code: def CheckpointSemiring(cls, min_size=0):
      class _Check(torch.autograd.Function):
          @staticmethod
          def forward(ctx, a, b):
              ctx.save_for_backward(a, b)
              return cls.matmul(a, b)
  
          @staticmethod
          def backward(ctx, grad_output):
              a, b = ctx.saved_tensors
              with torch.enable_grad():
                  q = cls.matmul(a, b)
                  return torch.autograd.grad(q, (a, b), grad_output)
  
      class _CheckBand(torch.autograd.Function):
          @staticmethod
          def forward(ctx, a, a_lu, a_ld, b, b_lu, b_ld):
              ctx.save_for_backward(
                  a, b, torch.LongTensor([a_lu, a_ld, b_lu, b_ld])
              )
              a = BandedMatrix(a, a_lu, a_ld)
              b = BandedMatrix(b, b_lu, b_ld)
              return cls.matmul(a, b).data
  
          @staticmethod
          def backward(ctx, grad_output):
              a, b, bands = ctx.saved_tensors
              a_lu, a_ld, b_lu, b_ld = bands.tolist()
              with torch.enable_grad():
                  q = cls.matmul(
                      BandedMatrix(a, a_lu, a_ld),
                      BandedMatrix(b, b_lu, b_ld),
                  )
                  grad_a, grad_b = torch.autograd.grad(
                      q.data, (a, b), grad_output
                  )
                  return grad_a, None, None, grad_b, None, None
  
      class _CheckpointSemiring(cls):
          @staticmethod
          def matmul(a, b):
              if has_genbmm and isinstance(a, genbmm.BandedMatrix):
                  lu = a.lu + b.lu
                  ld = a.ld + b.ld
                  c = _CheckBand.apply(
                      a.data, a.lu, a.ld, b.data, b.lu, b.ld
                  )
                  return BandedMatrix(c, lu, ld, cls.zero)
  
              if broadcast_size(a, b) > min_size:
                  return _Check.apply(a, b)
              else:
                  return cls.matmul(a, b)
  
      return _CheckpointSemiring
  
file_path: pytorch-struct/torch_struct/semirings/checkpoint.py
imports: import torch
label_desc: Use image node_id 3 for calling a global function with example usage: CheckpointSemiring(cls, min_size) and returns: _CheckpointSemiring, cls, cls, torch, grad_a,  None,  None,  grad_b,  None,  None, BandedMatrix, _Check, cls