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code/model.py

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+"""Simple, minimal implementation of Mamba in one file of PyTorch.
+
+Suggest reading the following before/while reading the code:
+    [1] Mamba: Linear-Time Sequence Modeling with Selective State Spaces (Albert Gu and Tri Dao)
+        https://arxiv.org/abs/2312.00752
+    [2] The Annotated S4 (Sasha Rush and Sidd Karamcheti)
+        https://srush.github.io/annotated-s4
+
+Glossary:
+    b: batch size                       (`B` in Mamba paper [1] Algorithm 2)
+    l: sequence length                  (`L` in [1] Algorithm 2)
+    d or d_model: hidden dim
+    n or d_state: latent state dim      (`N` in [1] Algorithm 2)
+    expand: expansion factor            (`E` in [1] Section 3.4)
+    d_in or d_inner: d * expand         (`D` in [1] Algorithm 2)
+    A, B, C, D: state space parameters  (See any state space representation formula)
+                                        (B, C are input-dependent (aka selective, a key innovation in Mamba); A, D are not)
+    Δ or delta: input-dependent step size
+    dt_rank: rank of Δ                  (See [1] Section 3.6 "Parameterization of ∆")
+
+"""
+from __future__ import annotations
+import math
+import json
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from dataclasses import dataclass
+from typing import Union
+from einops import rearrange, repeat, einsum
+from parallel_scan import pscan
+
+
+@dataclass
+class ModelArgs:
+    d_model: int
+    n_layer: int
+    vocab_size: int
+    d_state: int = 16
+    expand: int = 2
+    dt_rank: Union[int, str] = 'auto'
+    d_conv: int = 4 
+    pad_vocab_size_multiple: int = 8
+    conv_bias: bool = True
+    bias: bool = False
+    
+    def __post_init__(self):
+        self.d_inner = int(self.expand * self.d_model)
+        
+        if self.dt_rank == 'auto':
+            self.dt_rank = math.ceil(self.d_model / 16)
+            
+        if self.vocab_size % self.pad_vocab_size_multiple != 0:
+            self.vocab_size += (self.pad_vocab_size_multiple
+                                - self.vocab_size % self.pad_vocab_size_multiple)
+
+
+class Mamba(nn.Module):
+    def __init__(self, args: ModelArgs):
+        """Full Mamba model."""
+        super().__init__()
+        self.args = args
+        
+        self.embedding = nn.Embedding(args.vocab_size, args.d_model)
+        self.layers = nn.ModuleList([ResidualBlock(args) for _ in range(args.n_layer)])
+        self.norm_f = RMSNorm(args.d_model)
+
+        self.lm_head = nn.Linear(args.d_model, args.vocab_size, bias=False)
+        self.lm_head.weight = self.embedding.weight  # Tie output projection to embedding weights.
+                                                     # See "Weight Tying" paper
+
+
+    def forward(self, input_ids):
+        """
+        Args:
+            input_ids (long tensor): shape (b, l)    (See Glossary at top for definitions of b, l, d_in, n...)
+    
+        Returns:
+            logits: shape (b, l, vocab_size)
+
+        Official Implementation:
+            class MambaLMHeadModel, https://github.com/state-spaces/mamba/blob/main/mamba_ssm/models/mixer_seq_simple.py#L173
+
+        """
+        x = self.embedding(input_ids)
+        
+        for layer in self.layers:
+            x = layer(x)
+            
+        x = self.norm_f(x)
+        logits = self.lm_head(x)
+
+        return logits
+
+
+    @staticmethod
+    def from_config(pretrained_model_name: str):
+      from transformers.utils import CONFIG_NAME
+      from transformers.utils.hub import cached_file
+      
+      def load_config_hf(model_name):
+          resolved_archive_file = cached_file(model_name, CONFIG_NAME,
+                                              _raise_exceptions_for_missing_entries=False)
+          return json.load(open(resolved_archive_file))
+      config_data = load_config_hf(pretrained_model_name)
+      args = ModelArgs(
+          d_model=config_data['d_model'],
+          n_layer=config_data['n_layer'],
+          vocab_size=config_data['vocab_size']
+      )
+      model = Mamba(args)
+      return model
+
+    
+    @staticmethod
+    def from_pretrained(pretrained_model_name: str):
+        """Load pretrained weights from HuggingFace into model.
+    
+        Args:
+            pretrained_model_name: One of
+                * 'state-spaces/mamba-2.8b-slimpj'
+                * 'state-spaces/mamba-2.8b'
+                * 'state-spaces/mamba-1.4b'
+                * 'state-spaces/mamba-790m'
+                * 'state-spaces/mamba-370m'
+                * 'state-spaces/mamba-130m'
+                            
+        Returns:
+            model: Mamba model with weights loaded
+    
+        """
+        from transformers.utils import WEIGHTS_NAME, CONFIG_NAME
+        from transformers.utils.hub import cached_file
+        
+        def load_config_hf(model_name):
+            resolved_archive_file = cached_file(model_name, CONFIG_NAME,
+                                                _raise_exceptions_for_missing_entries=False)
+            return json.load(open(resolved_archive_file))
+        
+        
+        def load_state_dict_hf(model_name, device=None, dtype=None):
+            resolved_archive_file = cached_file(model_name, WEIGHTS_NAME,
+                                                _raise_exceptions_for_missing_entries=False)
+            return torch.load(resolved_archive_file, weights_only=True, map_location='cpu', mmap=True)
+        
+        config_data = load_config_hf(pretrained_model_name)
+        args = ModelArgs(
+            d_model=config_data['d_model'],
+            n_layer=config_data['n_layer'],
+            vocab_size=config_data['vocab_size']
+        )
+        model = Mamba(args)
+        
+        state_dict = load_state_dict_hf(pretrained_model_name)
+        new_state_dict = {}
+        for key in state_dict:
+            new_key = key.replace('backbone.', '')
+            new_state_dict[new_key] = state_dict[key]
+        model.load_state_dict(new_state_dict)
+        
+        return model
+
+
+class ResidualBlock(nn.Module):
+    def __init__(self, args: ModelArgs):
+        """Simple block wrapping Mamba block with normalization and residual connection."""
+        super().__init__()
+        self.args = args
+        self.mixer = MambaBlock(args)
+        self.norm = RMSNorm(args.d_model)
+        
+
+    def forward(self, x):
+        """
+        Args:
+            x: shape (b, l, d)    (See Glossary at top for definitions of b, l, d_in, n...)
+    
+        Returns:
+            output: shape (b, l, d)
+
+        Official Implementation:
+            Block.forward(), https://github.com/state-spaces/mamba/blob/main/mamba_ssm/modules/mamba_simple.py#L297
+            
+            Note: the official repo chains residual blocks that look like
+                [Add -> Norm -> Mamba] -> [Add -> Norm -> Mamba] -> [Add -> Norm -> Mamba] -> ...
+            where the first Add is a no-op. This is purely for performance reasons as this
+            allows them to fuse the Add->Norm.
+
+            We instead implement our blocks as the more familiar, simpler, and numerically equivalent
+                [Norm -> Mamba -> Add] -> [Norm -> Mamba -> Add] -> [Norm -> Mamba -> Add] -> ....
+            
+        """
+        output = self.mixer(self.norm(x)) + x
+
+        return output
+            
+
+class MambaBlock(nn.Module):
+    def __init__(self, args: ModelArgs):
+        """A single Mamba block, as described in Figure 3 in Section 3.4 in the Mamba paper [1]."""
+        super().__init__()
+        self.args = args
+
+        self.in_proj = nn.Linear(args.d_model, args.d_inner * 2, bias=args.bias)
+
+        self.conv1d = nn.Conv1d(
+            in_channels=args.d_inner,
+            out_channels=args.d_inner,
+            bias=args.conv_bias,
+            kernel_size=args.d_conv,
+            groups=args.d_inner,
+            padding=args.d_conv - 1,
+        )
+
+        # x_proj takes in `x` and outputs the input-specific Δ, B, C
+        self.x_proj = nn.Linear(args.d_inner, args.dt_rank + args.d_state * 2, bias=False)
+        
+        # dt_proj projects Δ from dt_rank to d_in
+        self.dt_proj = nn.Linear(args.dt_rank, args.d_inner, bias=True)
+
+        A = repeat(torch.arange(1, args.d_state + 1), 'n -> d n', d=args.d_inner)
+        self.A_log = nn.Parameter(torch.log(A))
+        self.D = nn.Parameter(torch.ones(args.d_inner))
+        self.out_proj = nn.Linear(args.d_inner, args.d_model, bias=args.bias)
+        
+
+    def forward(self, x):
+        """Mamba block forward. This looks the same as Figure 3 in Section 3.4 in the Mamba paper [1].
+    
+        Args:
+            x: shape (b, l, d)    (See Glossary at top for definitions of b, l, d_in, n...)
+    
+        Returns:
+            output: shape (b, l, d)
+        
+        Official Implementation:
+            class Mamba, https://github.com/state-spaces/mamba/blob/main/mamba_ssm/modules/mamba_simple.py#L119
+            mamba_inner_ref(), https://github.com/state-spaces/mamba/blob/main/mamba_ssm/ops/selective_scan_interface.py#L311
+            
+        """
+        (b, l, d) = x.shape
+        
+        x_and_res = self.in_proj(x)  # shape (b, l, 2 * d_in)
+        (x, res) = x_and_res.split(split_size=[self.args.d_inner, self.args.d_inner], dim=-1)
+
+        x = rearrange(x, 'b l d_in -> b d_in l')
+        x = self.conv1d(x)[:, :, :l]
+        x = rearrange(x, 'b d_in l -> b l d_in')
+        
+        x = F.silu(x)
+
+        y = self.ssm(x)
+        
+        y = y * F.silu(res)
+        
+        output = self.out_proj(y)
+
+        return output
+
+    
+    def ssm(self, x):
+        """Runs the SSM. See:
+            - Algorithm 2 in Section 3.2 in the Mamba paper [1]
+            - run_SSM(A, B, C, u) in The Annotated S4 [2]
+
+        Args:
+            x: shape (b, l, d_in)    (See Glossary at top for definitions of b, l, d_in, n...)
+    
+        Returns:
+            output: shape (b, l, d_in)
+
+        Official Implementation:
+            mamba_inner_ref(), https://github.com/state-spaces/mamba/blob/main/mamba_ssm/ops/selective_scan_interface.py#L311
+            
+        """
+        (d_in, n) = self.A_log.shape
+
+        # Compute ∆ A B C D, the state space parameters.
+        #     A, D are input independent (see Mamba paper [1] Section 3.5.2 "Interpretation of A" for why A isn't selective)
+        #     ∆, B, C are input-dependent (this is a key difference between Mamba and the linear time invariant S4,
+        #                                  and is why Mamba is called **selective** state spaces)
+        
+        A = -torch.exp(self.A_log.float())  # shape (d_in, n)
+        D = self.D.float()
+
+        x_dbl = self.x_proj(x)  # (b, l, dt_rank + 2*n)
+        
+        (delta, B, C) = x_dbl.split(split_size=[self.args.dt_rank, n, n], dim=-1)  # delta: (b, l, dt_rank). B, C: (b, l, n)
+        delta = F.softplus(self.dt_proj(delta))  # (b, l, d_in)
+        
+        y = self.selective_scan(x, delta, A, B, C, D)  # This is similar to run_SSM(A, B, C, u) in The Annotated S4 [2]
+        
+        return y
+
+    
+    def selective_scan(self, x, delta, A, B, C, D):
+        """Does selective scan algorithm. See:
+            - Section 2 State Space Models in the Mamba paper [1]
+            - Algorithm 2 in Section 3.2 in the Mamba paper [1]
+            - run_SSM(A, B, C, u) in The Annotated S4 [2]
+
+        This is the classic discrete state space formula:
+            x(t + 1) = Ax(t) + Bu(t)
+            y(t)     = Cx(t) + Du(t)
+        except B and C (and the step size delta, which is used for discretization) are dependent on the input x(t).
+    
+        Args:
+            u: shape (b, l, d_in)    (See Glossary at top for definitions of b, l, d_in, n...)
+            delta: shape (b, l, d_in)
+            A: shape (d_in, n)
+            B: shape (b, l, n)
+            C: shape (b, l, n)
+            D: shape (d_in,)
+    
+        Returns:
+            output: shape (b, l, d_in)
+    
+        Official Implementation:
+            selective_scan_ref(), https://github.com/state-spaces/mamba/blob/main/mamba_ssm/ops/selective_scan_interface.py#L86
+            Note: I refactored some parts out of `selective_scan_ref` out, so the functionality doesn't match exactly.
+            
+        """
+        # sequential scan
+        # (b, l, d_in) = u.shape
+        # n = A.shape[1]
+        
+        # # Discretize continuous parameters (A, B)
+        # # - A is discretized using zero-order hold (ZOH) discretization (see Section 2 Equation 4 in the Mamba paper [1])
+        # # - B is discretized using a simplified Euler discretization instead of ZOH. From a discussion with authors:
+        # #   "A is the more important term and the performance doesn't change much with the simplification on B"
+        # deltaA = torch.exp(einsum(delta, A, 'b l d_in, d_in n -> b l d_in n'))
+        # deltaB_u = einsum(delta, B, u, 'b l d_in, b l n, b l d_in -> b l d_in n')
+        
+        # # Perform selective scan (see scan_SSM() in The Annotated S4 [2])
+        # # Note that the below is sequential, while the official implementation does a much faster parallel scan that
+        # # is additionally hardware-aware (like FlashAttention).
+        # x = torch.zeros((b, d_in, n), device=deltaA.device)
+        # ys = []    
+        # for i in range(l):
+        #     x = deltaA[:, i] * x + deltaB_u[:, i]
+        #     y = einsum(x, C[:, i, :], 'b d_in n, b n -> b d_in')
+        #     ys.append(y)
+        # y = torch.stack(ys, dim=1)  # shape (b, l, d_in)
+        
+        # y = y + u * D
+    
+        # return y
+        # parallel scan
+        deltaA = torch.exp(delta.unsqueeze(-1) * A) # (B, L, ED, N)
+        deltaB = delta.unsqueeze(-1) * B.unsqueeze(2) # (B, L, ED, N)
+
+        BX = deltaB * (x.unsqueeze(-1)) # (B, L, ED, N)
+        
+        hs = pscan(deltaA, BX)
+
+        y = (hs @ C.unsqueeze(-1)).squeeze(3) # (B, L, ED, N) @ (B, L, N, 1) -> (B, L, ED, 1)
+
+        y = y + D * x
+
+        return y
+
+
+class RMSNorm(nn.Module):
+    def __init__(self,
+                 d_model: int,
+                 eps: float = 1e-5):
+        super().__init__()
+        self.eps = eps
+        self.weight = nn.Parameter(torch.ones(d_model))
+
+
+    def forward(self, x):
+        output = x * torch.rsqrt(x.pow(2).mean(-1, keepdim=True) + self.eps) * self.weight
+
+        return output        

code/parallel_scan.py

@@ -0,0 +1,226 @@
+import math
+
+import torch
+import torch.nn.functional as F
+
+"""
+
+An implementation of the parallel scan operation in PyTorch (Blelloch version).
+Please see docs/pscan.ipynb for a detailed explanation of what happens here.
+
+"""
+
+def npo2(len):
+    """
+    Returns the next power of 2 above len
+    """
+
+    return 2 ** math.ceil(math.log2(len))
+
+def pad_npo2(X):
+    """
+    Pads input length dim to the next power of 2
+
+    Args:
+        X : (B, L, D, N)
+
+    Returns:
+        Y : (B, npo2(L), D, N)
+    """
+
+    len_npo2 = npo2(X.size(1))
+    pad_tuple = (0, 0, 0, 0, 0, len_npo2 - X.size(1))
+    return F.pad(X, pad_tuple, "constant", 0)
+
+class PScan(torch.autograd.Function):
+    @staticmethod
+    def pscan(A, X):
+        # A : (B, D, L, N)
+        # X : (B, D, L, N)
+
+        # modifies X in place by doing a parallel scan.
+        # more formally, X will be populated by these values :
+        # H[t] = A[t] * H[t-1] + X[t] with H[0] = 0
+        # which are computed in parallel (2*log2(T) sequential steps (ideally), instead of T sequential steps)
+
+        # only supports L that is a power of two (mainly for a clearer code)
+        
+        B, D, L, _ = A.size()
+        num_steps = int(math.log2(L))
+
+        # up sweep (last 2 steps unfolded)
+        Aa = A
+        Xa = X
+        for _ in range(num_steps-2):
+            T = Xa.size(2)
+            Aa = Aa.view(B, D, T//2, 2, -1)
+            Xa = Xa.view(B, D, T//2, 2, -1)
+            
+            Xa[:, :, :, 1].add_(Aa[:, :, :, 1].mul(Xa[:, :, :, 0]))
+            Aa[:, :, :, 1].mul_(Aa[:, :, :, 0])
+
+            Aa = Aa[:, :, :, 1]
+            Xa = Xa[:, :, :, 1]
+
+        # we have only 4, 2 or 1 nodes left
+        if Xa.size(2) == 4:
+            Xa[:, :, 1].add_(Aa[:, :, 1].mul(Xa[:, :, 0]))
+            Aa[:, :, 1].mul_(Aa[:, :, 0])
+
+            Xa[:, :, 3].add_(Aa[:, :, 3].mul(Xa[:, :, 2] + Aa[:, :, 2].mul(Xa[:, :, 1])))
+        elif Xa.size(2) == 2:
+            Xa[:, :, 1].add_(Aa[:, :, 1].mul(Xa[:, :, 0]))
+            return
+        else:
+            return
+
+        # down sweep (first 2 steps unfolded)
+        Aa = A[:, :, 2**(num_steps-2)-1:L:2**(num_steps-2)]
+        Xa = X[:, :, 2**(num_steps-2)-1:L:2**(num_steps-2)]
+        Xa[:, :, 2].add_(Aa[:, :, 2].mul(Xa[:, :, 1]))
+        Aa[:, :, 2].mul_(Aa[:, :, 1])
+
+        for k in range(num_steps-3, -1, -1):
+            Aa = A[:, :, 2**k-1:L:2**k]
+            Xa = X[:, :, 2**k-1:L:2**k]
+
+            T = Xa.size(2)
+            Aa = Aa.view(B, D, T//2, 2, -1)
+            Xa = Xa.view(B, D, T//2, 2, -1)
+
+            Xa[:, :, 1:, 0].add_(Aa[:, :, 1:, 0].mul(Xa[:, :, :-1, 1]))
+            Aa[:, :, 1:, 0].mul_(Aa[:, :, :-1, 1])
+
+    @staticmethod
+    def pscan_rev(A, X):
+        # A : (B, D, L, N)
+        # X : (B, D, L, N)
+
+        # the same function as above, but in reverse
+        # (if you flip the input, call pscan, then flip the output, you get what this function outputs)
+        # it is used in the backward pass
+
+        # only supports L that is a power of two (mainly for a clearer code)
+
+        B, D, L, _ = A.size()
+        num_steps = int(math.log2(L))
+
+        # up sweep (last 2 steps unfolded)
+        Aa = A
+        Xa = X
+        for _ in range(num_steps-2):
+            T = Xa.size(2)
+            Aa = Aa.view(B, D, T//2, 2, -1)
+            Xa = Xa.view(B, D, T//2, 2, -1)
+                    
+            Xa[:, :, :, 0].add_(Aa[:, :, :, 0].mul(Xa[:, :, :, 1]))
+            Aa[:, :, :, 0].mul_(Aa[:, :, :, 1])
+
+            Aa = Aa[:, :, :, 0]
+            Xa = Xa[:, :, :, 0]
+
+        # we have only 4, 2 or 1 nodes left
+        if Xa.size(2) == 4:
+            Xa[:, :, 2].add_(Aa[:, :, 2].mul(Xa[:, :, 3]))
+            Aa[:, :, 2].mul_(Aa[:, :, 3])
+
+            Xa[:, :, 0].add_(Aa[:, :, 0].mul(Xa[:, :, 1].add(Aa[:, :, 1].mul(Xa[:, :, 2]))))
+        elif Xa.size(2) == 2:
+            Xa[:, :, 0].add_(Aa[:, :, 0].mul(Xa[:, :, 1]))
+            return
+        else:
+            return
+
+        # down sweep (first 2 steps unfolded)
+        Aa = A[:, :, 0:L:2**(num_steps-2)]
+        Xa = X[:, :, 0:L:2**(num_steps-2)]
+        Xa[:, :, 1].add_(Aa[:, :, 1].mul(Xa[:, :, 2]))
+        Aa[:, :, 1].mul_(Aa[:, :, 2])
+
+        for k in range(num_steps-3, -1, -1):
+            Aa = A[:, :, 0:L:2**k]
+            Xa = X[:, :, 0:L:2**k]
+
+            T = Xa.size(2)
+            Aa = Aa.view(B, D, T//2, 2, -1)
+            Xa = Xa.view(B, D, T//2, 2, -1)
+
+            Xa[:, :, :-1, 1].add_(Aa[:, :, :-1, 1].mul(Xa[:, :, 1:, 0]))
+            Aa[:, :, :-1, 1].mul_(Aa[:, :, 1:, 0])
+
+    @staticmethod
+    def forward(ctx, A_in, X_in):
+        """
+        Applies the parallel scan operation, as defined above. Returns a new tensor.
+        If you can, privilege sequence lengths that are powers of two.
+
+        Args:
+            A_in : (B, L, D, N)
+            X_in : (B, L, D, N)
+
+        Returns:
+            H : (B, L, D, N)
+        """
+
+        L = X_in.size(1)
+
+        # cloning is requiered because of the in-place ops
+        if L == npo2(L):
+            A = A_in.clone()
+            X = X_in.clone()
+        else:
+            # pad tensors (and clone btw)
+            A = pad_npo2(A_in) # (B, npo2(L), D, N)
+            X = pad_npo2(X_in) # (B, npo2(L), D, N)
+        
+        # prepare tensors
+        A = A.transpose(2, 1) # (B, D, npo2(L), N)
+        X = X.transpose(2, 1) # (B, D, npo2(L), N)
+
+        # parallel scan (modifies X in-place)
+        PScan.pscan(A, X)
+
+        ctx.save_for_backward(A_in, X)
+        
+        # slice [:, :L] (cut if there was padding)
+        return X.transpose(2, 1)[:, :L]
+    
+    @staticmethod
+    def backward(ctx, grad_output_in):
+        """
+        Flows the gradient from the output to the input. Returns two new tensors.
+
+        Args:
+            ctx : A_in : (B, L, D, N), X : (B, D, L, N)
+            grad_output_in : (B, L, D, N)
+
+        Returns:
+            gradA : (B, L, D, N), gradX : (B, L, D, N)
+        """
+
+        A_in, X = ctx.saved_tensors
+
+        L = grad_output_in.size(1)
+
+        # cloning is requiered because of the in-place ops
+        if L == npo2(L):
+            grad_output = grad_output_in.clone()
+            # the next padding will clone A_in
+        else:
+            grad_output = pad_npo2(grad_output_in) # (B, npo2(L), D, N)
+            A_in = pad_npo2(A_in) # (B, npo2(L), D, N)
+
+        # prepare tensors
+        grad_output = grad_output.transpose(2, 1)
+        A_in = A_in.transpose(2, 1) # (B, D, npo2(L), N)
+        A = torch.nn.functional.pad(A_in[:, :, 1:], (0, 0, 0, 1)) # (B, D, npo2(L), N) shift 1 to the left (see hand derivation)
+
+        # reverse parallel scan (modifies grad_output in-place)
+        PScan.pscan_rev(A, grad_output)
+
+        Q = torch.zeros_like(X)
+        Q[:, :, 1:].add_(X[:, :, :-1] * grad_output[:, :, 1:])
+
+        return Q.transpose(2, 1)[:, :L], grad_output.transpose(2, 1)[:, :L]
+    
+pscan = PScan.apply