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'''
num_replicas is the total number of times we'll replicate 
the batch samples for all cores.
'''
train_sampler = torch.utils.data.distributed.DistributedSampler(
                                                  im_train,
                                                  num_replicas=xm.xrt_world_size(),
                                                  rank=xm.get_ordinal(), 
                                                  shuffle=True
                 )

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# add your custom transforms and augmentations
T = transforms.Compose([
      transforms.ToTensor(),
      ...
    ])

# instructing the master node to download the dataset only ONCE
if not xm.is_master_ordinal():
  xm.rendezvous('download_only_once')

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def map_fn(index, flags):
  '''
  Contains the following:
    - data preprocessing
    - model instantiation
    - training loop
      - validation (optional)
    - testing
    
NOTE: all code beyond this belong inside this unless otherwise stated

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class MyCustomNet(nn.Module):
  def __init__(self, myparams):
    super().__init__()
    
    # define layers
    ...
    
  def forward(self, x):
    '''
    Pass your inputs through your layers as you normally would.

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# download and install PyTorch XLA
!pip install cloud-tpu-client==0.10 https://storage.googleapis.com/tpu-pytorch/wheels/torch_xla-1.8.1-cp37-cp37m-linux_x86_64.whl

# basic torch sub-modules (feel free to add on [eg: einops, time, random, etc.])
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim

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import os
assert os.environ['COLAB_TPU_ADDR'], 'Make sure to select TPU from Edit > Notebook settings > Hardware accelerator'

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CS2040s Week 12 Lecture 1

Notes from CS2040S Week 12 Lecture 21 on Minimum Spanning Trees

MST

• A spanning tree with minimum weight
• Covers all nodes once
• No cycles
• If you cut an MST, both pieces are MSTs
• For every cycle, max weight edge is not in the MST
• For ever cut D, the minimum weight edge that crosses the cut is in the MST

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CS2040s Week 10 Lecture 2

Notes from CS2040S Week 10 Lecture 2 on Directed Acyclic Graphs

Directed Acyclic Graphs

• Every edge has a direction between nodes
• No cycles in the graphs

Topological Ordering

• Ordering of nodes that respects the edges

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CS2040s Week 10 Lecture 1

Notes from CS2040S Week 10 Lecture 1 on Shortest Path Algorithms

Edge Weights

• Edges have weights on them that represent cost of traversal
  • Could be distance, money, energy needed
• Shortest path isn't necessarily the shortest
  • It's the path with the minimal total weight

Questions

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CS2040S Week 9 Lecture 2

Notes from Week 9 Lecture 2 on Graphs

BFS

Properties of parent edges

• They form a tree (shortest path tree)
  • There are no cycles – all nodes visited only once
• Parent edges are always shortest paths from starting node s
• For now, all edges have weight/distance 1