submission symmetry task-Avishikta Bhattacharjee

E2E_Hidden_Symmetry_Generator_Avishikta_Bhattacharjee/M_representation/README.md

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+### M representations
+M diagonal[1+a,1+b,1+c,1+d]

E2E_Hidden_Symmetry_Generator_Avishikta_Bhattacharjee/README.md

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+#  Symmetry Generator Learning: Install & Quickstart
+[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://github.com/gatetub/E2E/blob/main/E2E_Hidden_Symmetry_Generator_Avishikta_Bhattacharjee/generator-notebook.ipynb)
+
+### Summary
+This tutorial demonstrates how to learn latent symmetry generators that preserve a quadratic invariant $$\psi(x) = x^\top M x$$ using PyTorch, with a simple training loop and visualization utilities. It includes ready-to-run examples for SO(4) (Euclidean metric) and SO(1,3) Lorentz symmetry (Minkowski metric), and a plotting function to save generator heatmaps. The notebook is designed for quick experimentation, with configurable dimension, number of generators, data size, epochs, device, and series order for the transform.
+
+### Manifold method
+
+This tutorial treats the target symmetry group as the isometry group of a manifold defined by a metric $$M$$, and enforces invariance of the quadratic form $$\psi(x)=x^\top M x$$ under learned transformations to align generators with the manifold’s geometry.  
+
+- Geometry via metric: choose $$M=I$$ for Euclidean manifolds (SO(n)) or $$M=\mathrm{diag}(-1,1,\dots,1)$$ for Minkowski space (SO(1,n−1)), which fixes the notion of distance preserved by the group.  
+- Lie algebra constraint: learn generator matrices $$A$$ intended to satisfy the infinitesimal isometry condition $$A^\top M + M A = 0$$, implemented implicitly by minimizing the closure loss on $$\psi$$.  
+- Group action: approximate the exponential map with a truncated series $$g(\theta)$$ to transform data while preserving $$\psi$$, and use an orthogonality penalty to encourage distinct generators.
+
+### Install
+- Requirements: Python 3.11, PyTorch, Matplotlib, tqdm, optional CUDA GPU support for faster training.
+
+
+### Usage
+- Open generator-functions.ipynb and run cells top-to-bottom to train and visualize generators.
+- SO(4) example (Euclidean metric M=I) :
+```python
+import torch
+M = torch.eye(4, device="cuda:0")
+model = train_generic_lie_group(n=4, M=M)
+visualize_generators(model, filename="so4.png", group_name="SO(4)")
+```
+- Lorentz SO(1,3) example (Minkowski metric diag(-1,1,1,1)) :
+```python
+import torch
+
+def get_metric(n, device='cpu'):
+    M = torch.eye(n, device=device)
+    if n > 0:
+        M[0, 0] = -1.0
+    return M
+
+M = get_metric(4, device="cuda:0")
+model1 = train_generic_lie_group(n=4, M=M)
+visualize_generators(model1, filename="Lorentz4.png", group_name="L(4)")
+```

E2E_Hidden_Symmetry_Generator_Avishikta_Bhattacharjee/requirements.txt

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+
+torch
+matplotlib
+tqdm