Metadata-Version: 2.4
Name: idempotent-tropical
Version: 0.1.0
Summary: Zero-Multiplication Tropical Semiring Idempotent Attention & Max-Plus Algebraic Deep Learning
Author-email: "Dr. A. Emre ÇETİN" <aemre.cetin@gmail.com>
License: Proprietary - U.S. Patent Pending 64/148,668
Keywords: tropical-geometry,max-plus,idempotent-semiring,zero-multiplication,attention,fpga,neuromorphic,edge-ai,deep-learning
Requires-Python: >=3.10
Description-Content-Type: text/markdown
Requires-Dist: torch>=2.0.0
Requires-Dist: numpy>=1.22.0
Provides-Extra: dev
Requires-Dist: pytest>=7.0.0; extra == "dev"

# Idempotent-Tropical: Zero-Multiplication Tropical Semiring Attention

> **Zero-Multiplication Self-Attention Engine Powered by Max-Plus Idempotent Semiring Algebra for FPGA, Edge AI, and Neuromorphic Silicon.**  
> **Author:** Dr. A. Emre ÇETİN (`aemre.cetin@gmail.com`)  
> **Patent Base:** U.S. Patent Application No. `64/148,668` ("Patent Pending", Confirmation No. 5890)

---

## 1. Mathematical Foundations

In standard linear algebra over the field $(\mathbb{R}, +, \times)$, computing self-attention requires billions of floating-point multiplications:
$$\text{Attention}(Q, K, V) = \text{Softmax}\left(\frac{Q K^T}{\sqrt{d}}\right) V$$
For a standard sequence length ($T = 512, d = 64, H = 12, B = 4$), this entails **1,610,612,736 (1.61 Billion) floating-point multiplications per layer**.

`idempotent-tropical` maps the attention computation onto the **Tropical / Max-Plus Idempotent Semiring** $(\mathbb{R}_{\max}, \oplus, \otimes)$:
* **Set:** $\mathbb{R}_{\max} = \mathbb{R} \cup \{-\infty\}$
* **Tropical Addition ($\oplus$):** $a \oplus b = \max(a, b)$
  - **Inherent Idempotence:** $a \oplus a = \max(a, a) = a$
* **Tropical Multiplication ($\otimes$):** $a \otimes b = a + b$ (Classical addition acts as tropical multiplication!)
* **Tropical Matrix Product:**
  $$(A \odot_{\text{trop}} B)_{i, j} = \bigoplus_{k=1}^K (A_{i, k} \otimes B_{k, j}) = \max_{k=1}^K (A_{i, k} + B_{k, j})$$

### 100.00% Multiplication Reduction
Because classical multiplication is entirely replaced by addition ($+$) and classical addition is replaced by maximum ($\max$), **the core attention scoring and value routing stages require EXACTLY ZERO MULTIPLICATIONS.**

On silicon (ASICs, FPGAs, Neuromorphic chips), a floating-point multiplier requires $4\times - 8\times$ more silicon area and $3\times - 5\times$ more energy than an adder.

---

## 2. Installation

```bash
cd packages/idempotent-tropical
pip install -e .
```

---

## 3. Quickstart

```python
import torch
from idempotent_tropical import TropicalAttention

# Initialize zero-multiplication attention layer
attn = TropicalAttention(d_model=768, n_heads=12)
x = torch.randn(4, 256, 768)

# Differentiable training mode (Tropical soft-relaxation)
out_train, _ = attn(x, inference_mode=False)

# Pure zero-multiplication discrete inference mode (Max-Plus Algebra)
out_infer, _ = attn(x, inference_mode=True)
```

