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+# 🔢 Distributed Tensor
+
+## 📚 Table of Contents
+
+- [🔢 Distributed Tensor](#-distributed-tensor)
+  - [📚 Table of Contents](#-table-of-contents)
+  - [🔗 Introduction](#-introduction)
+  - [📝 Design](#-design)
+  - [🔨 Usage](#-usage)
+  - [🎈 Progress Log](#-progress-log)
+
+## 🔗 Introduction
+
+Distributed tensor is a type of tensor that is distributed across multiple devices. It is a wrapper of PyTorch tensor, and it is used to support distributed training.
+It can represent the device topology and tensor placement over the devices in the topology. It also provides a set of APIs to manipulate the distributed tensor.
+
+## 📝 Design
+
+Our implementation is inspired by the work [Alpa](https://arxiv.org/abs/2201.12023), which unifies data parallelism and tensor parallelism as intra-op parallelism. It uses notations `S` to represent the sharded dimension and `R` to represent the replicated dimension. For example, given a 2D matrix, `[S, R]` represents the tensor is sharded over the first dimension.
+
+Each sharded dimension will have a subscript to represent its placement over the devices. Assuming we have 4 GPUs and the GPUs are arranged in a 2 x 2 manner. Let's say we have a 2D matrix like below:
+
+
+```text
+    [1,  2,  3,  4 ]
+A = [4,  5,  6,  7 ]
+    [8,  9,  10, 11]
+    [12, 13, 14, 15]
+```
+
+`[S0, R]` would mean that the first dimension is sharded over the rows in the device topology.
+
+```text
+| --------------------—————————————————————-|
+|                     |                     |
+|  [1,  2,  3,  4 ]   |  [1,  2,  3,  4 ]   |
+|  [4,  5,  6,  7 ]   |  [4,  5,  6,  7 ]   |
+|                     |                     |
+| --------------------——————————————————-----
+|                     |                     |
+|  [8,  9,  10, 11]   |  [8,  9,  10, 11]   |
+|  [12, 13, 14, 15]   |  [12, 13, 14, 15]   |
+|                     |                     |
+| --------------------——————————————————-----
+```
+
+`[S01, R]` would mean that the first dimension is sharded over both the row and column in the device topology.
+
+```text
+| --------------------—————————————————————-|
+|                     |                     |
+|  [1,  2,  3,  4 ]   |  [4,  5,  6,  7 ]   |
+|                     |                     |
+| --------------------——————————————————-----
+|                     |                     |
+|  [8,  9,  10, 11]   |  [12, 13, 14, 15]   |
+|                     |                     |
+| --------------------——————————————————-----
+```
+
+## 🔨 Usage
+
+A sample API usage is given below.
+
+```python
+import torch
+
+import colossalai
+from colossalai.device.device_mesh import DeviceMesh
+from colossalai.tensor.d_tensor import DTensor, ShardingSpec
+
+colossalai.launch_from_torch(config={})
+
+# define your device mesh
+# assume you have 4 GPUs
+physical_mesh_id = torch.arange(0, 4)
+mesh_shape = (2, 2)
+device_mesh = DeviceMesh(physical_mesh_id, mesh_shape, init_process_group=True)
+
+# define a tensor
+a = torch.rand(16, 32).cuda()
+
+# create sharding spec for the tensor
+# assume the sharding spec is [S0, R]
+dim_partition_dict = {0: [0]}
+sharding_spec = ShardingSpec(a.dim(), dim_partition_dict)
+
+# create a distributed tensor
+d_tensor = DTensor(a, device_mesh, sharding_spec)
+print(d_tensor)
+
+global_tensor = d_tensor.to_global()
+print(global_tensor)
+```
+
+
+## 🎈 Progress Log
+
+- [x] Support layout conversion
+- [x] Support sharding on 2D device mesh
+- [ ] Support sharding on 3D device mesh
+- [ ] Support sharding 4D device mesh
+- [ ] Support sharding info saving and offline tensor merge (we can save tensor as dtensor and gather the tensors back to the global tensor based on the sharding info in a single process in CPU, useful for distributed training checkpoint load and save.)