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KAN.py

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+import torch
+import torch.nn.functional as F
+import math
+
+
+class KANLinear(torch.nn.Module):
+    """
+    Kolmogorov-Arnold Neural Network (KAN) layer.
+
+    Args:
+        in_features (int): Number of input features.
+        out_features (int): Number of output features.
+        grid_size (int): Number of grid points.
+        spline_order (int): Order of the spline.
+        scale_noise (float): Scale of the noise.
+        scale_base (float): Scale of the base weight.
+        scale_spline (float): Scale of the spline weight.
+        enable_standalone_scale_spline (bool): Whether to enable standalone scale for spline weight.
+        base_activation (torch.nn.Module): Activation function for the base weight.
+        grid_eps (float): Epsilon for the grid.
+        grid_range (list): Range of the grid.
+    """
+    def __init__(
+        self,
+        in_features,
+        out_features,
+        grid_size=5,
+        spline_order=3,
+        scale_noise=0.1,
+        scale_base=1.0,
+        scale_spline=1.0,
+        enable_standalone_scale_spline=True,
+        base_activation=torch.nn.SiLU,
+        grid_eps=0.02,
+        grid_range=[-1, 1],
+    ):
+        super(KANLinear, self).__init__()
+        self.in_features = in_features
+        self.out_features = out_features
+        self.grid_size = grid_size
+        self.spline_order = spline_order
+
+        h = (grid_range[1] - grid_range[0]) / grid_size
+        grid = (
+            (
+                torch.arange(-spline_order, grid_size + spline_order + 1) * h
+                + grid_range[0]
+            )
+            .expand(in_features, -1)
+            .contiguous()
+        )
+        self.register_buffer("grid", grid)
+
+        self.base_weight = torch.nn.Parameter(torch.Tensor(out_features, in_features))
+        self.spline_weight = torch.nn.Parameter(
+            torch.Tensor(out_features, in_features, grid_size + spline_order)
+        )
+        if enable_standalone_scale_spline:
+            self.spline_scaler = torch.nn.Parameter(
+                torch.Tensor(out_features, in_features)
+            )
+
+        self.scale_noise = scale_noise
+        self.scale_base = scale_base
+        self.scale_spline = scale_spline
+        self.enable_standalone_scale_spline = enable_standalone_scale_spline
+        self.base_activation = base_activation()
+        self.grid_eps = grid_eps
+
+        self.reset_parameters()
+
+    def reset_parameters(self):
+        torch.nn.init.kaiming_uniform_(self.base_weight, a=math.sqrt(5) * self.scale_base)
+        with torch.no_grad():
+            noise = (
+                (
+                    torch.rand(self.grid_size + 1, self.in_features, self.out_features)
+                    - 1 / 2
+                )
+                * self.scale_noise
+                / self.grid_size
+            )
+            self.spline_weight.data.copy_(
+                (self.scale_spline if not self.enable_standalone_scale_spline else 1.0)
+                * self.curve2coeff(
+                    self.grid.T[self.spline_order : -self.spline_order],
+                    noise,
+                )
+            )
+            if self.enable_standalone_scale_spline:
+                # torch.nn.init.constant_(self.spline_scaler, self.scale_spline)
+                torch.nn.init.kaiming_uniform_(self.spline_scaler, a=math.sqrt(5) * self.scale_spline)
+
+    def b_splines(self, x: torch.Tensor):
+        """
+        Compute the B-spline bases for the given input tensor.
+
+        Args:
+            x (torch.Tensor): Input tensor of shape (batch_size, in_features).
+
+        Returns:
+            torch.Tensor: B-spline bases tensor of shape (batch_size, in_features, grid_size + spline_order).
+        """
+        assert x.dim() == 2 and x.size(1) == self.in_features
+
+        grid: torch.Tensor = (
+            self.grid
+        )  # (in_features, grid_size + 2 * spline_order + 1)
+        x = x.unsqueeze(-1)
+        bases = ((x >= grid[:, :-1]) & (x < grid[:, 1:])).to(x.dtype)
+        for k in range(1, self.spline_order + 1):
+            bases = (
+                (x - grid[:, : -(k + 1)])
+                / (grid[:, k:-1] - grid[:, : -(k + 1)])
+                * bases[:, :, :-1]
+            ) + (
+                (grid[:, k + 1 :] - x)
+                / (grid[:, k + 1 :] - grid[:, 1:(-k)])
+                * bases[:, :, 1:]
+            )
+
+        assert bases.size() == (
+            x.size(0),
+            self.in_features,
+            self.grid_size + self.spline_order,
+        )
+        return bases.contiguous()
+
+    def curve2coeff(self, x: torch.Tensor, y: torch.Tensor):
+        """
+        Compute the coefficients of the curve that interpolates the given points.
+
+        Args:
+            x (torch.Tensor): Input tensor of shape (batch_size, in_features).
+            y (torch.Tensor): Output tensor of shape (batch_size, in_features, out_features).
+
+        Returns:
+            torch.Tensor: Coefficients tensor of shape (out_features, in_features, grid_size + spline_order).
+        """
+        assert x.dim() == 2 and x.size(1) == self.in_features
+        assert y.size() == (x.size(0), self.in_features, self.out_features)
+
+        A = self.b_splines(x).transpose(
+            0, 1
+        )  # (in_features, batch_size, grid_size + spline_order)
+        B = y.transpose(0, 1)  # (in_features, batch_size, out_features)
+        # cast to float32 to avoid torch.linalg.lstsq error
+        if A.dtype != torch.float32:
+            original_dtype = A.dtype
+            A = A.to(torch.float32)
+            B = B.to(torch.float32)
+        solution = torch.linalg.lstsq(
+            A, B
+        ).solution  # (in_features, grid_size + spline_order, out_features)
+        # cast back to original dtype
+        if A.dtype != solution.dtype:
+            solution = solution.to(original_dtype)
+        result = solution.permute(
+            2, 0, 1
+        )  # (out_features, in_features, grid_size + spline_order)
+
+        assert result.size() == (
+            self.out_features,
+            self.in_features,
+            self.grid_size + self.spline_order,
+        )
+        return result.contiguous()
+
+    @property
+    def scaled_spline_weight(self):
+        return self.spline_weight * (
+            self.spline_scaler.unsqueeze(-1)
+            if self.enable_standalone_scale_spline
+            else 1.0
+        )
+
+    def forward(self, x: torch.Tensor):
+        assert x.dim() == 2 and x.size(1) == self.in_features
+
+        base_output = F.linear(self.base_activation(x), self.base_weight)
+        spline_output = F.linear(
+            self.b_splines(x).view(x.size(0), -1),
+            self.scaled_spline_weight.view(self.out_features, -1),
+        )
+        return base_output + spline_output
+
+    @torch.no_grad()
+    def update_grid(self, x: torch.Tensor, margin=0.01):
+        assert x.dim() == 2 and x.size(1) == self.in_features
+        batch = x.size(0)
+
+        splines = self.b_splines(x)  # (batch, in, coeff)
+        splines = splines.permute(1, 0, 2)  # (in, batch, coeff)
+        orig_coeff = self.scaled_spline_weight  # (out, in, coeff)
+        orig_coeff = orig_coeff.permute(1, 2, 0)  # (in, coeff, out)
+        unreduced_spline_output = torch.bmm(splines, orig_coeff)  # (in, batch, out)
+        unreduced_spline_output = unreduced_spline_output.permute(
+            1, 0, 2
+        )  # (batch, in, out)
+
+        # sort each channel individually to collect data distribution
+        x_sorted = torch.sort(x, dim=0)[0]
+        grid_adaptive = x_sorted[
+            torch.linspace(
+                0, batch - 1, self.grid_size + 1, dtype=torch.int64, device=x.device
+            )
+        ]
+
+        uniform_step = (x_sorted[-1] - x_sorted[0] + 2 * margin) / self.grid_size
+        grid_uniform = (
+            torch.arange(
+                self.grid_size + 1, dtype=torch.float32, device=x.device
+            ).unsqueeze(1)
+            * uniform_step
+            + x_sorted[0]
+            - margin
+        )
+
+        grid = self.grid_eps * grid_uniform + (1 - self.grid_eps) * grid_adaptive
+        grid = torch.concatenate(
+            [
+                grid[:1]
+                - uniform_step
+                * torch.arange(self.spline_order, 0, -1, device=x.device).unsqueeze(1),
+                grid,
+                grid[-1:]
+                + uniform_step
+                * torch.arange(1, self.spline_order + 1, device=x.device).unsqueeze(1),
+            ],
+            dim=0,
+        )
+
+        self.grid.copy_(grid.T)
+        self.spline_weight.data.copy_(self.curve2coeff(x, unreduced_spline_output))
+
+    def regularization_loss(self, regularize_activation=1.0, regularize_entropy=1.0):
+        """
+        Compute the regularization loss.
+
+        This is a dumb simulation of the original L1 regularization as stated in the
+        paper, since the original one requires computing absolutes and entropy from the
+        expanded (batch, in_features, out_features) intermediate tensor, which is hidden
+        behind the F.linear function if we want an memory efficient implementation.
+
+        The L1 regularization is now computed as mean absolute value of the spline
+        weights. The authors implementation also includes this term in addition to the
+        sample-based regularization.
+        """
+        l1_fake = self.spline_weight.abs().mean(-1)
+        regularization_loss_activation = l1_fake.sum()
+        p = l1_fake / regularization_loss_activation
+        regularization_loss_entropy = -torch.sum(p * p.log())
+        return (
+            regularize_activation * regularization_loss_activation
+            + regularize_entropy * regularization_loss_entropy
+        )
+
+
+class KAN(torch.nn.Module):
+    def __init__(
+        self,
+        layers_hidden,
+        grid_size=5,
+        spline_order=3,
+        scale_noise=0.1,
+        scale_base=1.0,
+        scale_spline=1.0,
+        base_activation=torch.nn.SiLU,
+        grid_eps=0.02,
+        grid_range=[-1, 1],
+    ):
+        super(KAN, self).__init__()
+        self.grid_size = grid_size
+        self.spline_order = spline_order
+
+        self.layers = torch.nn.ModuleList()
+        for in_features, out_features in zip(layers_hidden, layers_hidden[1:]):
+            self.layers.append(
+                KANLinear(
+                    in_features,
+                    out_features,
+                    grid_size=grid_size,
+                    spline_order=spline_order,
+                    scale_noise=scale_noise,
+                    scale_base=scale_base,
+                    scale_spline=scale_spline,
+                    base_activation=base_activation,
+                    grid_eps=grid_eps,
+                    grid_range=grid_range,
+                )
+            )
+
+    def forward(self, x: torch.Tensor, update_grid=False):
+        for layer in self.layers:
+            if update_grid:
+                layer.update_grid(x)
+            x = layer(x)
+        return x
+
+    def regularization_loss(self, regularize_activation=1.0, regularize_entropy=1.0):
+        return sum(
+            layer.regularization_loss(regularize_activation, regularize_entropy)
+            for layer in self.layers
+        )

berkant_layers.py

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+# Copyright 2022 MosaicML Examples authors
+# SPDX-License-Identifier: Apache-2.0
+
+# Copyright 2018 The Google AI Language Team Authors and The HuggingFace Inc. team.
+# Copyright (c) 2018-2021, NVIDIA CORPORATION.  All rights reserved.
+# Copyright (c) 2022, Tri Dao.
+
+"""Implements Mosaic BERT, with an eye towards the Hugging Face API.
+
+Mosaic BERT improves performance over Hugging Face BERT through the following:
+
+1. ALiBi. This architectural change removes positional embeddings and instead encodes positional
+information through attention biases based on query-key position distance. It improves the effectiveness
+of training with shorter sequence lengths by enabling extrapolation to longer sequences.
+
+2. Gated Linear Units (GLU). This architectural change replaces the FFN component of the BERT layer
+to improve overall expressiveness, providing better convergence properties.
+
+3. Flash Attention. The Mosaic BERT's self-attention layer makes use of Flash Attention, which dramatically
+improves the speed of self-attention. Our implementation utilizes a bleeding edge implementation that
+supports attention biases, which allows us to use Flash Attention with ALiBi.
+
+4. Unpadding. Padding is often used to simplify batching across sequences of different lengths. Standard BERT
+implementations waste computation on padded tokens. Mosaic BERT internally unpads to reduce unnecessary computation
+and improve speed. It does this without changing how the user interfaces with the model, thereby
+preserving the simple API of standard implementations.
+
+
+Currently, Mosaic BERT is available for masked language modeling :class:`BertForMaskedLM` and sequence
+classification :class:`BertForSequenceClassification`. We aim to expand this catalogue in future releases.
+
+See :file:`./mosaic_bert.py` for utilities to simplify working with Mosaic BERT in Composer, and for example usage
+of the core Mosaic BERT classes.
+"""
+
+import copy
+import logging
+import math
+import warnings
+from typing import List, Optional, Tuple, Union
+
+import torch
+import torch.nn as nn
+from einops import rearrange
+from torch.nn.modules.utils import consume_prefix_in_state_dict_if_present
+from transformers.activations import ACT2FN
+from transformers.modeling_outputs import (MaskedLMOutput,
+                                           SequenceClassifierOutput)
+from transformers.models.bert.modeling_bert import BertPreTrainedModel
+
+from .berkant_padding import (index_first_axis,
+                                            index_put_first_axis, pad_input,
+                                            unpad_input, unpad_input_only)
+
+from .KAN import KANLinear
+try:
+    from .flash_attn_triton import flash_attn_qkvpacked_func
+except ImportError as e:
+    flash_attn_qkvpacked_func = None
+
+logger = logging.getLogger(__name__)
+
+class BerKANTEmbeddings(nn.Module):
+    """Construct the embeddings for words, ignoring position.
+
+    There are no positional embeddings since we use ALiBi and token_type
+    embeddings.
+
+    This module is modeled after the Hugging Face BERT's
+    :class:`~transformers.model.bert.modeling_bert.BertEmbeddings`, but is
+    modified as part of Mosaic BERT's ALiBi implementation. The key change is
+    that position embeddings are removed. Position information instead comes
+    from attention biases that scale linearly with the position distance
+    between query and key tokens.
+
+    This module ignores the `position_ids` input to the `forward` method.
+    """
+
+    def __init__(self, config):
+        super().__init__()
+        self.word_embeddings = nn.Embedding(config.vocab_size,
+                                            config.hidden_size,
+                                            padding_idx=config.pad_token_id)
+        # ALiBi doesn't use position embeddings
+        self.token_type_embeddings = nn.Embedding(config.type_vocab_size,
+                                                  config.hidden_size)
+
+        # self.LayerNorm is not snake-cased to stick with TensorFlow model
+        # variable name and be able to load any TensorFlow checkpoint file
+        self.LayerNorm = nn.LayerNorm(config.hidden_size,
+                                      eps=config.layer_norm_eps)
+        self.dropout = nn.Dropout(config.hidden_dropout_prob)
+        self.register_buffer('token_type_ids',
+                             torch.zeros(config.max_position_embeddings,
+                                         dtype=torch.long),
+                             persistent=False)
+
+    def forward(
+        self,
+        input_ids: Optional[torch.LongTensor] = None,
+        token_type_ids: Optional[torch.LongTensor] = None,
+        position_ids: Optional[torch.LongTensor] = None,
+        inputs_embeds: Optional[torch.FloatTensor] = None,
+        past_key_values_length: int = 0,
+    ) -> torch.Tensor:
+        if (input_ids is not None) == (inputs_embeds is not None):
+            raise ValueError('Must specify either input_ids or input_embeds!')
+        if input_ids is not None:
+            input_shape = input_ids.size()
+        else:
+            assert inputs_embeds is not None  # just for type checking
+            input_shape = inputs_embeds.size()[:-1]
+
+        seq_length = input_shape[1]
+
+        if position_ids is None:
+            # great! ALiBi
+            pass
+
+        # Setting the token_type_ids to the registered buffer in constructor
+        # where it is all zeros, which usually occurs when it's auto-generated;
+        # registered buffer helps users when tracing the model without passing
+        # token_type_ids, solves issue #5664
+        if token_type_ids is None:
+            if hasattr(self, 'token_type_ids'):
+                assert isinstance(self.token_type_ids, torch.LongTensor)
+                buffered_token_type_ids = self.token_type_ids[:, :seq_length]
+                buffered_token_type_ids_expanded = buffered_token_type_ids.expand(
+                    input_shape[0], seq_length)
+                token_type_ids = buffered_token_type_ids_expanded  # type: ignore
+            else:
+                token_type_ids = torch.zeros(input_shape,  # type: ignore
+                                             dtype=torch.long,
+                                             device=self.word_embeddings.device) # type: ignore  # yapf: disable
+
+        if inputs_embeds is None:
+            inputs_embeds = self.word_embeddings(input_ids)
+        token_type_embeddings = self.token_type_embeddings(token_type_ids)
+
+        embeddings = inputs_embeds + token_type_embeddings
+        # no position embeddings! ALiBi
+        embeddings = self.LayerNorm(embeddings)
+        embeddings = self.dropout(embeddings)
+        return embeddings
+
+
+class BerKANTUnpadSelfAttention(nn.Module):
+    """Performs multi-headed self attention on a batch of unpadded sequences.
+
+    If Triton is installed, this module uses Flash Attention to greatly improve throughput.
+    The Flash Attention implementation used in Mosaic BERT supports arbitrary attention biases (which
+    we use to implement ALiBi), but does not support attention dropout. If either Triton is not installed
+    or `config.attention_probs_dropout_prob > 0`, the implementation will default to a
+    math-equivalent pytorch version, which is much slower.
+
+    See `forward` method for additional detail.
+    """
+
+    def __init__(self, config):
+        super().__init__()
+        if config.hidden_size % config.num_attention_heads != 0 and not hasattr(
+                config, 'embedding_size'):
+            raise ValueError(
+                f'The hidden size ({config.hidden_size}) is not a multiple of the number of attention '
+                f'heads ({config.num_attention_heads})')
+
+        self.num_attention_heads = config.num_attention_heads
+        self.attention_head_size = int(config.hidden_size /
+                                       config.num_attention_heads)
+        self.all_head_size = self.num_attention_heads * self.attention_head_size
+        self.dropout = nn.Dropout(config.attention_probs_dropout_prob)
+        self.p_dropout = config.attention_probs_dropout_prob
+        self.Wqkv = KANLinear(self.all_head_size, 3 * config.hidden_size)
+
+        # Warn if defaulting to pytorch because of import issues
+        if flash_attn_qkvpacked_func is None:
+            warnings.warn(
+                'Unable to import Triton; defaulting MosaicBERT attention implementation to pytorch (this will reduce throughput when using this model).'
+            )
+
+    def forward(self, hidden_states: torch.Tensor, cu_seqlens: torch.Tensor,
+                max_seqlen_in_batch: int, indices: torch.Tensor,
+                attn_mask: torch.Tensor, bias: torch.Tensor) -> torch.Tensor:
+        """Perform self-attention.
+
+        If dropout is zero, then we can use the Triton kernel, so we do that. However, if not, we send through a standard PyTorch
+        implementation of self-attention.
+
+        The arguments are unpadded, and our implementations of attention require padded arguments,
+        so we first call `pad_input`. Once we compute attention, we re-unpad our outputs for the other layers.
+        The pad/unpad operations add overhead, but not sending pad tokens through ffs saves compute.
+        It is possible to write an unpadded implementation of attention (in Triton and PyTorch), which we will eventually do.
+
+        Args:
+            hidden_states: (total_nnz, dim)
+            cu_seqlens: (batch + 1,)
+            max_seqlen_in_batch: int
+            indices: (total_nnz,)
+            attn_mask: (batch, max_seqlen_in_batch)
+            bias: (batch, heads, max_seqlen_in_batch, max_seqlen_in_batch)
+
+        Returns:
+            attention: (total_nnz, dim)
+        """
+        qkv = self.Wqkv(hidden_states)
+        qkv = pad_input(qkv, indices, cu_seqlens.shape[0] - 1,
+                        max_seqlen_in_batch)  # batch, max_seqlen_in_batch, thd
+        qkv = rearrange(qkv,
+                        'b s (t h d) -> b s t h d',
+                        t=3,
+                        h=self.num_attention_heads)
+        if self.p_dropout or flash_attn_qkvpacked_func is None:
+            # if we have nonzero attention dropout (e.g. during fine-tuning) or no Triton, compute attention in PyTorch
+            q = qkv[:, :, 0, :, :].permute(0, 2, 1, 3)  # b h s d
+            k = qkv[:, :, 1, :, :].permute(0, 2, 3, 1)  # b h d s
+            v = qkv[:, :, 2, :, :].permute(0, 2, 1, 3)  # b h s d
+            attention_scores = torch.matmul(q, k) / math.sqrt(
+                self.attention_head_size)
+            attention_scores = attention_scores + bias
+            attention_probs = nn.functional.softmax(attention_scores, dim=-1)
+            attention_probs = self.dropout(attention_probs)
+            attention = torch.matmul(attention_probs, v).permute(0, 2, 1,
+                                                                 3)  # b s h d
+        else:
+            # Triton implementation only supports 0 attention dropout
+            convert_dtype = qkv.dtype not in [torch.float16, torch.bfloat16]
+            if convert_dtype:
+                # Triton implementation only supports fp16 and bf16
+                orig_dtype = qkv.dtype
+                qkv = qkv.to(torch.float16)
+                bias_dtype = bias.dtype
+                bias = bias.to(torch.float16)
+                attention = flash_attn_qkvpacked_func(qkv, bias)
+                attention = attention.to(orig_dtype)
+                bias = bias.to(bias_dtype)
+            else:
+                attention = flash_attn_qkvpacked_func(qkv, bias)
+
+        # attn_mask is 1 for attend and 0 for don't
+        attention = unpad_input_only(attention, torch.squeeze(attn_mask) == 1)
+        return rearrange(attention, 'nnz h d -> nnz (h d)')
+
+
+# Copy of transformer's library BertSelfOutput that will not be caught by surgery methods looking for HF BERT modules.
+class BerKANTSelfOutput(nn.Module):
+    """Computes the output of the attention layer.
+
+    This module is modeled after the Hugging Face BERT's
+    :class:`~transformers.model.bert.modeling_bert.BertSelfOutput`.
+    The implementation is identical. Rather than use the original module
+    directly, we re-implement it here so that Mosaic BERT's modules will not
+    be affected by any Composer surgery algorithm that modifies Hugging Face
+    BERT modules.
+    """
+
+    def __init__(self, config):
+        super().__init__()
+        self.dense = KANLinear(config.hidden_size, config.hidden_size)
+        self.LayerNorm = nn.LayerNorm(config.hidden_size,
+                                      eps=config.layer_norm_eps)
+        self.dropout = nn.Dropout(config.hidden_dropout_prob)
+
+    def forward(self, hidden_states: torch.Tensor,
+                input_tensor: torch.Tensor) -> torch.Tensor:
+        hidden_states = self.dense(hidden_states)
+        hidden_states = self.dropout(hidden_states)
+        hidden_states = self.LayerNorm(hidden_states + input_tensor)
+        return hidden_states
+
+
+class BerKANTUnpadAttention(nn.Module):
+    """Chains attention, Dropout, and LayerNorm for Mosaic BERT."""
+
+    def __init__(self, config):
+        super().__init__()
+        self.self = BerKANTUnpadSelfAttention(config)
+        self.output = BerKANTSelfOutput(config)
+
+    def forward(
+        self,
+        input_tensor: torch.Tensor,
+        cu_seqlens: torch.Tensor,
+        max_s: int,
+        subset_idx: Optional[torch.Tensor] = None,
+        indices: Optional[torch.Tensor] = None,
+        attn_mask: Optional[torch.Tensor] = None,
+        bias: Optional[torch.Tensor] = None,
+    ) -> torch.Tensor:
+        """Forward pass for scaled self-attention without padding.
+
+        Arguments:
+            input_tensor: (total_nnz, dim)
+            cu_seqlens: (batch + 1,)
+            max_s: int
+            subset_idx: () set of indices whose values we care about at the end of the layer
+                        (e.g., the masked tokens, if this is the final layer).
+            indices: None or (total_nnz,)
+            attn_mask: None or (batch, max_seqlen_in_batch)
+            bias: None or (batch, heads, max_seqlen_in_batch, max_seqlen_in_batch)
+        """
+        self_output = self.self(input_tensor, cu_seqlens, max_s, indices,
+                                attn_mask, bias)
+        if subset_idx is not None:
+            return self.output(index_first_axis(self_output, subset_idx),
+                               index_first_axis(input_tensor, subset_idx))
+        else:
+            return self.output(self_output, input_tensor)
+
+
+class BerKANTGatedLinearUnitMLP(nn.Module):
+    """Applies the FFN at the end of each Mosaic BERT layer.
+
+    Compared to the default BERT architecture, this block replaces :class:`~transformers.model.bert.modeling_bert.BertIntermediate`
+    and :class:`~transformers.model.bert.modeling_bert.SelfOutput` with a single module that has similar functionality, but
+    introduces Gated Linear Units.
+
+    Note: Mosaic BERT adds parameters in order to implement Gated Linear Units. To keep parameter count consistent with that of a
+    standard Hugging Face BERT, scale down `config.intermediate_size` by 2/3. For example, a Mosaic BERT constructed with
+    `config.intermediate_size=2048` will have the same parameter footprint as its Hugging Face BERT counterpart constructed
+    with the `config.intermediate_size=3072`.
+    However, in most cases it will not be necessary to adjust `config.intermediate_size` since, despite the increased
+    parameter size, Mosaic BERT typically offers a net higher throughput than a Hugging Face BERT built from the same `config`.
+    """
+
+    def __init__(self, config):
+        super().__init__()
+        self.config = config
+        self.gated_layers = KANLinear(config.hidden_size,
+                                      config.intermediate_size * 2)
+        self.act = nn.GELU(approximate='none')
+        self.wo = KANLinear(config.intermediate_size, config.hidden_size)
+        self.dropout = nn.Dropout(config.hidden_dropout_prob)
+        self.layernorm = nn.LayerNorm(config.hidden_size,
+                                      eps=config.layer_norm_eps)
+
+    def forward(self, hidden_states: torch.Tensor) -> torch.Tensor:
+        """Compute new hidden states from current hidden states.
+
+        Args:
+            hidden_states (torch.Tensor): The (unpadded) hidden states from
+                the attention layer [nnz, dim].
+        """
+        residual_connection = hidden_states
+        # compute the activation
+        hidden_states = self.gated_layers(hidden_states)
+        gated = hidden_states[:, :self.config.intermediate_size]
+        non_gated = hidden_states[:, self.config.intermediate_size:]
+        hidden_states = self.act(gated) * non_gated
+        hidden_states = self.dropout(hidden_states)
+        # multiply by the second matrix
+        hidden_states = self.wo(hidden_states)
+        # add the residual connection and post-LN
+        hidden_states = self.layernorm(hidden_states + residual_connection)
+        return hidden_states
+
+
+class BerKANTLayer(nn.Module):
+    """Composes the Mosaic BERT attention and FFN blocks into a single layer."""
+
+    def __init__(self, config):
+        super(BerKANTLayer, self).__init__()
+        self.attention = BerKANTUnpadAttention(config)
+        self.mlp = BerKANTGatedLinearUnitMLP(config)
+
+    def forward(
+        self,
+        hidden_states: torch.Tensor,
+        cu_seqlens: torch.Tensor,
+        seqlen: int,
+        subset_idx: Optional[torch.Tensor] = None,
+        indices: Optional[torch.Tensor] = None,
+        attn_mask: Optional[torch.Tensor] = None,
+        bias: Optional[torch.Tensor] = None,
+    ) -> torch.Tensor:
+        """Forward pass for a BERT layer, including both attention and MLP.
+
+        Args:
+            hidden_states: (total_nnz, dim)
+            cu_seqlens: (batch + 1,)
+            seqlen: int
+            subset_idx: () set of indices whose values we care about at the end of the layer
+                        (e.g., the masked tokens, if this is the final layer).
+            indices: None or (total_nnz,)
+            attn_mask: None or (batch, max_seqlen_in_batch)
+            bias: None or (batch, heads, max_seqlen_in_batch, max_seqlen_in_batch)
+        """
+        attention_output = self.attention(hidden_states, cu_seqlens, seqlen,
+                                          subset_idx, indices, attn_mask, bias)
+        layer_output = self.mlp(attention_output)
+        return layer_output
+
+
+class BerKANTEncoder(nn.Module):
+    """A stack of BERT layers providing the backbone of Mosaic BERT.
+
+    This module is modeled after the Hugging Face BERT's :class:`~transformers.model.bert.modeling_bert.BertEncoder`,
+    but with substantial modifications to implement unpadding and ALiBi.
+
+    Compared to the analogous Hugging Face BERT module, this module handles unpadding to reduce unnecessary computation
+    at padded tokens, and pre-computes attention biases to implement ALiBi.
+    """
+
+    def __init__(self, config):
+        super().__init__()
+        layer = BerKANTLayer(config)
+        self.layer = nn.ModuleList(
+            [copy.deepcopy(layer) for _ in range(config.num_hidden_layers)])
+
+        self.num_attention_heads = config.num_attention_heads
+
+        # The alibi mask will be dynamically expanded if it is too small for
+        # the input the model receives. But it generally helps to initialize it
+        # to a reasonably large size to help pre-allocate CUDA memory.
+        # The default `alibi_starting_size` is 512.
+        self._current_alibi_size = int(config.alibi_starting_size)
+        self.alibi = torch.zeros(
+            (1, self.num_attention_heads, self._current_alibi_size,
+             self._current_alibi_size))
+        self.rebuild_alibi_tensor(size=config.alibi_starting_size)
+
+    def rebuild_alibi_tensor(self,
+                             size: int,
+                             device: Optional[Union[torch.device, str]] = None):
+        # Alibi
+        # Following https://github.com/ofirpress/attention_with_linear_biases/issues/5 (Implementation 1)
+        # In the causal case, you can exploit the fact that softmax is invariant to a uniform translation
+        # of the logits, which makes the math work out *after* applying causal masking. If no causal masking
+        # will be applied, it is necessary to construct the diagonal mask.
+        n_heads = self.num_attention_heads
+
+        def _get_alibi_head_slopes(n_heads: int) -> List[float]:
+
+            def get_slopes_power_of_2(n_heads: int) -> List[float]:
+                start = (2**(-2**-(math.log2(n_heads) - 3)))
+                ratio = start
+                return [start * ratio**i for i in range(n_heads)]
+
+            # In the paper, they only train models that have 2^a heads for some a. This function
+            # has some good properties that only occur when the input is a power of 2. To
+            # maintain that even when the number of heads is not a power of 2, we use a
+            # workaround.
+            if math.log2(n_heads).is_integer():
+                return get_slopes_power_of_2(n_heads)
+
+            closest_power_of_2 = 2**math.floor(math.log2(n_heads))
+            slopes_a = get_slopes_power_of_2(closest_power_of_2)
+            slopes_b = _get_alibi_head_slopes(2 * closest_power_of_2)
+            slopes_b = slopes_b[0::2][:n_heads - closest_power_of_2]
+            return slopes_a + slopes_b
+
+        context_position = torch.arange(size, device=device)[:, None]
+        memory_position = torch.arange(size, device=device)[None, :]
+        relative_position = torch.abs(memory_position - context_position)
+        # [n_heads, max_token_length, max_token_length]
+        relative_position = relative_position.unsqueeze(0).expand(
+            n_heads, -1, -1)
+        slopes = torch.Tensor(_get_alibi_head_slopes(n_heads)).to(device)
+        alibi = slopes.unsqueeze(1).unsqueeze(1) * -relative_position
+        # [1, n_heads, max_token_length, max_token_length]
+        alibi = alibi.unsqueeze(0)
+        assert alibi.shape == torch.Size([1, n_heads, size, size])
+
+        self._current_alibi_size = size
+        self.alibi = alibi
+
+    def forward(
+        self,
+        hidden_states: torch.Tensor,
+        attention_mask: torch.Tensor,
+        output_all_encoded_layers: Optional[bool] = True,
+        subset_mask: Optional[torch.Tensor] = None,
+    ) -> List[torch.Tensor]:
+
+        extended_attention_mask = attention_mask.unsqueeze(1).unsqueeze(2)
+        extended_attention_mask = extended_attention_mask.to(
+            dtype=next(self.parameters()).dtype)  # fp16 compatibility
+        extended_attention_mask = (1.0 - extended_attention_mask) * -10000.0
+
+        attention_mask_bool = attention_mask.bool()
+        batch, seqlen = hidden_states.shape[:2]
+        # Unpad inputs and mask. It will remove tokens that are padded.
+        # Assume ntokens is total number of tokens (padded and non-padded)
+        # and ntokens_unpad is total number of non-padded tokens.
+        # Then unpadding performs the following compression of the inputs:
+        # hidden_states[ntokens,hidden] -> hidden_states[ntokens_unpad,hidden]
+        hidden_states, indices, cu_seqlens, _ = unpad_input(
+            hidden_states, attention_mask_bool)
+
+        # Add alibi matrix to extended_attention_mask
+        if self._current_alibi_size < seqlen:
+            # Rebuild the alibi tensor when needed
+            warnings.warn(
+                f'Increasing alibi size from {self._current_alibi_size} to {seqlen}'
+            )
+            self.rebuild_alibi_tensor(size=seqlen, device=hidden_states.device)
+        elif self.alibi.device != hidden_states.device:
+            # Device catch-up
+            self.alibi = self.alibi.to(hidden_states.device)
+        alibi_bias = self.alibi[:, :, :seqlen, :seqlen]
+        attn_bias = extended_attention_mask[:, :, :seqlen, :seqlen]
+        alibi_attn_mask = attn_bias + alibi_bias
+
+        all_encoder_layers = []
+        if subset_mask is None:
+            for layer_module in self.layer:
+                hidden_states = layer_module(hidden_states,
+                                             cu_seqlens,
+                                             seqlen,
+                                             None,
+                                             indices,
+                                             attn_mask=attention_mask,
+                                             bias=alibi_attn_mask)
+                if output_all_encoded_layers:
+                    all_encoder_layers.append(hidden_states)
+            # Pad inputs and mask. It will insert back zero-padded tokens.
+            # Assume ntokens is total number of tokens (padded and non-padded)
+            # and ntokens_unpad is total number of non-padded tokens.
+            # Then padding performs the following de-compression:
+            #     hidden_states[ntokens_unpad,hidden] -> hidden_states[ntokens,hidden]
+            hidden_states = pad_input(hidden_states, indices, batch, seqlen)
+        else:
+            for i in range(len(self.layer) - 1):
+                layer_module = self.layer[i]
+                hidden_states = layer_module(hidden_states,
+                                             cu_seqlens,
+                                             seqlen,
+                                             None,
+                                             indices,
+                                             attn_mask=attention_mask,
+                                             bias=alibi_attn_mask)
+                if output_all_encoded_layers:
+                    all_encoder_layers.append(hidden_states)
+            subset_idx = torch.nonzero(subset_mask[attention_mask_bool],
+                                       as_tuple=False).flatten()
+            hidden_states = self.layer[-1](hidden_states,
+                                           cu_seqlens,
+                                           seqlen,
+                                           subset_idx=subset_idx,
+                                           indices=indices,
+                                           attn_mask=attention_mask,
+                                           bias=alibi_attn_mask)
+
+        if not output_all_encoded_layers:
+            all_encoder_layers.append(hidden_states)
+        return all_encoder_layers
+
+
+class BerKANTPooler(nn.Module):
+
+    def __init__(self, config):
+        super(BerKANTPooler, self).__init__()
+        self.dense = KANLinear(config.hidden_size, config.hidden_size)
+        self.activation = nn.Tanh()
+
+    def forward(self,
+                hidden_states: torch.Tensor,
+                pool: Optional[bool] = True) -> torch.Tensor:
+        # We "pool" the model by simply taking the hidden state corresponding
+        # to the first token.
+        first_token_tensor = hidden_states[:, 0] if pool else hidden_states
+        pooled_output = self.dense(first_token_tensor)
+        pooled_output = self.activation(pooled_output)
+        return pooled_output
+
+
+class BerKANTPredictionHeadTransform(nn.Module):
+
+    def __init__(self, config):
+        super().__init__()
+        self.dense = nn.Linear(config.hidden_size, config.hidden_size)
+        if isinstance(config.hidden_act, str):
+            self.transform_act_fn = ACT2FN[config.hidden_act]
+        else:
+            self.transform_act_fn = config.hidden_act
+        self.LayerNorm = torch.nn.LayerNorm(config.hidden_size, eps=1e-12)
+
+    def forward(self, hidden_states: torch.Tensor) -> torch.Tensor:
+        hidden_states = self.dense(hidden_states)
+        hidden_states = self.transform_act_fn(hidden_states)
+        hidden_states = self.LayerNorm(hidden_states)
+        return hidden_states
+
+
+class BerKANTModel(BertPreTrainedModel):
+    """Overall BERT model.
+
+    Args:
+        config: a BertConfig class instance with the configuration to build a new model
+
+    Inputs:
+        `input_ids`: a torch.LongTensor of shape [batch_size, sequence_length]
+            with the word token indices in the vocabulary(see the tokens preprocessing logic in the scripts
+            `extract_features.py`, `run_classifier.py` and `run_squad.py`)
+        `token_type_ids`: an optional torch.LongTensor of shape [batch_size, sequence_length] with the token
+            types indices selected in [0, 1]. Type 0 corresponds to a `sentence A` and type 1 corresponds to
+            a `sentence B` token (see BERT paper for more details).
+        `attention_mask`: an optional torch.LongTensor of shape [batch_size, sequence_length] with indices
+            selected in [0, 1]. It's a mask to be used if the input sequence length is smaller than the max
+            input sequence length in the current batch. It's the mask that we typically use for attention when
+            a batch has varying length sentences.
+        `output_all_encoded_layers`: boolean which controls the content of the `encoded_layers` output as described below. Default: `True`.
+
+    Outputs: Tuple of (encoded_layers, pooled_output)
+        `encoded_layers`: controlled by `output_all_encoded_layers` argument:
+            - `output_all_encoded_layers=True`: outputs a list of the full sequences of encoded-hidden-states at the end
+                of each attention block (i.e. 12 full sequences for BERT-base, 24 for BERT-large), each
+                encoded-hidden-state is a torch.FloatTensor of size [batch_size, sequence_length, hidden_size],
+            - `output_all_encoded_layers=False`: outputs only the full sequence of hidden-states corresponding
+                to the last attention block of shape [batch_size, sequence_length, hidden_size],
+        `pooled_output`: a torch.FloatTensor of size [batch_size, hidden_size] which is the output of a
+            classifier pretrained on top of the hidden state associated to the first character of the
+            input (`CLS`) to train on the Next-Sentence task (see BERT's paper).
+
+    Example usage:
+    ```python
+    # Already been converted into WordPiece token ids
+    input_ids = torch.LongTensor([[31, 51, 99], [15, 5, 0]])
+    input_mask = torch.LongTensor([[1, 1, 1], [1, 1, 0]])
+    token_type_ids = torch.LongTensor([[0, 0, 1], [0, 1, 0]])
+    config = modeling.BertConfig(vocab_size_or_config_json_file=32000, hidden_size=768,
+        num_hidden_layers=12, num_attention_heads=12, intermediate_size=3072)
+    model = BertModel(config=config)
+    all_encoder_layers, pooled_output = model(input_ids, token_type_ids, input_mask)
+    ```
+    """
+
+    def __init__(self, config, add_pooling_layer=True):
+        super(BerKANTModel, self).__init__(config)
+        self.embeddings = BerKANTEmbeddings(config)
+        self.encoder = BerKANTEncoder(config)
+        self.pooler = BerKANTPooler(config) if add_pooling_layer else None
+        self.post_init()
+
+    def get_input_embeddings(self):
+        return self.embeddings.word_embeddings
+
+    def set_input_embeddings(self, value):
+        self.embeddings.word_embeddings = value
+
+    def forward(
+        self,
+        input_ids: torch.Tensor,
+        token_type_ids: Optional[torch.Tensor] = None,
+        attention_mask: Optional[torch.Tensor] = None,
+        position_ids: Optional[torch.Tensor] = None,
+        output_all_encoded_layers: Optional[bool] = False,
+        masked_tokens_mask: Optional[torch.Tensor] = None,
+        **kwargs
+    ) -> Tuple[Union[List[torch.Tensor], torch.Tensor], Optional[torch.Tensor]]:
+        if attention_mask is None:
+            attention_mask = torch.ones_like(input_ids)
+        if token_type_ids is None:
+            token_type_ids = torch.zeros_like(input_ids)
+
+        embedding_output = self.embeddings(input_ids, token_type_ids,
+                                           position_ids)
+
+        subset_mask = []
+        first_col_mask = []
+
+        if masked_tokens_mask is None:
+            subset_mask = None
+        else:
+            first_col_mask = torch.zeros_like(masked_tokens_mask)
+            first_col_mask[:, 0] = True
+            subset_mask = masked_tokens_mask | first_col_mask
+
+        encoder_outputs = self.encoder(
+            embedding_output,
+            attention_mask,
+            output_all_encoded_layers=output_all_encoded_layers,
+            subset_mask=subset_mask)
+
+        if masked_tokens_mask is None:
+            sequence_output = encoder_outputs[-1]
+            pooled_output = self.pooler(
+                sequence_output) if self.pooler is not None else None
+        else:
+            # TD [2022-03-01]: the indexing here is very tricky.
+            attention_mask_bool = attention_mask.bool()
+            subset_idx = subset_mask[attention_mask_bool]  # type: ignore
+            sequence_output = encoder_outputs[-1][
+                masked_tokens_mask[attention_mask_bool][subset_idx]]
+            if self.pooler is not None:
+                pool_input = encoder_outputs[-1][
+                    first_col_mask[attention_mask_bool][subset_idx]]
+                pooled_output = self.pooler(pool_input, pool=False)
+            else:
+                pooled_output = None
+
+        if not output_all_encoded_layers:
+            encoder_outputs = sequence_output
+
+        if self.pooler is not None:
+            return encoder_outputs, pooled_output
+
+        return encoder_outputs, None
+
+
+###################
+# Bert Heads
+###################
+class BerKANTLMPredictionHead(nn.Module):
+
+    def __init__(self, config, bert_model_embedding_weights):
+        super().__init__()
+        self.transform = BerKANTPredictionHeadTransform(config)
+        # The output weights are the same as the input embeddings, but there is
+        # an output-only bias for each token.
+        self.decoder = nn.Linear(bert_model_embedding_weights.size(1),
+                                 bert_model_embedding_weights.size(0))
+        self.decoder.weight = bert_model_embedding_weights
+
+    def forward(self, hidden_states: torch.Tensor) -> torch.Tensor:
+        hidden_states = self.transform(hidden_states)
+        hidden_states = self.decoder(hidden_states)
+        return hidden_states
+
+
+class BerKANTOnlyMLMHead(nn.Module):
+
+    def __init__(self, config, bert_model_embedding_weights):
+        super().__init__()
+        self.predictions = BerKANTLMPredictionHead(config,
+                                                bert_model_embedding_weights)
+
+    def forward(self, sequence_output: torch.Tensor) -> torch.Tensor:
+        prediction_scores = self.predictions(sequence_output)
+        return prediction_scores
+
+
+class BerKANTOnlyNSPHead(nn.Module):
+
+    def __init__(self, config):
+        super().__init__()
+        self.seq_relationship = KANLinear(config.hidden_size, 2)
+
+    def forward(self, pooled_output: torch.Tensor) -> torch.Tensor:
+        seq_relationship_score = self.seq_relationship(pooled_output)
+        return seq_relationship_score
+
+
+#####################
+# Various Bert models
+#####################
+
+
+class BerKANTForPreTraining(BertPreTrainedModel):
+    #TBD: Coming in Future Commit
+    pass
+
+
+class BerKANTLMHeadModel(BertPreTrainedModel):
+    #TBD: Coming in Future Commit
+    pass
+
+
+class BerKANTForMaskedLM(BertPreTrainedModel):
+
+    def __init__(self, config):
+        super().__init__(config)
+
+        if config.is_decoder:
+            warnings.warn(
+                'If you want to use `BertForMaskedLM` make sure `config.is_decoder=False` for '
+                'bi-directional self-attention.')
+
+        self.bert = BerKANTModel(config, add_pooling_layer=False)
+        self.cls = BerKANTOnlyMLMHead(config,
+                                   self.bert.embeddings.word_embeddings.weight)
+
+        # Initialize weights and apply final processing
+        self.post_init()
+
+    @classmethod
+    def from_composer(cls,
+                      pretrained_checkpoint,
+                      state_dict=None,
+                      cache_dir=None,
+                      from_tf=False,
+                      config=None,
+                      *inputs,
+                      **kwargs):
+        """Load from pre-trained."""
+        model = cls(config, *inputs, **kwargs)
+        if from_tf:
+            raise ValueError(
+                'Mosaic BERT does not support loading TensorFlow weights.')
+
+        state_dict = torch.load(pretrained_checkpoint)
+        # If the state_dict was saved after wrapping with `composer.HuggingFaceModel`, it takes on the `model` prefix
+        consume_prefix_in_state_dict_if_present(state_dict, prefix='model.')
+        missing_keys, unexpected_keys = model.load_state_dict(state_dict,
+                                                              strict=False)
+
+        if len(missing_keys) > 0:
+            logger.warning(
+                f"Found these missing keys in the checkpoint: {', '.join(missing_keys)}"
+            )
+        if len(unexpected_keys) > 0:
+            logger.warning(
+                f"Found these unexpected keys in the checkpoint: {', '.join(unexpected_keys)}"
+            )
+
+        return model
+
+    def get_output_embeddings(self):
+        return self.cls.predictions.decoder
+
+    def set_output_embeddings(self, new_embeddings):
+        self.cls.predictions.decoder = new_embeddings
+
+    def forward(
+        self,
+        input_ids: Optional[torch.Tensor] = None,
+        attention_mask: Optional[torch.Tensor] = None,
+        token_type_ids: Optional[torch.Tensor] = None,
+        position_ids: Optional[torch.Tensor] = None,
+        head_mask: Optional[torch.Tensor] = None,
+        inputs_embeds: Optional[torch.Tensor] = None,
+        encoder_hidden_states: Optional[torch.Tensor] = None,
+        encoder_attention_mask: Optional[torch.Tensor] = None,
+        labels: Optional[torch.Tensor] = None,
+        output_attentions: Optional[bool] = None,
+        output_hidden_states: Optional[bool] = None,
+        return_dict: Optional[bool] = None,
+    ) -> Union[Tuple[torch.Tensor], MaskedLMOutput]:
+        # labels should be a `torch.LongTensor` of shape
+        # `(batch_size, sequence_length)`. These are used for computing the
+        #  masked language modeling loss.
+        #
+        # Indices should be in `[-100, 0, ..., config.vocab_size]` (see
+        # `input_ids` docstring) Tokens with indices set to `-100` are ignored
+        # (masked), the loss is only computed for the tokens with labels in `[0,
+        # ..., config.vocab_size]`
+        #
+        # Prediction scores are only computed for masked tokens and the (bs,
+        # seqlen) dimensions are flattened
+        if (input_ids is not None) == (inputs_embeds is not None):
+            raise ValueError('Must specify either input_ids or input_embeds!')
+
+        if labels is None:
+            masked_tokens_mask = None
+        else:
+            masked_tokens_mask = labels > 0
+
+        return_dict = return_dict if return_dict is not None else self.config.use_return_dict
+
+        outputs = self.bert(
+            input_ids,
+            attention_mask=attention_mask,
+            token_type_ids=token_type_ids,
+            position_ids=position_ids,
+            head_mask=head_mask,
+            inputs_embeds=inputs_embeds,
+            encoder_hidden_states=encoder_hidden_states,
+            encoder_attention_mask=encoder_attention_mask,
+            output_attentions=output_attentions,
+            output_hidden_states=output_hidden_states,
+            return_dict=return_dict,
+            masked_tokens_mask=masked_tokens_mask,
+        )
+
+        sequence_output = outputs[0]
+        prediction_scores = self.cls(sequence_output)
+
+        loss = None
+        if labels is not None:
+            # Compute loss
+            loss_fct = nn.CrossEntropyLoss()
+            masked_token_idx = torch.nonzero(labels.flatten() > 0,
+                                             as_tuple=False).flatten()
+            loss = loss_fct(prediction_scores,
+                            labels.flatten()[masked_token_idx])
+
+            assert input_ids is not None, 'Coding error; please open an issue'
+            batch, seqlen = input_ids.shape[:2]
+            prediction_scores = rearrange(index_put_first_axis(
+                prediction_scores, masked_token_idx, batch * seqlen),
+                                          '(b s) d -> b s d',
+                                          b=batch)
+
+        if not return_dict:
+            output = (prediction_scores,) + outputs[2:]
+            return ((loss,) + output) if loss is not None else output
+
+        return MaskedLMOutput(
+            loss=loss,
+            logits=prediction_scores,
+            hidden_states=None,
+            attentions=None,
+        )
+
+    def prepare_inputs_for_generation(self, input_ids: torch.Tensor,
+                                      attention_mask: torch.Tensor,
+                                      **model_kwargs):
+        input_shape = input_ids.shape
+        effective_batch_size = input_shape[0]
+
+        #  add a dummy token
+        if self.config.pad_token_id is None:
+            raise ValueError('The PAD token should be defined for generation')
+
+        attention_mask = torch.cat([
+            attention_mask,
+            attention_mask.new_zeros((attention_mask.shape[0], 1))
+        ],
+                                   dim=-1)
+        dummy_token = torch.full((effective_batch_size, 1),
+                                 self.config.pad_token_id,
+                                 dtype=torch.long,
+                                 device=input_ids.device)
+        input_ids = torch.cat([input_ids, dummy_token], dim=1)
+
+        return {'input_ids': input_ids, 'attention_mask': attention_mask}
+
+
+class BerKANTForNextSentencePrediction(BertPreTrainedModel):
+    #TBD: Push in future commit
+    pass
+
+
+class BerKANTForSequenceClassification(BertPreTrainedModel):
+    """Bert Model transformer with a sequence classification/regression head.
+
+    This head is just a linear layer on top of the pooled output. Used for,
+    e.g., GLUE tasks.
+    """
+
+    def __init__(self, config):
+        super().__init__(config)
+        self.num_labels = config.num_labels
+        self.config = config
+
+        self.bert = BerKANTModel(config)
+        classifier_dropout = (config.classifier_dropout
+                              if config.classifier_dropout is not None else
+                              config.hidden_dropout_prob)
+        self.dropout = nn.Dropout(classifier_dropout)
+        self.classifier = KANLinear(config.hidden_size, config.num_labels)
+
+        # Initialize weights and apply final processing
+        self.post_init()
+
+    @classmethod
+    def from_composer(cls,
+                      pretrained_checkpoint,
+                      state_dict=None,
+                      cache_dir=None,
+                      from_tf=False,
+                      config=None,
+                      *inputs,
+                      **kwargs):
+        """Load from pre-trained."""
+        model = cls(config, *inputs, **kwargs)
+        if from_tf:
+            raise ValueError(
+                'Mosaic BERT does not support loading TensorFlow weights.')
+
+        state_dict = torch.load(pretrained_checkpoint)
+        # If the state_dict was saved after wrapping with `composer.HuggingFaceModel`, it takes on the `model` prefix
+        consume_prefix_in_state_dict_if_present(state_dict, prefix='model.')
+        missing_keys, unexpected_keys = model.load_state_dict(state_dict,
+                                                              strict=False)
+
+        if len(missing_keys) > 0:
+            logger.warning(
+                f"Found these missing keys in the checkpoint: {', '.join(missing_keys)}"
+            )
+        if len(unexpected_keys) > 0:
+            logger.warning(
+                f"Found these unexpected keys in the checkpoint: {', '.join(unexpected_keys)}"
+            )
+
+        return model
+
+    def forward(
+        self,
+        input_ids: Optional[torch.Tensor] = None,
+        attention_mask: Optional[torch.Tensor] = None,
+        token_type_ids: Optional[torch.Tensor] = None,
+        position_ids: Optional[torch.Tensor] = None,
+        head_mask: Optional[torch.Tensor] = None,
+        inputs_embeds: Optional[torch.Tensor] = None,
+        labels: Optional[torch.Tensor] = None,
+        output_attentions: Optional[bool] = None,
+        output_hidden_states: Optional[bool] = None,
+        return_dict: Optional[bool] = None,
+    ) -> Union[Tuple[torch.Tensor], SequenceClassifierOutput]:
+        # labels (`torch.LongTensor` of shape `(batch_size,)`, *optional*):
+        # Labels for computing the sequence classification/regression loss.
+        # Indices should be in `[0, ..., config.num_labels - 1]`.
+        # If `config.num_labels == 1` a regression loss is computed
+        # (mean-square loss). If `config.num_labels > 1` a classification loss
+        # is computed (cross-entropy).
+
+        return_dict = return_dict if return_dict is not None else self.config.use_return_dict
+
+        outputs = self.bert(
+            input_ids,
+            attention_mask=attention_mask,
+            token_type_ids=token_type_ids,
+            position_ids=position_ids,
+            head_mask=head_mask,
+            inputs_embeds=inputs_embeds,
+            output_attentions=output_attentions,
+            output_hidden_states=output_hidden_states,
+            return_dict=return_dict,
+        )
+
+        pooled_output = outputs[1]
+
+        pooled_output = self.dropout(pooled_output)
+        logits = self.classifier(pooled_output)
+
+        loss = None
+        if labels is not None:
+            # Compute loss
+            if self.config.problem_type is None:
+                if self.num_labels == 1:
+                    self.config.problem_type = 'regression'
+                elif self.num_labels > 1 and (labels.dtype == torch.long or
+                                              labels.dtype == torch.int):
+                    self.config.problem_type = 'single_label_classification'
+                else:
+                    self.config.problem_type = 'multi_label_classification'
+
+            if self.config.problem_type == 'regression':
+                loss_fct = nn.MSELoss()
+                if self.num_labels == 1:
+                    loss = loss_fct(logits.squeeze(), labels.squeeze())
+                else:
+                    loss = loss_fct(logits, labels)
+            elif self.config.problem_type == 'single_label_classification':
+                loss_fct = nn.CrossEntropyLoss()
+                loss = loss_fct(logits.view(-1, self.num_labels),
+                                labels.view(-1))
+            elif self.config.problem_type == 'multi_label_classification':
+                loss_fct = nn.BCEWithLogitsLoss()
+                loss = loss_fct(logits, labels)
+
+        if not return_dict:
+            output = (logits,) + outputs[2:]
+            return ((loss,) + output) if loss is not None else output
+
+        return SequenceClassifierOutput(
+            loss=loss,
+            logits=logits,
+            hidden_states=None,
+            attentions=None,
+        )
+
+
+class BerKANTForMultipleChoice(BertPreTrainedModel):
+    #TBD: Push in future commit
+    pass
+
+
+class BerKANTForTokenClassification(BertPreTrainedModel):
+    #TBD: Push in future commit
+    pass
+
+
+class BerKANTForQuestionAnswering(BertPreTrainedModel):
+    """Bert Model with a span classification head.
+
+    This is used for extractive question-answering tasks like SQuAD (a linear
+    layers on top of the hidden states' output to compute `span start logits`
+    and `span end logits`).
+    """
+    #TBD: Push in future commit
+
+# from transformers import AutoModelForMaskedLM
+
+# AutoModelForMaskedLM.register("labiium-berkant", BerKANTForMaskedLM)

berkant_padding.py

@@ -0,0 +1,159 @@
+# Copyright 2022 MosaicML Examples authors
+# SPDX-License-Identifier: Apache-2.0
+
+# Adapted from https://github.com/HazyResearch/flash-attention/blob/main/flash_attn/bert_padding.py
+# Which was adapted from https://github.com/mlcommons/training_results_v1.1/blob/main/NVIDIA/benchmarks/bert/implementations/pytorch/padding.py
+
+"""Helper functions for padding and unpadding batches.
+
+These functions are used extensively throughout the Mosaic BERT implementation
+in `bert_layers.py`.
+"""
+
+from typing import Tuple, cast
+
+import torch
+import torch.nn.functional as F
+from einops import rearrange, repeat
+
+
+class IndexFirstAxis(torch.autograd.Function):
+
+    @staticmethod
+    def forward(ctx, input: torch.Tensor,
+                indices: torch.Tensor) -> torch.Tensor:
+        """Get just the values of `input` which are at `indices`.
+
+        Arguments:
+            ctx: the autograd context object
+            input: (b, ...) 2+ dimensional tensor
+            indices: (num_idx) 1D tensor
+        """
+        ctx.save_for_backward(indices)
+        assert input.ndim >= 2
+        ctx.first_axis_dim, other_shape = input.shape[0], input.shape[
+            1:]  # type: ignore
+        second_dim = other_shape.numel(
+        )  # product of sizes of all but first dimension
+        # TD [2022-03-04] For some reason torch.gather is a bit faster than indexing.
+        return torch.gather(
+            rearrange(input, 'b ... -> b (...)'),  # (b, ...) -> (b, second_dim)
+            0,
+            repeat(indices, 'z -> z d',
+                   d=second_dim)  # (indices,) -> (indices, second_dim)
+        ).reshape(-1, *other_shape)  # (num_idx, ...)
+
+    @staticmethod
+    def backward(ctx, grad_output: torch.Tensor) -> Tuple[torch.Tensor, None]:
+        indices, = ctx.saved_tensors
+        assert grad_output.ndim >= 2
+        other_shape = grad_output.shape[1:]
+        grad_output = rearrange(grad_output, 'b ... -> b (...)')
+        grad_input = torch.zeros([ctx.first_axis_dim, grad_output.shape[1]],
+                                 device=grad_output.device,
+                                 dtype=grad_output.dtype)
+        # TD [2022-03-04] For some reason torch.scatter is a bit faster than indexing.
+        # grad_input[indices] = grad_output
+        grad_input.scatter_(0,
+                            repeat(indices, 'z -> z d', d=grad_output.shape[1]),
+                            grad_output)
+        return grad_input.reshape(ctx.first_axis_dim, *other_shape), None
+
+
+index_first_axis = IndexFirstAxis.apply
+
+
+class IndexPutFirstAxis(torch.autograd.Function):
+
+    @staticmethod
+    def forward(ctx, values: torch.Tensor, indices: torch.Tensor,
+                first_axis_dim) -> torch.Tensor:
+        ctx.save_for_backward(indices)
+        assert indices.ndim == 1
+        assert values.ndim >= 2
+        output = torch.zeros(first_axis_dim,
+                             *values.shape[1:],
+                             device=values.device,
+                             dtype=values.dtype)
+        output[indices] = values
+        return output
+
+    @staticmethod
+    def backward(ctx,
+                 grad_output: torch.Tensor) -> Tuple[torch.Tensor, None, None]:
+        indices, = ctx.saved_tensors
+        grad_values = grad_output[indices]
+        return grad_values, None, None
+
+
+index_put_first_axis = IndexPutFirstAxis.apply
+
+
+def unpad_input(
+    hidden_states: torch.Tensor,
+    attention_mask: torch.Tensor,
+) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, int]:
+    """Remove padding from input sequences.
+
+    Arguments:
+        hidden_states: (batch, seqlen, ...)
+        attention_mask: (batch, seqlen), bool / int, 1 means valid and 0 means not valid.
+
+    Returns:
+        hidden_states: (total_nnz, ...), where total_nnz = number of tokens in selected in attention_mask.
+        indices: (total_nnz)
+        cu_seqlens: (batch + 1), the cumulative sequence lengths, used to index into hidden_states.
+        max_seqlen_in_batch: int ()
+    """
+    seqlens_in_batch = attention_mask.sum(dim=-1, dtype=torch.int32)
+    indices = torch.nonzero(attention_mask.flatten(), as_tuple=False).flatten()
+    max_seqlen_in_batch = int(seqlens_in_batch.max().item())
+    cu_seqlens = F.pad(torch.cumsum(seqlens_in_batch, dim=0, dtype=torch.int32),
+                       (1, 0))
+    # TD [2022-03-04] We don't want to index with a bool mask, because Pytorch will expand the
+    # bool mask, then call nonzero to get the indices, then index with those. The indices is @dim
+    # times larger than it needs to be, wasting memory. It's faster and more memory-efficient to
+    # index with integer indices. Moreover, torch's index is a bit slower than it needs to be,
+    # so we write custom forward and backward to make it a bit faster.
+    hidden_states = cast(
+        torch.Tensor,
+        index_first_axis(rearrange(hidden_states, 'b s ... -> (b s) ...'),
+                         indices))
+    return hidden_states, indices, cu_seqlens, max_seqlen_in_batch
+
+
+def unpad_input_only(
+    hidden_states: torch.Tensor,
+    attention_mask: torch.Tensor,
+) -> torch.Tensor:
+    """Like unpad_input, but only return the unpadded first tensor.
+
+    Save a small amount of overhead.
+
+    Arguments:
+        hidden_states: (batch, seqlen, ...)
+        attention_mask: (batch, seqlen), bool / int, 1 means valid and 0 means not valid.
+
+    Returns:
+        hidden_states: (total_nnz, ...), where total_nnz = number of tokens in selected in attention_mask.
+    """
+    indices = torch.nonzero(attention_mask.flatten(), as_tuple=False).flatten()
+    return index_first_axis(rearrange(hidden_states, 'b s ... -> (b s) ...'),
+                            indices)
+
+
+def pad_input(hidden_states: torch.Tensor, indices: torch.Tensor, batch: int,
+              seqlen: int) -> torch.Tensor:
+    """Add padding to sequences.
+
+    Arguments:
+        hidden_states: (total_nnz, ...), where total_nnz = number of tokens in selected in attention_mask.
+        indices: (total_nnz)
+        batch: int batch_size
+        seqlen: int max sequence length
+
+    Returns:
+        hidden_states: (batch, seqlen, ...)
+    """
+    output = index_put_first_axis(hidden_states, indices, batch * seqlen)
+    return rearrange(output, '(b s) ... -> b s ...', b=batch)

configuration_berkant.py

@@ -0,0 +1,25 @@
+# Copyright 2022 MosaicML Examples authors
+# SPDX-License-Identifier: Apache-2.0
+
+from transformers import BertConfig as TransformersBertConfig
+
+
+class BerKANTConfig(TransformersBertConfig):
+
+    def __init__(
+        self,
+        alibi_starting_size: int = 512,
+        attention_probs_dropout_prob: float = 0.0,
+        **kwargs,
+    ):
+        """Configuration class for MosaicBert.
+        Args:
+            alibi_starting_size (int): Use `alibi_starting_size` to determine how large of an alibi tensor to
+                create when initializing the model. You should be able to ignore this parameter in most cases.
+                Defaults to 512.
+            attention_probs_dropout_prob (float): By default, turn off attention dropout in Mosaic BERT
+                (otherwise, Flash Attention will be off by default). Defaults to 0.0.
+        """
+        super().__init__(
+            attention_probs_dropout_prob=attention_probs_dropout_prob, **kwargs)
+        self.alibi_starting_size = alibi_starting_size

flash_attn_triton.py

@@ -0,0 +1,1112 @@
+# Copyright 2022 MosaicML Examples authors
+# SPDX-License-Identifier: Apache-2.0
+
+"""Triton implementation of Flash Attention.
+
+# Copyright (c) 2022, Tri Dao.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+*Experimental* implementation of FlashAttention in Triton.
+We use the FlashAttention implementation from Phil Tillet a starting point.
+https://github.com/openai/triton/blob/master/python/tutorials/06-fused-attention.py
+
+Changes:
+- Implement both causal and non-causal attention.
+- Implement both self-attention and cross-attention.
+- Support arbitrary seqlens (not just multiples of 128), for both forward and backward.
+- Support all head dimensions up to 128 (not just 16, 32, 64, 128), for both forward and backward.
+- Support attention bias.
+- Speed up the forward pass a bit, and only store the LSE instead of m and l.
+- Make the backward for d=128 much faster by reducing register spilling.
+- Optionally parallelize the backward pass across seqlen_k, to deal with the case of
+small batch size * nheads.
+
+Caution:
+- If you plan to use headdim other than 64 and 128, you should test for race conditions
+(due to the Triton compiler), as done in tests/test_flash_attn.py
+"test_flash_attn_triton_race_condition". I've tested and fixed many race conditions
+for different head dimensions (40, 48, 64, 128, 80, 88, 96), but I'm still not 100% confident
+that there are none left for other head dimensions.
+Differences between this Triton version and the CUDA version:
+- Triton version doesn't support dropout.
+- Triton forward is generally faster than CUDA forward.
+- Triton backward is faster than CUDA backward when batch * nheads is small, and when headdim=64.
+It is slightly slower when headdim=128 and batch * nheads is large.
+- Triton version doesn't yet support different sequence lengths in a batch (i.e., RaggedTensor/NestedTensor).
+"""
+
+import math
+
+import torch
+import triton  # type: ignore (reportMissingImports)
+import triton.language as tl  # type: ignore (reportMissingImports)
+from einops import repeat
+
+
+@triton.autotune(
+    configs=[
+        triton.Config({
+            'BLOCK_M': 128,
+            'BLOCK_N': 128
+        },
+                      num_warps=8,
+                      num_stages=1),
+        # This config has a race condition when EVEN_M == False, disabling it for now.
+        # triton.Config({"BLOCK_M": 64, "BLOCK_N": 64}, num_warps=4, num_stages=1),
+    ],
+    key=[
+        'CACHE_KEY_SEQLEN_Q', 'CACHE_KEY_SEQLEN_K', 'BIAS_TYPE', 'IS_CAUSAL',
+        'BLOCK_HEADDIM'
+    ])
+@triton.heuristics({
+    'EVEN_M': lambda args: args['seqlen_q'] % args['BLOCK_M'] == 0,
+    'EVEN_N': lambda args: args['seqlen_k'] % args['BLOCK_N'] == 0,
+    'EVEN_HEADDIM': lambda args: args['headdim'] == args['BLOCK_HEADDIM'],
+})
+@triton.jit
+def _fwd_kernel(
+    Q,
+    K,
+    V,
+    Bias,
+    Out,
+    Lse,
+    TMP,  # NOTE: TMP is a scratchpad buffer to workaround a compiler bug
+    softmax_scale,
+    stride_qb,
+    stride_qh,
+    stride_qm,
+    stride_kb,
+    stride_kh,
+    stride_kn,
+    stride_vb,
+    stride_vh,
+    stride_vn,
+    stride_bb,
+    stride_bh,
+    stride_bm,
+    stride_ob,
+    stride_oh,
+    stride_om,
+    nheads,
+    seqlen_q,
+    seqlen_k,
+    seqlen_q_rounded,
+    headdim,
+    CACHE_KEY_SEQLEN_Q,
+    CACHE_KEY_SEQLEN_K,
+    BIAS_TYPE: tl.constexpr,
+    IS_CAUSAL: tl.constexpr,
+    BLOCK_HEADDIM: tl.constexpr,
+    EVEN_M: tl.constexpr,
+    EVEN_N: tl.constexpr,
+    EVEN_HEADDIM: tl.constexpr,
+    BLOCK_M: tl.constexpr,
+    BLOCK_N: tl.constexpr,
+):
+    start_m = tl.program_id(0)
+    off_hb = tl.program_id(1)
+    off_b = off_hb // nheads
+    off_h = off_hb % nheads
+    # off_b = tl.program_id(1)
+    # off_h = tl.program_id(2)
+    # off_hb = off_b * nheads + off_h
+    # initialize offsets
+    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
+    offs_n = tl.arange(0, BLOCK_N)
+    offs_d = tl.arange(0, BLOCK_HEADDIM)
+    # Initialize pointers to Q, K, V
+    # Adding parenthesis around indexing might use int32 math instead of int64 math?
+    # https://github.com/openai/triton/issues/741
+    # I'm seeing a tiny bit of difference (5-7us)
+    q_ptrs = Q + off_b * stride_qb + off_h * stride_qh + (
+        offs_m[:, None] * stride_qm + offs_d[None, :])
+    k_ptrs = K + off_b * stride_kb + off_h * stride_kh + (
+        offs_n[:, None] * stride_kn + offs_d[None, :])
+    v_ptrs = V + off_b * stride_vb + off_h * stride_vh + (
+        offs_n[:, None] * stride_vn + offs_d[None, :])
+    if BIAS_TYPE == 'vector':
+        b_ptrs = Bias + off_b * stride_bb + off_h * stride_bh + offs_n
+    elif BIAS_TYPE == 'matrix':
+        b_ptrs = Bias + off_b * stride_bb + off_h * stride_bh + (
+            offs_m[:, None] * stride_bm + offs_n[None, :])
+    else:
+        raise ValueError("BIAS_TYPE must be one of {'vector', 'matrix'}")
+    # initialize pointer to m and l
+    t_ptrs = TMP + off_hb * seqlen_q_rounded + offs_m
+    lse_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float('inf')
+    m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float('inf')
+    acc_o = tl.zeros([BLOCK_M, BLOCK_HEADDIM], dtype=tl.float32)
+    # load q: it will stay in SRAM throughout
+    # [2022-10-30] TD: Triton bug - in the case of EVEN_M=True and EVEN_N=False, if we just call
+    # tl.load(q_ptrs), we get the wrong output!
+    if EVEN_M & EVEN_N:
+        if EVEN_HEADDIM:
+            q = tl.load(q_ptrs)
+        else:
+            q = tl.load(q_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
+    else:
+        if EVEN_HEADDIM:
+            q = tl.load(q_ptrs, mask=offs_m[:, None] < seqlen_q, other=0.0)
+        else:
+            q = tl.load(q_ptrs,
+                        mask=(offs_m[:, None] < seqlen_q) &
+                        (offs_d[None, :] < headdim),
+                        other=0.0)
+    # loop over k, v and update accumulator
+    end_n = seqlen_k if not IS_CAUSAL else tl.minimum(
+        (start_m + 1) * BLOCK_M, seqlen_k)
+    for start_n in range(0, end_n, BLOCK_N):
+        start_n = tl.multiple_of(start_n, BLOCK_N)
+        # -- compute qk ----
+        if EVEN_N & EVEN_M:  # If we just do "if EVEN_N", there seems to be some race condition
+            if EVEN_HEADDIM:
+                k = tl.load(k_ptrs + start_n * stride_kn)
+            else:
+                k = tl.load(k_ptrs + start_n * stride_kn,
+                            mask=offs_d[None, :] < headdim,
+                            other=0.0)
+        else:
+            if EVEN_HEADDIM:
+                k = tl.load(k_ptrs + start_n * stride_kn,
+                            mask=(start_n + offs_n)[:, None] < seqlen_k,
+                            other=0.0)
+            else:
+                k = tl.load(k_ptrs + start_n * stride_kn,
+                            mask=((start_n + offs_n)[:, None] < seqlen_k) &
+                            (offs_d[None, :] < headdim),
+                            other=0.0)
+        qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
+        qk += tl.dot(q, k, trans_b=True)
+        # Trying to combine the two masks seem to make the result wrong
+        if not EVEN_N:  # Need to mask out otherwise the softmax is wrong
+            qk += tl.where((start_n + offs_n)[None, :] < seqlen_k, 0,
+                           float('-inf'))
+        if IS_CAUSAL:
+            qk += tl.where(offs_m[:, None] >= (start_n + offs_n)[None, :], 0,
+                           float('-inf'))
+        if BIAS_TYPE != 'none':
+            if BIAS_TYPE == 'vector':
+                if EVEN_N:
+                    bias = tl.load(b_ptrs + start_n).to(tl.float32)
+                else:
+                    bias = tl.load(b_ptrs + start_n,
+                                   mask=(start_n + offs_n) < seqlen_k,
+                                   other=0.0).to(tl.float32)
+                bias = bias[None, :]
+            elif BIAS_TYPE == 'matrix':
+                if EVEN_M & EVEN_N:
+                    bias = tl.load(b_ptrs + start_n).to(tl.float32)
+                else:
+                    bias = tl.load(b_ptrs + start_n,
+                                   mask=(offs_m[:, None] < seqlen_q) &
+                                   ((start_n + offs_n)[None, :] < seqlen_k),
+                                   other=0.0).to(tl.float32)
+            else:
+                raise ValueError(
+                    "BIAS_TYPE must be one of {'vector', 'matrix'}")
+            # Slightly faster to multiply the softmax_scale in the tl.exp below since the compiler
+            # can then fuse the mult and add into an fma instruction. But if we have bias we need to
+            # to multiply with softmax_scale here.
+            qk = qk * softmax_scale + bias
+            m_ij = tl.maximum(tl.max(qk, 1), lse_i)
+            p = tl.exp(qk - m_ij[:, None])
+        else:
+            m_ij = tl.maximum(tl.max(qk, 1) * softmax_scale, lse_i)
+            p = tl.exp(qk * softmax_scale - m_ij[:, None])
+        l_ij = tl.sum(p, 1)
+
+        # scale acc_o
+        acc_o_scale = tl.exp(m_i - m_ij)
+
+        # # -- update output accumulator --
+        # BUG: have to store and immediately load
+        tl.store(t_ptrs, acc_o_scale)
+        acc_o_scale = tl.load(t_ptrs)
+        acc_o = acc_o * acc_o_scale[:, None]
+        # update acc_o
+        if EVEN_N & EVEN_M:  # If we just do "if EVEN_N", there seems to be some race condition
+            if EVEN_HEADDIM:
+                v = tl.load(v_ptrs + start_n * stride_vn)
+            else:
+                v = tl.load(v_ptrs + start_n * stride_vn,
+                            mask=offs_d[None, :] < headdim,
+                            other=0.0)
+        else:
+            if EVEN_HEADDIM:
+                v = tl.load(v_ptrs + start_n * stride_vn,
+                            mask=(start_n + offs_n)[:, None] < seqlen_k,
+                            other=0.0)
+            else:
+                v = tl.load(v_ptrs + start_n * stride_vn,
+                            mask=((start_n + offs_n)[:, None] < seqlen_k) &
+                            (offs_d[None, :] < headdim),
+                            other=0.0)
+        p = p.to(v.dtype)
+        acc_o += tl.dot(p, v)
+
+        # -- update statistics
+        m_i = m_ij
+        l_i_new = tl.exp(lse_i - m_ij) + l_ij
+        lse_i = m_ij + tl.log(l_i_new)
+
+    o_scale = tl.exp(m_i - lse_i)
+    # BUG: have to store and immediately load
+    tl.store(t_ptrs, o_scale)
+    o_scale = tl.load(t_ptrs)
+    acc_o = acc_o * o_scale[:, None]
+    # rematerialize offsets to save registers
+    start_m = tl.program_id(0)
+    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
+    # write back l and m
+    lse_ptrs = Lse + off_hb * seqlen_q_rounded + offs_m
+    tl.store(lse_ptrs, lse_i)
+    # initialize pointers to output
+    offs_n = tl.arange(0, BLOCK_HEADDIM)
+    out_ptrs = Out + off_b * stride_ob + off_h * stride_oh + (
+        offs_m[:, None] * stride_om + offs_n[None, :])
+    if EVEN_M:
+        if EVEN_HEADDIM:
+            tl.store(out_ptrs, acc_o)
+        else:
+            tl.store(out_ptrs, acc_o, mask=offs_d[None, :] < headdim)
+    else:
+        if EVEN_HEADDIM:
+            tl.store(out_ptrs, acc_o, mask=offs_m[:, None] < seqlen_q)
+        else:
+            tl.store(out_ptrs,
+                     acc_o,
+                     mask=(offs_m[:, None] < seqlen_q) &
+                     (offs_d[None, :] < headdim))
+
+
+@triton.jit
+def _bwd_preprocess_do_o_dot(
+    Out,
+    DO,
+    Delta,
+    stride_ob,
+    stride_oh,
+    stride_om,
+    stride_dob,
+    stride_doh,
+    stride_dom,
+    nheads,
+    seqlen_q,
+    seqlen_q_rounded,
+    headdim,
+    BLOCK_M: tl.constexpr,
+    BLOCK_HEADDIM: tl.constexpr,
+):
+    start_m = tl.program_id(0)
+    off_hb = tl.program_id(1)
+    off_b = off_hb // nheads
+    off_h = off_hb % nheads
+    # initialize offsets
+    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
+    offs_d = tl.arange(0, BLOCK_HEADDIM)
+    # load
+    o = tl.load(Out + off_b * stride_ob + off_h * stride_oh +
+                offs_m[:, None] * stride_om + offs_d[None, :],
+                mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim),
+                other=0.0).to(tl.float32)
+    do = tl.load(DO + off_b * stride_dob + off_h * stride_doh +
+                 offs_m[:, None] * stride_dom + offs_d[None, :],
+                 mask=(offs_m[:, None] < seqlen_q) &
+                 (offs_d[None, :] < headdim),
+                 other=0.0).to(tl.float32)
+    delta = tl.sum(o * do, axis=1)
+    # write-back
+    tl.store(Delta + off_hb * seqlen_q_rounded + offs_m, delta)
+
+
+@triton.jit
+def _bwd_kernel_one_col_block(
+    start_n,
+    Q,
+    K,
+    V,
+    Bias,
+    DO,
+    DQ,
+    DK,
+    DV,
+    LSE,
+    D,
+    softmax_scale,
+    stride_qm,
+    stride_kn,
+    stride_vn,
+    stride_bm,
+    stride_dom,
+    stride_dqm,
+    stride_dkn,
+    stride_dvn,
+    seqlen_q,
+    seqlen_k,
+    headdim,
+    ATOMIC_ADD: tl.constexpr,
+    BIAS_TYPE: tl.constexpr,
+    IS_CAUSAL: tl.constexpr,
+    BLOCK_HEADDIM: tl.constexpr,
+    EVEN_M: tl.constexpr,
+    EVEN_N: tl.constexpr,
+    EVEN_HEADDIM: tl.constexpr,
+    BLOCK_M: tl.constexpr,
+    BLOCK_N: tl.constexpr,
+):
+    # We need to make sure begin_m is a multiple of BLOCK_M (not BLOCK_N)
+    begin_m = 0 if not IS_CAUSAL else ((start_n * BLOCK_N) // BLOCK_M) * BLOCK_M
+    # initialize row/col offsets
+    offs_qm = begin_m + tl.arange(0, BLOCK_M)
+    offs_n = start_n * BLOCK_N + tl.arange(0, BLOCK_N)
+    offs_m = tl.arange(0, BLOCK_M)
+    offs_d = tl.arange(0, BLOCK_HEADDIM)
+    # initialize pointers to value-like data
+    q_ptrs = Q + (offs_qm[:, None] * stride_qm + offs_d[None, :])
+    k_ptrs = K + (offs_n[:, None] * stride_kn + offs_d[None, :])
+    v_ptrs = V + (offs_n[:, None] * stride_vn + offs_d[None, :])
+    do_ptrs = DO + (offs_qm[:, None] * stride_dom + offs_d[None, :])
+    dq_ptrs = DQ + (offs_qm[:, None] * stride_dqm + offs_d[None, :])
+    if BIAS_TYPE == 'vector':
+        b_ptrs = Bias + offs_n
+    elif BIAS_TYPE == 'matrix':
+        b_ptrs = Bias + (offs_qm[:, None] * stride_bm + offs_n[None, :])
+    else:
+        raise ValueError("BIAS_TYPE must be one of {'vector', 'matrix'}")
+    # initialize dv and dk
+    dv = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32)
+    dk = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32)
+    # k and v stay in SRAM throughout
+    # [2022-10-30] TD: Same bug as the fwd. In the case of EVEN_N=True and EVEN_M=False,
+    # if we just call tl.load(k_ptrs), we get the wrong output!
+    if EVEN_N & EVEN_M:
+        if EVEN_HEADDIM:
+            k = tl.load(k_ptrs)
+            v = tl.load(v_ptrs)
+        else:
+            k = tl.load(k_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
+            v = tl.load(v_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
+    else:
+        if EVEN_HEADDIM:
+            k = tl.load(k_ptrs, mask=offs_n[:, None] < seqlen_k, other=0.0)
+            v = tl.load(v_ptrs, mask=offs_n[:, None] < seqlen_k, other=0.0)
+        else:
+            k = tl.load(k_ptrs,
+                        mask=(offs_n[:, None] < seqlen_k) &
+                        (offs_d[None, :] < headdim),
+                        other=0.0)
+            v = tl.load(v_ptrs,
+                        mask=(offs_n[:, None] < seqlen_k) &
+                        (offs_d[None, :] < headdim),
+                        other=0.0)
+    # loop over rows
+    num_block_m = tl.cdiv(seqlen_q, BLOCK_M)
+    for start_m in range(begin_m, num_block_m * BLOCK_M, BLOCK_M):
+        start_m = tl.multiple_of(start_m, BLOCK_M)
+        offs_m_curr = start_m + offs_m
+        # load q, k, v, do on-chip
+        # Same bug as below. Otherwise gives wrong result for headdim=40, seqlen=(128, 117)
+        if EVEN_M & EVEN_HEADDIM:
+            q = tl.load(q_ptrs)
+        else:
+            if EVEN_HEADDIM:
+                q = tl.load(q_ptrs,
+                            mask=offs_m_curr[:, None] < seqlen_q,
+                            other=0.0)
+            else:
+                q = tl.load(q_ptrs,
+                            mask=(offs_m_curr[:, None] < seqlen_q) &
+                            (offs_d[None, :] < headdim),
+                            other=0.0)
+        # recompute p = softmax(qk, dim=-1).T
+        qk = tl.dot(q, k, trans_b=True)
+        # Trying to combine the two masks seem to make the result wrong
+        if not EVEN_N:  # Need to mask out otherwise the softmax is wrong
+            qk = tl.where(offs_n[None, :] < seqlen_k, qk, float('-inf'))
+        if IS_CAUSAL:
+            qk = tl.where(offs_m_curr[:, None] >= (offs_n[None, :]), qk,
+                          float('-inf'))
+        if BIAS_TYPE != 'none':
+            if BIAS_TYPE == 'vector':
+                if EVEN_N:
+                    bias = tl.load(b_ptrs).to(tl.float32)
+                else:
+                    bias = tl.load(b_ptrs, mask=offs_n < seqlen_k,
+                                   other=0.0).to(tl.float32)
+                bias = bias[None, :]
+            elif BIAS_TYPE == 'matrix':
+                if EVEN_M & EVEN_N:
+                    bias = tl.load(b_ptrs).to(tl.float32)
+                else:
+                    bias = tl.load(b_ptrs,
+                                   mask=(offs_m_curr[:, None] < seqlen_q) &
+                                   (offs_n[None, :] < seqlen_k),
+                                   other=0.0).to(tl.float32)
+            else:
+                raise ValueError(
+                    "BIAS_TYPE must be one of {'vector', 'matrix'}")
+            qk = qk * softmax_scale + bias
+        # There seems to be a race condition when headdim=48/96, and dq, dk, dv are wrong.
+        # Also wrong for headdim=64.
+        if not (EVEN_M & EVEN_HEADDIM):
+            tl.debug_barrier()
+        lse_i = tl.load(LSE + offs_m_curr)
+        if BIAS_TYPE == 'none':
+            p = tl.exp(qk * softmax_scale - lse_i[:, None])
+        else:
+            p = tl.exp(qk - lse_i[:, None])
+        # compute dv
+        # [2022-10-30] TD: A Triton bug: if EVEN_M=True and EVEN_HEADDIM=False, if we call
+        # do = tl.load(do_ptrs, mask=offs_d[None, :] < headdim, other=0.0), we get wrong outputs
+        # in the case of headdim=48/96, seqlen_q & seqlen_k >= 512. If headdim=40 or seqlen < 512,
+        # the output is correct.
+        if EVEN_M & EVEN_HEADDIM:
+            do = tl.load(do_ptrs)
+        else:
+            # [2022-11-01] TD: Triton bug, there's a race condition if we just use m_mask and not d_mask.
+            do = tl.load(do_ptrs,
+                         mask=(offs_m_curr[:, None] < seqlen_q) &
+                         (offs_d[None, :] < headdim),
+                         other=0.0)
+        # if EVEN_M:
+        #     if EVEN_HEADDIM:
+        #         do = tl.load(do_ptrs)
+        #     else:
+        #         do = tl.load(do_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
+        # else:
+        #     if EVEN_HEADDIM:
+        #         do = tl.load(do_ptrs, mask=offs_m_curr[:, None] < seqlen_q, other=0.0)
+        #     else:
+        #         do = tl.load(do_ptrs, mask=(offs_m_curr[:, None] < seqlen_q)
+        #                                    & (offs_d[None, :] < headdim), other=0.0)
+        dv += tl.dot(p.to(do.dtype), do, trans_a=True)
+        # compute dp = dot(v, do)
+        # There seems to be a race condition when headdim=48/96, and dq, dk are wrong.
+        # Also wrong for headdim=128, seqlen=(108, 256), and ATOMIC_ADD=True
+        # Also wrong for headdim=64, seqlen=(1023, 1024), and ATOMIC_ADD=False
+        if not (EVEN_M & EVEN_HEADDIM):
+            tl.debug_barrier()
+        dp = tl.dot(do, v, trans_b=True)
+        # There's a race condition for headdim=48
+        if not EVEN_HEADDIM:
+            tl.debug_barrier()
+        # compute ds = p * (dp - delta[:, None])
+        # Putting the subtraction after the dp matmul (instead of before) is slightly faster
+        Di = tl.load(D + offs_m_curr)
+        # Converting ds to q.dtype here reduces register pressure and makes it much faster
+        # for BLOCK_HEADDIM=128
+        ds = (p * (dp - Di[:, None]) * softmax_scale).to(q.dtype)
+        # compute dk = dot(ds.T, q)
+        dk += tl.dot(ds, q, trans_a=True)
+        # compute dq
+        if not ATOMIC_ADD:
+            if EVEN_M & EVEN_HEADDIM:  # Race condition if we just do EVEN_M
+                dq = tl.load(dq_ptrs, eviction_policy='evict_last')
+                dq += tl.dot(ds, k)
+                tl.store(dq_ptrs, dq, eviction_policy='evict_last')
+            else:
+                if EVEN_HEADDIM:
+                    dq = tl.load(dq_ptrs,
+                                 mask=offs_m_curr[:, None] < seqlen_q,
+                                 other=0.0,
+                                 eviction_policy='evict_last')
+                    dq += tl.dot(ds, k)
+                    tl.store(dq_ptrs,
+                             dq,
+                             mask=offs_m_curr[:, None] < seqlen_q,
+                             eviction_policy='evict_last')
+                else:
+                    dq = tl.load(dq_ptrs,
+                                 mask=(offs_m_curr[:, None] < seqlen_q) &
+                                 (offs_d[None, :] < headdim),
+                                 other=0.0,
+                                 eviction_policy='evict_last')
+                    dq += tl.dot(ds, k)
+                    tl.store(dq_ptrs,
+                             dq,
+                             mask=(offs_m_curr[:, None] < seqlen_q) &
+                             (offs_d[None, :] < headdim),
+                             eviction_policy='evict_last')
+        else:  # If we're parallelizing across the seqlen_k dimension
+            dq = tl.dot(ds, k)
+            if EVEN_M & EVEN_HEADDIM:  # Race condition if we just do EVEN_M
+                tl.atomic_add(dq_ptrs, dq)
+            else:
+                if EVEN_HEADDIM:
+                    tl.atomic_add(dq_ptrs,
+                                  dq,
+                                  mask=offs_m_curr[:, None] < seqlen_q)
+                else:
+                    tl.atomic_add(dq_ptrs,
+                                  dq,
+                                  mask=(offs_m_curr[:, None] < seqlen_q) &
+                                  (offs_d[None, :] < headdim))
+        # increment pointers
+        dq_ptrs += BLOCK_M * stride_dqm
+        q_ptrs += BLOCK_M * stride_qm
+        do_ptrs += BLOCK_M * stride_dom
+        if BIAS_TYPE == 'matrix':
+            b_ptrs += BLOCK_M * stride_bm
+    # write-back
+    dv_ptrs = DV + (offs_n[:, None] * stride_dvn + offs_d[None, :])
+    dk_ptrs = DK + (offs_n[:, None] * stride_dkn + offs_d[None, :])
+    # [2022-11-01] TD: Same bug. In the case of EVEN_N=True and EVEN_M=False,
+    # if we just call tl.store(dv_ptrs), there's a race condition
+    if EVEN_N & EVEN_M:
+        if EVEN_HEADDIM:
+            tl.store(dv_ptrs, dv)
+            tl.store(dk_ptrs, dk)
+        else:
+            tl.store(dv_ptrs, dv, mask=offs_d[None, :] < headdim)
+            tl.store(dk_ptrs, dk, mask=offs_d[None, :] < headdim)
+    else:
+        if EVEN_HEADDIM:
+            tl.store(dv_ptrs, dv, mask=offs_n[:, None] < seqlen_k)
+            tl.store(dk_ptrs, dk, mask=offs_n[:, None] < seqlen_k)
+        else:
+            tl.store(dv_ptrs,
+                     dv,
+                     mask=(offs_n[:, None] < seqlen_k) &
+                     (offs_d[None, :] < headdim))
+            tl.store(dk_ptrs,
+                     dk,
+                     mask=(offs_n[:, None] < seqlen_k) &
+                     (offs_d[None, :] < headdim))
+
+
+def init_to_zero(name):
+    return lambda nargs: nargs[name].zero_()
+
+
+@triton.autotune(
+    configs=[
+        triton.Config(
+            {
+                'BLOCK_M': 128,
+                'BLOCK_N': 128,
+                'SEQUENCE_PARALLEL': False
+            },
+            num_warps=8,
+            num_stages=1,
+            pre_hook=init_to_zero('DQ')),
+        triton.Config(
+            {
+                'BLOCK_M': 128,
+                'BLOCK_N': 128,
+                'SEQUENCE_PARALLEL': True
+            },
+            num_warps=8,
+            num_stages=1,
+            pre_hook=init_to_zero('DQ')),
+        # Other configs seem to give wrong results when seqlen_q % 128 != 0, disabling them for now
+        # # Kernel is buggy (give wrong result) if we set BLOCK_m=128, BLOCK_n=64, num_warps=*4*
+        # triton.Config({"BLOCK_M": 128, "BLOCK_N": 64, "SEQUENCE_PARALLEL": False}, num_warps=8, num_stages=1, pre_hook=init_to_zero('DQ')),
+        # triton.Config({"BLOCK_M": 128, "BLOCK_N": 64, "SEQUENCE_PARALLEL": True}, num_warps=8, num_stages=1, pre_hook=init_to_zero('DQ')),
+        # triton.Config({"BLOCK_M": 64, "BLOCK_N": 64, "SEQUENCE_PARALLEL": False}, num_warps=4, num_stages=1, pre_hook=init_to_zero('DQ')),
+        # triton.Config({"BLOCK_M": 64, "BLOCK_N": 64, "SEQUENCE_PARALLEL": True}, num_warps=4, num_stages=1, pre_hook=init_to_zero('DQ')),
+    ],
+    key=[
+        'CACHE_KEY_SEQLEN_Q', 'CACHE_KEY_SEQLEN_K', 'BIAS_TYPE', 'IS_CAUSAL',
+        'BLOCK_HEADDIM'
+    ],
+)
+@triton.heuristics({
+    'EVEN_M': lambda args: args['seqlen_q'] % args['BLOCK_M'] == 0,
+    'EVEN_N': lambda args: args['seqlen_k'] % args['BLOCK_N'] == 0,
+    'EVEN_HEADDIM': lambda args: args['headdim'] == args['BLOCK_HEADDIM'],
+})
+@triton.jit
+def _bwd_kernel(
+    Q,
+    K,
+    V,
+    Bias,
+    DO,
+    DQ,
+    DK,
+    DV,
+    LSE,
+    D,
+    softmax_scale,
+    stride_qb,
+    stride_qh,
+    stride_qm,
+    stride_kb,
+    stride_kh,
+    stride_kn,
+    stride_vb,
+    stride_vh,
+    stride_vn,
+    stride_bb,
+    stride_bh,
+    stride_bm,
+    stride_dob,
+    stride_doh,
+    stride_dom,
+    stride_dqb,
+    stride_dqh,
+    stride_dqm,
+    stride_dkb,
+    stride_dkh,
+    stride_dkn,
+    stride_dvb,
+    stride_dvh,
+    stride_dvn,
+    nheads,
+    seqlen_q,
+    seqlen_k,
+    seqlen_q_rounded,
+    headdim,
+    CACHE_KEY_SEQLEN_Q,
+    CACHE_KEY_SEQLEN_K,
+    BIAS_TYPE: tl.constexpr,
+    IS_CAUSAL: tl.constexpr,
+    BLOCK_HEADDIM: tl.constexpr,
+    SEQUENCE_PARALLEL: tl.constexpr,
+    EVEN_M: tl.constexpr,
+    EVEN_N: tl.constexpr,
+    EVEN_HEADDIM: tl.constexpr,
+    BLOCK_M: tl.constexpr,
+    BLOCK_N: tl.constexpr,
+):
+    off_hb = tl.program_id(1)
+    off_b = off_hb // nheads
+    off_h = off_hb % nheads
+    # offset pointers for batch/head
+    Q += off_b * stride_qb + off_h * stride_qh
+    K += off_b * stride_kb + off_h * stride_kh
+    V += off_b * stride_vb + off_h * stride_vh
+    DO += off_b * stride_dob + off_h * stride_doh
+    DQ += off_b * stride_dqb + off_h * stride_dqh
+    DK += off_b * stride_dkb + off_h * stride_dkh
+    DV += off_b * stride_dvb + off_h * stride_dvh
+    if BIAS_TYPE != 'none':
+        Bias += off_b * stride_bb + off_h * stride_bh
+    # pointer to row-wise quantities in value-like data
+    D += off_hb * seqlen_q_rounded
+    LSE += off_hb * seqlen_q_rounded
+    if not SEQUENCE_PARALLEL:
+        num_block_n = tl.cdiv(seqlen_k, BLOCK_N)
+        for start_n in range(0, num_block_n):
+            _bwd_kernel_one_col_block(start_n,
+                                      Q,
+                                      K,
+                                      V,
+                                      Bias,
+                                      DO,
+                                      DQ,
+                                      DK,
+                                      DV,
+                                      LSE,
+                                      D,
+                                      softmax_scale,
+                                      stride_qm,
+                                      stride_kn,
+                                      stride_vn,
+                                      stride_bm,
+                                      stride_dom,
+                                      stride_dqm,
+                                      stride_dkn,
+                                      stride_dvn,
+                                      seqlen_q,
+                                      seqlen_k,
+                                      headdim,
+                                      ATOMIC_ADD=False,
+                                      BIAS_TYPE=BIAS_TYPE,
+                                      IS_CAUSAL=IS_CAUSAL,
+                                      BLOCK_HEADDIM=BLOCK_HEADDIM,
+                                      EVEN_M=EVEN_M,
+                                      EVEN_N=EVEN_N,
+                                      EVEN_HEADDIM=EVEN_HEADDIM,
+                                      BLOCK_M=BLOCK_M,
+                                      BLOCK_N=BLOCK_N)
+    else:
+        start_n = tl.program_id(0)
+        _bwd_kernel_one_col_block(start_n,
+                                  Q,
+                                  K,
+                                  V,
+                                  Bias,
+                                  DO,
+                                  DQ,
+                                  DK,
+                                  DV,
+                                  LSE,
+                                  D,
+                                  softmax_scale,
+                                  stride_qm,
+                                  stride_kn,
+                                  stride_vn,
+                                  stride_bm,
+                                  stride_dom,
+                                  stride_dqm,
+                                  stride_dkn,
+                                  stride_dvn,
+                                  seqlen_q,
+                                  seqlen_k,
+                                  headdim,
+                                  ATOMIC_ADD=True,
+                                  BIAS_TYPE=BIAS_TYPE,
+                                  IS_CAUSAL=IS_CAUSAL,
+                                  BLOCK_HEADDIM=BLOCK_HEADDIM,
+                                  EVEN_M=EVEN_M,
+                                  EVEN_N=EVEN_N,
+                                  EVEN_HEADDIM=EVEN_HEADDIM,
+                                  BLOCK_M=BLOCK_M,
+                                  BLOCK_N=BLOCK_N)
+
+
+def _flash_attn_forward(q, k, v, bias=None, causal=False, softmax_scale=None):
+    # shape constraints
+    batch, seqlen_q, nheads, d = q.shape
+    _, seqlen_k, _, _ = k.shape
+    assert k.shape == (batch, seqlen_k, nheads, d)
+    assert v.shape == (batch, seqlen_k, nheads, d)
+    assert d <= 128, 'FlashAttention only support head dimensions up to 128'
+    assert q.dtype == k.dtype == v.dtype, 'All tensors must have the same type'
+    assert q.dtype in [torch.float16,
+                       torch.bfloat16], 'Only support fp16 and bf16'
+    assert q.is_cuda and k.is_cuda and v.is_cuda
+    softmax_scale = softmax_scale or 1.0 / math.sqrt(d)
+
+    has_bias = bias is not None
+    bias_type = 'none'
+    if has_bias:
+        assert bias.dtype in [q.dtype, torch.float]
+        assert bias.is_cuda
+        assert bias.dim() == 4
+        if bias.stride(-1) != 1:
+            bias = bias.contiguous()
+        if bias.shape[2:] == (1, seqlen_k):
+            bias_type = 'vector'
+        elif bias.shape[2:] == (seqlen_q, seqlen_k):
+            bias_type = 'matrix'
+        else:
+            raise RuntimeError('Last 2 dimensions of bias must be (1, seqlen_k)'
+                               ' or (seqlen_q, seqlen_k)')
+        if bias.shape[:2] == (1, nheads):
+            bias = repeat(bias, '1 h ... -> b h ...', b=batch)
+        elif bias.shape[:2] == (batch, 1):
+            bias = repeat(bias, 'b 1 ... -> b h ...', h=nheads)
+        elif bias.shape[:2] == (1, 1):
+            bias = repeat(bias, '1 h ... -> b h ...', b=batch)
+            bias = repeat(bias, 'b 1 ... -> b h ...', h=nheads)
+        assert bias.shape[:2] == (
+            batch, nheads
+        ), f'First 2 dimensions of bias must be broadcastible to (batch, nheads) = ({batch, nheads}). Bias has shape: {bias.shape}'
+    assert bias is not None  # for type checking
+    bias_strides = (bias.stride(0), bias.stride(1),
+                    bias.stride(2)) if has_bias else (0, 0, 0)
+
+    seqlen_q_rounded = math.ceil(seqlen_q / 128) * 128
+    lse = torch.empty((batch, nheads, seqlen_q_rounded),
+                      device=q.device,
+                      dtype=torch.float32)
+    tmp = torch.empty((batch, nheads, seqlen_q_rounded),
+                      device=q.device,
+                      dtype=torch.float32)
+    o = torch.empty_like(q)
+
+    BLOCK_HEADDIM = max(triton.next_power_of_2(d), 16)
+    # BLOCK = 128
+    # num_warps = 4 if d <= 64 else 8
+    grid = lambda META: (triton.cdiv(seqlen_q, META['BLOCK_M']), batch * nheads)
+    _fwd_kernel[grid](  # type: ignore
+        q,
+        k,
+        v,
+        bias,
+        o,
+        lse,
+        tmp,
+        softmax_scale,
+        q.stride(0),
+        q.stride(2),
+        q.stride(1),
+        k.stride(0),
+        k.stride(2),
+        k.stride(1),
+        v.stride(0),
+        v.stride(2),
+        v.stride(1),
+        *bias_strides,
+        o.stride(0),
+        o.stride(2),
+        o.stride(1),
+        nheads,
+        seqlen_q,
+        seqlen_k,
+        seqlen_q_rounded,
+        d,
+        seqlen_q // 32,
+        seqlen_k // 32,  # key for triton cache (limit number of compilations)
+        # Can't use kwargs here because triton autotune expects key to be args, not kwargs
+        # IS_CAUSAL=causal, BLOCK_HEADDIM=d,
+        bias_type,
+        causal,
+        BLOCK_HEADDIM,
+        # BLOCK_M=BLOCK, BLOCK_N=BLOCK,
+        # num_warps=num_warps,
+        # num_stages=1,
+    )
+    return o, lse, softmax_scale  # softmax_scale could have been updated
+
+
+def _flash_attn_backward(do,
+                         q,
+                         k,
+                         v,
+                         o,
+                         lse,
+                         dq,
+                         dk,
+                         dv,
+                         bias=None,
+                         causal=False,
+                         softmax_scale=None):
+    # Make sure that the last dimension is contiguous
+    if do.stride(-1) != 1:
+        do = do.contiguous()
+    batch, seqlen_q, nheads, d = q.shape
+    _, seqlen_k, _, _ = k.shape
+    # assert d in {16, 32, 64, 128}
+    assert d <= 128
+    seqlen_q_rounded = math.ceil(seqlen_q / 128) * 128
+    assert lse.shape == (batch, nheads, seqlen_q_rounded)
+    assert q.stride(-1) == k.stride(-1) == v.stride(-1) == o.stride(-1) == 1
+    assert dq.stride(-1) == dk.stride(-1) == dv.stride(-1) == 1
+    softmax_scale = softmax_scale or 1.0 / math.sqrt(d)
+    # dq_accum = torch.zeros_like(q, dtype=torch.float32)
+    dq_accum = torch.empty_like(q, dtype=torch.float32)
+    delta = torch.empty_like(lse)
+    # delta = torch.zeros_like(lse)
+
+    BLOCK_HEADDIM = max(triton.next_power_of_2(d), 16)
+    grid = lambda META: (triton.cdiv(seqlen_q, META['BLOCK_M']), batch * nheads)
+    _bwd_preprocess_do_o_dot[grid](  # type: ignore
+        o,
+        do,
+        delta,
+        o.stride(0),
+        o.stride(2),
+        o.stride(1),
+        do.stride(0),
+        do.stride(2),
+        do.stride(1),
+        nheads,
+        seqlen_q,
+        seqlen_q_rounded,
+        d,
+        BLOCK_M=128,
+        BLOCK_HEADDIM=BLOCK_HEADDIM,
+    )
+
+    has_bias = bias is not None
+    bias_type = 'none'
+    if has_bias:
+        assert bias.dtype in [q.dtype, torch.float]
+        assert bias.is_cuda
+        assert bias.dim() == 4
+        assert bias.stride(-1) == 1
+        if bias.shape[2:] == (1, seqlen_k):
+            bias_type = 'vector'
+        elif bias.shape[2:] == (seqlen_q, seqlen_k):
+            bias_type = 'matrix'
+        else:
+            raise RuntimeError('Last 2 dimensions of bias must be (1, seqlen_k)'
+                               ' or (seqlen_q, seqlen_k)')
+        if bias.shape[:2] == (1, nheads):
+            bias = repeat(bias, '1 h ... -> b h ...', b=batch)
+        elif bias.shape[:2] == (batch, 1):
+            bias = repeat(bias, 'b 1 ... -> b h ...', h=nheads)
+        elif bias.shape[:2] == (1, 1):
+            bias = repeat(bias, '1 h ... -> b h ...', b=batch)
+            bias = repeat(bias, 'b 1 ... -> b h ...', h=nheads)
+        assert bias.shape[:2] == (
+            batch, nheads
+        ), f'First 2 dimensions of bias must be broadcastible to (batch, nheads) = ({batch, nheads}). Bias has shape: {bias.shape}'
+    assert bias is not None  # type checking
+    bias_strides = (bias.stride(0), bias.stride(1),
+                    bias.stride(2)) if has_bias else (0, 0, 0)
+
+    # BLOCK_M = 128
+    # BLOCK_N = 64
+    # num_warps = 4
+    grid = lambda META: (triton.cdiv(seqlen_k, META['BLOCK_N'])
+                         if META['SEQUENCE_PARALLEL'] else 1, batch * nheads)
+    _bwd_kernel[grid](  # type: ignore
+        q,
+        k,
+        v,
+        bias,
+        do,
+        dq_accum,
+        dk,
+        dv,
+        lse,
+        delta,
+        softmax_scale,
+        q.stride(0),
+        q.stride(2),
+        q.stride(1),
+        k.stride(0),
+        k.stride(2),
+        k.stride(1),
+        v.stride(0),
+        v.stride(2),
+        v.stride(1),
+        *bias_strides,
+        do.stride(0),
+        do.stride(2),
+        do.stride(1),
+        dq_accum.stride(0),
+        dq_accum.stride(2),
+        dq_accum.stride(1),
+        dk.stride(0),
+        dk.stride(2),
+        dk.stride(1),
+        dv.stride(0),
+        dv.stride(2),
+        dv.stride(1),
+        nheads,
+        seqlen_q,
+        seqlen_k,
+        seqlen_q_rounded,
+        d,
+        seqlen_q // 32,
+        seqlen_k // 32,  # key for triton cache (limit number of compilations)
+        # Can't use kwargs here because triton autotune expects key to be args, not kwargs
+        # IS_CAUSAL=causal, BLOCK_HEADDIM=d,
+        bias_type,
+        causal,
+        BLOCK_HEADDIM,
+        # SEQUENCE_PARALLEL=False,
+        # BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N,
+        # num_warps=num_warps,
+        # num_stages=1,
+    )
+    dq.copy_(dq_accum)
+
+
+class _FlashAttnQKVPackedFunc(torch.autograd.Function):
+
+    @staticmethod
+    def forward(ctx, qkv, bias=None, causal=False, softmax_scale=None):
+        """Forward pass for packed FlashAttention.
+
+        Args:
+            ctx: autograd context
+            qkv: (batch, seqlen, 3, nheads, headdim)
+            bias: optional, shape broadcastible to (batch, nheads, seqlen, seqlen).
+                For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen).
+                ALiBi mask for non-causal would have shape (1, nheads, seqlen, seqlen)
+            causal (bool): whether to incorporate causal attention masking
+            softmax_scale (float, optional): scale factor for softmax
+        """
+        # Make sure that the last dimension is contiguous
+        if qkv.stride(-1) != 1:
+            qkv = qkv.contiguous()
+        o, lse, ctx.softmax_scale = _flash_attn_forward(
+            qkv[:, :, 0],
+            qkv[:, :, 1],
+            qkv[:, :, 2],
+            bias=bias,
+            causal=causal,
+            softmax_scale=softmax_scale)
+        ctx.save_for_backward(qkv, o, lse, bias)
+        ctx.causal = causal
+        return o
+
+    @staticmethod
+    def backward(ctx, do):
+        qkv, o, lse, bias = ctx.saved_tensors
+        assert not ctx.needs_input_grad[
+            1], 'FlashAttention does not support bias gradient yet'
+        # Triton's autotune causes the Tensor._version to change, and so Pytorch autograd
+        # does a memcpy. To avoid this we run in inference_mode, which doesn't track the version.
+        with torch.inference_mode():
+            dqkv = torch.empty_like(qkv)
+            _flash_attn_backward(do,
+                                 qkv[:, :, 0],
+                                 qkv[:, :, 1],
+                                 qkv[:, :, 2],
+                                 o,
+                                 lse,
+                                 dqkv[:, :, 0],
+                                 dqkv[:, :, 1],
+                                 dqkv[:, :, 2],
+                                 bias=bias,
+                                 causal=ctx.causal,
+                                 softmax_scale=ctx.softmax_scale)
+        return dqkv, None, None, None
+
+
+flash_attn_qkvpacked_func = _FlashAttnQKVPackedFunc.apply
+
+
+class _FlashAttnFunc(torch.autograd.Function):
+
+    @staticmethod
+    def forward(ctx, q, k, v, bias=None, causal=False, softmax_scale=None):
+        """Forward pass for FlashAttention.
+
+        Args:
+            ctx: autograd context
+            q: (batch_size, seqlen_q, nheads, headdim)
+            k: (batch_size, seqlen_k, nheads, headdim)
+            v: (batch_size, seqlen_k, nheads, headdim)
+            bias: optional, shape broadcastible to (batch, nheads, seqlen_q, seqlen_k).
+                For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen_k).
+                ALiBi mask for non-causal would have shape (1, nheads, seqlen_q, seqlen_k)
+            causal (bool): whether to incorporate causal attention masking
+            softmax_scale (float, optional): scale factor for softmax
+        """
+        # Make sure that the last dimension is contiguous
+        q, k, v = [
+            x if x.stride(-1) == 1 else x.contiguous() for x in [q, k, v]
+        ]
+        o, lse, ctx.softmax_scale = _flash_attn_forward(
+            q, k, v, bias=bias, causal=causal, softmax_scale=softmax_scale)
+        ctx.save_for_backward(q, k, v, o, lse, bias)
+        ctx.causal = causal
+        return o
+
+    @staticmethod
+    def backward(ctx, do):
+        q, k, v, o, lse, bias = ctx.saved_tensors
+        assert not ctx.needs_input_grad[
+            3], 'FlashAttention does not support bias gradient yet'
+        # Triton's autotune causes the Tensor._version to change, and so Pytorch autograd
+        # does a memcpy. To avoid this we run in inference_mode, which doesn't track the version.
+        with torch.inference_mode():
+            dq = torch.empty_like(q)
+            dk = torch.empty_like(k)
+            dv = torch.empty_like(v)
+            _flash_attn_backward(do,
+                                 q,
+                                 k,
+                                 v,
+                                 o,
+                                 lse,
+                                 dq,
+                                 dk,
+                                 dv,
+                                 bias=bias,
+                                 causal=ctx.causal,
+                                 softmax_scale=ctx.softmax_scale)
+        return dq, dk, dv, None, None, None
+
+
+flash_attn_func = _FlashAttnFunc.apply