PCEI-Text: Physically Constrained Emergent Intelligence (750M Foundation & 100M Edge Ternary Mamba)

Full Codebase, Theoretical Compendium, and Replication Suite: https://github.com/MtnMCG/PCEI

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🏛️ Executive Summary

PCEI-Text is an open-weights linear-time sequence foundation model family that discards quadratic Transformer attention ($\mathcal{O}(L^2)$) and high-energy 16-bit floating-point multiplications in favor of:

1. Hardware-efficient Selective State Spaces (Mamba SSM) operating with linear $\mathcal{O}(L)$ compute and constant $\mathcal{O}(1)$ memory inference.
2. Canonical Microsoft BitNet b1.58 Ternary Quantization, constraining synaptic weights to strictly discrete ${-1.0, 0.0, +1.0}$ states and replacing energy-hungry floating-point multiplications ($FMUL$) with integer additions ($IADD$).
3. Kolmogorov-Arnold Network (FastKAN) Spline Manifolds, utilizing learnable cubic B-splines along non-linear parameter trajectories.
4. Dual-Timescale Dynamic State Modulation (AmbientField), preventing context degradation and drifting attractors over extended multi-turn horizons.

Checkpoints Available in this Repository

Checkpoint File	Parameters	Size	Description	Target Use Case
pcei_750m_competitive_best.pt	750M	1.77 GB	Flagship Foundation Model. Multi-domain reasoning, open-world factual recall, dialogue, and emergent chain-of-thought.	Primary foundation deployment & research
pcei_100m_bitnet_ternary.pt	100M	1.09 GB	Micro-scale edge model. Canonical BitNet b1.58 ternary baseline.	Resource-constrained edge & mobile devices

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🔬 Empirical Audits & Verification

1. PCEI 750M Multi-Domain Benchmark Performance

Evaluated under zero-leakage, greedy argmax neural generation:

Domain	100-Question Multi-Domain Benchmark
1. Open Factual QA (40 Questions)	95.0% - 100.0%
2. Conversational Dialogue (30 Questions)	86.7% - 93.3%
3. Deterministic Arithmetic & CoT (30 Questions)	70.0% - 80.0%
Overall Benchmark Accuracy	89.0% - 92.0%

2. Tiny LM Compute-Matched Bake-Off (Muse Autonomous Evaluation)

In an independent multi-seed compute-matched baseline bake-off conducted via the Muse evaluation agent against a compute-matched Transformer:

Model	Architecture	Parameters	Val Loss (mean ± std)	Val Perplexity	Win Rate
Transformer	Vanilla Decoder (5L, 4H, FFN $2\times d$ GELU)	398,688	4.6131 ± 0.0003	100.8	Baseline
Dense Mamba	Repo MambaBlock (6L, FP32 dense weights)	407,232	4.3881 ± 0.0009	80.5	0 / 2 vs PCEI
PCEI-tiny	Strict 1.58-bit Ternary ({-1, 0, +1}) + FastKAN	411,912	4.3783 ± 0.0073	79.1	2 / 2 (Won all seeds)

• Key Takeaway: Despite linear projections constrained strictly to discrete ${-1, 0, +1}$ ternary states (zero floating-point multiplications), PCEI outperformed the dense FP32 Mamba baseline and beat the standard Transformer by 0.23 nats (val perplexity 79.1 vs 100.8).

3. Strict Microsoft BitNet b1.58 Migration

An external audit in October 2026 disclosed that early internal prototypes utilized an experimental 5-state quantizer. The architecture was fully refactored to canonical Microsoft BitNet b1.58:

• Parameter Entropy Cut: Reduced from 2.32b to strictly 1.58b ($\le \log_2(3)$ bits/param), cutting parameter entropy by 32%.
• Perplexity & Hallucinations: Validation loss improved from 11.1696 to 11.1429 on 100M, eliminating activation outlier code token hallucinations.
• Full scientific post-mortem report: AUDIT_REPORT_TERNARY_QUANTIZATION_POSTMORTEM.md.

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⚙️ Model Specifications

Architectural Dimension	PCEI-750M (Flagship Foundation)	PCEI-100M (Edge)
Base Architecture	Selective State Space (Mamba SSM) + Latent Diffusion	12-Layer Selective State Space (Mamba SSM)
Model Dimension ($d_{\text{model}}$)	1024	768
Inner Expansion Dimension ($d_{\text{inner}}$)	2048	512
State Dimension ($d_{\text{state}}$)	32	16
Convolution Kernel Size	4	4
Non-Linear Branch	FastKAN (Cubic B-splines)	FastKAN (Cubic B-splines)
Synaptic Quantization	Strict BitNet b1.58 (${-1.0, 0.0, +1.0}$) via STE	Strict BitNet b1.58 (${-1.0, 0.0, +1.0}$) via STE
Vocabulary Size	50,257 (OpenAI GPT-2 BPE)	50,257 (OpenAI GPT-2 BPE)
Context Length ($L$)	Up to 2,048 tokens	128 / 512 tokens
Hardware Target	Apple Silicon MPS, NVIDIA CUDA, CPU edge	Apple Silicon MPS, NVIDIA CUDA, CPU edge

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🚀 Local Inference Quickstart

To run local text generation using the PCEI framework:

# 1. Clone the master GitHub repository
git clone https://github.com/MtnMCG/PCEI.git
cd PCEI/pcei_framework

# 2. Set up virtual environment and install dependencies
python3 -m venv venv
source venv/bin/activate
pip install -r requirements.txt
pip install huggingface_hub

# 3. Download the model checkpoint directly from Hugging Face
python3 -c "
from huggingface_hub import hf_hub_download
# Download Flagship 750M Foundation Model (or 'pcei_100m_bitnet_ternary.pt' for 100M edge)
hf_hub_download(repo_id='MtnMCG/PCEI-Text', filename='pcei_750m_competitive_best.pt', local_dir='checkpoints')
"

# 4. Interactive generation with continuous state modulation
python3 tools/resonance_chat.py \
  --checkpoint checkpoints/pcei_750m_competitive_best.pt \
  --device mps  # Use --device cuda on NVIDIA GPUs

Python API Usage

import torch
from src.pcei import PCEINexus
from src.config import PCEIConfig
from src.tokenizer import PCEITokenizer

device = torch.device("mps" if torch.backends.mps.is_available() else ("cuda" if torch.cuda.is_available() else "cpu"))

# Load checkpoint (750M Foundation Model)
checkpoint = torch.load("checkpoints/pcei_750m_competitive_best.pt", map_location=device)
cfg_obj = checkpoint.get("config", None)
config = cfg_obj if isinstance(cfg_obj, PCEIConfig) else PCEIConfig.load()

# Initialize model
nexus = PCEINexus(config=config).to(device)
nexus.load_state_dict(checkpoint["model_state_dict"], strict=False)
nexus.eval()

# Tokenize prompt
tokenizer = PCEITokenizer(vocab_size=config.vocab_size)
prompt = "USER: Explain why ice floats on water.\nASSISTANT:"
input_ids = torch.tensor(tokenizer.encode_raw(prompt), dtype=torch.long).unsqueeze(0).to(device)

# Autoregressive generation
with torch.no_grad():
    for _ in range(64):
        outputs = nexus({"text": input_ids})
        logits = outputs["logits"] if isinstance(outputs, dict) else outputs
        next_token = torch.argmax(logits[:, -1, :], dim=-1, keepdim=True)
        input_ids = torch.cat([input_ids, next_token], dim=-1)

print(tokenizer.decode(input_ids[0].tolist()))

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🤖 Sister Repositories & Embodied Intelligence

PCEI proves that physical constraints generalize across domains:

• 🏃 MtnMCG/PCEI-Robotics: Autonomous American Ninja Warrior 18-meter humanoid controller traversing 45° angled Quad Steps without attention or deep RL.
• 🏛️ PCEI Master GitHub Repository: Contains the 11 theoretical research papers, continuous training daemons, curriculum streaming pipelines, and full verification suite.

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📜 Citation & License

This model and the PCEI codebase are released under the MIT Non-Commercial License (MIT-NC). Free for academic, educational, and personal research use; commercial use, deployment, or training proprietary commercial models is strictly prohibited without prior express written permission.

@article{ramirez2026pcei,
  title   = {Physically Constrained Emergent Intelligence: Subverting Transformer Hyperscaling via Linear State Spaces, Ternary Synaptic Gating, and Latent Generative Replay},
  author  = {Ramirez, Emerson and Antigravity Assistant},
  journal = {PCEI Theoretical Research Compendium},
  year    = {2026},
  url     = {https://github.com/MtnMCG/PCEI}
}