›”)
            โ””โ”€โ”€ Token B โ”€โ”€โ”€โ–ถ State C โ”€โ”€โ”€โ–ถ Goal / Closing '}' โœ…
  (Preemptively prunes any branch that cannot reach Goal in <= T_rem steps)
FeatureStandard Forward DFA (Outlines / SGLang)**GCLM (Ours)**
Masking BasisCurrent state validity (s_curr -> s')Time-bounded backward reachability (s_curr -> s' ->* S_goal in โ‰ค T_rem - 1 steps)
Dead-End TrapsโŒ May enter valid forward branches that lead to dead-endsโœ… Preemptively masked before entering trap
Token Budget ExceededโŒ Outputs truncated/broken syntax when budget endsโœ… Forces early syntax closure before budget exhaustion
Per-Token OverheadO(1) table lookupStrict O(1) vectorized PyTorch lookup (< 0.1ms)
Complexity ScalingScales with active state transitionsZero runtime dependence on state count (S)

๐Ÿ“ Mathematical Formulation

1. Offline Backward BFS Table Builder

Given an FSM (S, ฮฃ, ฮด, s_0, S_goal) and maximum token budget T_max, we precompute a reachability tensor R of shape (T_max + 1, |S|) via vectorized backward BFS:

python
# Base Step (t = 0):
R[0, s] = 1  if (s in S_goal)  else 0

# Vectorized Backward BFS (for t = 1 ... T_max):
R[t, s] = R[t-1, s]  OR  (โˆƒ v โˆˆ V such that ฮด(s, v) >= 0 and R[t-1, ฮด(s, v)] == 1)

2. Strict O(1) Runtime Logits Masking

At decoding step k with remaining token budget T_rem = T_max - k:

python
# Step 1: Vectorized check for valid transitions within remaining budget
ValidTokens(v) = (ฮด(s_curr, v) >= 0)  AND  R[min(T_rem - 1, T_max), clamp(ฮด(s_curr, v), 0)]

# Step 2: In-place O(1) logit masking
Logits[v] = Logits[v]  if ValidTokens(v) == 1  else -inf

๐Ÿ“ Repository Structure

gclm_project/
โ”œโ”€โ”€ core/
โ”‚   โ”œโ”€โ”€ __init__.py
โ”‚   โ”œโ”€โ”€ fsm_builder.py          # Transitions tensor & vectorized backward BFS reachability table
โ”‚   โ”œโ”€โ”€ logit_processor.py      # Hugging Face LogitsProcessor compatible O(1) in-place masker
โ”‚   โ””โ”€โ”€ compiler.py             # Tokenizer-aware grammar/pattern compiler
โ”œโ”€โ”€ benchmarks/
โ”‚   โ”œโ”€โ”€ synthetic_deadend.py    # Experiment 1: Dead-end trap avoidance benchmark
โ”‚   โ”œโ”€โ”€ json_budget_bench.py    # Experiment 2: Real-world strict budget JSON benchmark
โ”‚   โ”œโ”€โ”€ tool_calling_bench.py   # Experiment 3: Multi-step agent action budget benchmark
โ”‚   โ”œโ”€โ”€ scaling_bench.py        # Experiment 4: Complexity scaling (|S|=10~10,000) & plot generator
โ”‚   โ”œโ”€โ”€ real_model_bench.py     # Experiment 5: Real lightweight LLM (Qwen2.5) E2E benchmark
โ”‚   โ””โ”€โ”€ latency_bench.py        # Per-token runtime overhead benchmark
โ”œโ”€โ”€ examples/
โ”‚   โ””โ”€โ”€ run_generation.py       # Live interactive generation demo with Transformers
โ”œโ”€โ”€ tests/
โ”‚   โ”œโ”€โ”€ test_fsm_builder.py     # Unit tests for BFS reachability & multi-goal
โ”‚   โ””โ”€โ”€ test_logit_processor.py # Unit tests for batch masking & state progression
โ”œโ”€โ”€ paper_figure_scaling.png    # Publication-ready 300-DPI scaling figure
โ”œโ”€โ”€ requirements.txt
โ””โ”€โ”€ README.md

๐Ÿ“Š Comprehensive Experimental Results

1. Real Lightweight LLM End-to-End Benchmark (Qwen2.5-0.5B)

Tested on real model weights generating JSON responses under strict token limits.
Token Budget (T_max)Vanilla SamplingForward DFA (Outlines Style)**GCLM (Ours)**Latency / Sample (GCLM)
T_max = 6 tokens0.0%30.0%100.0%615.90 ms (Fastest, early closure)
T_max = 10 tokens0.0%70.0%100.0%1,086.02 ms
T_max = 16 tokens0.0%85.0%100.0%992.39 ms

2. Strict Budget JSON Schema Parsing Benchmark

Complex nested JSON schema tested across 500 trials per budget.
Budget (T_max)VanillaForward DFA (Outlines Style)**GCLM (Ours)**Key Insight
T_max = 42.4%55.4%100.0%Forces safe `{}` closure when fields cannot finish
T_max = 62.4%45.6%100.0%Prunes deep nested object paths
T_max = 82.2%65.2%100.0%Eliminates dangling commas
T_max = 161.4%91.8%100.0%Complete 100% parse rate across all budgets

3. Multi-Step Agent Tool-Calling & Action Budget Benchmark

ReAct-style multi-tool workflow evaluating goal completion within action limits.
Action BudgetVanillaForward DFA**GCLM (Ours)**Key Finding
3 Actions0.00%16.80%100.00%Dynamically forces 3-step shortest path
4 Actions0.00%33.20%100.00%Prunes unfinishable deep search subtrees
8 Actions0.60%65.20%100.00%Completely avoids infinite retry trap loops

4. FSM Complexity & Strict O(1) Runtime Scaling

Scaling state count |S| from 10 to 10,000 (1,000x increase). Plot saved as paper_figure_scaling.png.
Vocabulary Size (V)State Count (S)Offline BFS TimeMemory FootprintOnline Latency per Token
V = 32,000 (LLaMA)S = 1029.55 ms2.44 MB388.72 ยตs
V = 32,000S = 100240.10 ms24.42 MB335.10 ยตs
V = 32,000S = 1,0002,111.82 ms244.19 MB340.84 ยตs
V = 32,000S = 10,00025,790.14 ms2.44 GB356.29 ยตs (O(1) verified)
V = 151,643 (Qwen2.5)S = 10159.29 ms11.57 MB601.92 ยตs
V = 151,643S = 10,000147,702.79 ms11.56 GB666.22 ยตs (O(1) verified)

๐Ÿš€ Quick Start

1. Installation

From Hugging Face:

bash
git clone https://huggingface.co/uuugi/gclm-constrained-decoding
cd gclm-constrained-decoding
pip install -r requirements.txt

From GitHub:

bash
git clone https://github.com/uuuugi/Goal-Conditioned-Reachability-Logit-Masker.git
cd Goal-Conditioned-Reachability-Logit-Masker
pip install -r requirements.txt

2. Basic Usage with Hugging Face Transformers

python
import torch
from transformers import AutoModelForCausalLM, AutoTokenizer, LogitsProcessorList
from core.fsm_builder import ReachabilityFSM
from core.logit_processor import GoalReachabilityLogitsProcessor

# 1. Load model and tokenizer
model_id = "Qwen/Qwen2.5-0.5B"
tokenizer = AutoTokenizer.from_pretrained(model_id)
model = AutoModelForCausalLM.from_pretrained(model_id)

vocab_size = model.config.vocab_size
max_budget = 15

# 2. Define FSM & Goal state
fsm = ReachabilityFSM(num_states=5, vocab_size=vocab_size)
fsm.add_transition(from_state=0, token_id=101, to_state=1)
fsm.add_transition(from_state=1, token_id=102, to_state=2)
fsm.set_goal_states([2])

# 3. Precompute reachability table (one-time offline step)
fsm.build_reachability(max_steps=max_budget)

# 4. Attach GCLM to Hugging Face LogitsProcessorList
gclm_processor = GoalReachabilityLogitsProcessor(fsm=fsm, max_budget=max_budget)
logits_processors = LogitsProcessorList([gclm_processor])

# 5. Generate with guaranteed reachability
inputs = tokenizer("Your prompt here", return_tensors="pt")
outputs = model.generate(
    **inputs,
    max_new_tokens=max_budget,
    logits_processor=logits_processors
)
print(tokenizer.decode(outputs[0]))

๐Ÿงช Reproducing Experiments

bash
# Run Unit Tests
python -m pytest tests/ -v

# Run Experiment 1: Synthetic Dead-End Benchmark
python -m benchmarks.synthetic_deadend

# Run Experiment 2: Strict Budget JSON Benchmark
python -m benchmarks.json_budget_bench

# Run Experiment 3: Agent Tool-Calling Benchmark
python -m benchmarks.tool_calling_bench

# Run Experiment 4: Scaling Benchmark & Generate Paper Plots
python -m benchmarks.scaling_bench

# Run Experiment 5: Real Lightweight LLM Benchmark (Qwen2.5)
python -m benchmarks.real_model_bench --model Qwen/Qwen2.5-0.5B

๐Ÿ“‘ Paper & Citation

๐Ÿ“„ Paper PDF: **Download `paper.pdf`** ๐Ÿ’ป GitHub Repository: **uuuugi/Goal-Conditioned-Reachability-Logit-Masker** ๐Ÿค— Hugging Face Model: **uuugi/gclm-constrained-decoding**

bibtex
@article{an2026gclm,
  title={Goal-Conditioned Reachability Logit Masker: Guaranteed Goal Satisfaction for Constrained LLM Generation in O(1) Time},
  author={An, ByeongUk},
  journal={arXiv preprint},
  year={2026}
}

Author: ByeongUk An Email: hhjjkk7186@gmail.com ORCID: `0009-0007-5612-5602`


๐Ÿ“„ License

MIT License