import operator import warnings from dataclasses import dataclass from functools import reduce # Required in Python 3 from typing import Tuple, Optional import torch import bitsandbytes.functional as F # math.prod not compatible with python < 3.8 def prod(iterable): return reduce(operator.mul, iterable, 1) tensor = torch.Tensor # The inverse transformation for the colTuring and colAmpere format were contributed by Alex Borzunov: # https://github.com/bigscience-workshop/petals/blob/main/src/petals/utils/linear8bitlt_patch.py """ This class pools outlier dimensions across layers. This is particularly important for small models where outlier features are less systematic and occur with low frequency. """ class GlobalOutlierPooler: _instance = None def __init__(self): raise RuntimeError("Call get_instance() instead") def initialize(self): self.outliers = set() self.model_dim = None @classmethod def get_instance(cls): if cls._instance is None: cls._instance = cls.__new__(cls) cls._instance.initialize() return cls._instance def add_outliers(self, outlier_idx, feature_dim): if self.model_dim is None: self.model_dim = feature_dim if feature_dim != self.model_dim: return # we do not encode outliers for the 2nd FFN layer self.outliers.update(outlier_idx.tolist()) def get_current_outlier_idx(self): return torch.Tensor(list(self.outliers)).to(torch.int64) def get_inverse_transform_indices(transform_tile: callable, tile_size: Tuple[int, int]): """ Compute a permutation of indices that invert the specified (tiled) matrix transformation :param transform_tile: a function that applies forward transform to a tensor of shape [dim1, dim2] :param tile_size: higher-level tile dimensions, i.e. (8, 32) for Turing and (32, 32) for Ampere :note: we assume that tile_transform applies to a cpu-based int8 tensor of shape tile_size :example: transform_tile function for the turing layout (bitsandbytes.functional as F) :returns: indices """ d1, d2 = tile_size assert 0 < d1 * d2 < 2**64 tile_indices = torch.arange(d1 * d2, dtype=torch.int64).view(d1, d2) # encode each position in tile as a tuple of <= 8 unique bytes permuted_tile_indices = torch.zeros_like(tile_indices) for i in range(8): # select i-th byte, apply transformation and trace where each index ended up ith_dim_indices = torch.div(tile_indices, 256**i, rounding_mode="trunc") % 256 sample_tile_i = (ith_dim_indices - 128).to(torch.int8).contiguous() assert torch.all(sample_tile_i.int() + 128 == ith_dim_indices), "int overflow" permuted_tile_i = transform_tile(sample_tile_i) ith_permuted_indices = permuted_tile_i.to(tile_indices.dtype) + 128 permuted_tile_indices += ith_permuted_indices * (256**i) if d1 * d2 < 256**i: break # if all indices fit in i bytes, stop early return permuted_tile_indices def undo_layout(permuted_tensor: torch.Tensor, tile_indices: torch.LongTensor) -> torch.Tensor: """ Undo a tiled permutation such as turing or ampere layout :param permuted_tensor: torch tensor in a permuted layout :param tile_indices: reverse transformation indices, from get_inverse_transform_indices :return: contiguous row-major tensor """ (rows, cols), (tile_rows, tile_cols) = permuted_tensor.shape, tile_indices.shape assert rows % tile_rows == cols % tile_cols == 0, "tensor must contain a whole number of tiles" tensor = permuted_tensor.reshape(-1, tile_indices.numel()).t() outputs = torch.empty_like(tensor) # note: not using .index_copy because it was slower on cuda outputs[tile_indices.flatten()] = tensor outputs = outputs.reshape(tile_rows, tile_cols, cols // tile_cols, rows // tile_rows) outputs = outputs.permute(3, 0, 2, 1) # (rows // tile_rows, tile_rows), (cols // tile_cols, tile_cols) return outputs.reshape(rows, cols).contiguous() class MatMul8bit(torch.autograd.Function): @staticmethod def forward(ctx, A, B, out=None, quant_type="vector", precision=None): if precision is None: precision = [8, 8, 8] if precision[0] != 8: with torch.no_grad(): output = torch.matmul(A, B) else: if len(B.shape) == 2: dim = 0 else: dim = 1 qA, SA = F.vectorwise_quant(A, dim=-1, quant_type=quant_type) qB, SB = F.vectorwise_quant(B, dim=dim, quant_type=quant_type) iout = F.igemm(qA, qB) output = F.vectorwise_mm_dequant(iout, SA, SB, A.dtype, quant_type) if A.requires_grad or B.requires_grad: ctx.save_for_backward(A, B) ctx.quant_type = quant_type ctx.precision = precision return output @staticmethod def backward(ctx, grad_output): A, B = ctx.saved_tensors quant_type = ctx.quant_type precision = ctx.precision grad_A = grad_B = None if B.requires_grad: if len(A.shape) == 3: dims = [0, 1] # bsi -> ibs permute_dim = [0, 2, 1] else: dims = [0] # bs -> sb permute_dim = [1, 0] if precision[1] != 8: with torch.no_grad(): grad_B = torch.matmul(A.permute(permute_dim), grad_output) else: if len(B.shape) == 2 and len(A.shape) == 3: grad_output = grad_output.contiguous() if not grad_output.is_contiguous(): grad_output.contiguous() qgrad_output, S1 = F.vectorwise_quant( grad_output.view(-1, grad_output.shape[2]), dim=0, quant_type=quant_type, ) if not A.is_contiguous(): A = A.contiguous() qA, S2 = F.vectorwise_quant( A.view(-1, A.shape[2]), dim=0, quant_type=quant_type ) igrad_B = F.igemm(qA.t(), qgrad_output) grad_B = F.vectorwise_mm_dequant( igrad_B, S2.t(), S1, grad_output.dtype, quant_type ) else: qgrad_output, S1 = F.vectorwise_quant( grad_output, dim=dims, quant_type=quant_type ) qA, S2 = F.vectorwise_quant( A, dim=dims, quant_type=quant_type ) igrad_B = F.igemm(qA.permute(permute_dim), qgrad_output) grad_B = F.vectorwise_mm_dequant( igrad_B, S2.permute(permute_dim), S1, grad_output.dtype, quant_type, ) if A.requires_grad: if len(grad_output.shape) == 3: dims = [2] else: dims = [1] if len(B.shape) == 3: # bio -> boi permute_dim = [0, 2, 1] dim_B = dims else: # io -> oi permute_dim = [1, 0] dim_B = [1] if precision[2] != 8: with torch.no_grad(): grad_A = torch.matmul(grad_output, B.permute(permute_dim)) else: qgrad_output, S1 = F.vectorwise_quant( grad_output, dim=dims, quant_type=quant_type ) qB, S3 = F.vectorwise_quant(B, dim=dim_B, quant_type=quant_type) igrad_A = F.igemm(qgrad_output, qB.permute(permute_dim)) grad_A = F.vectorwise_mm_dequant( igrad_A, S1, S3.permute(permute_dim), grad_output.dtype, quant_type, ) return grad_A, grad_B, None, None, None mm_cublas = MatMul8bit.apply bmm_cublas = MatMul8bit.apply matmul_cublas = MatMul8bit.apply @dataclass class MatmulLtState: tile_indices: Optional[torch.Tensor] = None force_no_igemmlt: bool = False CB = None CxB = None SB = None SCB = None CxBt = None SBt = None CBt = None subB = None outlier_pool = None has_accumulated_gradients = False threshold = 0.0 idx = None is_training = True has_fp16_weights = True memory_efficient_backward = False use_pool = False formatB = F.get_special_format_str() def reset_grads(self): self.CB = None self.CxB = None self.SB = None self.SCB = None self.CxBt = None self.SBt = None self.CBt = None def get_tile_size(self): assert self.formatB in ( "col_turing", "col_ampere", ), f"please find this assert and manually enter tile size for {self.formatB}" return (8, 32) if self.formatB == "col_turing" else (32, 32) class MatMul8bitLt(torch.autograd.Function): # forward is the same, but we added the fallback for pre-turing GPUs # backward is mostly the same, but adds one extra clause (see "elif state.CxB is not None") @staticmethod def forward(ctx, A, B, out=None, bias=None, state=MatmulLtState): using_igemmlt = torch.cuda.get_device_capability(device=A.device) >= (7, 5) and not state.force_no_igemmlt # default of pytorch behavior if inputs are empty ctx.is_empty = False if prod(A.shape) == 0: ctx.is_empty = True ctx.A = A ctx.B = B ctx.bias = bias if A.shape[-1] == B.shape[0]: return torch.empty(A.shape[:-1] + B.shape[1:], dtype=A.dtype, device=A.device) else: return torch.empty(A.shape[:-1] + B.shape[:1], dtype=A.dtype, device=A.device) # 1. Quantize A # 2. Quantize B # 3. Matmul # 4. Mixed-precision decomposition matmul # 5. Save state formatB = state.formatB input_shape = A.shape if state.outlier_pool is None: state.outlier_pool = GlobalOutlierPooler.get_instance() # Cast A to fp16 if A.dtype != torch.float16: warnings.warn(f"MatMul8bitLt: inputs will be cast from {A.dtype} to float16 during quantization") # 1. Quantize A if len(A.shape) == 3: A = A.view(-1, A.shape[-1]).contiguous() CA, CAt, SCA, SCAt, coo_tensorA = F.double_quant(A.to(torch.float16), threshold=state.threshold) if state.threshold > 0.0 and coo_tensorA is not None: if state.has_fp16_weights: idx = torch.unique(coo_tensorA.colidx).long() CA[:, idx] = 0 CAt[:, idx] = 0 subA = A[:, idx] state.subB = B[:, idx].t().contiguous() state.idx = idx else: if state.CxB is None and using_igemmlt: # B in in 8-bit row-major, we can transform it back to 16-bit to extract outlier dimensions # we also need to convert it to the turing/ampere format state.CxB, state.SB = F.transform(state.CB, to_order=formatB) else: if not state.has_fp16_weights and state.CxB is None and using_igemmlt: state.CxB, state.SB = F.transform(state.CB, to_order=formatB) subA = None # 2. Quantize B if state.has_fp16_weights: has_grad = True if (getattr(B, "grad", None) is not None) else False is_transposed = not B.is_contiguous() and B.shape[0] == B.stride(1) if is_transposed: B = B.contiguous() if (state.is_training and not has_grad) or state.CxB is None: state.reset_grads() ( CB, state.CBt, state.SCB, state.SCBt, coo_tensorB, ) = F.double_quant(B.to(torch.float16)) if using_igemmlt: state.CxB, state.SB = F.transform(CB, to_order=formatB) else: state.CB = CB else: has_grad = False if coo_tensorA is not None and not state.has_fp16_weights: # extract outliers outlier_idx = torch.unique(coo_tensorA.colidx) state.idx = outlier_idx # state.outlier_pool.add_outliers(outlier_idx, A.shape[-1]) # if state.use_pool and state.outlier_pool.model_dim == A.shape[-1]: # # do not use pool for 2nd FFN layer # state.idx = state.outlier_pool.get_current_outlier_idx().to(A.device) # else: # state.idx = outlier_idx if state.CxB is not None: outliers = F.extract_outliers(state.CxB, state.SB, state.idx.int()) else: outliers = state.CB[:, state.idx.long()].clone() state.subB = (outliers * state.SCB.view(-1, 1) / 127.0).t().contiguous().to(A.dtype) CA[:, state.idx.long()] = 0 CAt[:, state.idx.long()] = 0 subA = A[:, state.idx.long()] shapeB = state.SB[0] if state.SB else B.shape if len(input_shape) == 3: output_shape = (input_shape[0], input_shape[1], shapeB[0]) else: output_shape = (input_shape[0], shapeB[0]) # 3. Matmul if using_igemmlt: C32A, SA = F.transform(CA, "col32") out32, Sout32 = F.igemmlt(C32A, state.CxB, SA, state.SB) if bias is None or bias.dtype == torch.float16: # we apply the fused bias here output = F.mm_dequant(out32, Sout32, SCA, state.SCB, bias=bias) output = output.to(A.dtype) else: # apply bias separately output = F.mm_dequant(out32, Sout32, SCA, state.SCB, bias=None) output = output.to(A.dtype).add_(bias) else: A_wo_outliers = A.clone() if state.idx is not None: A_wo_outliers[:, state.idx.long()] = 0 output = torch.nn.functional.linear(A_wo_outliers, state.CB.to(A.dtype)) output = output.mul_(state.SCB.unsqueeze(0).mul(1.0 / 127.0)) if bias is not None: output = output.add_(bias) # 4. Mixed-precision decomposition matmul if coo_tensorA is not None and subA is not None: output += torch.matmul(subA, state.subB) # 5. Save state ctx.state = state ctx.formatB = formatB ctx.grad_shape = input_shape ctx.dtype_A, ctx.dtype_B, ctx.dtype_bias = A.dtype, B.dtype, None if bias is None else bias.dtype if any(ctx.needs_input_grad[:2]): ctx.tensors = (CAt, subA) ctx.tensor_states = (SCAt, state.idx) else: ctx.tensors = [None, None] ctx.tensor_states = (None, None) ctx.save_for_backward(None, None) clone_func = torch.clone if len(output_shape) == 3 else lambda x: x return clone_func(output.view(output_shape)) @staticmethod def backward(ctx, grad_output): if ctx.is_empty: bias_grad = None if ctx.bias is None else torch.zeros_like(ctx.bias) return torch.zeros_like(ctx.A), torch.zeros_like(ctx.B), None, bias_grad, None req_gradA, req_gradB, _, req_gradBias, _ = ctx.needs_input_grad CAt, subA = ctx.tensors SCAt, idx = ctx.tensor_states formatB = ctx.formatB state = ctx.state grad_A = grad_B = grad_bias = None if req_gradBias: # compute grad_bias first before changing grad_output dtype grad_bias = grad_output.sum(0, dtype=ctx.dtype_bias) # Cast grad_output to fp16 if len(grad_output.shape) == 3: grad_output = grad_output.reshape(-1, grad_output.shape[-1]).contiguous() Cgrad, Cgradt, SCgrad, SCgradt, coo_tensor = F.double_quant(grad_output.to(torch.float16)) if req_gradB: CxAt, SAt = F.transform(CAt, formatB, transpose=True) C32grad, Sgrad = F.transform(Cgradt, "col32", transpose=True) gradB32, SgradB32 = F.igemmlt(C32grad, CxAt, Sgrad, SAt) grad_B = F.mm_dequant(gradB32, SgradB32, SCgradt, SCAt) if state.threshold > 0.0 and subA is not None: grad_B[:, idx] += torch.matmul(grad_output.t(), subA) if req_gradA: if state.CBt is not None: C32grad, Sgrad = F.transform(Cgrad, "col32") if state.CxBt is None: state.CxBt, state.SBt = F.transform(state.CBt, to_order=formatB, transpose=True) gradA32, SgradA32 = F.igemmlt(C32grad, state.CxBt, Sgrad, state.SBt) grad_A = F.mm_dequant(gradA32, SgradA32, SCgrad, state.SCBt).view(ctx.grad_shape).to(ctx.dtype_A) elif state.CB is not None: CB = state.CB.to(ctx.dtype_A, copy=True).mul_(state.SCB.unsqueeze(1).mul(1.0 / 127.0)) grad_A = torch.matmul(grad_output, CB).view(ctx.grad_shape).to(ctx.dtype_A) elif state.CxB is not None: if state.tile_indices is None: order, tile_size = state.formatB, state.get_tile_size() transform = lambda x: F.transform(x.cuda(), from_order="row", to_order=order)[0].to(x.device) with torch.no_grad(): state.tile_indices = get_inverse_transform_indices(transform, tile_size).to(state.CxB.device) CB = ( undo_layout(state.CxB, state.tile_indices) .to(ctx.dtype_A) .mul_(state.SCB.unsqueeze(1).mul(1.0 / 127.0)) ) grad_A = torch.matmul(grad_output, CB).view(ctx.grad_shape).to(ctx.dtype_A) else: raise Exception("State must contain either CBt or CB or CxB matrix for backward") return grad_A, grad_B, None, grad_bias, None def matmul( A: tensor, B: tensor, out: tensor = None, state: MatmulLtState = None, threshold=0.0, bias=None ): state = state or MatmulLtState() if threshold > 0.0: state.threshold = threshold return MatMul8bitLt.apply(A, B, out, bias, state)