assistant> Hello! Yes, I can definitely help you with that. First, let’s briefly go over the concepts of a Decision Transformer and a Perceiver AR architecture.

A Decision Transformer is an attention-based model that extends the Transformer architecture to perform structured prediction tasks, such as sequence labeling and graph classification. It introduces a new layer, the decision layer, which enables the model to make decisions based on a given context.

A Perceiver AR architecture, on the other hand, is a hybrid architecture that combines the attention mechanism of Transformers with the memory-based approach of associative retrieval (AR). It uses a learned index to map queries to memories and performs attention over them to retrieve the relevant information.

To combine these two ideas, we can use the Perceiver AR architecture as our base model and then add a decision layer on top of it. We can also modify the attention mechanism to incorporate the decision information.

Let’s start with the dataclasses. We’ll create a base class for the Perceiver AR and a subclass for the Decision Transformer. We’ll also define the required parameters for each class.

from dataclasses import dataclass
from typing import Any, List

import torch
import torch.nn as nn

@dataclass
class PerceiverARConfig:
    num_latent_tokens: int
    num_memory_tokens: int
    num_dimensions: int
    num_heads: int
    num_iterations: int
    num_latent_blocks: int
    num_memory_blocks: int
    output_dim: int
    latent_init_std: float = 1.0
    memory_init_std: float = 0.02
    query_init_std: float = 0.02

@dataclass
class DecisionTransformerConfig(PerceiverARConfig):
    num_categories: int

Next, we’ll define the Perceiver AR model using Einops.

class PerceiverAR(nn.Module):
    def __init__(self, config: PerceiverARConfig):
        super().__init__()
        self.latents = nn.Parameter(torch.randn(config.num_latent_tokens, config.num_dimensions) * config.latent_init_std)
        self.memories = nn.Parameter(torch.randn(config.num_memory_tokens, config.num_dimensions) * config.memory_init_std)
        self.queries_weights = nn.Parameter(torch.randn(config.num_dimensions, config.num_heads) * config.query_init_std, requires_grad=True)
        self.keys_weights = nn.Parameter(torch.randn(config.num_dimensions, config.num_heads) * config.query_init_std, requires_grad=True)
        self.values_weights = nn.Parameter(torch.randn(config.num_dimensions, config.num_heads) * config.query_init_std, requires_grad=True)

        self.latent_blocks = nn.ModuleList([
            nn.ModuleList([
                nn.LayerNorm(config.num_dimensions),
                nn.Linear(config.num_dimensions, 4 * config.num_dimensions),
                nn.GELU(),
                nn.Linear(4 * config.num_dimensions, config.num_dimensions),
                nn.GELU(),
            ])
            for _ in range(config.num_latent_blocks)
        ])
        self.memory_blocks = nn.ModuleList([
            nn.ModuleList([
                nn.LayerNorm(config.num_dimensions),
                nn.Linear(config.num_dimensions, 4 * config.num_dimensions),
                nn.GELU(),
                nn.Linear(4 * config.num_dimensions, config.num_dimensions),
                nn.GELU(),
            ])
            for _ in range(config.num_memory_blocks)
        ])

        self.out_block = nn.Sequential(
            nn.LayerNorm(config.num_dimensions),
            nn.Linear(config.num_dimensions, config.output_dim)
        )

    def forward(self, inputs: torch.Tensor) -> torch.Tensor:
        batch_size, seq_len, _ = inputs.shape

        queries = inputs @ self.queries_weights
        keys = self.memories @ self.keys_weights
        values = self.memories @ self.values_weights

        softmax_dim = -1
        queries = queries.permute(1, 0, 2)
        keys = keys.permute(1, 2, 0)
        values = values.permute(1, 2, 0)

        for _ in range(self.num_iterations):
            for latent_block in self.latent_blocks:
                queries += self.latents.unsqueeze(0)

                queries = latent_block[0](queries)
                queries = einops.rearrange(queries, 'b n d -> n b d')

                queries = einops.rearrange(queries, 'n b d -> n b () d')
                keys = einops.rearrange(keys, 'b h n d -> b h n () d')
                values = einops.rearrange(values, 'b h n d -> b h n () d')

                attention = (queries @ keys.transpose(-2, -1))
                attention = attention.softmax(dim=softmax_dim)
                out = attention @ values
                out = einops.rearrange(out, 'n b h m d -> n b (h d m)')

                out = latent_block[1](out)
                out = latent_block[2](out)
                out = latent_block[3](out)
                out = latent_block[4](out)

                out = einops.rearrange(out, 'n b () d -> n b d')
                queries += out

            for memory_block in self.memory_blocks:
                queries += inputs

                queries = memory_block[0](queries)
                queries = einops.rearrange(queries, 'b n d -> n b d')

                queries = einops.rearrange(queries, 'n b d -> n b () d')
                keys = einops.rearrange(keys, 'b h n d -> b h n () d')
                values = einops.rearrange(values, 'b h n d -> b h n () d')

                attention = (queries @ keys.transpose(-2, -1))
                attention = attention.softmax(dim=softmax_dim)
                out = attention @ values
                out = einops.rearrange(out, 'n b h m d -> n b (h d m)')

                out = memory_block[1](out)
                out = memory_block[2](out)
                out = memory_block[3](out)
                out = memory_block[4](out)

                out = einops.rearrange(out, 'n b () d -> n b d')
                queries += out

        queries = queries.permute(1, 0, 2)

        return self.out_block(queries[-1])

Finally, we’ll add the decision layer to the model. The decision layer adds an additional output dimension for the decision logits. It also modifies the attention mechanism to include the decision information. Note that we’re using the Decision Transformer’s configuration for this step, as it includes the number of categories for the output.

class DecisionTransformer(PerceiverAR):
    def __init__(self, config: DecisionTransformerConfig):
        super().__init__(config)
        self.decision_weights = nn.Parameter(torch.randn(config.num_dimensions, config.num_categories) * config.query_init_std, requires_grad=True)

    def forward(self, inputs: torch.Tensor) -> List[torch.Tensor]:
        batch_size, seq_len, _ = inputs.shape

        queries = inputs @ self.queries_weights
        keys = self.memories @ self.keys_weights
        values = self.memories @ self.values_weights
        decisions = torch.zeros(batch_size, seq_len, self.num_categories)

        softmax_dim = -1
        queries = queries.permute(1, 0, 2)
        keys = keys.permute(1, 2, 0)
        values = values.permute(1, 2, 0)

        for step in range(self.num_iterations):
            for latent_block in self.latent_blocks:
                queries += self.latents.unsqueeze(0)
                decision = decisions[:, step, :]

                queries = latent_block[0](queries)
                queries = einops.rearrange(queries, 'b n d -> n b d')

                queries = einops.rearrange(queries, 'n b d -> n b () d')
                keys = einops.rearrange(keys, 'b h n d -> b h n () d')
                values = einops.rearrange(values, 'b h n d -> b h n () d')
                decision = einops.rearrange(decision, 'b c -> b () () c')

                queries_dec = torch.cat([queries, decision], dim=-1)
                keys_dec = torch.cat([keys, keys], dim=-1)
                values_dec = torch.cat([values, values], dim=-1)

                attention = (queries_dec @ keys_dec.transpose(-2, -1))
                attention = attention / (self.num_dimensions ** 0.5)
                attention = attention.softmax(dim=softmax_dim)

                out = attention @ values_dec
                out = einops.rearrange(out, 'n b h m d -> n b (h d m)')
                out = out[:, :, :self.num_dimensions]  # remove decision information

                out = latent_block[1](out)
                out = latent_block[2](out)
                out = latent_block[3](out)
                out = latent_block[4](out)

                out = einops.rearrange(out, 'n b () d -> n b d')
                queries += out

            for memory_block in self.memory_blocks:
                queries += inputs

                queries = memory_block[0](queries)
                queries = einops.rearrange(queries, 'b n d -> n b d')

                queries = einops.rearrange(queries, 'n b d -> n b () d')
                keys = einops.rearrange(keys, 'b h n d -> b h n () d')
                values = einops.rearrange(values, 'b h n d -> b h n () d')
                decision = einops.rearrange(decision, 'b c -> b () () c')

                queries_dec = torch.cat([queries, decision], dim=-1)
                keys_dec = torch.cat([keys, keys], dim=-1)
                values_dec = torch.cat([values, values], dim=-1)

                attention = (queries_dec @ keys_dec.transpose(-2, -1))
                attention = attention / (self.num_dimensions ** 0.5)
                attention = attention.softmax(dim=softmax_dim)

                out = attention @ values_dec
                out = einops.rearrange(out, 'n b h m d -> n b (h d m)')
                out = out[:, :, :self.num_dimensions]  # remove decision information

                out = memory_block[1](out)
                out = memory_block[2](out)
                out = memory_block[3](out)
                out = memory_block[4](out)

                out = einops.rearrange(out, 'n b () d -> n b d')
                queries += out

            decision_logits = self.out_block(queries[-1]) @ self.decision_weights
            decision_logits = einops.rearrange(decision_logits, 'b n c -> b n () c')
            decisions[:, step, :] = decision_logits.squeeze(1).softmax(dim=-1)

        return [self.out_block(queries[-1]), decisions]

And that’s it! You can now use the Decision Transformer class to perform structured prediction tasks with decision-making capabilities.

assistant> Sure! Here’s an example training code for a mock task using the Decision Transformer model we just defined:

import torch.optim as optim
from torch.utils.data import TensorDataset, DataLoader

# define mock data
input_size = 10  # number of features in input
seq_len = 20  # length of sequence
num_categories = 3  # number of possible decision categories
batch_size = 4

inputs = torch.randn(batch_size, seq_len, input_size)
output_labels = torch.randint(0, num_categories, size=(batch_size, seq_len))

# create dataset and data loader
dataset = TensorDataset(inputs, output_labels)
data_loader = DataLoader(dataset, batch_size=batch_size)

# define model and loss
config = DecisionTransformerConfig(num_latent_tokens=64, num_memory_tokens=64, num_dimensions=256, num_heads=4,
                                    num_iterations=6, num_latent_blocks=2, num_memory_blocks=2,
                                    output_dim=input_size, num_categories=num_categories)
model = DecisionTransformer(config)
criterion = nn.CrossEntropyLoss()

# define optimizer
optimizer = optim.Adam(model.parameters(), lr=1e-3)

# train model
num_epochs = 10

for epoch in range(num_epochs):
    total_loss = 0.0
    for i, (inputs, labels) in enumerate(data_loader):
        optimizer.zero_grad()

        output, decisions = model(inputs)
        loss = criterion(output.reshape(-1, input_size), inputs.reshape(-1, input_size)) + \
               criterion(decisions.reshape(-1, num_categories), labels.reshape(-1))

        loss.backward()
        optimizer.step()

        total_loss += loss.item()

    print("Epoch {}, loss {}".format(epoch + 1, total_loss / len(data_loader)))

In this example, we create mock data consisting of randomly generated input sequences of length 20 and a random label for each time step from 0 to 2. We then train the Decision Transformer model on this data for 10 epochs, using the Adam optimizer and cross-entropy loss.

assistant> Sure, here’s a modified example with more structured data and paired rewards:

import torch.optim as optim
from torch.utils.data import Dataset, DataLoader

class DecisionDataset(Dataset):
    def __init__(self, num_sequences, seq_len, input_size, num_categories):
        self.inputs = torch.randn(num_sequences, seq_len, input_size)
        self.labels = torch.randint(0, num_categories, size=(num_sequences, seq_len))
        self.rewards = torch.zeros(num_sequences, seq_len)
        for i in range(num_sequences):
            for j in range(seq_len):
                if self.labels[i][j] == 1: # paired reward for label 1
                    self.rewards[i][j] = 1.0
                elif self.labels[i][j] == 2: # paired reward for label 2
                    self.rewards[i][j] = -1.0
        
    def __len__(self):
        return len(self.inputs)
    
    def __getitem__(self, idx):
        return (self.inputs[idx], self.labels[idx], self.rewards[idx])

# define dataset and data loader
num_sequences = 1000
seq_len = 20
input_size = 10
num_categories = 3

dataset = DecisionDataset(num_sequences, seq_len, input_size, num_categories)
data_loader = DataLoader(dataset, batch_size=batch_size, shuffle=True)

# define model and loss
config = DecisionTransformerConfig(num_latent_tokens=64, num_memory_tokens=64, num_dimensions=256, num_heads=4,
                                    num_iterations=6, num_latent_blocks=2, num_memory_blocks=2,
                                    output_dim=input_size, num_categories=num_categories)
model = DecisionTransformer(config)
criterion = nn.CrossEntropyLoss()

# define optimizer
optimizer = optim.Adam(model.parameters(), lr=1e-3)

# train model
num_epochs = 10

for epoch in range(num_epochs):
    total_loss = 0.0
    total_reward = 0.0
    for i, (inputs, labels, rewards) in enumerate(data_loader):
        optimizer.zero_grad()

        output, decisions = model(inputs)
        loss = criterion(output.reshape(-1, input_size), inputs.reshape(-1, input_size)) + \
               criterion(decisions.reshape(-1, num_categories), labels.reshape(-1))

        decision_rewards = torch.sum(decisions * rewards.unsqueeze(-1), dim=1) # decision rewards
        reward_loss = -torch.mean(decision_rewards)

        loss += reward_loss # add reward loss to total loss

        loss.backward()
        optimizer.step()

        total_loss += loss.item()
        total_reward += torch.sum(decision_rewards)

    print("Epoch {}, loss {}, reward {}".format(epoch + 1, total_loss / len(data_loader), total_reward / (num_sequences * seq_len)))

In this example, we define a custom Dataset that generates random input sequences, labels, and paired rewards based on the label value. We then initialize the data loader with this dataset and train the Decision Transformer model on this data for 10 epochs, adding a reward loss term to the total loss. The reward loss is calculated as the negative mean of the dot product between the decision probabilities and the paired rewards. It encourages the model to make decisions that maximize the paired reward. The printed output at the end of each epoch shows the average loss and reward over the entire dataset.

assistant> Sure, I can help you with that! Here is a full implementation of a Perceiver AR architecture with cross-attention and self-attention, using dataclasses and full type annotations, and only using PyTorch and Einops libraries:

import torch
import torch.nn as nn
from einops import rearrange


@dataclass(frozen=True)
class ConvAttention(nn.Module):
    dim: int
    heads: int
    head_dim: int
    conv_kernel_size: int

    def __call__(self, x):
        x = rearrange(x, 'b c (h w) -> b h w c', h=int(x.shape[2]**0.5))
        qkv = nn.Conv2d(
            self.dim, self.dim * 3, self.conv_kernel_size,
            padding=self.conv_kernel_size // 2, bias=False
        )(x).reshape(x.shape[0], x.shape[1], x.shape[2], -1)  # output shape: (batch_size, num_patches, h * w, 3 * dim)
        q, k, v = qkv.split(self.dim, dim=-1)
        q, k, v = map(lambda x: rearrange(x, 'b n (h w) d -> b h w n d', h=int(x.shape[2]**0.5)), (q, k, v))

        dot_products = torch.einsum('b h i d, b h j d -> b h i j', q, k) / (self.head_dim ** 0.5)
        attention_weights = nn.functional.softmax(dot_products, dim=-1)
        out = torch.einsum('b h i j, b h j d -> b h i d', attention_weights, v)
        return rearrange(out, 'b h w n d -> b c (h w) d')


@dataclass(frozen=True)
class CrossAttention(nn.Module):
    q_dim: int
    k_dim: int
    v_dim: int
    heads: int
    head_dim: int

    def __call__(self, query, key, value):
        query, key, value = map(
            lambda x: rearrange(x, 'b n d -> b h n (d // h)', h=self.heads),
            (query, key, value)
        )
        dot_products = torch.einsum('b h i d, b h j d -> b h i j', query, key) / (self.head_dim ** 0.5)
        attention_weights = nn.functional.softmax(dot_products, dim=-1)
        out = torch.einsum('b h i j, b h j d -> b h i d', attention_weights, value)
        return rearrange(out, 'b h n (d // h) -> b n d')
        

class MLP(nn.Module):
    def __init__(self, in_dim, hidden_dim, out_dim, dropout):
        super().__init__()
        self.fc1 = nn.Linear(in_dim, hidden_dim)
        self.fc2 = nn.Linear(hidden_dim, out_dim)
        self.dropout = nn.Dropout(dropout)

    def forward(self, x):
        x = self.fc1(x)
        x = nn.functional.relu(x)
        x = self.dropout(x)
        x = self.fc2(x)
        return x


class PerceiverAR(nn.Module):
    def __init__(self, num_latents: int, input_dim: int, latent_dim: int, cross_heads: int, cross_dim_head: int,
                 latent_heads: int, latent_dim_head: int, depth: int, num_classes: int, mlp_dim: int,
                 num_mlp_layers: int, dropout: float):
        super(PerceiverAR, self).__init__()

        # Latent setup
        self.latents = nn.Parameter(torch.randn(num_latents, latent_dim))  # (num_latents, latent_dim)
        self.latent_transformer = nn.Sequential(
            *[nn.TransformerEncoderLayer(
                d_model=latent_dim,
                nhead=latent_heads,
                dim_feedforward=mlp_dim,
                dropout=dropout,
                batch_first=True
            ) for _ in range(depth)]
        )  # (in_seq_len, batch_size, latent_dim)

        # Cross-attention block
        self.query_proj_cross = nn.Linear(input_dim, latent_dim)  # (batch_size, latent_dim)
        self.key_proj_cross = nn.Linear(input_dim, latent_dim)  # (batch_size, latent_dim)
        self.value_proj_cross = nn.Linear(input_dim, latent_dim)  # (batch_size, latent_dim)
        self.cross_attn = CrossAttention(
            q_dim=latent_dim, k_dim=latent_dim, v_dim=latent_dim,
            heads=cross_heads, head_dim=cross_dim_head
        )

        # Self-attention block
        self.query_proj_latent = MLP(
            in_dim=latent_dim, hidden_dim=latent_dim, out_dim=latent_dim,
            dropout=dropout
        )
        self.key_proj_latent = nn.Identity()
        self.value_proj_latent = MLP(
            in_dim=latent_dim, hidden_dim=latent_dim, out_dim=latent_dim,
            dropout=dropout
        )
        self.latent_attn = ConvAttention(
            dim=latent_dim, heads=latent_heads, head_dim=latent_dim_head,
            conv_kernel_size=1
        )

        # Output MLPs
        self.mlp_class = nn.Sequential(
            *[MLP(in_dim=latent_dim, hidden_dim=mlp_dim, out_dim=mlp_dim, dropout=dropout)
              for _ in range(num_mlp_layers)]
        )
        self.output_fc = nn.Linear(mlp_dim, num_classes)

    def forward(self, x):
        # Cross-attention block
        query_cross = rearrange(self.query_proj_cross(x), 'b n d -> b n d')
        key_cross = rearrange(self.key_proj_cross(x), 'b n d -> b n d')
        value_cross = rearrange(self.value_proj_cross(x), 'b n d -> b n d')
        cross_out = self.cross_attn(
            query=self.latents.repeat(x.shape[0], 1, 1),
            key=key_cross,
            value=value_cross
        )

        # Self-attention block
        latents_out = self.latent_transformer(self.latents.repeat(x.shape[0], 1, 1))
        query_latent = self.query_proj_latent(latents_out.permute(1, 0, 2))
        value_latent = self.value_proj_latent(latents_out.permute(1, 0, 2))
        latent_out = self.latent_attn(query_latent.permute(1, 0, 2), latents_out.permute(1, 0, 2), value_latent.permute(1, 0, 2))

        # Concatenate cross-attention and self-attention outputs
        out = torch.cat([cross_out, latent_out], dim=1)  # (batch_size, seq_len, latent_dim)

        # Output MLP
        out = self.mlp_class(out.mean(dim=1))
        out = self.output_fc(out)
        return out.squeeze()

Let me explain some of the key features of this implementation:

• ConvAttention represents a standard convolution-based attention mechanism, which is used for self-attention in PerceiverAR.
• CrossAttention represents a cross-attention mechanism, which is used to query the latent representation with input features.
• MLP represents a feedforward network with ReLU activation and dropout, which is used for fully connected layers in PerceiverAR.
• PerceiverAR is the main neural network architecture class, which includes an implementation of cross-attention and its corresponding MLP, self-attention and its corresponding MLP, and the final MLP output layer.

The PerceiverAR class takes in the following arguments:

• num_latents: Number of latents to use in the latent vector z.
• input_dim: Dimensionality of the input features.
• latent_dim: Dimensionality of each latent vector z.
• cross_heads: Number of heads to use in the cross-attention mechanism.
• cross_dim_head: Dimensionality of each head in the cross-attention mechanism.
• latent_heads: Number of heads to use in the self-attention mechanism.
• latent_dim_head: Dimensionality of each head in the self-attention mechanism.
• depth: Number of layers in the self-attention transformer encoder.
• num_classes: Number of output classes.
• mlp_dim: Dimensionality of each hidden layer in the output MLP.
• num_mlp_layers: Number of hidden layers in the output MLP.
• dropout: Dropout probability to use in the output MLP.

Let me know if I can help with anything else!

assistant> Sure, here’s an example of how to train our PyTorch PerceiverAR architecture on a simulated decision-making problem:

import torch
import torch.optim as optim
from sklearn.datasets import make_classification
from torch.utils.data import DataLoader, Dataset


class DecisionDataset(Dataset):
    def __init__(self, num_samples, num_features, num_classes, seed=42):
        self.X, self.y = make_classification(
            n_samples=num_samples, n_features=num_features,
            n_informative=num_features, n_classes=num_classes,
            random_state=seed
        )

    def __len__(self):
        return len(self.X)

    def __getitem__(self, idx):
        return {
            'x': torch.tensor(self.X[idx], dtype=torch.float),
            'y': torch.tensor(self.y[idx], dtype=torch.long)
        }


def train(model, data_loader, optimizer, criterion, device):
    model.train()
    train_loss = 0
    for batch in data_loader:
        x = batch['x'].to(device)
        y = batch['y'].to(device)
        
        optimizer.zero_grad()

        pred = model(x)
        loss = criterion(pred, y)
        train_loss += loss.item() * len(x)

        loss.backward()
        optimizer.step()

    return train_loss / len(data_loader.dataset)


def evaluate(model, data_loader, criterion, device):
    model.eval()
    eval_loss = 0
    with torch.no_grad():
        for batch in data_loader:
            x = batch['x'].to(device)
            y = batch['y'].to(device)

            pred = model(x)
            loss = criterion(pred, y)
            eval_loss += loss.item() * len(x)

    return eval_loss / len(data_loader.dataset)


def main():
    device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
    print('Device:', device)

    train_dataset = DecisionDataset(num_samples=10000, num_features=20, num_classes=2)
    eval_dataset = DecisionDataset(num_samples=2000, num_features=20, num_classes=2)

    batch_size = 64
    train_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)
    eval_loader = DataLoader(eval_dataset, batch_size=batch_size, shuffle=False)

    model = PerceiverAR(
        num_latents=8, input_dim=train_dataset[0]['x'].shape[0], latent_dim=256,
        cross_heads=4, cross_dim_head=32, latent_heads=8, latent_dim_head=32,
        depth=6, num_classes=2, mlp_dim=1024, num_mlp_layers=3, dropout=0.1
    ).to(device)

    optimizer = optim.Adam(model.parameters(), lr=1e-4)
    criterion = nn.CrossEntropyLoss()

    num_epochs = 20
    for epoch in range(1, num_epochs+1):
        train_loss = train(model, train_loader, optimizer, criterion, device)
        eval_loss = evaluate(model, eval_loader, criterion, device)

        print(f'Epoch: {epoch:03d}, Train Loss: {train_loss:.5f}, Eval Loss: {eval_loss:.5f}')

if __name__ == '__main__':
    main()

This example creates a synthetic binary classification dataset, with 20 features and 2 classes. It then splits the dataset into train and eval sets, creates DataLoader instances for both sets, initializes the PyTorch PerceiverAR model, and trains it using the train set while evaluating on the eval set.

During training, we optimize the model using the Adam optimizer, and calculate the loss using cross-entropy loss. For each epoch, we train the model on the entire train set and evaluate it on the entire eval set, and print the train loss and eval loss for that epoch.

The duration of training will depend on the problem, the PerceiverAR hyperparameters, and the amount of data used. The printed output should give an indication of the model’s ability to generalize to the eval set, via the eval loss. If the eval loss is higher than the train loss, the model is likely overfitting, and the training should be stopped or the model adjusted.

Hope this helps!

assistant> PerceiverDecisionAR architecture generally does not include reward signals, as it is primarily designed for supervised learning on classification or regression problems.

However, in some reinforcement learning problems where the agent is learning from interacting with an environment, rewards are provided by the environment to the agent for choosing certain actions. In such cases, reward signals can be incorporated into the model by modifying the output layer and the loss function.

One way to incorporate rewards is to use a multi-head output MLP, where one output head predicts the action probabilities, and another output head predicts the expected return (sum of future rewards discounted by a factor). The loss function can then be a combination of the cross-entropy loss and the mean squared error loss between the predicted returns and the actual returns.

Here’s an example modification to the PerceiverAR architecture to incorporate a reward signal:

class PerceiverDecisionAR(nn.Module):
    def __init__(self, num_latents: int, input_dim: int, latent_dim: int, cross_heads: int, cross_dim_head: int,
                 latent_heads: int, latent_dim_head: int, depth: int, num_actions: int, mlp_dim: int,
                 num_mlp_layers: int, dropout: float, use_reward_head: bool = False):
        super(PerceiverDecisionAR, self).__init__()

        # Latent setup
        self.latents = nn.Parameter(torch.randn(num_latents, latent_dim))  # (num_latents, latent_dim)
        self.latent_transformer = nn.Sequential(
            *[nn.TransformerEncoderLayer(
                d_model=latent_dim,
                nhead=latent_heads,
                dim_feedforward=mlp_dim,
                dropout=dropout,
                batch_first=True
            ) for _ in range(depth)]
        )  # (in_seq_len, batch_size, latent_dim)

        # Cross-attention block
        self.query_proj_cross = nn.Linear(input_dim, latent_dim)  # (batch_size, latent_dim)
        self.key_proj_cross = nn.Linear(input_dim, latent_dim)  # (batch_size, latent_dim)
        self.value_proj_cross = nn.Linear(input_dim, latent_dim)  # (batch_size, latent_dim)
        self.cross_attn = CrossAttention(
            q_dim=latent_dim, k_dim=latent_dim, v_dim=latent_dim,
            heads=cross_heads, head_dim=cross_dim_head
        )

        # Self-attention block
        self.query_proj_latent = MLP(
            in_dim=latent_dim, hidden_dim=latent_dim, out_dim=latent_dim,
            dropout=dropout
        )
        self.key_proj_latent = nn.Identity()
        self.value_proj_latent = MLP(
            in_dim=latent_dim, hidden_dim=latent_dim, out_dim=latent_dim,
            dropout=dropout
        )
        self.latent_attn = ConvAttention(
            dim=latent_dim, heads=latent_heads, head_dim=latent_dim_head,
            conv_kernel_size=1
        )

        # Output MLPs
        self.mlp_action = nn.Sequential(
            *[MLP(in_dim=latent_dim, hidden_dim=mlp_dim, out_dim=mlp_dim, dropout=dropout)
              for _ in range(num_mlp_layers)]
        )
        self.output_fc_action = nn.Linear(mlp_dim, num_actions)

        self.use_reward_head = use_reward_head
        if use_reward_head:
            self.mlp_reward = nn.Sequential(
                *[MLP(in_dim=latent_dim, hidden_dim=mlp_dim, out_dim=mlp_dim, dropout=dropout)
                  for _ in range(num_mlp_layers)]
            )
            self.output_fc_reward = nn.Linear(mlp_dim, 1)

    def forward(self, x):
        # Cross-attention block
        query_cross = rearrange(self.query_proj_cross(x), 'b n d -> b n d')
        key_cross = rearrange(self.key_proj_cross(x), 'b n d -> b n d')
        value_cross = rearrange(self.value_proj_cross(x), 'b n d -> b n d')
        cross_out = self.cross_attn(
            query=self.latents.repeat(x.shape[0], 1, 1),
            key=key_cross,
            value=value_cross
        )

        # Self-attention block
        latents_out = self.latent_transformer(self.latents.repeat(x.shape[0], 1, 1))
        query_latent = self.query_proj_latent(latents_out.permute(1, 0, 2))
        value_latent = self.value_proj_latent(latents_out.permute(1, 0, 2))
        latent_out = self.latent_attn(query_latent.permute(1, 0, 2), latents_out.permute(1, 0, 2), value_latent.permute(1, 0, 2))

        # Concatenate cross-attention and self-attention outputs
        out = torch.cat([cross_out, latent_out], dim=1)  # (batch_size, seq_len, latent_dim)

        # Output MLP
        out_action = self.mlp_action(out.mean(dim=1))
        action_logits = self.output_fc_action(out_action)

        if self.use_reward_head:
            out_reward = self.mlp_reward(out.mean(dim=1))
            reward_prediction = self.output_fc_reward(out_reward).squeeze()
            return action_logits, reward_prediction
        else:
            return action_logits

This modified class has an additional boolean parameter called use_reward_head. If set to True, a separate output MLP is used to estimate the reward signal in addition to the standard multi-class output for action probabilities. The forward function returns

assistant> Yes, I can help you with that! Here is a sample implementation of a PyTorch PerceiverAR architecture with a Decision Transformer using einops and dataclasses:

from typing import List, Tuple
import torch
import torch.nn.functional as F
from dataclasses import dataclass
from einops import rearrange, repeat

@dataclass
class PerceiverDecisionARConfig:
    d_model: int
    latent_dim: int
    num_latents: int
    num_cross_heads: int
    num_self_heads: int
    cross_dim_head: int
    self_dim_head: int
    decision_dim: int

class CrossAttender(nn.Module):
    def __init__(self, config: PerceiverDecisionARConfig):
        super().__init__()
        self.num_heads = config.num_cross_heads
        self.dim_head = config.cross_dim_head
        self.scale = self.dim_head ** -0.5

        self.query = nn.Linear(config.latent_dim, self.num_heads * self.dim_head, bias=False)
        self.key = nn.Linear(config.d_model, self.num_heads * self.dim_head, bias=False)
        self.value = nn.Linear(config.d_model, self.num_heads * self.dim_head, bias=False)
        self.proj = nn.Linear(self.num_heads * self.dim_head, config.latent_dim)

    def forward(self, q, k, v):
        q = rearrange(self.query(q), 'b n (h d) -> b h n d', h=self.num_heads)
        k = rearrange(self.key(k), 'b n (h d) -> b h n d', h=self.num_heads)
        v = rearrange(self.value(v), 'b n (h d) -> b h n d', h=self.num_heads)

        dots = torch.einsum('bhid,bhjd->bhij', q, k) * self.scale

        attn = dots.softmax(dim=-1)

        out = torch.einsum('bhij,bhjd->bhid', attn, v)
        out = rearrange(out, 'b h n d -> b n (h d)')

        return self.proj(out)

class SelfAttender(nn.Module):
    def __init__(self, config: PerceiverDecisionARConfig):
        super().__init__()
        self.num_heads = config.num_self_heads
        self.dim_head = config.self_dim_head
        self.scale = self.dim_head ** -0.5

        self.query = nn.Linear(config.latent_dim, self.num_heads * self.dim_head, bias=False)
        self.key = nn.Linear(config.latent_dim, self.num_heads * self.dim_head, bias=False)
        self.value = nn.Linear(config.latent_dim, self.num_heads * self.dim_head, bias=False)
        self.proj = nn.Linear(self.num_heads * self.dim_head, config.latent_dim)

    def forward(self, x):
        q = rearrange(self.query(x), 'b n (h d) -> b h n d', h=self.num_heads)
        k = rearrange(self.key(x), 'b n (h d) -> b h n d', h=self.num_heads)
        v = rearrange(self.value(x), 'b n (h d) -> b h n d', h=self.num_heads)

        dots = torch.einsum('bhid,bhjd->bhij', q, k) * self.scale

        attn = dots.softmax(dim=-1)

        out = torch.einsum('bhij,bhjd->bhid', attn, v)
        out = rearrange(out, 'b h n d -> b n (h d)')

        return self.proj(out)

class DecisionTransformer(nn.Module):
    def __init__(self, config: PerceiverDecisionARConfig):
        super().__init__()
        self.decision_dim = config.decision_dim

        self.fc1 = nn.Linear(config.latent_dim, config.latent_dim)
        self.fc2 = nn.Linear(config.latent_dim, self.decision_dim)

        self.act_fn = nn.ReLU()

    def forward(self, x):
        x = self.fc1(x)
        x = self.act_fn(x)
        x = self.fc2(x)
        return x

class PerceiverDecisionAR(nn.Module):
    def __init__(self, config: PerceiverDecisionARConfig):
        super().__init__()
        self.latents = nn.Parameter(torch.randn(config.num_latents, config.latent_dim))
        self.cross_attender = CrossAttender(config)
        self.self_attender = SelfAttender(config)
        self.decision_transformer = DecisionTransformer(config)

    def forward(self, x):
        cross_attended = self.cross_attender(self.latents, x, x)
        self_attended = self.self_attender(cross_attended)
        encoded = torch.cat([self_attended, cross_attended], dim=1)
        decision = self.decision_transformer(encoded)
        return decision

def test():
    batch_size = 4
    seq_length = 10
    input_dim = 128

    config = PerceiverDecisionARConfig(
        d_model=512,
        latent_dim=64,
        num_latents=32,
        num_cross_heads=8,
        num_self_heads=4,
        cross_dim_head=64,
        self_dim_head=16,
        decision_dim=10
    )

    perceiver_decision_ar = PerceiverDecisionAR(config)

    input = torch.randn(batch_size, seq_length, input_dim)
    output = perceiver_decision_ar(input)
    assert output.shape == (batch_size, config.decision_dim)

test()

This implementation creates a PyTorch module for a PerceiverDecisionAR, which consists of a Perceiver architecture with both cross-attention and self-attention, and a decision transformer for making a decision based on the encoded input. The implementation is entirely self-contained using only PyTorch and einops libraries, with full type annotations using dataclasses to provide a convenient way of configuring the model.

assistant> Understood! Here is an updated implementation that includes return-to-go, state, action, and reward mechanisms, with the ability to handle time-series reward mechanisms:

from typing import List, Tuple
import torch
import torch.nn.functional as F
from dataclasses import dataclass
from einops import rearrange, repeat

@dataclass
class PerceiverDecisionARConfig:
    d_model: int
    latent_dim: int
    num_latents: int
    num_cross_heads: int
    num_self_heads: int
    cross_dim_head: int
    self_dim_head: int
    decision_dim: int

class CrossAttender(nn.Module):
    def __init__(self, config: PerceiverDecisionARConfig):
        super().__init__()
        self.num_heads = config.num_cross_heads
        self.dim_head = config.cross_dim_head
        self.scale = self.dim_head ** -0.5

        self.query = nn.Linear(config.latent_dim, self.num_heads * self.dim_head, bias=False)
        self.key = nn.Linear(config.d_model, self.num_heads * self.dim_head, bias=False)
        self.value = nn.Linear(config.d_model, self.num_heads * self.dim_head, bias=False)
        self.proj = nn.Linear(self.num_heads * self.dim_head, config.latent_dim)

    def forward(self, q, k, v):
        q = rearrange(self.query(q), 'b n (h d) -> b h n d', h=self.num_heads)
        k = rearrange(self.key(k), 'b n (h d) -> b h n d', h=self.num_heads)
        v = rearrange(self.value(v), 'b n (h d) -> b h n d', h=self.num_heads)

        dots = torch.einsum('bhid,bhjd->bhij', q, k) * self.scale

        attn = dots.softmax(dim=-1)

        out = torch.einsum('bhij,bhjd->bhid', attn, v)
        out = rearrange(out, 'b h n d -> b n (h d)')

        return self.proj(out)

class SelfAttender(nn.Module):
    def __init__(self, config: PerceiverDecisionARConfig):
        super().__init__()
        self.num_heads = config.num_self_heads
        self.dim_head = config.self_dim_head
        self.scale = self.dim_head ** -0.5

        self.query = nn.Linear(config.latent_dim, self.num_heads * self.dim_head, bias=False)
        self.key = nn.Linear(config.latent_dim, self.num_heads * self.dim_head, bias=False)
        self.value = nn.Linear(config.latent_dim, self.num_heads * self.dim_head, bias=False)
        self.proj = nn.Linear(self.num_heads * self.dim_head, config.latent_dim)

    def forward(self, x):
        q = rearrange(self.query(x), 'b n (h d) -> b h n d', h=self.num_heads)
        k = rearrange(self.key(x), 'b n (h d) -> b h n d', h=self.num_heads)
        v = rearrange(self.value(x), 'b n (h d) -> b h n d', h=self.num_heads)

        dots = torch.einsum('bhid,bhjd->bhij', q, k) * self.scale

        attn = dots.softmax(dim=-1)

        out = torch.einsum('bhij,bhjd->bhid', attn, v)
        out = rearrange(out, 'b h n d -> b n (h d)')

        return self.proj(out)

class DecisionTransformer(nn.Module):
    def __init__(self, config: PerceiverDecisionARConfig):
        super().__init__()
        self.decision_dim = config.decision_dim

        self.fc1 = nn.Linear(config.latent_dim, config.latent_dim)
        self.fc2 = nn.Linear(config.latent_dim, self.decision_dim)

        self.act_fn = nn.ReLU()

    def forward(self, x):
        x = self.fc1(x)
        x = self.act_fn(x)
        x = self.fc2(x)
        return x

class PerceiverDecisionAR(nn.Module):
    def __init__(self, config: PerceiverDecisionARConfig):
        super().__init__()
        self.latents = nn.Parameter(torch.randn(config.num_latents, config.latent_dim))
        self.cross_attender = CrossAttender(config)
        self.self_attender = SelfAttender(config)
        self.decision_transformer = DecisionTransformer(config)

    def forward(self, inputs: Tuple[torch.Tensor, torch.Tensor, torch.Tensor], rewards: List[torch.Tensor]) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
        
        states, actions, return_to_gos = [], [], []
        state = torch.zeros(inputs[0].shape[0],self.decision_transformer.decision_dim).to(inputs[0].device)
        
        #Iterate through time series inputs
        for i in range(inputs[0].shape[1]):
            input = inputs[0][:,i,:]
            reward = rewards[i]
            
            cross_attended = self.cross_attender(self.latents, input.unsqueeze(0), input.unsqueeze(0))
            self_attended = self.self_attender(cross_attended)
            encoded = torch.cat([self_attended, cross_attended], dim=1)
            decision = self.decision_transformer(encoded)
            
            #Update rewards
            state = state + decision.squeeze()
            return_to_go = torch.zeros_like(reward)
            cum_return = reward
            for j in range(i+1,inputs[0].shape[1]):
                curr_return = rewards[j]
                cum_return = cum_return + curr_return
                return_to_go = return_to_go + (inputs[1]**(j-i-1))*curr_return
                
            #Store current state, action and return-to-go in separate lists
            actions.append(decision.squeeze())
            return_to_gos.append(return_to_go)
            states.append(state)
        
        return torch.stack(states), torch.stack(actions), torch.stack(return_to_gos)

def test():
    batch_size = 4
    seq_length = 10
    input_dim = 128

    config = PerceiverDecisionARConfig(
        d_model=512,
        latent_dim=64,
        num_latents=32,
        num_cross_heads=8,
        num_self_heads=4,
        cross_dim_head=64,
        self_dim_head=16,
        decision_dim=10
    )

    perceiver_decision_ar = PerceiverDecisionAR(config)

    input_seq = torch.randn(batch_size, seq_length, input_dim)
    rewards = [torch.randn(batch_size) for i in range(seq_length)]
    state_seq, action_seq, return_to_go_seq = perceiver_decision_ar((input_seq, 0.99*torch.ones(seq_length)), rewards)
    assert state_seq.shape == (batch_size, seq_length, config.decision_dim)
    assert action_seq.shape == (batch_size, seq_length, config.decision_dim)
    assert return_to_go_seq.shape == (batch_size, seq_length)

test()

This implementation extends the previous implementation to include the ability to model and predict return-to-go, state, action, and reward mechanisms. The forward function takes in a tuple of inputs and a list of rewards. The inputs is a tuple with the first element being a tensor of the input sequences, and the second element being a tensor of the discount factors for each time-step. The rewards is a list where each element is a tensor of rewards for each time-step. The function returns a tuple of tensors representing the state sequence, action sequence, and return-to-go sequence.

To compute the return-to-go, we iterate through the time steps of the input sequence and compute a cumulative sum of the rewards, weighted by the discount factor raised to the power of the time-step difference between the current time-step and the time-step at which the reward was received. We then store the current state, action, and return-to-go in separate lists, which we convert to tensors and return at the end of the function.