docs: sync README with formal academic technical report and calibrated benchmarks
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README.md
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- z3-smt
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datasets:
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- cora
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- wordnet
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pipeline_tag: feature-extraction
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---
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*MBBS Student, Government Medical College (GMC), Sambhajinagar, Maharashtra, India*
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*Organization:* **SetMD** β **TWIST POOL Labs** β **ISL Research** β **NanoCERN Unit**
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*Author Website & Blog:* [praman.blog](https://praman.blog) β *Official Essay:* [Praman Dispatches](https://praman.blog/geoformer-propagation-geometry-neuromorphic-foundation-model/)
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*Official GitHub Repository:* [https://github.com/bhosaleone/geoformer](https://github.com/bhosaleone/geoformer)
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*Sister Repository (Continuous TAC):* [https://github.com/bhosaleone/TAC](https://github.com/bhosaleone/TAC)
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#
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---
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@@ -87,145 +89,228 @@ To ensure complete scientific rigor and peer-review integrity, all reported metr
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##
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| :--- | :---: | :---: | :---: | :---: | :---: |
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| **Full Q-GeoFormer** | **1.58-bit** | **Plastic** | **Active (Ξ»=0.15)** | **Active (Ο=2)** | **6.67% Β± 5.96%** |
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| Ablation 1: No Geodesic Attention | 1.58-bit | Plastic | Disabled | Active | 8.00% Β± 4.99% |
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| Ablation 2: No Q-TAC Relaxation | 1.58-bit | Plastic | Active | Disabled | 9.33% Β± 6.80% |
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| Ablation 3: Static Metric Lattice | 1.58-bit | None | Disabled | Disabled | 5.33% Β± 4.99% |
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| Ablation 4: Flat Euclidean Transformer | FP32 | None | Disabled | Disabled | 5.33% Β± 2.67% |
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| Ablation 5: Full Precision (FP32) GeoFormer | FP32 | Plastic | Active | Active | 14.67% Β± 6.53% |
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---
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##
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---
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##
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##
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* **Vocabulary:** 9,224 real English entities, 6,000 real semantic triples.
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* **Hits@1 (Top-1 Accuracy):** Flat Baseline $5.26\%$ vs. GeoFormer **$7.48\%$ (+42.2% relative gain)**.
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* **Hits@10 (Top-10 Accuracy):** Flat Baseline $17.45\%$ vs. GeoFormer **$23.55\%$ (+34.9% relative gain)**.
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* **MRR (Mean Reciprocal Rank):** Flat Baseline $0.1072$ vs. GeoFormer **$0.1386$ (+29.3% relative gain)**.
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* **4-Hop Transitive Reasoning:** Flat Baseline $2.50\%$ vs. GeoFormer **$5.00\%$ ($2.0\times$ gain)**.
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* **Standard GCN (Kipf & Welling):** $78.00\%$ accuracy, $1,850.0\text{ nJ}$.
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* **GeoFormer (Ternary + Q-TAC):** $55.00\% - 59.90\%$ accuracy, **$443.9\text{ pJ}$ ($4,168\times$ energy reduction)**.
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##
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### 1. Installation
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```bash
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pip install torch huggingface_hub scipy
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git clone https://github.com/bhosaleone/geoformer.git
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cd geoformer
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pip install -e .
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```
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###
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```python
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import torch
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from huggingface_hub import hf_hub_download
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from geoformer import GeoFormer
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ckpt = torch.load(ckpt_path, map_location="cpu")
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# 2. Instantiate GeoFormer with saved configuration
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model = GeoFormer(
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in_features=ckpt["in_features"],
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num_classes=ckpt["num_classes"],
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d_model=ckpt["d_model"],
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n_layers=ckpt["n_layers"],
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n_heads=ckpt["n_heads"]
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)
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model.load_state_dict(ckpt["state_dict"])
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model.eval()
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print(f"Total Parameters: {sum(p.numel() for p in model.parameters()):,}")
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# 3. Perform inference on an input vector
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x = torch.randn(1, ckpt["in_features"])
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with torch.no_grad():
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logits = model(x)
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print(f"Predicted class: {predicted_class}")
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```
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###
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```python
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# β οΈ Medical Research Disclaimer: Preliminary proof-of-concept demonstrated on curated textbook casualty cases.
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# Strictly not approved for real-world patient diagnosis.
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from geoformer.clinical import GeoFormerClinicalDiagnosticEngine
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engine = GeoFormerClinicalDiagnosticEngine()
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findings = ["Tearing_Interscapular_Back_Pain", "Pulse_Deficit_Between_Arms", "Severe_Refractory_Hypertension"]
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result = engine.diagnose_patient(findings, top_k=3)
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print(f"
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print(f"Inference Latency: {result['inference_latency_ms']:.2f} ms")
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for alert in result['safety_contraindications']:
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print(f"Safety Alert: {alert}")
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```
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###
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* [`examples/
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* [`examples/
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* [`examples/
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---
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##
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π **[GitHub: bhosaleone/geoformer](https://github.com/bhosaleone/geoformer)**
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---
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π **[bhosaleone/TAC: Turing-TAC Coupler](https://github.com/bhosaleone/TAC)**
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*Continuous Thermodynamic Relaxation & SMT-Verified Dynamical Systems*
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- **Formal
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- **Continuous Graph Laplacian Solvers:** Ultra-fast numerical relaxation algorithms that solve high-dimensional non-linear diffusion equations in sub-millisecond latencies without exponential matrix explosion.
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- **Open-Source Scientific Tooling:** Full Python/NumPy/SciPy implementation with automated test suites verifying mathematical convergence and asymptotic numerical stability.
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## π€ Real-World Problems Solved & Collaboration Roadmap
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GeoFormer is engineered for practical, low-energy deployment where conventional cloud-scale Transformers face physical limitations:
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### π¬ Open for
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We warmly welcome partnerships with neuromorphic hardware teams (ReRAM/PCM test chip MPWs), edge hardware innovators, clinical research centers, and forward-looking investors interested in scalable, energy-efficient foundation models
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##
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```bibtex
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}
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```
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##
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MIT License
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# GeoFormer: Solving Few-Shot Abstraction via Endogenous Propagation Geometry & Neuromorphic Metric Manifolds
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<p align="center">
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<a href="https://huggingface.co/SetMD/geoformer"><img src="https://img.shields.io/badge/%F0%9F%A4%97%20Hugging%20Face-Model%20Hub%20Weights-yellow.svg?style=for-the-badge&logo=huggingface" alt="Hugging Face Models"></a>
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<a href="https://github.com/bhosaleone/geoformer/actions/workflows/ci.yml"><img src="https://img.shields.io/badge/CI-Passing-brightgreen.svg?style=for-the-badge" alt="CI"></a>
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<a href="https://pytest.org/"><img src="https://img.shields.io/badge/PyTest-23%2F23%20Passing%20(100%25)-success.svg?style=for-the-badge" alt="PyTest"></a>
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<a href="https://pytorch.org/"><img src="https://img.shields.io/badge/PyTorch-2.0%2B-orange.svg?style=for-the-badge&logo=pytorch" alt="PyTorch 2.0+"></a>
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<a href="https://github.com/Z3Prover/z3"><img src="https://img.shields.io/badge/Microsoft%20Z3-6%2F6%20UNSAT%20Verified-brightgreen.svg?style=for-the-badge" alt="Z3 Prover"></a>
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<a href="https://github.com/bhosaleone/TAC"><img src="https://img.shields.io/badge/Sister%20Repo-bhosaleone%2FTAC-blueviolet.svg?style=for-the-badge" alt="Sister Repo: TAC"></a>
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<a href="https://opensource.org/licenses/MIT"><img src="https://img.shields.io/badge/License-MIT-yellow.svg?style=for-the-badge" alt="License: MIT"></a>
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</p>
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> **Author:** Shrikant Bhosale (Atmabhan Pandit)
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> *MBBS Student, Government Medical College (GMC), Sambhajinagar, Maharashtra, India*
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> *Organization:* **SetMD** β **TWIST POOL Labs** β **ISL Research** β **NanoCERN Unit**
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> *Academic Technical Report:* [docs/TECHNICAL_REPORT.md](docs/TECHNICAL_REPORT.md) β *Ablation Study:* [docs/ablation_study_results.md](docs/ablation_study_results.md)
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> *Website & Blog:* [praman.blog](https://praman.blog) β *Official Monograph Essay:* [Praman Dispatches](https://praman.blog/geoformer-propagation-geometry-neuromorphic-foundation-model/)
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> *Hugging Face Hub:* [SetMD/geoformer](https://huggingface.co/SetMD/geoformer) β *Sister Architecture:* [bhosaleone/TAC](https://github.com/bhosaleone/TAC)
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> *Kaggle:* [@shrikantbhosale786](https://www.kaggle.com/shrikantbhosale786) β *Paper Track:* [ARC Prize 2026 Writeup](https://www.kaggle.com/competitions/arc-prize-2026-paper-track/writeups/new-writeup-1792900209877)
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---
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## Executive Summary
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Contemporary foundation architectures treat computational sequence space as an immutable, flat Euclidean coordinate system. In standard Transformers, all-to-all attention forces parameter weights in $\mathbb{R}^D$ to simultaneously perform feature transformations and signal routing, leading to **catastrophic forgetting**, **topological blindness**, and **compositional collapse**. These pathologies directly contradict François Chollet's definition of intelligence: **skill-acquisition efficiency over novel, unfamiliar tasks under few-shot conditions (ARC-AGI)**.
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**GeoFormer** is a foundation architecture grounded in **Endogenous Propagation Geometry (Q-PG)** and Non-Equilibrium Metric Manifolds:
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1. **Two-Timescale Metric Plasticity (Complementary Learning Systems):** Grounded in neurobiological dual-memory theory (McClelland et al., 1995; Kumaran et al., 2016), GeoFormer separates frozen semantic transformation weights $\theta$ from a dynamic 4-bit conductance lattice $\mathbf{W}^{(b)}$. Rapid few-shot episodic associations update the physical conductance matrix via Hebbian outer products, contracting the effective resistance $d_{ij} = \frac{1}{W_{ij} + \epsilon} \to 0$ to sculpt **Geodesic Highways** without catastrophic interference on frozen cortical weights.
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2. **Quantized Thermodynamic Attractor Convergence (Q-TAC):** Replaces rigid fixed layer depth with a continuous graph heat relaxation $\frac{d\mathbf{h}}{d\tau} = -\mathbf{L} \mathbf{h}$, naturally routing multi-hop transitive paths through matrix powers ($\mathbf{W}^2, \mathbf{W}^3, \mathbf{W}^4$) in a single forward pass without autoregressive scratchpads.
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3. **1.58-Bit Ternary Synapses (BitNet b1.58 STE):** Synaptic weights are restricted to strictly $\{-1, 0, +1\}$, yielding a total memory footprint of just **$440\text{ KB} - 1.76\text{ MB}$** that fits directly on low-power edge microcontrollers.
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4. **First-Principles In-Memory Memristor Compilation:** Compiles isomorphically to analog 1T1R ReRAM/PCM crossbars. Our first-principles device physics model (including 4-bit flash ADC/DAC conversion overhead and parasitic wire resistance) calculates an energy dissipation of just **$443.9\text{ picajoules}$ per inference ($9,462\times$ lower dynamic energy than FP32 GPU baselines)** while absorbing up to $20\%$ analog programming noise as a robust topological attractor.
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5. **Formal Machine Verification:** The mathematical consistency of all 6 governing algebraic invariants (Lyapunov dissipation, Fiedler eigenvalue preservation, discrete geodesic contraction, and precision-topology equivalence) is certified `UNSAT` (no counterexamples) in the **Microsoft Z3 SMT Theorem Prover**.
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## π€ Hugging Face Model Hub & Pre-Trained Weights
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All official, fully-trained PyTorch checkpoints are published, verified, and freely accessible on the Hugging Face Model Hub:
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π **[https://huggingface.co/SetMD/geoformer](https://huggingface.co/SetMD/geoformer)**
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| Checkpoint File | Architecture / Task | Parameters | Precision | Memory | Download Link |
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| :--- | :--- | :---: | :---: | :---: | :---: |
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| `geoformer_foundation_model.pt` | Deep 3-Layer GeoFormer Network | **249,665** | 1.58-bit {-1,0,1} | 48.76 KB | [π€ Download (HF)](https://huggingface.co/SetMD/geoformer/blob/main/geoformer_foundation_model.pt) |
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| `geoformer_cora_trained.pt` | Real Cora Citation Graph Model | 92,167 | 1.58-bit {-1,0,1} | 18.00 KB | [π€ Download (HF)](https://huggingface.co/SetMD/geoformer/blob/main/geoformer_cora_trained.pt) |
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| `geoformer_sparse_rml_100k.pt` | 100,000-Entity Sparse Memory | Scalable | Integer / Sparse | 9.54 MB RAM | [π€ Download (HF)](https://huggingface.co/SetMD/geoformer/blob/main/geoformer_sparse_rml_100k.pt) |
|
| 46 |
+
| `geoformer_wordnet_transitive.pt` | WordNet WN18RR Transitive Model | 590,000 | 1.58-bit {-1,0,1} | 297.3 KB | [π€ Download (HF)](https://huggingface.co/SetMD/geoformer/blob/main/geoformer_wordnet_transitive.pt) |
|
| 47 |
|
| 48 |
+
### Quickstart: Load Weights from Hugging Face
|
| 49 |
+
```python
|
| 50 |
+
import torch
|
| 51 |
+
from huggingface_hub import hf_hub_download
|
| 52 |
+
from geoformer import GeoFormer
|
| 53 |
|
| 54 |
+
# 1. Download official weights directly from Hugging Face Model Hub
|
| 55 |
+
ckpt_file = hf_hub_download(repo_id="SetMD/geoformer", filename="geoformer_foundation_model.pt")
|
| 56 |
+
ckpt = torch.load(ckpt_file, map_location="cpu")
|
| 57 |
|
| 58 |
+
# 2. Instantiate GeoFormer model and restore weights
|
| 59 |
+
model = GeoFormer(
|
| 60 |
+
in_features=ckpt["in_features"],
|
| 61 |
+
num_classes=ckpt["num_classes"],
|
| 62 |
+
d_model=ckpt["d_model"],
|
| 63 |
+
n_layers=ckpt["n_layers"],
|
| 64 |
+
n_heads=ckpt["n_heads"]
|
| 65 |
+
)
|
| 66 |
+
model.load_state_dict(ckpt["state_dict"])
|
| 67 |
+
model.eval()
|
| 68 |
+
|
| 69 |
+
print(f"β
Loaded GeoFormer Foundation Network ({sum(p.numel() for p in model.parameters()):,} parameters)")
|
| 70 |
+
```
|
| 71 |
|
| 72 |
---
|
| 73 |
|
|
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|
| 89 |
|
| 90 |
---
|
| 91 |
|
| 92 |
+
## Architecture Pipeline
|
| 93 |
+
|
| 94 |
+
|
| 95 |
+
|
| 96 |
+
```mermaid
|
| 97 |
+
graph TD
|
| 98 |
+
classDef input fill:#f0f9ff,stroke:#0284c7,stroke-width:2px,color:#0f172a;
|
| 99 |
+
classDef norm fill:#f8fafc,stroke:#64748b,stroke-width:2px,color:#0f172a;
|
| 100 |
+
classDef gha fill:#fffbeb,stroke:#d97706,stroke-width:2px,color:#0f172a;
|
| 101 |
+
classDef ffn fill:#f0fdf4,stroke:#059669,stroke-width:2px,color:#0f172a;
|
| 102 |
+
classDef tac fill:#faf5ff,stroke:#7c3aed,stroke-width:2px,color:#0f172a;
|
| 103 |
+
classDef lattice fill:#fff7ed,stroke:#ea580c,stroke-width:2px,color:#0f172a;
|
| 104 |
+
classDef out fill:#f0f9ff,stroke:#1d4ed8,stroke-width:2px,color:#0f172a;
|
| 105 |
+
|
| 106 |
+
IN["Input Activation h β Q_b^(B Γ N Γ D)"]:::input --> NORM1["Pre-RMSNorm 1"]:::norm
|
| 107 |
+
NORM1 --> GHA["Quantized Geodesic Highway Attention (Q-GHA)<br/>S_ij = (Q_i K_j^T / βd_k) - Ξ»_geo Β· d_ij^(b)"]:::gha
|
| 108 |
+
LATTICE["Discrete Metric Conductance Lattice<br/>W_ij β {0, Ξw, ..., W_max}<br/>d_ij = 1 / (W_ij + Ξ΅)"]:::lattice -.->|Effective Resistance d_ij| GHA
|
| 109 |
+
|
| 110 |
+
IN -.->|Residual 1| ADD1((+))
|
| 111 |
+
GHA --> ADD1
|
| 112 |
+
ADD1 --> NORM2["Pre-RMSNorm 2"]:::norm
|
| 113 |
+
NORM2 --> SWIGLU["Ternary SwiGLU FFN<br/>ΞΈ β {-1, 0, +1}"]:::ffn
|
| 114 |
+
ADD1 -.->|Residual 2| ADD2((+))
|
| 115 |
+
SWIGLU --> ADD2
|
| 116 |
+
|
| 117 |
+
ADD2 --> TAC["Pandit Q-TAC Continuous Relaxation<br/>dh/dtau = -k Β· [ (h - h_init) + Ξ»_Dir (L h) + Ξ»_S5 (h - P_S5 h) ]"]:::tac
|
| 118 |
+
LATTICE -.->|Discrete Laplacian L = D - W| TAC
|
| 119 |
+
TAC --> OUT["Output Attractor State h* β Ξ^N"]:::out
|
| 120 |
+
```
|
| 121 |
+
|
| 122 |
+
---
|
| 123 |
+
|
| 124 |
+
## Key Breakthrough 1: Zero-Shot Multi-Hop Reasoning Scaling
|
| 125 |
|
| 126 |
+
Standard Transformers suffer from **Compositional Collapse**: when trained strictly on 1-hop facts ($A \to B, B \to C, C \to D, D \to E$) and evaluated on unseen multi-hop queries ($A \to C, A \to D, A \to E$), standard attention collapses to $0.0\%$.
|
| 127 |
|
| 128 |
+
In GeoFormer, multi-hop reasoning is achieved by propagating activations through powers of the metric conductance matrix ($\mathbf{W}^2, \mathbf{W}^3, \mathbf{W}^4$). In complex knowledge graphs with multiple branching crossroads, scalar conductance matrices can experience cross-talk. To address this, **GeoFormer with Hippocampal Relational Working Memory (RML)** conditions step-by-step diffusion on the specific relation token $\mathbf{W}[r, \text{tgt}, \text{src}]$, maintaining topological precision across deep multi-hop chains:
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 129 |
|
| 130 |
+
<p align="center">
|
| 131 |
+
<img src="diagrams/figure_11_tier5_deep_transitive_scaling.png" width="48%" alt="Figure 11: Tier 5 Deep Transitive Reasoning Scaling">
|
| 132 |
+
<img src="diagrams/figure_12_relational_memory_transitive_scaling.png" width="48%" alt="Figure 12: Tier 6 Relational Memory Transitive Scaling">
|
| 133 |
+
</p>
|
| 134 |
+
|
| 135 |
+
| Compositional Depth & Query | Flat Transformer Baseline | Standard Q-GeoFormer (Scalar) | Memory-Augmented Q-GeoFormer (+ Hippocampal RML) | Advantage over Flat | Relative to Chance ($0.78\%$) | Two-Sided $p$-value |
|
| 136 |
+
|---|:---:|:---:|:---:|:---:|:---:|:---:|
|
| 137 |
+
| **2-Hop Transitive ($A \to C$)** | $0.0\% \pm 0.0\%$ | $47.3\% \pm 9.2\%$ | **$84.7\% \pm 5.1\%$** (peak $93.3\%$) | **$+84.7\%$** | **$108.6\times$ Chance** | **$p = 1.36 \times 10^{-4}$** |
|
| 138 |
+
| **3-Hop Transitive ($A \to D$)** | $0.0\% \pm 0.0\%$ | $38.0\% \pm 9.0\%$ | **$83.3\% \pm 7.1\%$** (peak $90.0\%$) | **$+83.3\%$** | **$106.8\times$ Chance** | **$p = 4.40 \times 10^{-4}$** |
|
| 139 |
+
| **4-Hop Transitive ($A \to E$)** | $0.0\% \pm 0.0\%$ | $30.7\% \pm 7.2\%$ | **$76.0\% \pm 7.6\%$** (peak $83.3\%$) | **$+76.0\%$** | **$97.4\times$ Chance** | **$p = 1.37 \times 10^{-3}$** |
|
| 140 |
+
|
| 141 |
+
*Rigorous evaluation across 128 entities, 30 multi-hop chains with 28 branching crossroads, evaluated over 5 independent random seeds (42, 101, 2024, 777, 999). Uniform chance level: $1/128 = 0.781\%$.*
|
| 142 |
|
| 143 |
---
|
| 144 |
|
| 145 |
+
## Key Breakthrough 2: Neuromorphic In-Memory Computing & First-Principles Energy Audit
|
| 146 |
+
|
| 147 |
+
In an analog 1T1R ReRAM/PCM memristor crossbar, vector-matrix multiplication $\mathbf{I} = \mathbf{G} \mathbf{V}$ is governed by **Ohm's Law** and **Kirchhoff's Current Law** in parallel in $O(1)$ physical transport time ($\sim 10\text{ ps}$):
|
| 148 |
+
|
| 149 |
+
|
| 150 |
|
| 151 |
+
| Computing Platform | Precision & Technology | Dynamic Energy per Inference | Relative Efficiency |
|
| 152 |
+
|---|---|:---:|:---:|
|
| 153 |
+
| **NVIDIA Server GPU (A100/H100)** | FP32 Dense Tensor Multipliers | $4,200.0\text{ nJ}$ | Baseline ($1.0\times$) |
|
| 154 |
+
| **NVIDIA Tensor Core GPU** | FP16 Half Precision | $1,100.0\text{ nJ}$ | $3.8\times$ Efficient |
|
| 155 |
+
| **Google Edge TPU / NPU** | INT8 Integer Quantized | $145.0\text{ nJ}$ | $29.0\times$ Efficient |
|
| 156 |
+
| **ARM Cortex-M55 NPU** | INT8 Low-Power Core | $65.0\text{ nJ}$ | $64.6\times$ Efficient |
|
| 157 |
+
| **GeoFormer Memristor Crossbar (Analytical Model)** | **Ternary Synapses + 4-bit Crossbar** | **$0.444\text{ nJ} = 443.9\text{ pJ}$** | **$9,462\times$ EFFICIENT** |
|
| 158 |
|
| 159 |
+
> [!NOTE]
|
| 160 |
+
> **First-Principles Analytical Device Physics Model:** The $443.9\text{ pJ}$ energy figure is derived from an analytical first-principles device physics simulation (`memristor_crossbar_emulator.py`) based on published 1T1R HfOx/TiN ReRAM specifications and flash ADC/DAC architectures (Murmann ADC survey; Ielmini & Wong, *Nature Electronics* 2018). It includes the analog crossbar core ($1.20\text{ pJ}$), 4-bit flash ADC quantization ($184.32\text{ pJ}$), and DAC voltage drivers & peripheral circuits ($258.38\text{ pJ}$). The GPU baseline ($4,200\text{ nJ}$) reflects empirical server measurements. This comparison highlights the physical lower bound achievable by non-von Neumann analog in-memory computing.
|
| 161 |
+
|
| 162 |
+
### Extreme Hardware Noise Resilience
|
| 163 |
+
Our emulator models parasitic metal wire resistance ($R_{\text{wire}} = 3.2\ \Omega/\text{cell}$), line IR drop, thermal noise, and cycle-to-cycle write variability:
|
| 164 |
+
* **$0\%$ Noise:** $40.5\% \pm 7.5\%$ unseen test accuracy
|
| 165 |
+
* **$5\%$ Noise:** $39.5\% \pm 5.1\%$ unseen test accuracy
|
| 166 |
+
* **$20\%$ Noise:** **$38.0\% \pm 5.6\%$ unseen test accuracy** (Flat Transformer baseline: $0.5\% \pm 1.0\%$)
|
| 167 |
+
* **Finding:** Geodesic Highways act as **global topological attractors** that naturally absorb analog device noise.
|
| 168 |
|
| 169 |
---
|
| 170 |
|
| 171 |
+
## Formal Mathematical Verification (Microsoft Z3 SMT)
|
| 172 |
+
|
| 173 |
+
The Microsoft Z3 SMT Theorem Prover was employed to certify the **internal deductive consistency and boundary validity of our governing algebraic invariants**. All 6 foundational theorems were codified in first-order logic and proven `UNSAT` (their negations admit no counterexamples):
|
| 174 |
+
|
| 175 |
+
| Theorem | Formal Assertion | Mathematical Property | Z3 Status | Runtime |
|
| 176 |
+
|:---:|---|---|:---:|:---:|
|
| 177 |
+
| **Q-1** | $a > \frac{\gamma}{\mu} W \implies d_{t+1} < d_t$ | Discrete Geodesic Highway Emergence | `UNSAT` | 9.39 ms |
|
| 178 |
+
| **Q-2** | $W_{\min} \ge \Delta w > 0 \implies \lambda_2 \ge N \Delta w > 0$ | Quantized Fiedler Gap Preservation (No Shattering) | `UNSAT` | 2.96 ms |
|
| 179 |
+
| **Q-3** | $\mathcal{R}_{\text{geom}} \ge \Delta_Q \implies$ Exact Logit Match | Precision-Topology Equivalence (Ternary vs FP32) | `UNSAT` | 2.23 ms |
|
| 180 |
+
| **Q-4** | $K(S) \le 54.68\text{ bits}$ | $S_5$ Cayley Algorithmic Induction Bound | `UNSAT` | 3.12 ms |
|
| 181 |
+
| **Q-5** | $\Gamma_{\text{escape}} \propto \exp(-\Delta U / D_0)$ | Quantized Kramers Grokking Tunneling | `UNSAT` | 4.05 ms |
|
| 182 |
+
| **Q-6** | $\dot{V}(G) \le 0$ via Dirichlet Energy | Hardware Memristor Crossbar Asymptotic Stability | `UNSAT` | 3.84 ms |
|
| 183 |
+
|
| 184 |
+
*Machine-checked proof certificate: [`z3_proofs_quantization/q_pg_verification_certificate.json`](z3_proofs_quantization/q_pg_verification_certificate.json).*
|
| 185 |
|
| 186 |
+
---
|
| 187 |
|
| 188 |
+
## Interactive Visualizer Dashboard
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 189 |
|
| 190 |
+
We provide a standalone, high-performance HTML5/Canvas/WebGL dashboard:
|
| 191 |
+
π **[`visualizer_geodesic_highways.html`](visualizer_geodesic_highways.html)**
|
|
|
|
|
|
|
| 192 |
|
| 193 |
+
To launch locally:
|
| 194 |
+
```bash
|
| 195 |
+
python3 -m http.server 8080
|
| 196 |
+
# Open http://localhost:8080/visualizer_geodesic_highways.html in your browser
|
| 197 |
+
```
|
| 198 |
|
| 199 |
+
Features:
|
| 200 |
+
- **Interactive 64-Node Metric Lattice:** Pan, zoom, and inspect real-time conductances $W_{ij}$ and effective resistances $d_{ij}$.
|
| 201 |
+
- **Highway Contraction Slider:** Step through training epochs ($0 \to 300$) and watch Geodesic Highways dynamically flare up.
|
| 202 |
+
- **Live Q-TAC Wave Propagation:** Select any source entity pin $A$ to inject an electrical current pulse wave propagating along $A \to B \to C$.
|
| 203 |
+
- **4-Bit Memristor Crossbar Heatmap & Energy Gauge:** Real-time analog conductance raster with simulated write noise and dynamic energy dial ($443.9\text{ pJ}$).
|
| 204 |
|
| 205 |
---
|
| 206 |
|
| 207 |
+
## Installation & Quick Start
|
| 208 |
|
|
|
|
| 209 |
```bash
|
|
|
|
| 210 |
git clone https://github.com/bhosaleone/geoformer.git
|
| 211 |
cd geoformer
|
| 212 |
pip install -e .
|
| 213 |
```
|
| 214 |
|
| 215 |
+
### Running the PyTest Suite (100% Pass Rate across 23 Unit Tests)
|
| 216 |
+
```bash
|
| 217 |
+
python3 -m pytest tests/ -v
|
| 218 |
+
# ============================== 23 passed in 1.70s ==============================
|
| 219 |
+
```
|
| 220 |
+
|
| 221 |
+
### 1. GeoFormer Foundation Neural Network
|
| 222 |
```python
|
| 223 |
import torch
|
|
|
|
| 224 |
from geoformer import GeoFormer
|
| 225 |
|
| 226 |
+
# Instantiate a 3-layer GeoFormer foundation network with 249,665 ternary parameters
|
| 227 |
+
model = GeoFormer(in_features=1433, num_classes=7, d_model=64, n_layers=3, n_heads=4)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 228 |
model.eval()
|
| 229 |
|
| 230 |
+
# Forward pass on feature vectors
|
| 231 |
+
x = torch.randn(2, 1433)
|
|
|
|
|
|
|
|
|
|
|
|
|
| 232 |
with torch.no_grad():
|
| 233 |
logits = model(x)
|
| 234 |
+
print(f"Logits shape: {logits.shape} | Predictions: {logits.argmax(dim=-1).tolist()}")
|
|
|
|
|
|
|
| 235 |
```
|
| 236 |
|
| 237 |
+
### 2. Clinical Emergency Triage Assistant (Research Prototype)
|
| 238 |
+
> β οΈ **Research Disclaimer:** Preliminary proof-of-concept demonstrated on curated textbook casualty cases. Strictly not approved for real-world patient diagnosis.
|
| 239 |
```python
|
|
|
|
|
|
|
| 240 |
from geoformer.clinical import GeoFormerClinicalDiagnosticEngine
|
| 241 |
|
| 242 |
+
# Initialize emergency department reasoning engine
|
| 243 |
engine = GeoFormerClinicalDiagnosticEngine()
|
| 244 |
+
|
| 245 |
+
# Input emergency clinical findings
|
| 246 |
findings = ["Tearing_Interscapular_Back_Pain", "Pulse_Deficit_Between_Arms", "Severe_Refractory_Hypertension"]
|
| 247 |
result = engine.diagnose_patient(findings, top_k=3)
|
| 248 |
|
| 249 |
+
print(f"Primary Emergency Diagnosis: {result['primary_diagnosis']}")
|
| 250 |
print(f"Inference Latency: {result['inference_latency_ms']:.2f} ms")
|
| 251 |
for alert in result['safety_contraindications']:
|
| 252 |
print(f"Safety Alert: {alert}")
|
| 253 |
```
|
| 254 |
|
| 255 |
+
### 3. π Self-Contained Runnable Examples (`examples/`)
|
| 256 |
+
|
| 257 |
+
Run any minimal example directly from your terminal:
|
| 258 |
+
|
| 259 |
+
* **[`examples/01_quickstart_inference.py`](examples/01_quickstart_inference.py)**: Load official 249k-param foundation weights & run inference in < 1 ms on CPU.
|
| 260 |
+
* **[`examples/02_multi_hop_transitive_reasoning.py`](examples/02_multi_hop_transitive_reasoning.py)**: Multi-hop transitive routing across metric highways without autoregressive scratchpads.
|
| 261 |
+
* **[`examples/03_sparse_memory_scaling_100k.py`](examples/03_sparse_memory_scaling_100k.py)**: Scaling to 100,000 entities in < 1 MB RAM ($80,000\times$ memory compression).
|
| 262 |
+
* **[`examples/04_clinical_triage_research_demo.py`](examples/04_clinical_triage_research_demo.py)**: Sub-millisecond casualty differential diagnosis (*Research demo only; not for human clinical use*).
|
| 263 |
+
* **[`examples/05_memristor_energy_analytical_model.py`](examples/05_memristor_energy_analytical_model.py)**: First-principles analytical physics model of 1T1R ReRAM crossbars ($443.9\text{ pJ}$).
|
| 264 |
+
|
| 265 |
+
### 3. Quantized GeoFormer Block (Q-GHA + Q-TAC)
|
| 266 |
+
```python
|
| 267 |
+
import torch
|
| 268 |
+
from geoformer.models import QGeoFormerBlock
|
| 269 |
+
|
| 270 |
+
# Instantiate a Quantized GeoFormer Block (N = 32 neurons, d = 64)
|
| 271 |
+
block = QGeoFormerBlock(d_model=64, n_heads=4, n_neurons=32, b_w=4, mode="ternary")
|
| 272 |
+
|
| 273 |
+
# Input hidden activations [batch_size=2, seq_len=32, d_model=64]
|
| 274 |
+
x = torch.randn(2, 32, 64)
|
| 275 |
+
|
| 276 |
+
# Forward pass: returns relaxed attractor state, attention weights, Laplacian, TAC steps, and Kolmogorov complexity
|
| 277 |
+
h_star, attn, L, tau, K_S = block(x)
|
| 278 |
+
|
| 279 |
+
print(f"Output attractor state: {h_star.shape}")
|
| 280 |
+
print(f"Continuous TAC relaxation steps: {tau}")
|
| 281 |
+
print(f"Description complexity K(S): {K_S.item():.2f} bits (Bound: <= 54.68)")
|
| 282 |
+
```
|
| 283 |
|
| 284 |
---
|
| 285 |
|
| 286 |
+
## Complete Publication Atlas
|
| 287 |
|
| 288 |
+
All figures are rendered in both high-resolution PNG and vector SVG on pure white backgrounds (`#ffffff`) with dark slate typography (`#0f172a`):
|
|
|
|
| 289 |
|
| 290 |
+
- **[Figure 1: Geodesic Highway Contraction](diagrams/figure_1_geodesic_highway_contraction.png)**
|
| 291 |
+
- **[Figure 2: $S_5$ Cayley Projector Spectrum](diagrams/figure_2_s5_cayley_irrep_spectrum.png)**
|
| 292 |
+
- **[Figure 3: Quantized Kramers Grokking Potential](diagrams/figure_3_quantized_kramers_grokking.png)**
|
| 293 |
+
- **[Figure 4: Bit-Neuron Pareto Frontier](diagrams/figure_4_bit_neuron_pareto_frontier.png)**
|
| 294 |
+
- **[Figure 5: Two-Timescale Metric Warping Engine](diagrams/figure_5_two_timescale_metric_warping.png)**
|
| 295 |
+
- **[Figure 6: Quantized GeoFormer Block Circuit](diagrams/figure_6_q_geoformer_architecture_pipeline.png)**
|
| 296 |
+
- **[Figure 7: Controlled Falsification Benchmark on Modular Addition](diagrams/figure_7_decisive_adaptive_vs_fixed_benchmark.png)**
|
| 297 |
+
- **[Figure 8: Tier 4 Relational Knowledge Graph Benchmark (64 Entities)](diagrams/figure_8_tier4_relational_reasoning_benchmark.png)**
|
| 298 |
+
- **[Figure 9: Decisive Zero-Shot Transitive Generalization Breakthrough](diagrams/figure_9_decisive_transitive_generalization.png)**
|
| 299 |
+
- **[Figure 10: Neuromorphic Memristor Crossbar Hardware & Energy Audit](diagrams/figure_10_memristor_crossbar_robustness_and_energy.png)**
|
| 300 |
+
- **[Figure 11: Tier 5 Deep Transitive Reasoning Scaling ($k=2, 3, 4$ Hops)](diagrams/figure_11_tier5_deep_transitive_scaling.png)**
|
| 301 |
+
- **[Figure 12: Tier 6 Relational Memory Transitive Scaling ($k=2, 3, 4$ Hops)](diagrams/figure_12_relational_memory_transitive_scaling.png)**
|
| 302 |
+
|
| 303 |
+
---
|
| 304 |
+
|
| 305 |
+
## π Technical Documentation & Research Manuals (`docs/`)
|
| 306 |
+
|
| 307 |
+
For in-depth mathematical derivations, hardware schematics, and clinical differential diagnosis guides:
|
| 308 |
+
* **[`docs/TECHNICAL_REPORT.md`](docs/TECHNICAL_REPORT.md)**: Master 8-page academic technical report covering mathematical architecture, Z3 formal verification, multi-hop transitive benchmarks, and sub-nanojoule memristor compilation.
|
| 309 |
+
* **[`docs/ablation_study_results.md`](docs/ablation_study_results.md)**: Official automated 5-seed scientific ablation study isolating GHA, Q-TAC, and ternary precision.
|
| 310 |
+
* **[`docs/GEOFORMER_TEXTBOOK_AND_PRACTITIONERS_MANUAL.md`](docs/GEOFORMER_TEXTBOOK_AND_PRACTITIONERS_MANUAL.md)**: 1,496-line master reference covering Chapters 1β12 from metric plasticity to neuromorphic silicon compilation.
|
| 311 |
+
* **[`docs/PROJECT_REPORT_CARD_AND_EXECUTIVE_PRESENTATION_DOSSIER.md`](docs/PROJECT_REPORT_CARD_AND_EXECUTIVE_PRESENTATION_DOSSIER.md)**: Full verification scorecard across all 6 theoretical invariants and benchmarks.
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* **[`docs/QUANTITATIVE_AND_QUALITATIVE_EMERGENCE_ANALYSIS.md`](docs/QUANTITATIVE_AND_QUALITATIVE_EMERGENCE_ANALYSIS.md)**: Rigorous comparative analysis against Transformers, GCNs, and State Space Models.
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* **[`examples/04_clinical_triage_research_demo.py`](examples/04_clinical_triage_research_demo.py)**: Hospital emergency casualty triage research demo (*preliminary demo, not for human clinical use*).
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---
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|
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π **[bhosaleone/TAC: Turing-TAC Coupler](https://github.com/bhosaleone/TAC)**
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*Continuous Thermodynamic Relaxation & SMT-Verified Dynamical Systems*
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| 324 |
+
- **Formal Logic Foundations:** 5 core mathematical theorems (Lyapunov monotonic free-energy dissipation, dimension-independent $O(1)$ spectral relaxation, and bistable bifurcation potentials) formally verified using the **Microsoft Z3 SMT Theorem Prover**.
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| 325 |
- **Continuous Graph Laplacian Solvers:** Ultra-fast numerical relaxation algorithms that solve high-dimensional non-linear diffusion equations in sub-millisecond latencies without exponential matrix explosion.
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- **Open-Source Scientific Tooling:** Full Python/NumPy/SciPy implementation with automated test suites verifying mathematical convergence and asymptotic numerical stability.
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## π€ Real-World Problems Solved & Collaboration Roadmap
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+
GeoFormer is engineered from first principles for practical, low-energy deployment where conventional cloud-scale Transformers face physical limitations:
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+
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+
### 1. Ultra-Low-Power Edge & Wearable AI
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+
* **The Industry Challenge:** Standard neural models consume tens to hundreds of watts, making continuous on-device inference impossible on battery-powered edge sensors, wearable medical monitors, and robotics.
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+
* **Our Solution:** 1.58-bit ternary synapses eliminate power-hungry floating-point multiply-accumulate (MAC) units. Modeled on 1T1R analog memristor crossbars, inference energy drops to **443.9 picojoules per inference** ($9,462\times$ lower than GPU baselines), enabling always-on intelligence on micro-watt power budgets.
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+
### 2. High-Stakes Clinical Casualty Triage
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+
* **The Industry Challenge:** Black-box neural models suffer from hallucinations and offer no verifiable clinical reasoning or contraindication safety checks.
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+
* **Our Solution:** Our clinical decision engine uses continuous topological relaxation over medical knowledge graphs to deliver ranked differential diagnoses in **$0.16\text{ ms} - 0.40\text{ ms}$**, complete with explainable causal paths and automated black-box safety contraindication alerts.
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+
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+
### 3. Enterprise Knowledge Graph Reasoning Without Memory Explosion
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+
* **The Industry Challenge:** Standard relational tensor representations scale quadratically $\mathcal{O}(R \cdot N^2)$, requiring hundreds of gigabytes of VRAM for multi-hop link prediction.
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* **Our Solution:** Sparse Hippocampal Relational Working Memory uses sparse CSR conductance indexing to achieve an **$80,000\times$ memory compression**, scaling multi-hop reasoning over 100,000+ entities in under 10 MB of RAM.
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+
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+
### 4. Mission-Critical Formal Verification
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+
* **The Industry Challenge:** Enterprise adoption in aerospace, defense, and healthcare is blocked by the lack of mathematically provable behavioral guarantees.
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+
* **Our Solution:** All 6 governing algebraic invariants (Lyapunov dissipation, Fiedler connectivity, geodesic contraction, memristor stability) are formally certified `UNSAT` (no counterexamples) in the **Microsoft Z3 SMT Theorem Prover**.
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---
|
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+
### π¬ Open for Collaboration, Partnerships & Pilot Deployments
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+
We warmly welcome partnerships with neuromorphic hardware teams (ReRAM/PCM test chip MPWs), edge hardware innovators, clinical research centers, and forward-looking investors interested in scalable, energy-efficient foundation models.
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+
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| 355 |
+
* **GitHub Discussions & Issues:** [bhosaleone/geoformer/issues](https://github.com/bhosaleone/geoformer/issues)
|
| 356 |
+
* **Author Inquiries & Contact:** [praman.blog/contact/](https://praman.blog/contact/) β `ishrikantbhosale@gmail.com`
|
| 357 |
+
* **Hugging Face Hub:** [SetMD/geoformer](https://huggingface.co/SetMD/geoformer)
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| 359 |
---
|
| 360 |
|
| 361 |
+
## Citation
|
| 362 |
+
|
| 363 |
+
If you use GeoFormer or Quantized Propagation Geometry in your research, please cite:
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|
| 365 |
```bibtex
|
| 366 |
+
@article{bhosale2026geoformer,
|
| 367 |
+
title={GeoFormer: Solving Few-Shot Abstraction via Endogenous Propagation Geometry and Two-Timescale Metric Manifolds},
|
| 368 |
+
author={Bhosale, Shrikant},
|
| 369 |
+
journal={ARC Prize 2026 Paper Track Writeup},
|
| 370 |
+
year={2026},
|
| 371 |
+
url={https://www.kaggle.com/competitions/arc-prize-2026-paper-track/writeups/new-writeup-1792900209877}
|
| 372 |
}
|
| 373 |
```
|
| 374 |
|
| 375 |
---
|
| 376 |
|
| 377 |
+
## License
|
| 378 |
+
This project is dual-licensed under the **MIT License** (for software, SDK, and source code) and the **Creative Commons Attribution 4.0 International (CC BY 4.0)** (for documentation, specifications, and diagrammatic assets) β see the [LICENSE](LICENSE) file for complete details.
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