# inspired by https://github.com/karpathy/micrograd/blob/master/micrograd/engine.py from __future__ import annotations import time, math from collections import defaultdict from functools import partialmethod, reduce from itertools import accumulate import numpy as np from typing import List, Tuple, Callable, Optional, ClassVar, Type, Union, Sequence, Any, Iterable, Set from tinygrad.helpers import ImageDType, argfix, make_pair, getenv, IMAGE, DEBUG, flatten, DType, dtypes, prod, all_int from tinygrad.lazy import LazyBuffer from tinygrad.ops import Device, LoadOps from tinygrad.shape.symbolic import sint from tinygrad.realize import run_schedule # An instantiation of the Function is the Context class Function: def __init__(self, device:str, *tensors:Tensor): self.device = device self.needs_input_grad = [t.requires_grad for t in tensors] self.requires_grad = True if any(self.needs_input_grad) else None if None in self.needs_input_grad else False if self.requires_grad: self.parents = tensors def forward(self, *args, **kwargs): raise NotImplementedError(f"forward not implemented for {type(self)}") def backward(self, *args, **kwargs): raise RuntimeError(f"backward not implemented for {type(self)}") @classmethod def apply(fxn:Type[Function], *x:Tensor, **kwargs) -> Tensor: ctx = fxn(x[0].device, *x) ret = Tensor(ctx.forward(*[t.lazydata for t in x], **kwargs), device=ctx.device, requires_grad=ctx.requires_grad) if ctx.requires_grad and not Tensor.no_grad: ret._ctx = ctx # used by autograd engine return ret import tinygrad.mlops as mlops # **** start with two base classes, Tensor and Function **** class Tensor: __slots__ = "lazydata", "requires_grad", "grad", "_ctx" __deletable__ = ('_ctx',) training: ClassVar[bool] = False class train: def __init__(self, val=True): self.val = val def __enter__(self): self.prev = Tensor.training Tensor.training = self.val def __exit__(self, exc_type: Any, exc_value: Any, traceback: Any): Tensor.training = self.prev no_grad: ClassVar[bool] = False default_type: ClassVar[DType] = dtypes.float32 def __init__(self, data:Union[int, float, list, LazyBuffer, np.ndarray], device:Optional[str]=None, dtype:Optional[DType]=None, requires_grad:Optional[bool]=None): assert dtype is None or isinstance(dtype, DType), f"invalid dtype {dtype}" device = Device.canonicalize(device) # tensors have gradients, buffers do not self.grad: Optional[Tensor] = None # NOTE: this can be in three states. False and None: no gradient, True: gradient # None (the default) will be updated to True if it's put in an optimizer self.requires_grad: Optional[bool] = requires_grad # internal variables used for autograd graph construction self._ctx: Optional[Function] = None if isinstance(data, LazyBuffer): assert dtype is None or dtype == data.dtype, "dtype doesn't match, and casting isn't supported" elif isinstance(data, (int, float)): data = LazyBuffer.loadop(LoadOps.CONST, tuple(), dtype or Tensor.default_type, device, data) elif data.__class__ is list: assert dtype is None or dtype.np is not None, f"{dtype} doesn't have a numpy dtype" data = LazyBuffer.fromCPU(np.array(data, dtype=(dtype or Tensor.default_type).np)) elif isinstance(data, np.ndarray): assert dtype is None or dtype.np is not None, f"{dtype} doesn't have a numpy dtype" if data.shape == (): data = LazyBuffer.loadop(LoadOps.CONST, tuple(), dtype or dtypes.from_np(data.dtype), device, data.item()) else: data = LazyBuffer.fromCPU(data.astype(dtype.np) if dtype is not None and dtype.np is not None else data) else: raise RuntimeError(f"can't create Tensor from {data}") # data is a LazyBuffer, but it might be on the wrong device self.lazydata = data if data.device == device else data.copy_to_device(device) def __repr__(self): return f"" # Python has a non moving GC, so this should be okay def __hash__(self): return id(self) @property def device(self) -> str: return self.lazydata.device @property def shape(self) -> Tuple[sint, ...]: return self.lazydata.shape @property def dtype(self) -> DType: return self.lazydata.dtype # ***** data handlers **** @staticmethod def corealize(lst:Iterable[Tensor]): seen:Set[LazyBuffer] = set() sched = [] for t in lst: sched += t.lazydata.schedule(seen) run_schedule(sched) def realize(self) -> Tensor: run_schedule(self.lazydata.schedule()) return self def assign(self, x) -> Tensor: # TODO: this is a hack for writing to DISK if self.device.startswith("DISK"): if x.__class__ is not Tensor: x = Tensor(x, device="CPU", dtype=self.dtype) self.contiguous().realize().lazydata.realized._copyin(x.numpy()) # type: ignore return self if x.__class__ is not Tensor: x = Tensor(x, device=self.device, dtype=self.dtype) assert self.shape == x.shape and self.device == x.device, f"assign shape mismatch {self.shape} != {x.shape} or device mismatch {self.device} != {x.device}" assert not x.requires_grad # self requires_grad is okay? if DEBUG >= 4: print(f"assign {self.lazydata} <- {x.lazydata}") if self.dtype == x.dtype and self.lazydata.realized is not None and not getenv("DISALLOW_ASSIGN"): x.lazydata.output_buffer = self.lazydata.realized self.lazydata = x.lazydata return self def detach(self) -> Tensor: return Tensor(self.lazydata, device=self.device, requires_grad=False) def numpy(self) -> np.ndarray: assert all_int(self.shape), f"no numpy if shape is symbolic, {self.shape=}" assert self.dtype.np is not None, f"no numpy dtype for {self.dtype}" return self.detach().cast(dtypes.from_np(self.dtype.np)).contiguous().to('CPU').realize().lazydata.realized.toCPU().reshape(self.shape) # TODO: if things are realized this won't work def to_(self, device:str): assert self.lazydata.realized is None self.lazydata.device = device if self.grad: self.grad.to_(device) def to(self, device:str) -> Tensor: ret = Tensor(self.lazydata, device) if self.grad: ret.grad = self.grad.to(device) return ret # ***** creation llop entrypoint ***** @staticmethod def _loadop(op, sz, device:Optional[str]=None, dtype:Optional[DType]=None, arg=None, **kwargs): return Tensor(LazyBuffer.loadop(op, (sz,), Tensor.default_type if dtype is None else dtype, Device.canonicalize(device), arg), dtype=dtype, device=device, **kwargs) @staticmethod def empty(*shape, **kwargs): assert all_int(shape), f"cannot create with symbolic shape {shape}" return Tensor._loadop(LoadOps.EMPTY, prod(shape), **kwargs).reshape(shape) _seed: int = int(time.time()) @staticmethod def manual_seed(seed=0): Tensor._seed = seed @staticmethod def rand(*shape, **kwargs): assert all_int(shape), f"cannot create with symbolic shape {shape}" Tensor._seed += 1 return Tensor._loadop(LoadOps.RAND, prod(shape), arg=Tensor._seed, **kwargs).reshape(shape) # ***** creation helper functions ***** @staticmethod def full(shape:Tuple[sint, ...], fill_value, **kwargs): return Tensor(fill_value, **kwargs).reshape([1]*len(new_shape := argfix(shape))).expand(new_shape) @staticmethod def zeros(*shape, **kwargs): return Tensor.full(argfix(*shape), 0, **kwargs) @staticmethod def ones(*shape, **kwargs): return Tensor.full(argfix(*shape), 1, **kwargs) @staticmethod def arange(start, stop=None, step=1, **kwargs): if stop is None: stop, start = start, 0 return Tensor.full((math.ceil((stop-start)/step),), step, **kwargs).cumsum() + (start - step) @staticmethod def eye(dim:int, **kwargs): return Tensor.full((dim,1),1,**kwargs).pad(((0,0),(0,dim))).reshape(dim*(dim+1)).shrink(((0,dim*dim),)).reshape(dim, dim) def full_like(self, fill_value, **kwargs): return Tensor.full(self.shape, fill_value=fill_value, dtype=kwargs.pop("dtype", self.dtype), device=kwargs.pop("device", self.device), **kwargs) def zeros_like(self, **kwargs): return self.full_like(0, **kwargs) def ones_like(self, **kwargs): return self.full_like(1, **kwargs) # ***** rng hlops ***** @staticmethod def randn(*shape, dtype:Optional[DType]=None, **kwargs) -> Tensor: # https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform src = Tensor.rand(2, *shape, **kwargs) return src[0].mul(2*math.pi).cos().mul((1 - src[1]).log().mul(-2).sqrt()).cast(Tensor.default_type if dtype is None else dtype) @staticmethod def normal(*shape, mean=0.0, std=1.0, **kwargs) -> Tensor: return (std * Tensor.randn(*shape, **kwargs)) + mean @staticmethod def uniform(*shape, low=0.0, high=1.0, **kwargs) -> Tensor: dtype = kwargs.pop("dtype", Tensor.default_type) return ((high-low) * Tensor.rand(*shape, **kwargs)).cast(dtype) + low @staticmethod def scaled_uniform(*shape, **kwargs) -> Tensor: return Tensor.uniform(*shape, low=-1.0, high=1.0, **kwargs).mul(prod(shape)**-0.5) # https://www.tensorflow.org/api_docs/python/tf/keras/initializers/GlorotUniform @staticmethod def glorot_uniform(*shape, **kwargs) -> Tensor: return Tensor.uniform(*shape, low=-1.0, high=1.0, **kwargs).mul((6/(shape[0]+prod(shape[1:])))**0.5) # https://pytorch.org/docs/stable/_modules/torch/nn/init.html#kaiming_uniform_ @staticmethod def kaiming_uniform(*shape, a:float = 0.01, **kwargs) -> Tensor: bound = math.sqrt(3.0) * math.sqrt(2.0 / (1 + a ** 2)) / math.sqrt(prod(shape[1:])) return Tensor.uniform(*shape, low=-bound, high=bound, **kwargs) # https://pytorch.org/docs/stable/_modules/torch/nn/init.html#kaiming_normal_ @staticmethod def kaiming_normal(*shape, a:float = 0.01, **kwargs) -> Tensor: std = math.sqrt(2.0 / (1 + a ** 2)) / math.sqrt(prod(shape[1:])) return Tensor.normal(*shape, mean=0.0, std=std, **kwargs) # ***** toposort and backward pass ***** def deepwalk(self): def _deepwalk(node, visited, nodes): visited.add(node) if getattr(node, "_ctx", None): for i in node._ctx.parents: if i not in visited: _deepwalk(i, visited, nodes) nodes.append(node) return nodes return _deepwalk(self, set(), []) def backward(self): assert self.shape == tuple(), f"backward can only be called for scalar tensors, but it has shape {self.shape})" # fill in the first grad with one. don't use Tensor.ones because we don't need contiguous # this is "implicit gradient creation" self.grad = Tensor(1, device=self.device, requires_grad=False) for t0 in reversed(self.deepwalk()): assert (t0.grad is not None) grads = t0._ctx.backward(t0.grad.lazydata) grads = [Tensor(g, device=self.device, requires_grad=False) if g is not None else None for g in ([grads] if len(t0._ctx.parents) == 1 else grads)] for t, g in zip(t0._ctx.parents, grads): if g is not None and t.requires_grad: assert g.shape == t.shape, f"grad shape must match tensor shape, {g.shape!r} != {t.shape!r}" t.grad = g if t.grad is None else (t.grad + g) del t0._ctx # ***** movement mlops ***** def reshape(self, shape, *args) -> Tensor: new_shape = argfix(shape, *args) assert 0 not in new_shape, f"zeros not allowed in shape {new_shape}" return mlops.Reshape.apply(self, shape=tuple([-prod(self.shape) // prod(new_shape) if s == -1 else s for s in new_shape])) def expand(self, shape, *args) -> Tensor: return mlops.Expand.apply(self, shape=tuple([x if x != -1 else s for s,x in zip(self.shape, argfix(shape, *args))])) def permute(self, order, *args) -> Tensor: return mlops.Permute.apply(self, order=argfix(order, *args)) def flip(self, axis, *args) -> Tensor: return mlops.Flip.apply(self, axis=[x if x >= 0 else x+len(self.shape) for x in argfix(axis, *args)]) def shrink(self, arg:Tuple[Tuple[sint, sint], ...]) -> Tensor: return mlops.Shrink.apply(self, arg=arg) if any(x != (0,s) for x,s in zip(arg, self.shape)) else self def pad(self, arg: Tuple[Tuple[int, int], ...], value:float=0) -> Tensor: ret = mlops.Pad.apply(self, arg=arg) if any(x != (0, 0) for x in arg) else self return ret if 0 == value else ret + mlops.Pad.apply(Tensor.ones_like(self), arg=arg).where(0, value) # ***** movement hlops ***** # - Negative indices are taken relative to the end of the sequence, so X[-2] returns the 2nd-to-last element # - A slice i:j returns the elements with indices in [i, j) # - If omitted, i and j will default to 0 and N, respectively, where N is the length of the sequence # - Negative values for i and j are taken relative to the end of the sequence # - Both i and j will be clamped to the range (-N, N], where N in the length of the sequence # - Indexing with None on a given axis will add a new dimension of size one before that axis # - Empty slices are not allowed (tensors with 0s in shape have to be supported first, for all backends). # - For a slice [i:j:k] finding the correct indices is delegated to slice.indices(len). # - Strides > 1 and < 0 are now allowed!: # - This works by applying Shrink -> [[Flip -> ] Pad -> Reshape -> Shrink] -> Reshape (ops in brackets are optional) # - Idea of stride < 0 support: # - Do the slice first, flip the axes were slice.step is negative, do slice.step -> -slice.step. Go to steps below. # - Idea of stride `s` > 1 support (Pad -> Reshape -> Shrink): # - Instead of doing [::s] on axis [dim_sz], do [:, 0] on axes [dim_sz_padded // s, s]. # - So pad dim_sz with as many zeros as needed (dim_sz -> dim_sz_padded) so that reshape to [dim_sz_padded // s, s] # is possible. # - Apply Shrink to do the slice [:, 0] on axes of shapes [dim_sz_padded // s, s]. # - Fancy indexing and combined indexing is supported # - Combined indexing works by letting regular slicing finish first -> computing the resulting dims w.r.t to Tensors passed in -> fancy indexing # - Any Tensors passed in __getitem__ will perform (CMPEQ with arange -> MUL with self -> SUM_REDUCE) iteratively # - The first iteration will expand the dim of self while consecutive iterations will reduce the dim # - There's a special case where a permute is needed at the end: # - if first Tensor passed in (expand dims) is not at dim 0 # - and following Tensors does not follow consecutively to the end of fancy indexing's dims def __getitem__(self, val): # val: Union[int, slice, Tensor, None, Ellipsis, Tuple[Union[int, slice, Tensor, None, Ellipsis], ...]] def normalize_int(e, i, dim_sz): if -dim_sz <= e < dim_sz: return e if e != -1 else dim_sz-1 raise IndexError(f"index {e} is out of bounds for dimension {i} with size {self.shape[i]}") orig_slices = list(val) if isinstance(val, tuple) else [val] count = defaultdict(list) for i,v in enumerate(orig_slices): count[type(v)].append(i) if (num_slices := len(count[int]) + len(count[slice]) + len(count[Tensor])) > len(self.shape): raise IndexError(f"too many indices for tensor of dimension {len(self.shape)}") if len(ellipsis_found := count[type(Ellipsis)]) > 1: raise IndexError("an index can only have a single ellipsis ('...')") ellipsis_idx = ellipsis_found[0] if ellipsis_found else len(orig_slices) orig_slices[ellipsis_idx:ellipsis_idx+1] = [slice(None)] * (len(self.shape) - num_slices) valid_slices = [v for v in orig_slices if v is not None] valid_slices = [v if isinstance(v, slice) else slice(y_ := normalize_int(v, i, dim_sz), y_+1) if isinstance(v, int) else slice(None) for i, (v, dim_sz) in enumerate(zip(valid_slices, self.shape))] start, stop, strides = zip(*y) if (y := [s.indices(dim_sz) for s, dim_sz in zip(valid_slices, self.shape)]) else ((), (), ()) new_slice = tuple((s, e) if st > 0 else (e+1, s+1) for s, e, st in zip(start, stop, strides)) sliced_tensor = self.shrink(new_slice).flip(axis=[i for i, s in enumerate(strides) if s < 0]) new_shape = sliced_tensor.shape if any(abs(s) != 1 for s in strides): strides = tuple(abs(s) for s in strides) # Pad: add pad at the end: [dim_sz] -> [dim_sz_padded] padded_tensor = sliced_tensor.pad(tuple((0, s-(dim_sz % s) if dim_sz % s != 0 else 0) for s, dim_sz in zip(strides, sliced_tensor.shape))) # Reshape: [dim_sz_padded] -> [dim_sz_padded // s, s] reshaped_tensor = padded_tensor.reshape(flatten([sh // s, s] for sh, s in zip(padded_tensor.shape, strides))) new_shape = reshaped_tensor.shape[::2] # Shrink: do [:, 0] sliced_tensor = reshaped_tensor.shrink(tuple(flatten(((0, sh), (0, 1)) for sh in new_shape))) final_shape, it_shape, dim, tensors, dim_collapsed = [], iter(new_shape), [], [], 0 for i,s in enumerate(orig_slices): if s is None: final_shape.append(1) else: # s is int or slice or Tensor dim_shape = next(it_shape) if isinstance(s, int): dim_collapsed += 1 else: assert isinstance(dim_shape, int), f"does not support symbolic shape {dim_shape}" final_shape.append(dim_shape) if isinstance(s, Tensor): tensors.append(s) dim.append(i-dim_collapsed) ret = sliced_tensor.reshape(tuple(final_shape)) if tensors: # Fancy/tensor indexing # normalize idx # TODO: first contiguous fixes torch+cpu_only CI, but it causes llvm to fail. Second one fixes llvm idx = [t.sign().contiguous().__neg__().contiguous().relu() * ret.shape[d] + t for d,t in zip(dim, tensors)] max_dim = max(i.ndim for i in idx) # compute sum_dim, arange, and idx sum_dim = [d if n==0 else d+max_dim-n for n,d in enumerate(dim)] arange = [Tensor.arange(ret.shape[d], dtype=dtypes.int32, requires_grad=False, device=self.device).reshape(*[1]*sd, ret.shape[d], *[1]*(ret.ndim + max_dim - n - sd - 1)) for n,(sd,d) in enumerate(zip(sum_dim, dim))] first_idx = [idx[0].reshape(*[1]*dim[0], *[1]*(1 + max_dim - idx[0].ndim), *idx[0].shape, *[1]*(ret.ndim - dim[0] - 1))] rest_idx = [i.reshape(*[1]*dim[0], *[1]*(max_dim - i.ndim), *i.shape, *[1]*(ret.ndim - dim[0] - n)) for n,i in enumerate(idx[1:], 1)] idx = first_idx + rest_idx ret = ret.reshape(*ret.shape[:sum_dim[0]+1], *[1]*max_dim, *ret.shape[sum_dim[0]+1:]) # iteratively fancy index for a,i,sd in zip(arange, idx, sum_dim): ret = (a==i).mul(ret).sum(sd) # special permute case if dim[0] != 0 and len(dim) != 1 and dim != list(range(dim[0], dim[-1]+1)): ret_dims = list(range(ret.ndim)) ret = ret.permute(ret_dims[dim[0]:dim[0]+max_dim] + ret_dims[:dim[0]] + ret_dims[dim[0]+max_dim:]) return ret def __setitem__(self,s,v): return self.__getitem__(s).assign(v) # NOTE: using slice is discouraged and things should migrate to pad and shrink def slice(self, arg:Sequence[Optional[Tuple[int, sint]]], value:float=0) -> Tensor: arg_ = tuple([a if a is not None else (0,s) for s,a in zip(self.shape, arg)]) padding = tuple([(max(0, -p[0]), max(0, p[1]-self.shape[i])) for i,p in enumerate(arg_)]) return self.pad(padding, value=value).shrink(tuple([(p[0] + padding[i][0], p[1] + padding[i][0]) for i,p in enumerate(arg_)])) def gather(self: Tensor, idx: Tensor, dim: int): assert idx.ndim == self.ndim, "self.ndim must equal idx.ndim" assert all(s >= i for s,i in zip(self.shape, idx.shape)), "all dim of idx.shape must be smaller than self.shape" if dim < 0: dim += self.ndim idx = idx.transpose(ax1=dim, ax2=0).unsqueeze(-1) permarg = list(range(self.ndim)) permarg = permarg[1:dim] + [permarg[0]] + permarg[dim+1:] + [permarg[dim]] if dim != 0 else permarg[1:] + [permarg[0]] return ((idx == Tensor.arange(self.shape[dim], dtype=dtypes.int32, requires_grad=False, device=self.device)) * self.permute(*permarg).shrink(tuple([*[(0,sh) for sh in idx.shape[1:-1]], (0,self.shape[dim])])).unsqueeze(0)).sum(-1).transpose(ax1=0, ax2=dim) def cat(self, *args, dim=0): dim = (dim + len(self.shape)) if dim < 0 else dim assert all(len(y.shape) == len(self.shape) and all(y.shape[i] == s for i,s in enumerate(self.shape) if i != dim) for y in args) catargs = [self, *args] assert all(t.shape for t in catargs), "zero-dimensional tensor cannot be concatenated" shapes = [s.shape[dim] for s in catargs] shape_cumsum = [0, *accumulate(shapes)] slc = [[(0, 0) for _ in self.shape] for _ in catargs] for shp,k,s in zip(shapes, shape_cumsum[:-1], slc): s[dim] = (k, shape_cumsum[-1] - k - shp) return reduce(Tensor.__add__, [arg.pad(tuple(s)) for arg,s in zip(catargs, slc)]) @staticmethod def stack(tensors, dim=0): first = tensors[0].unsqueeze(dim) unsqueezed_tensors = [tensor.unsqueeze(dim) for tensor in tensors[1:]] # checks for shapes and number of dimensions delegated to cat return first.cat(*unsqueezed_tensors, dim=dim) def repeat(self, repeats): base_shape = (1,) * (len(repeats) - self.ndim) + self.shape new_shape = [x for b in base_shape for x in [1, b]] expand_shape = [x for rs in zip(repeats, base_shape) for x in rs] final_shape = [r*s for r,s in zip(repeats, base_shape)] return self.reshape(new_shape).expand(expand_shape).reshape(final_shape) def chunk(self, num:int, dim:int) -> List[Tensor]: assert all_int(self.shape), f"does not support symbolic shape {self.shape}" dim, step = dim + self.ndim if dim < 0 else dim, math.ceil(self.shape[dim]/num) slice_params = [[slice(None)]*dim + [slice(k, k + step)] for k in range(0, self.shape[dim], step)] return [self[tuple(sl)] for sl in slice_params] def squeeze(self, dim=None): if dim is None: return self if 1 not in self.shape else self.reshape(*[size for size in self.shape if size != 1]) if dim <= 0 and self.ndim == 0: return self # This is to match PyTorch behavior if not -self.ndim <= dim < self.ndim: raise IndexError(f"Dimension out of range (expected to be in range of [{-self.ndim if self.ndim > 0 else self.ndim-1}, {self.ndim-1 if self.ndim > 0 else self.ndim}], but got {dim})") if dim < 0: dim += self.ndim return self if self.shape[dim] != 1 else self.reshape(*[size for idx, size in enumerate(self.shape) if idx != dim]) def unsqueeze(self, dim): if dim < 0: dim = len(self.shape) + dim + 1 return self.reshape(self.shape[:dim] + (1,) + self.shape[dim:]) # (padding_left, padding_right, padding_top, padding_bottom) def pad2d(self, padding:Union[List[int], Tuple[int, ...]], value:float=0): slc = [(-p0, s+p1) for p0,p1,s in zip(padding[::2], padding[1::2], self.shape[::-1])][::-1] return self.slice([(0,s) for s in self.shape[:-(len(padding)//2)]] + slc, value=value) @property def T(self) -> Tensor: return self.transpose() def transpose(self, ax1=1, ax2=0) -> Tensor: order = list(range(len(self.shape))) order[ax1], order[ax2] = order[ax2], order[ax1] return self.permute(order) def flatten(self, start_dim=0): return self.reshape(shape=self.shape[:start_dim] + (-1,)) # ***** reduce ops ***** def _reduce(self, fxn:Type[Function], axis:Optional[Union[int, Tuple[int, ...]]]=None, keepdim=False) -> Tensor: axis_: List[int] = list(range(len(self.shape))) if axis is None else ([axis] if axis.__class__ is int else list(axis)) # type: ignore axis_ = [x if x >= 0 else x+len(self.shape) for x in axis_] shape = [s for i,s in enumerate(self.shape) if i not in axis_] ret = fxn.apply(self, new_shape=tuple([1 if i in axis_ else s for i,s in enumerate(self.shape)])) return ret if keepdim else ret.reshape(shape=shape) def sum(self, axis=None, keepdim=False): return self._reduce(mlops.Sum, axis, keepdim) def max(self, axis=None, keepdim=False): return self._reduce(mlops.Max, axis, keepdim) def min(self, axis=None, keepdim=False): return -((-self).max(axis=axis, keepdim=keepdim)) def mean(self, axis=None, keepdim=False): assert all_int(self.shape), "does not support symbolic shape" out = self.sum(axis=axis, keepdim=keepdim) return out.mul(prod(out.shape)/prod(self.shape)) def std(self, axis=None, keepdim=False, correction=1): assert all_int(self.shape), "does not support symbolic shape" square_sum = ((self - self.mean(axis=axis, keepdim=True)).square()).sum(axis=axis, keepdim=keepdim) return square_sum.div(prod(self.shape)/prod(square_sum.shape)-correction).sqrt() def _softmax(self, axis): m = self - self.max(axis=axis, keepdim=True) e = m.exp() return m, e, e.sum(axis=axis, keepdim=True) def softmax(self, axis=-1): _, e, ss = self._softmax(axis) return e.div(ss) def log_softmax(self, axis=-1): m, _, ss = self._softmax(axis) return m - ss.log() def argmax(self, axis=None, keepdim=False): if axis is None: idx = (self == self.max(axis)) * Tensor.arange(prod(self.shape)-1,-1,-1, dtype=dtypes.int32, requires_grad=False, device=self.device).reshape(self.shape) return prod(self.shape) - idx.max() - 1 axis = axis + len(self.shape) if axis < 0 else axis m = self == self.max(axis=axis, keepdim=True) idx = m * Tensor.arange(self.shape[axis]-1,-1,-1, dtype=dtypes.int32, requires_grad=False, device=self.device).reshape(self.shape[axis], *[1]*(self.ndim-axis-1)) return self.shape[axis]-idx.max(axis=axis, keepdim=keepdim)-1 def argmin(self, axis=None, keepdim=False): return (-self).argmax(axis=axis, keepdim=keepdim) # ***** processing ops ***** def _pool(self, k_:Tuple[int, ...], stride:Union[Tuple[int, ...], int]=1, dilation:Union[Tuple[int, ...], int]=1) -> Tensor: assert len(self.shape) >= len(k_), f"can't pool {self.shape} with {k_}" assert all_int(self.shape), f"does not support symbolic shape {self.shape}" s_, d_ = make_pair(stride, len(k_)), make_pair(dilation, len(k_)) assert len(k_) == len(s_) and len(k_) == len(d_), f"stride/dilation mismatch kernel:{k_} stride:{s_} dilation:{d_}" slc_prefix, prefix, i_ = [(0,x) for x in self.shape[0:-len(k_)]], self.shape[0:-len(k_)], self.shape[-len(k_):] if any(k > s for k,s in zip(k_, s_)) or any(d != 1 for d in d_): o_ = [(i - d * (k-1) - 1)//s + 1 for i,d,k,s in zip(i_, d_, k_, s_)] e_ = [math.ceil(k*(i+d) / i) for k,i,d in zip(k_, i_, d_)] # expands such that we don't need padding xup = self.reshape(*prefix, *flatten((1,i) for i in i_)).expand(*prefix, *flatten((e,i) for e,i in zip(e_, i_))).reshape(*prefix, *[e*i for e,i in zip(e_, i_)]) # slide by dilation xup = xup.slice(slc_prefix + [(0,k*(i+d)) for k,i,d in zip(k_, i_, d_)]) xup = xup.reshape(*prefix, *flatten((k,i+d) for k,i,d in zip(k_, i_, d_))) xup = xup.slice(slc_prefix + flatten(((0,k), (0,o*s)) for k,o,s in zip(k_, o_, s_))) # handle stride, and permute to move reduce to the end xup = xup.reshape(*prefix, *flatten((k,o,s) for k,o,s in zip(k_, o_, s_))) xup = xup.slice(slc_prefix + flatten(((0,k), (0,o), (0,1)) for k,o in zip(k_, o_))) xup = xup.reshape(*prefix, *flatten((k,o) for k,o in zip(k_, o_))) return xup.permute(*range(len(prefix)), *[len(prefix)+i*2+1 for i in range(len(k_))], *[len(prefix)+i*2 for i in range(len(k_))]) # TODO: once the shapetracker can optimize well, remove this alternative implementation. or not if the CPU implementation doesn't use ShapeTracker o_ = [(i+(s-k))//s for i,s,k in zip(i_, s_, k_)] xup = self.slice(slc_prefix + [(0,o*s) for o,s in zip(o_, s_)]) xup = xup.reshape(*prefix, *flatten(((o, s) for o,s in zip(o_, s_)))) xup = xup.slice(slc_prefix + flatten(((0,o), (0,k)) for o,k in zip(o_, k_))) return xup.permute(*range(len(prefix)), *[len(prefix)+i*2 for i in range(len(k_))], *[len(prefix)+i*2+1 for i in range(len(k_))]) # NOTE: these work for more than 2D def avg_pool2d(self, kernel_size=(2,2), stride=None): return self._pool(make_pair(kernel_size), stride if stride is not None else kernel_size).mean(axis=tuple(range(0-len(make_pair(kernel_size)), 0))) def max_pool2d(self, kernel_size=(2,2), stride=None, dilation=1): return self._pool(make_pair(kernel_size), stride if stride is not None else kernel_size, dilation).max(axis=tuple(range(0-len(make_pair(kernel_size)), 0))) def conv_transpose2d(self, weight:Tensor, bias:Optional[Tensor]=None, groups=1, stride=1, dilation=1, padding=0, output_padding=0) -> Tensor: HW, trailing = weight.shape[2:], list(range(3, len(weight.shape)+1)) x, w = self, weight.reshape(groups, weight.shape[0]//groups, weight.shape[1], *weight.shape[2:]).permute(0,2,1,*trailing).flip(trailing) stride = make_pair(stride, len(HW)) if any(s>1 for s in stride): x = x.reshape(*x.shape[:2], *flatten((k,1) for k in x.shape[2:])) x = x.pad(((0,0), (0,0), *flatten(((0,0),(0,s-1)) for s in stride))) x = x.reshape(*x.shape[:2], *[k*s for k,s in zip(x.shape[2::2], stride)]) x = x.shrink(((0,x.shape[0]), (0,x.shape[1]), *[(0,k-(s-1)) for k,s in zip(x.shape[2:], stride)])) padding = flatten((((k-1)*d-p,(k-1)*d-p+op) for k,d,p,op in reversed(list(zip(HW, make_pair(dilation, len(HW)), make_pair(padding, len(HW)), make_pair(output_padding, len(HW))))))) return x.conv2d(w.reshape(w.shape[0]*w.shape[1],*w.shape[2:]), groups=groups, bias=bias, dilation=dilation, padding=padding) wino = int(getenv("WINO", "0")) def conv2d(self, weight:Tensor, bias:Optional[Tensor]=None, groups=1, stride=1, dilation=1, padding=0) -> Tensor: (bs,cin_), (cout,cin), HW = self.shape[:2], weight.shape[:2], weight.shape[2:] assert groups*cin == cin_ and len(self.shape) == len(weight.shape), f"Input Tensor shape {self.shape} does not match the shape of the weights {weight.shape}. ({groups*cin} vs. {cin_})" if isinstance(padding, (tuple,list)): assert len(padding) == 2*len(HW) or len(padding) == len(HW), f"Expected padding of length {2*len(HW)} or {len(HW)}, but got {len(padding)} for tensor of shape {self.shape}" padding_ = [padding]*2*len(HW) if isinstance(padding, int) else (padding if len(padding) == 2*len(HW) else [p for p in padding for _ in range(2)][::-1]) # conv2d is a pooling op (with padding) x = self.pad2d(padding_)._pool(HW, stride, dilation) # (bs, groups*cin, oy, ox, H, W) rcout, oyx = cout//groups, x.shape[2:-len(HW)] if not all(x == 3 for x in HW) or stride != 1 or dilation != 1 or not Tensor.wino: # normal conv x = x.reshape(bs, groups, cin, 1, *oyx, *HW).expand(bs, groups, cin, rcout, *oyx, *HW).permute(0,1,3,*[4+i for i in range(len(oyx))],2,*[4+len(oyx)+i for i in range(len(HW))]) # conv! broadcasted to (bs, groups, rcout, *oyx, cin, *HW) ret = (x * weight.reshape(1, groups, rcout, *[1] * len(oyx), cin, *HW)).sum([-1-i for i in range(1+len(oyx))], keepdim=True).reshape(bs, cout, *oyx) return ret if bias is None else ret.add(bias.reshape(1, -1, *[1] * len(HW))) # winograd conv 3 kernel f(4x4,3x3) see: http://arxiv.org/abs/1509.09308 def apply_matrix(mat, t, dim=0): return t if dim == len(HW) else Tensor.stack([apply_matrix(mat, sum(mm*t[j] for j,mm in enumerate(m) if mm), dim=dim+1) for m in mat]) HWI, HWO = (6,) * len(HW), (4,) * len(HW) # F(4x4,3x3) winograd tiles winograd_Bt = [[4, 0, -5, 0, 1, 0], [0, -4, -4, 1, 1, 0], [0, 4, -4, -1, 1, 0], [0, -2, -1, 2, 1, 0], [0, 2, -1, -2, 1, 0], [0, 4, 0, -5, 0, 1]] winograd_G = [[1/4, 0, 0], [-1/6, -1/6, -1/6], [-1/6, 1/6, -1/6], [1/24, 1/12, 1/6], [1/24, -1/12, 1/6], [0, 0, 1]] winograd_At = [[1, 1, 1, 1, 1, 0], [0, 1, -1, 2, -2, 0], [0, 1, 1, 4, 4, 0], [0, 1, -1, 8, -8, 1]] # applying At in pre-order almost doubles compilation time # todo: stride == dilation # use padding to round up to 4x4 output tiles d = self.pad2d(sum([[padding_[i*2], padding_[i*2+1] + (-(dim + sum(padding_[i * 2:(i + 1) * 2]) - 2) % 4)] for i, dim in enumerate(self.shape[-len(HW):])], []))._pool(HWI, HWO) # (bs, cin_, tyx, HWI) d = d.permute(*range(len(d.shape)-len(HW),len(d.shape)), *range(len(d.shape)-len(HW))).contiguous_backward() # move HW to the front: # (HWI, bs, cin_, tyx) tyx = d.shape[-len(HWI):] # dim of tiling g = weight.permute(*range(len(weight.shape)-len(HW),len(weight.shape)), *range(len(weight.shape)-len(HW))) # move HW to the front # compute 6x6 winograd tiles: GgGt, BtdB gfactors = apply_matrix(winograd_G, g).contiguous().reshape(*HWI, 1, groups, rcout, cin, *([1]*len(tyx))) # (HWI, groups * rcout, cin) -> (HWI, bs=1, groups, rcout, cin, tyx=(1,1)) dfactors = apply_matrix(winograd_Bt, d).contiguous().reshape(*HWI, bs, groups, 1, cin, *tyx) # (HWI, bs, cin_, tyx) -> (HWI, bs, groups, 1 ,cin, *tyx) ret = apply_matrix(winograd_At, (gfactors * dfactors).sum(axis=-1-len(HW))) # matmul; sum across cin: (HWI, bs, groups, rcout, *tyx); then HWI -> HWO: (HWO, bs, groups, rcout, *tyx) ret = ret.permute([*range(len(HW), len(ret.shape)-len(HW)), *[i+o for i in range(len(HW)) for o in [len(ret.shape)-len(HW),0]]]) # interleave tyx and HWO: (bs, groups, rcout, oy, HO, ox, WO) ret = ret.reshape(bs, cout, *[c * HWO[i] for i, c in enumerate(tyx)]).shrink(tuple((0, s) for s in [bs, cout, *oyx])) # merge groups and rcout, tyx and HWO: (bs, groups, cout, *yx), shrink to final return (ret if bias is None else ret.add(bias.reshape(1, -1, *[1 for _ in range(len(HW))]))).contiguous().contiguous_backward() def dot(self, w:Tensor) -> Tensor: n1, n2 = len(self.shape), len(w.shape) assert n1 != 0 and n2 != 0, f"both arguments to matmul need to be at least 1D, but they are {n1}D and {n2}D" assert self.shape[-1] == w.shape[-min(n2, 2)], f"Input Tensor shapes {self.shape} and {w.shape} cannot be multiplied ({self.shape[-1]} != {w.shape[-min(n2, 2)]})" x = self.reshape(*self.shape[0:-1], *[1]*min(n1-1, n2-1, 1), self.shape[-1]) w = w.reshape(*w.shape[0:-2], *[1]*min(n1-1, n2-1, 1), *w.shape[-min(n2, 2):]).transpose(-1, -min(n2, 2)) return (x*w).sum(-1) def cumsum(self, axis:int=0) -> Tensor: return self.transpose(axis,-1).pad2d((self.shape[axis]-1,0))._pool((self.shape[axis],)).sum(-1).transpose(axis,-1) # ***** mlops (unary) ***** def __neg__(self): return mlops.Neg.apply(self) def contiguous(self): return mlops.Contiguous.apply(self) def contiguous_backward(self): return mlops.ContiguousBackward.apply(self) def log(self): return mlops.Log.apply(self) def log2(self): return mlops.Log.apply(self)/math.log(2) def exp(self): return mlops.Exp.apply(self) def exp2(self): return mlops.Exp.apply(self*math.log(2)) def relu(self): return mlops.Relu.apply(self) def sigmoid(self): return mlops.Sigmoid.apply(self) def sin(self): return mlops.Sin.apply(self) def sqrt(self): return mlops.Sqrt.apply(self) def rsqrt(self): return (1/self).sqrt() def cos(self): return ((math.pi/2)-self).sin() def tan(self): return self.sin() / self.cos() @staticmethod def _tri(r:int, c:int, k:int=0, **kwargs) -> Tensor: return Tensor.arange(r, **kwargs).unsqueeze(1).expand(r,c) <= Tensor.arange(-k, c-k, **kwargs).unsqueeze(0).expand(r,c) def triu(self, k:int=0) -> Tensor: assert all_int(self.shape), f"does not support symbolic shape {self.shape}" return Tensor._tri(self.shape[-2], self.shape[-1], k=k, dtype=self.dtype, device=self.device).where(self, Tensor.zeros_like(self)) def tril(self, k:int=0) -> Tensor: assert all_int(self.shape), f"does not support symbolic shape {self.shape}" return Tensor._tri(self.shape[-2], self.shape[-1], k=k+1, dtype=self.dtype, device=self.device).where(Tensor.zeros_like(self), self) # ***** math functions (unary) ***** def trunc(self: Tensor) -> Tensor: return self.cast(dtypes.int32).contiguous().cast(self.dtype) def ceil(self: Tensor) -> Tensor: return (self > (b := self.trunc())).where(b+1, b) def floor(self: Tensor) -> Tensor: return (self < (b := self.trunc())).where(b-1, b) def square(self): return self*self def clip(self, min_, max_): return self.maximum(min_).minimum(max_) def abs(self): return self.relu() + (-self).relu() def sign(self): return self / (self.abs() + 1e-10) def reciprocal(self): return 1.0/self # ***** activation functions (unary) ***** def elu(self, alpha=1.0): return self.relu() - alpha*(1-self.exp()).relu() def celu(self, alpha=1.0): return self.maximum(0) + (alpha * ((self / alpha).exp() - 1)).minimum(0) def swish(self): return self * self.sigmoid() def silu(self): return self.swish() # The SiLU function is also known as the swish function. def relu6(self): return self.relu() - (self-6).relu() def hardswish(self): return self * (self+3).relu6() * (1/6) def tanh(self): return 2.0 * ((2.0 * self).sigmoid()) - 1.0 def hardtanh(self, min_val=-1, max_val=1): return self.clip(min_val, max_val) def gelu(self): return 0.5 * self * (1 + (self * 0.7978845608 * (1 + 0.044715 * self * self)).tanh()) def quick_gelu(self): return self * (self * 1.702).sigmoid() def leakyrelu(self, neg_slope=0.01): return self.relu() - (-neg_slope*self).relu() def mish(self): return self * self.softplus().tanh() def softplus(self, beta=1): return (1/beta) * (1 + (self*beta).exp()).log() def softsign(self): return self / (1 + self.abs()) # ***** broadcasted binary mlops ***** def _broadcasted(self, y:Union[Tensor, float], reverse:bool=False) -> Tuple[Tensor, Tensor]: x: Tensor = self if not isinstance(y, Tensor): y = Tensor(y, device=self.device, requires_grad=False, dtype=self.dtype if self.dtype != dtypes.bool and self.dtype.__class__ is not ImageDType else dtypes.float32) if reverse: x, y = y, x if (xshape:=x.shape) == (yshape:=y.shape): return (x, y) shape_delta = len(xshape) - len(yshape) if shape_delta > 0: y = y.reshape((1,) * shape_delta + yshape) elif shape_delta < 0: x = x.reshape((1,) * -shape_delta + xshape) if (xshape:=x.shape) == (yshape:=y.shape): return (x, y) shape_ret = tuple([max(x, y) for x, y in zip(xshape, yshape)]) if xshape != shape_ret: x = x.expand(shape_ret) if yshape != shape_ret: y = y.expand(shape_ret) return (x, y) def _to_float(self, x:Union[Tensor, float]): return x.lazydata.op.arg if isinstance(x, Tensor) and not x.lazydata.realized and x.lazydata.op.op == LoadOps.CONST and not x.requires_grad \ and x.lazydata.st.contiguous and self._broadcasted(x)[0].shape == self.shape else x def add(self, x:Union[Tensor, float], reverse=False) -> Tensor: x = self._to_float(x) return mlops.Add.apply(*self._broadcasted(x, reverse)) if x.__class__ is Tensor or x else self def sub(self, x:Union[Tensor, float], reverse=False) -> Tensor: x = self._to_float(x) return mlops.Sub.apply(*self._broadcasted(x, reverse)) if x.__class__ is Tensor or x else (-self if reverse else self) def mul(self, x:Union[Tensor, float], reverse=False) -> Tensor: x = self._to_float(x) if x.__class__ is not Tensor and x == 0.0: return mlops.Zero.apply(self) if x.__class__ is not Tensor and x == -1.0: return -self return mlops.Mul.apply(*self._broadcasted(x, reverse)) if x.__class__ is Tensor or x != 1.0 else self def div(self, x:Union[Tensor, float], reverse=False) -> Tensor: x = self._to_float(x) return mlops.Div.apply(*self._broadcasted(x, reverse)) if x.__class__ is Tensor or reverse or not x or not dtypes.is_float(self.dtype) else self.mul(1/x) def pow(self, x:Union[Tensor, float], reverse=False) -> Tensor: x = self._to_float(x) if x.__class__ is not Tensor and not reverse: # simple pow identities if x < 0: return self.reciprocal().pow(-x) if x == 3.0: return self*self*self if x == 2.0: return self*self if x == 1.0: return self if x == 0.5: return self.sqrt() if not isinstance(x, Tensor) and reverse and x > 0: return self.mul(math.log(x)).exp() ar = self.abs().log().mul(x).exp() if not reverse or isinstance(x, Tensor) else self.mul(math.log(abs(x))).exp() # correct sign of negative numbers raised to a power (cos has a period of 2pi so we use it here to get the oddness of the power) sign = (x * math.pi).cos() if isinstance(x, Tensor) else math.cos(x * math.pi) if not reverse else (self * math.pi).cos() # we only need to correct the sign if the base is negative base_sign = ((self.sign() if not reverse else x.sign() if isinstance(x, Tensor) else math.copysign(1, x)) - 1) / -2 # we need 0 to be positive so we need to correct base_sign when the base is 0 base_sign = base_sign - (1.5 * (1 - (self.sign().abs() if not reverse else x.sign().abs() if isinstance(x, Tensor) else abs(int(bool(x)))))) # inject nan if the base is negative and the power is not an integer to_nan = (((x - x.trunc()) * 1e10).abs().clip(0, 1) if isinstance(x, Tensor) else int(bool(x - int(x))) if not reverse else ((self - self.trunc()) * 1e10).abs().clip(0, 1)) * base_sign inject_nan = ((((-to_nan) * 2) + 1)).log().add(1) if isinstance(to_nan, Tensor) else 1 if not to_nan else float("nan") return ar.mul(sign * base_sign + (1 - base_sign)).mul(inject_nan) def matmul(self, x:Tensor, reverse=False) -> Tensor: return x.dot(self) if reverse else self.dot(x) def maximum(self, x:Union[Tensor, float]) -> Tensor: return (selfx).detach().where(self, (self+x)/2)) def minimum(self, x:Union[Tensor, float]) -> Tensor: return -((-self).maximum(-x)) def where(self:Tensor, input_:Union[Tensor, float], other:Union[Tensor, float]): x_,y = self._broadcasted(input_) x,z = x_._broadcasted(other) return mlops.Where.apply(x, *y._broadcasted(z)) # ***** binary op wrappers (18 wasted lines to make the typechecker happy) ***** # NOTE: __pow__ and friends are broken in mypyc with the ** operator def __add__(self, x) -> Tensor: return self.add(x) def __sub__(self, x) -> Tensor: return self.sub(x) def __mul__(self, x) -> Tensor: return self.mul(x) def __pow__(self, x) -> Tensor: return self.pow(x) def __truediv__(self, x) -> Tensor: return self.div(x) def __matmul__(self, x) -> Tensor: return self.matmul(x) def __radd__(self, x) -> Tensor: return self.add(x, True) def __rsub__(self, x) -> Tensor: return self.sub(x, True) def __rmul__(self, x) -> Tensor: return self.mul(x, True) def __rpow__(self, x) -> Tensor: return self.pow(x, True) def __rtruediv__(self, x) -> Tensor: return self.div(x, True) def __rmatmul__(self, x) -> Tensor: return self.matmul(x, True) def __iadd__(self, x) -> Tensor: return self.assign(self.add(x)) def __isub__(self, x) -> Tensor: return self.assign(self.sub(x)) def __imul__(self, x) -> Tensor: return self.assign(self.mul(x)) def __ipow__(self, x) -> Tensor: return self.assign(self.pow(x)) def __itruediv__(self, x) -> Tensor: return self.assign(self.div(x)) def __imatmul__(self, x) -> Tensor: return self.assign(self.matmul(x)) def __lt__(self, x) -> Tensor: return mlops.Less.apply(*self._broadcasted(x, False)) def __gt__(self, x) -> Tensor: return mlops.Less.apply(*self._broadcasted(x, True)) def __ge__(self, x) -> Tensor: return 1.0-(self Tensor: return 1.0-(self>x) def __ne__(self, x) -> Tensor: return (selfx) # type: ignore def __eq__(self, x) -> Tensor: return 1.0-(self != x) # type: ignore # ***** functional nn ops ***** def linear(self, weight:Tensor, bias:Optional[Tensor]=None): x = self.mul(weight) if len(weight.shape) == 1 else self.dot(weight) return x.add(bias) if bias is not None else x def sequential(self, ll:List[Callable[[Tensor], Tensor]]): return reduce(lambda x,f: f(x), ll, self) def layernorm(self, axis=-1, eps:float=1e-5) -> Tensor: y = (self - self.mean(axis, keepdim=True)) return y.mul((y*y).mean(axis, keepdim=True).add(eps).rsqrt()) def batchnorm(self, weight:Optional[Tensor], bias:Optional[Tensor], mean:Tensor, invstd:Tensor) -> Tensor: x = (self - mean.reshape(shape=[1, -1, 1, 1])) if weight: x = x * weight.reshape(shape=[1, -1, 1, 1]) ret = x.mul(invstd.reshape(shape=[1, -1, 1, 1]) if len(invstd.shape) == 1 else invstd) return (ret + bias.reshape(shape=[1, -1, 1, 1])) if bias else ret def dropout(self, p=0.5) -> Tensor: if not Tensor.training or p == 0: return self mask = (Tensor.rand(*self.shape, requires_grad=False, device=self.device) >= p).cast(dtypes.bool) return self * mask * (1/(1.0 - p)) def scaled_dot_product_attention(self, key:Tensor, value:Tensor, attn_mask:Optional[Tensor]=None, dropout_p:float=0.0, is_causal:bool=False) -> Tensor: # NOTE: it works if key, value have symbolic shape assert all_int(self.shape), f"does not support symbolic shape {self.shape}" if is_causal: attn_mask = Tensor.ones(self.shape[-2], key.shape[-2], requires_grad=False, device=self.device).tril(0).cast(dtypes.bool) if attn_mask is not None and attn_mask.dtype == dtypes.bool: attn_mask = (attn_mask == 0).where(-float("inf"), attn_mask) return (self @ key.transpose(-2,-1) / math.sqrt(self.shape[-1]) + attn_mask).softmax(-1).dropout(dropout_p) @ value def binary_crossentropy(self, y:Tensor) -> Tensor: return (-y*self.log() - (1-y)*(1-self).log()).mean() def binary_crossentropy_logits(self, y:Tensor) -> Tensor: return (self.maximum(0) - y * self + (1 + self.abs().__neg__().exp()).log()).mean() def sparse_categorical_crossentropy(self, Y, ignore_index=-1) -> Tensor: loss_mask = Y != ignore_index y_counter = Tensor.arange(self.shape[-1], dtype=dtypes.int32, requires_grad=False, device=self.device).unsqueeze(0).expand(Y.numel(), self.shape[-1]) y = ((y_counter == Y.flatten().reshape(-1, 1)).where(-1.0, 0) * loss_mask.reshape(-1, 1)).reshape(*Y.shape, self.shape[-1]) return self.log_softmax().mul(y).sum() / loss_mask.sum() # ***** cast ops ***** def cast(self, dtype:DType) -> Tensor: return mlops.Cast.apply(self, dtype=dtype) if self.dtype != dtype else self def bitcast(self, dtype:DType) -> Tensor: assert self.dtype.itemsize == dtype.itemsize, "can't bitcast mismatched dtype itemsizes" return mlops.Cast.apply(self, dtype=dtype, bitcast=True) if self.dtype != dtype else self def float(self) -> Tensor: return self.cast(dtypes.float32) def half(self) -> Tensor: return self.cast(dtypes.float16) # ***** convenience stuff ***** @property def ndim(self) -> int: return len(self.shape) def numel(self) -> sint: return prod(self.shape) def element_size(self) -> int: return self.dtype.itemsize def nbytes(self) -> int: return self.numel() * self.element_size() def is_floating_point(self) -> bool: return dtypes.is_float(self.dtype) # register functions to move between devices for device in Device._buffers: setattr(Tensor, f"{device.lower()}", partialmethod(Tensor.to, device)) setattr(Tensor, f"{device.lower()}_", partialmethod(Tensor.to_, device)) if IMAGE: # if IMAGE>0 we install these replacement functions in Tensor (hack!) from tinygrad.features.image import image_conv2d, image_dot setattr(Tensor, "conv2d", image_conv2d) setattr(Tensor, "dot", image_dot)