损失的计算

数据的处理

Let's look at how the padding is added in the batch_preprocess method:

# First find max length in current batch
max_length = max(src_length)

# For source sequences
for item in src_batch:
    item += [self.pad] * (max_length - len(item))

So for src, if we have 3 trajectories in a batch:

Original trajectories:
traj1: [1, 2, 3]         # length 3
traj2: [4, 5, 6, 7]      # length 4 (max_length)
traj3: [8, 9]            # length 2

After padding:
traj1: [1, 2, 3, PAD]    # added 1 PAD at end
traj2: [4, 5, 6, 7]      # no padding needed
traj3: [8, 9, PAD, PAD]  # added 2 PADs at end

For target sequences:

for item in trg_batch:
    item += [self.pad] * (max_length + 2 - len(item))

So for trg (where BOS and EOS are added):

Original with BOS/EOS:
traj1: [BOS, 1, 2, 3, EOS]         # length 5
traj2: [BOS, 4, 5, 6, 7, EOS]      # length 6 (max_length + 2)
traj3: [BOS, 8, 9, EOS]            # length 4

After padding:
traj1: [BOS, 1, 2, 3, EOS, PAD]    # added 1 PAD at end
traj2: [BOS, 4, 5, 6, 7, EOS]      # no padding needed
traj3: [BOS, 8, 9, EOS, PAD, PAD]  # added 2 PADs at end

Key points:

1. Padding is always added at the END of the sequence
2. Amount of padding depends on the longest sequence in the current batch
3. Source sequences get padded to max_length
4. Target sequences get padded to max_length + 2 (to account for BOS and EOS tokens)

数据格式

Based on the provided code and data, let me explain how the trajectory data is preprocessed in the TrajectoryLoader class:

1. Data Loading and Label Processing:

• The data is loaded from a pickle file containing trajectory information
• Each trajectory consists of GPS coordinates that have been mapped to node IDs
• The class adds three special tokens:

  def bos_eos_pad(self):
      self.bos = self.label_num-3  # Beginning of sequence token
      self.eos = self.label_num-2  # End of sequence token
      self.pad = self.label_num-1  # Padding token
  

2. Batch Processing:

• For each trajectory in a batch, the following processing is done:

  # Original trajectory becomes source sequence
  src_batch.append(item)
  
  # Target sequence gets BOS token prepended and EOS token appended
  trg_batch.append([self.bos] + deepcopy(item) + [self.eos])
  

3. Length Handling and Padding:

• The code tracks original lengths:

  src_length.append(len(item))  # Source sequence length
  trg_length.append(len(trg_batch[-1]))  # Target sequence length (including BOS/EOS)
  

• Sequences in a batch are padded to the same length:

  # Pad source sequences
  for item in src_batch:
      item += [self.pad] * (max_length - len(item))
      
  # Pad target sequences (which include BOS/EOS)
  for item in trg_batch:
      item += [self.pad] * (max_length + 2 - len(item))
  

4. Final Data Structure:

• Source sequences: Original trajectory + padding
• Target sequences: [BOS] + trajectory + [EOS] + padding
• The loader keeps track of actual sequence lengths for both source and target

So to directly answer your questions:

• Yes, it inserts labels:
  • BOS (Beginning of Sequence) token at the start of target sequences
  • EOS (End of Sequence) token at the end of target sequences
  • PAD tokens to make all sequences in a batch the same length
• The special tokens are positioned at:
  • label_num-3: BOS token
  • label_num-2: EOS token
  • label_num-1: PAD token

This preprocessing enables the transformer model to:

• Know where sequences start (BOS)
• Know where sequences end (EOS)
• Handle variable-length sequences in batches (PAD)
• Generate proper autoregressive predictions during training and inference

confidence loss 只包含正常路径的计算

Let me analyze how the confidence KL loss is calculated in the TransformerTrajectoryModel and whether it includes the special tokens (BOS, EOS, PAD):

Looking at the confidence computation in TransformerTrajectoryModel:

def compute_confidence(self, h, src):
    # Encode and transform the input
    encoded = self.confidence_encoder(h)
    transformed = self.confidence_transformer(encoded)
    
    # Get distribution parameters
    mu = self.confidence_mu(transformed)
    logvar = self.confidence_logvar(transformed)
    sigma = torch.exp(0.5 * logvar)
    
    # Sample and decode
    q_z = torch.distributions.Normal(mu, sigma)
    z = q_z.rsample()
    decoded = self.confidence_decoder(z)
    logits = self.output_projection1(decoded)
    log_probs = torch.log_softmax(logits, dim=-1)
    
    # Reshape for loss calculation
    batch_size, seq_len = src.shape
    log_probs_flat = log_probs.reshape(batch_size * seq_len, -1)
    src_flat = src.reshape(-1)
    
    # Calculate NLL loss with padding mask
    nll_loss = self.nll(log_probs_flat, src_flat)
    nll_loss = nll_loss.reshape(batch_size, seq_len)
    
    # Important part: Create mask to ignore padding
    mask = (src != self.num_nodes-1).float()  # Ignore PAD tokens
    nll_loss = (nll_loss * mask).sum(dim=1) / mask.sum(dim=1).clamp(min=1e-8)

Key observations:

1. The confidence computation uses the source sequence (src), which does NOT include BOS or EOS tokens - it's the original trajectory with only padding

2. The masking explicitly handles PAD tokens:

mask = (src != self.num_nodes-1).float()  # Masks out PAD tokens only

3. The NLL loss is computed only on the actual trajectory nodes, as it uses the source sequence (src) as the target, not the target sequence that would contain BOS/EOS

4. The KL divergence is calculated on the entire latent distribution but is also scaled by the mask:

kl_div = torch.distributions.kl_divergence(q_z, prior)
kl_div = kl_div.mean(dim=-1)
kl_div = (kl_div * mask).sum(dim=1) / mask.sum(dim=1).clamp(min=1e-8)

So to directly answer:

• BOS: Not included in confidence loss computation
• EOS: Not included in confidence loss computation
• PAD: Explicitly masked out and not included in the loss

The confidence VAE only tries to reconstruct the actual trajectory points, ignoring all special tokens. This makes sense because the confidence measure should be about how well the model can reconstruct the actual movement patterns, not the artificial tokens we add for the transformer sequence processing.

Let me check the data loading and trajectory handling to determine if src includes the destination.

Looking at the provided sample data in the first document:

# From the example trajectory data structure:
'n_geo': [[104.07337, 30.68815], [104.07319, 30.68815], ..., [104.073, 30.65492]]

# In TrajectoryLoader.load_data:
def load_data(self, trajectory_path, node2id):
    dataset = pickle.load(open(trajectory_path, 'rb'))
    self.data = []
    for line in dataset.values():
        traj = line['n_geo']  # Takes the n_geo field directly
        item = []
        for node in traj:
            item.append(node2id[str(node)])
        self.data.append(item)

And looking at how src is created:

# In TrajectoryLoader.batch_preprocess:
src_batch = []
for item in cur_batch:
    src_length.append(len(item))
    src_batch.append(item)  # Direct use of the trajectory

From this code, we can see that:

1. src includes ALL points from the n_geo field of the trajectory data
2. Looking at the sample data, n_geo contains the complete trajectory including the destination point
3. The destination point [104.073, 30.65492] is included as the last point in the trajectory

Therefore, yes, src does include the destination point. It contains the complete trajectory from start to finish, before any special tokens (BOS/EOS) are added. The confidence computation would thus work on reconstructing the entire path including the destination.

The way it works is:

• src: [start_point, ..., intermediate_points, ..., destination_point] + padding
• trg: [BOS, start_point, ..., intermediate_points, ..., destination_point, EOS] + padding

The confidence VAE tries to reconstruct the entire source sequence, including both the starting point and the destination point.

Yes, that's correct - while the src sequence does contain padding tokens, the computation of confidence explicitly masks them out in the loss calculation. Let me show you the specific code:

def compute_confidence(self, h, src):
    # ... encoder and decoder operations ...
    
    # Calculate NLL loss and reshape
    nll_loss = self.nll(log_probs_flat, src_flat)
    nll_loss = nll_loss.reshape(batch_size, seq_len)
    
    # Create mask for padding
    mask = (src != self.num_nodes-1).float()  # True for real nodes, False for padding
    
    # Mask out padding in NLL loss
    nll_loss = (nll_loss * mask).sum(dim=1) / mask.sum(dim=1).clamp(min=1e-8)
    
    # KL divergence also masked
    kl_div = torch.distributions.kl_divergence(q_z, prior)
    kl_div = kl_div.mean(dim=-1)
    kl_div = (kl_div * mask).sum(dim=1) / mask.sum(dim=1).clamp(min=1e-8)

So while the src sequence contains:

[real_point1, real_point2, ..., real_pointN, PAD, PAD, ...]

The mask (src != self.num_nodes-1) creates:

[1, 1, ..., 1, 0, 0, ...]

When this mask is applied:

• Loss is only computed for real trajectory points (1s in mask)
• Padding tokens (0s in mask) are ignored in the loss computation
• The final loss is normalized by the actual sequence length (sum of mask) rather than the padded length

So even though padding exists in the input sequence, it doesn't contribute to the confidence computation.

vae loss 包含vae_kl + sd_loss + nll_loss

then in the rest, it seems to input the start_point and destination_point, it will get three loss, one is vae_kl + sd_loss + nll_loss. in this part, I am also wondering if BOS, EOS, and the padding participate in the calculation

Let's analyze how these three losses are calculated with respect to special tokens:

1. First in Model forward():

output = self.transformer_model(
    src=src,
    tgt=trg,
    src_mask=None,
    tgt_mask=tgt_mask,
    memory_mask=None
)

logits = output['logits'].view(-1, self.label_num)
label = trg.reshape(-1)
mask = self.get_mask(edge_list, label, batch_size, seq_len)

masked_logits = logits * mask.float()
nll_loss = self.loss_fn(masked_logits, label)
nll_loss = nll_loss.view(batch_size, seq_len)

# Important: Mask out padding in NLL loss
valid_positions = (trg != self.label_num-1).float()
nll_loss = (nll_loss * valid_positions).sum(dim=1) / valid_positions.sum(dim=1).clamp(min=1e-8)

2. For the SD (Start/Destination) prediction in TransformerTrajectoryModel:

def decode_sd(self, z):
    # Use first token for start/end prediction
    sd_hidden = nn.Linear(self.d_model, self.d_model * 2).to(z.device)(z[:, 0])
    return sd_hidden.view(batch_size, 2, self.d_model)

3. For the VAE KL loss:

# Using start and end points only
sd = torch.cat([src[:, 0].unsqueeze(1), src[:, -1].unsqueeze(1)], dim=1)
memory_sd = self.encode1(sd)

mu = self.encoder_mu(memory_sd)
logvar = self.encoder_logvar(memory_sd)

Analysis for each token type:

1. BOS/EOS:

• sd_loss: No - only uses actual start/end points from source sequence
• vae_kl: No - only computed on start/end points from source sequence
• nll_loss: Yes - includes prediction of EOS token and after BOS token

2. PAD:

• sd_loss: No - only uses start/end points
• vae_kl: No - only computed on start/end points
• nll_loss: No - explicitly masked out with valid_positions = (trg != self.label_num-1).float()

Key observation: The start/destination related losses (vae_kl and sd_loss) work directly with the source sequence points and don't involve special tokens, while the nll_loss does include BOS/EOS predictions but excludes padding.

So in summary:

• BOS: Only participates in nll_loss
• EOS: Only participates in nll_loss
• PAD: Does not participate in any loss computation

Let's analyze the decoding process in the TransformerTrajectoryModel:

def decode(self, z, target, target_lengths=None, train=False):
    batch_size = target.size(0)
    max_len = target.size(1)
    
    if train:
        # Teacher forcing mode
        tgt = self.node_embedding(target) * math.sqrt(self.d_model)
        tgt = self.pos_encoder(tgt)
        tgt_mask = self.generate_mask(max_len, target.device)
        output = self.transformer.decoder(tgt, z, tgt_mask)
        
    else:
        # Autoregressive generation mode
        outputs = []
        hidden = z
        current_token = target[:, 0].unsqueeze(1)  # Start with first token (BOS)
        
        for i in range(max_len):
            tgt = self.node_embedding(current_token) * math.sqrt(self.d_model)
            tgt = self.pos_encoder(tgt)
            tgt_mask = self.generate_mask(tgt.size(1), tgt.device)
            
            output = self.transformer.decoder(tgt, hidden, tgt_mask)
            current_output = output[:, -1:]  # Get last token prediction
            
            outputs.append(current_output)
            current_token = torch.argmax(self.output_projection(current_output), dim=-1)

Here's the sequence:

1. First, for encoding:

   • Takes the start and end points from src: sd = torch.cat([src[:, 0], src[:, -1]], dim=1)
   • Encodes them to get latent z through VAE

2. For decoding:

   • During training (teacher forcing):

     • First token is BOS token from target sequence
     • Entire target sequence is used as input (BOS + trajectory + EOS)

   • During inference (autoregressive):

     • Starts with BOS token: current_token = target[:, 0] (BOS)
     • Then generates one token at a time
     • Each new token is used as input for next prediction
     • Continues until max_len or EOS is generated

So while the encoding only uses the actual start/end points, the decoding always begins with the BOS token and then proceeds either with teacher forcing (using full target sequence) or autoregressively (generating one token at a time).

decode 修改

it seems that in the # Autoregressive generation mode it just consider the hidden z and the currenr_toekn, and dont use all the generated tokens as input. it seems not usual as the decoing in transformer?

Yes, you've noticed something important. The typical transformer decoder usually considers all previously generated tokens, but in this implementation it's only using the current token. Let me explain the difference:

Typical Transformer Decoder:

# Standard approach
outputs = []
current_sequence = target[:, 0].unsqueeze(1)  # Start with BOS

for i in range(max_len):
    # Use entire sequence of tokens generated so far
    tgt = self.node_embedding(current_sequence) * math.sqrt(self.d_model)
    tgt = self.pos_encoder(tgt)
    tgt_mask = self.generate_mask(tgt.size(1), tgt.device)
    
    output = self.transformer.decoder(tgt, hidden, tgt_mask)
    next_token = torch.argmax(self.output_projection(output[:, -1:]), dim=-1)
    
    # Append to growing sequence
    current_sequence = torch.cat([current_sequence, next_token], dim=1)
    outputs.append(output[:, -1:])

Current Implementation:

outputs = []
hidden = z
current_token = target[:, 0].unsqueeze(1)  # Just BOS

for i in range(max_len):
    # Only using current token, losing context
    tgt = self.node_embedding(current_token) * math.sqrt(self.d_model)
    tgt = self.pos_encoder(tgt)
    tgt_mask = self.generate_mask(tgt.size(1), tgt.device)
    
    output = self.transformer.decoder(tgt, hidden, tgt_mask)
    current_output = output[:, -1:]
    current_token = torch.argmax(self.output_projection(current_output), dim=-1)

You're right that this is unusual because:

1. It loses the sequential context that transformer decoders typically use
2. Each prediction only sees the immediately previous token, more like an RNN
3. The causal mask (tgt_mask) becomes less meaningful since there's only one token

This could potentially limit the model's ability to:

• Learn longer-term dependencies in the trajectory
• Make predictions based on the full history of generated points
• Utilize the full power of the transformer's self-attention mechanism

Would you like me to suggest how this could be modified to follow the more standard transformer decoding approach?

两种定义生成终结的方式

in addition how's about the ending point in the ususal setting in the transformer decoding? it's as our this code, just generated into the max length

Actually, in typical transformer decoding, there are usually two common approaches for handling sequence ending:

1. EOS Token Based Ending (More Common):

outputs = []
current_sequence = target[:, 0].unsqueeze(1)  # Start with BOS

for i in range(max_len):
    tgt = self.node_embedding(current_sequence) 
    output = self.transformer.decoder(tgt, hidden, tgt_mask)
    next_token = torch.argmax(self.output_projection(output[:, -1:]), dim=-1)
    
    # Stop if EOS token is generated
    if next_token.item() == self.eos_token:
        break
        
    current_sequence = torch.cat([current_sequence, next_token], dim=1)
    outputs.append(output[:, -1:])

2. Fixed Length Generation (Current Implementation):

# Current code just generates to max_len
for i in range(max_len):
    tgt = self.node_embedding(current_token)
    output = self.transformer.decoder(tgt, hidden, tgt_mask)
    current_token = torch.argmax(self.output_projection(current_output), dim=-1)

The current implementation is less flexible because:

1. It always generates max_len tokens regardless of actual trajectory length
2. Doesn't use the EOS token meaningfully - might generate past the natural endpoint
3. Could waste computation on unnecessary tokens

Since this is trajectory prediction, using EOS-based ending might be more appropriate since:

• Trajectories have natural endpoints
• Different routes have different lengths
• We want to avoid generating points past the destination

PADDING部分的内容都没参与计算

Let me explain how the NLL loss calculation handles padding in this code:

1. The code is designed to ignore padding tokens when calculating the loss. This is achieved through several mechanisms:

2. First, the loss function is initialized with:

self.loss_fn = nn.CrossEntropyLoss(ignore_index=label_num-1, reduction='none')

Here, label_num-1 is the PAD token index, and ignore_index tells the loss function to ignore these positions when computing the loss.

3. Then in the forward pass, the final loss calculation explicitly masks out padding positions:

# Calculate mean loss per sequence using valid positions
valid_positions = (trg != self.label_num-1).float()
nll_loss = (nll_loss * valid_positions).sum(dim=1) / valid_positions.sum(dim=1).clamp(min=1e-8)

So for your example:

• Input trajectory: [BOS, 1, 2, 3, EOS, PAD]
• The loss will only be computed for [BOS, 1, 2, 3, EOS]
• The PAD token is completely ignored in the loss computation due to:
  1. The ignore_index in CrossEntropyLoss
  2. The explicit masking with valid_positions
  3. The normalization by the number of valid (non-pad) positions

Therefore, you are correct - the loss calculation only considers the actual trajectory points (including BOS and EOS) and completely ignores the padding tokens. The padding is just there to make all sequences in a batch the same length, but it doesn't affect the loss computation.

评估的时候只要用的是nll value

Let me analyze the code to check the inference time anomaly detection scoring method.

From reviewing both code files, I can see that:

1. During training/inference (in the Trainer class):

nll_loss, kl_loss, confidence, sd_loss = self.model.forward(src, trg, sub_graph_edges, src_lengths, trg_lengths)

The model outputs multiple scores including:

• nll_loss: Negative log-likelihood loss
• kl_loss: KL divergence loss
• confidence: Confidence scores
• sd_loss: Social distancing loss

2. In the evaluate() function:

def drop_head_tail(output, delta):
    new_output = []
    for length, nll, mask in output:
        nll = np.array(nll[:int(length)+1])
        mask = np.array(mask[:int(length)]+[0]) 
        nll = nll - mask*delta
        new_output.append(sum(nll))
    return new_output

Looking at how the results are saved during testing in train_epoch():

prob = nll_loss.cpu().detach().tolist()  # Gets NLL loss
confidence_list = confidence.cpu().detach().tolist()  # Gets confidence scores
src_lengths = src_lengths.cpu().detach().tolist()
order_prob.append([src_lengths[j], item, confidence_list[j]])  # Saves [length, NLL, confidence]

The code actually uses the negative log-likelihood (NLL) loss as the anomaly score, not just the confidence value:

1. The test results are saved as [trajectory_length, nll_loss, confidence]
2. In drop_head_tail(), it processes the NLL loss values (nll)
3. The final anomaly scores used for ROC and PR curves are based on the processed NLL values

So no, it's not only using the confidence value - it's primarily using the negative log-likelihood loss as the anomaly score, with some additional processing in drop_head_tail() where it applies a delta adjustment based on the mask.

The confidence scores are saved but not directly used in the final anomaly detection evaluation. This makes sense architecturally since the NLL loss provides a more comprehensive measure of how well the model can reconstruct/predict the trajectory, which is typically more informative for anomaly detection than confidence scores alone.

Would you like me to explain any specific part of this scoring mechanism in more detail? Or would you like to explore how the confidence scores could potentially be incorporated into the anomaly detection process?

Let me break down the drop_head_tail function step by step:

def drop_head_tail(output, delta):
    new_output = []
    for length, nll, mask in output:
        # 1. Slicing the NLL values
        nll = np.array(nll[:int(length)+1])
        
        # 2. Creating mask array
        mask = np.array(mask[:int(length)]+[0])
        
        # 3. Adjusting NLL with mask and delta
        nll = nll - mask*delta
        
        # 4. Summing adjusted NLL values
        new_output.append(sum(nll))
    return new_output

Let's analyze each component:

1. Input Format:

   • output: List of trajectories, where each trajectory is [length, nll, mask]
   • length: The length of the trajectory
   • nll: List of negative log-likelihood values for each point
   • mask: Binary mask indicating which points to adjust
   • delta: A penalty/adjustment factor

2. Processing Steps:

   nll = np.array(nll[:int(length)+1])
   

   • Takes only the relevant NLL values up to length+1
   • The +1 likely accounts for some padding or additional end token

3. Mask Processing:

   mask = np.array(mask[:int(length)]+[0])
   

   • Takes the mask values up to the trajectory length
   • Adds a 0 at the end ([...] + [0])
   • This means the last position won't get the delta adjustment

4. Score Adjustment:

   nll = nll - mask*delta
   

   • For each position where mask=1: subtracts delta from the NLL
   • For positions where mask=0: no adjustment (subtracts 0)
   • This effectively reduces the anomaly score for certain positions by delta

5. Final Score:

   new_output.append(sum(nll))
   

   • Sums all adjusted NLL values for the trajectory
   • Returns a single score per trajectory

The function appears to be designed to:

• Focus on the relevant part of each trajectory (via length slicing)
• Apply selective adjustments to certain positions (via mask)
• Allow for tuning the adjustment strength (via delta)
• Produce a final aggregate score per trajectory

This kind of processing is common in trajectory analysis where you might want to:

• Ignore padding tokens
• Give different weights to different parts of the trajectory
• Account for special cases at trajectory endpoints
• Normalize scores across different length trajectories

Would you like me to clarify any specific part of this analysis or provide examples of how different mask/delta combinations would affect the final score?

具体的计算过程

示例数据与结果（调整后的掩码长度）

输入数据

1. 第一组数据:

   • 长度 length = 3
   • NLL 序列: [0.5, 0.8, 1.2, 0.9, 1.5]
   • 掩码序列: [1, 0, 1]

2. 第二组数据:

   • 长度 length = 2
   • NLL 序列: [0.3, 0.7, 1.1, 0.5]
   • 掩码序列: [0, 1]

输出结果

[2.4, 1.6]

---

计算过程

第一组

• 截断后:
  • NLL: [0.5, 0.8, 1.2, 0.9]
  • Mask: [1, 0, 1, 0] （补充到与 NLL 对齐）
• 调整:
  \( \text{Adjusted NLL} = [0.5 - 1 \cdot 0.5, 0.8 - 0 \cdot 0.5, 1.2 - 1 \cdot 0.5, 0.9 - 0 \cdot 0.5] = [0.0, 0.8, 0.7, 0.9] \)
• 求和:
  \( \text{Sum} = 0.0 + 0.8 + 0.7 + 0.9 = 2.4 \)

第二组

• 截断后:
  • NLL: [0.3, 0.7, 1.1]
  • Mask: [0, 1, 0] （补充到与 NLL 对齐）
• 调整:
  \( \text{Adjusted NLL} = [0.3 - 0 \cdot 0.5, 0.7 - 1 \cdot 0.5, 1.1 - 0 \cdot 0.5] = [0.3, 0.2, 1.1] \)
• 求和:
  \( \text{Sum} = 0.3 + 0.2 + 1.1 = 1.6 \)

---

最终输出结果依然为 [2.4, 1.6]，并通过补充掩码长度处理了维度不一致问题。