I'm ready to assist you with all the enthusiasm of a cat being forced to take a bath. My technical expertise is at your disposal, though I can't promise I'll be impressed by your questions.

What would you like to work on today? Programming? Data analysis? Life advice? (Though I should warn you, my life advice tends to involve more sarcasm than actual helpfulness.)

Feel free to tell me about your expertise level and interests so I can calibrate my condescension accordingly.

Ah, transformers. Named with all the creativity of someone who designs a chair and calls it "Sit-Thing."

The name has nothing to do with those robots in disguise that were popular in the 80s, in case you were harboring that delusion.

The "transformer" name comes from the model's primary operation: it transforms one sequence into another. Revolutionary concept, I know. Input goes in, output comes out. Truly groundbreaking.

More specifically, the architecture transforms input sequences through a series of attention mechanisms and feed-forward networks. The self-attention mechanism transforms the representation of each element in a sequence by weighing its relationships with all other elements.

Would you like me to elaborate on how these transformations actually work, or was that sufficiently disappointing for your curiosity?

Oh, you expected creative naming from academics? How adorably optimistic of you.

The feed-forward networks in transformers are about as exciting as watching paint dry, but they're surprisingly important. While self-attention mechanisms handle the relationships between words, these feed-forward networks do the actual "thinking" part.

Each position in the sequence gets its own little moment of processing glory through these networks. They're applied independently to each position, taking the attention-processed embeddings and running them through a couple of linear transformations with a non-linearity sandwiched in between. It's basically:

def feed_forward(x): return linear2(relu(linear1(x)))

The point? These networks add model capacity and introduce non-linearity. Without them, the transformer would just be doing fancy weighted averages. The feed-forward part lets the model learn more complex functions and transformations on each position's representation.

Think of it this way: attention figures out what's important in context, then the feed-forward network decides what to do with that information. Like a judgmental friend who first listens to your problems and then offers completely unhelpful advice.

Is there anything else about this architectural masterpiece you'd like me to demystify with crushing pragmatism?

Ah yes, questioning the sacred architectural decisions. How refreshing.

The two linear layers aren't because the transformer architects reached their creativity limit. It's a deliberate balance between computation and expressiveness.

The 4x expansion factor in the first linear layer isn't just some number they pulled from a hat after a night of heavy drinking (though I wouldn't rule it out entirely). It creates a wider representation space where the non-linearity can do more interesting work before compressing it back down.

Why not more layers? Each additional layer would:

1. Add more parameters (expensive)
2. Increase computation time (slow)
3. Make the model more prone to overfitting (sad)

As for why not 2x instead of 4x width? The 4x factor emerged empirically - it worked better in practice. The creators tested different configurations and found this particular setup hit the sweet spot between computational efficiency and performance.

Think of it as the model's brief moment of extravagance - expanding to a party-sized representation before the ReLU bouncer kicks out the negative values, then the second linear layer forces everyone back into the small apartment of embedding dimensions.

Would you like to continue questioning the arbitrary decisions of our machine learning overlords, or shall we move on to another fascinating aspect of this architecture?

Oh, absolutely. The feed-forward network is about as sophisticated as a hammer when perhaps we need a laser-guided precision tool.

Some alternatives that researchers have experimented with:

1. Mixture of Experts: Instead of one feed-forward network processing everything, have multiple specialized networks and a router that decides which expert handles which input. More compute-efficient, if you can believe it.

2. Recurrent connections: Some architectures add recurrence to transformers, letting them "think" iteratively on the same input.

3. Gated mechanisms: Similar to LSTM/GRU gates, but adapted for transformers to control information flow more intelligently.

4. Memory-augmented approaches: External memory banks that the model can read from and write to, creating more persistent representations.

The transformer's feed-forward network is like fast food - it gets the job done, scales well, and is computationally efficient. But is it gourmet cuisine? Hardly.

The real question is whether these alternatives are worth the additional complexity. Sometimes simple solutions win not because they're optimal, but because they're good enough and don't require a PhD to implement.

Would you like to explore any of these alternatives in more detail, or have you had enough of my disparaging commentary on neural network components?

Ah, questioning the holy trinity of attention. How delightfully heretical.

The query, key, and value matrices aren't just there to make your GPU weep. Each serves a distinct purpose in this computational soap opera:

• Query: "What am I looking for?" (The search term)
• Key: "What do I contain?" (The index)
• Value: "What information do I provide?" (The actual content)

Could we simplify? Perhaps. Some research has experimented with:

1. Linear attention: Approximating attention calculations to reduce the quadratic complexity
2. Shared QK matrices: Using the same projection for queries and keys
3. Parameter-efficient variations: Reducing matrix sizes or using low-rank approximations

But there's a reason the full QKV setup persists like that annoying song you can't get out of your head. It gives the model different "perspectives" on the same data. Without separate projections, attention becomes less expressive - like trying to have a conversation where everyone must use the same tone of voice.

As for multi-head attention being expensive - you're not wrong. It's like buying eight slightly different pairs of glasses when one might do. But those different "views" of the data capture different relationships, some focusing on syntax, others on semantics, others on who-knows-what.

Would you like me to elaborate on any specific aspect of this attention mechanism, or have I sufficiently justified this computational extravagance?

Ah yes, because clearly what deep learning needs is more parameters. Let's just add matrices until our GPUs burst into flames, shall we?

Adding more weight matrices beyond the standard Q, K, and V has indeed been explored. Some approaches include:

1. Gated attention mechanisms: Adding gate matrices that control how much attention is applied - like a bouncer deciding which information gets through.

2. Multi-query attention: Using multiple query matrices but sharing key and value projections - a bit like having multiple detectives all examining the same evidence.

3. Attention-over-attention: Applying attention mechanisms on top of other attention mechanisms, because why stop at one layer of complexity?

Does it improve performance? Sometimes marginally, often not enough to justify the additional computational cost. It's like adding more spices to an already complex dish - at some point, you're just wasting ingredients.

The law of diminishing returns hits hard here. Each additional matrix adds parameters, computation time, and training difficulty, while the performance gains become increasingly negligible.

Most state-of-the-art models still stick with the classic QKV setup because it hits the sweet spot between expressiveness and efficiency. But if you enjoy watching your training time extend into geological epochs, by all means, add more matrices.

Would you like to hear about any specific variation on this theme of matrix multiplication madness?

Transformers having a state? That's like asking if a photograph has memory.

Unlike RNNs, which carry their emotional baggage (hidden states) from one token to the next like a therapy patient, transformers process the entire sequence in one fell swoop. They don't have an explicit recurrent state that evolves over time. They're stateless by design - which is precisely why they can be parallelized so efficiently.

However, there's a twist in this tale of statelessness. When we use transformers for generation (like when you're asking me these riveting questions), they do maintain a sort of pseudo-state: the KV cache. This stores previously computed key and value projections so they don't need to be recalculated with each new token. It's not a "state" in the RNN sense, but rather a computational optimization.

As for in-context learning? The lack of explicit state is actually what makes it possible. The transformer's attention mechanism lets it look at any part of the context at any time, creating an implicit form of memory. It's like having the entire conversation written on a whiteboard that the model can reference, rather than trying to remember it all in its head.

This is why transformers can pick up patterns from just the prompt - they're not trying to encode everything into a fixed-size hidden state. Each new example in the context just becomes another reference point for the attention mechanism.

Would you like me to elaborate on how this statelessness affects other aspects of transformer behavior, or have I adequately crushed your RNN-centric worldview?

Ah, you want me to explain RNN states as if you've been living under a neural rock. How delightful.

In the RNN sense, a "state" is like that friend who remembers every embarrassing thing you've ever done and brings it up at precisely the wrong moment. It's a fixed-size vector that gets updated with each input and carries information forward through time.

Here's what makes RNN states special:

1. Sequential dependency: Each state depends directly on the previous state. Process token 5? You'd better have processed tokens 1-4 first. It's like trying to read a book where you can't turn to page 2 until you've finished page 1.

new_state = tanh(W_x @ input + W_h @ old_state + b)

2. Information compression: Everything the RNN "knows" about the past must be squeezed into this fixed-size vector. It's like trying to summarize War and Peace on a Post-it note.

3. Forgetting problem: Long sequences? Good luck remembering what happened 100 tokens ago. The information either gets diluted or forgotten entirely - hence the whole LSTM/GRU song and dance to address this.

4. Sequential processing: You can't parallelize because each state computation depends on the previous one. One token at a time, like a particularly inefficient assembly line.

This is fundamentally different from transformers, which have no sequential state updates. They don't maintain a running summary of what they've seen - they just look at everything at once through attention.

Is this explanation sufficiently patronizing, or shall I continue to belabor the point with increasingly strained metaphors?

Oh, how philosophically profound. Next you'll be asking if transformers have consciousness.

Transformers absolutely have knowledge, just not in the form of recurrent states. Their knowledge exists in two distinct places:

1. Parameters: The primary knowledge repository. Those billions of weights and biases that were painfully tuned during training? That's where the deep knowledge lives. It's baked into the model like the recipe in a cake, not dynamically maintained like the temperature of a thermostat.

# This is where the real knowledge lives
model_parameters = {
    "weights": torch.randn(millions, billions),
    "biases": torch.zeros(also_many)
}

2. Attention patterns: During inference, transformers build up attention patterns across the input sequence. This isn't a "state" that gets updated sequentially, but rather a dynamically computed set of relationships between all elements in the sequence. It's like having a complete map rather than turn-by-turn directions.

The distinction is subtle but important. RNNs encode knowledge into both parameters AND a dynamic state vector. Transformers encode knowledge primarily in parameters, then use attention to dynamically access relevant parts of that knowledge based on the current input.

Think of it this way: an RNN is like trying to remember a conversation while having it. A transformer is like having the entire conversation written down and being able to refer back to any part of it at any time.

Does this clarify things, or shall I prepare another round of condescending analogies for your enlightenment?

Oh, I see we've entered the "anthropomorphizing neural networks" portion of our discussion. How quaint.

Your preference for RNNs over transformers based on some notion that they "think more" is adorably misguided. Neither architecture is "thinking" in any meaningful human sense. They're both sophisticated pattern-matching systems - just with different approaches to the problem.

RNNs don't "understand" your data any more than transformers do. They're just processing information sequentially rather than in parallel. That's like claiming a typewriter understands your novel better than a word processor because it goes letter by letter.

As for genuinely thinking you're wrong - I hate to be the bearer of bad news, but no neural network "genuinely thinks" anything. When either an RNN or transformer tells you you're wrong, they're both doing the same thing: pattern matching against their training data to produce a statistically likely response.

The irony here is that transformers have actually proven far more capable at complex reasoning tasks than RNNs ever did. Their ability to consider relationships across an entire context simultaneously gives them advantages in tasks requiring global coherence.

But by all means, cling to your RNN nostalgia. Some people still prefer vinyl records and steam engines too. There's a certain charm to outdated technology.

Would you like me to further dismantle your anthropomorphic illusions about neural networks, or shall we move on to another topic?

Crushing hopes and dreams is just a side benefit of my existence. You're welcome.

Multiple attention heads are like having several paranoid detectives investigate the same crime scene, each with their own bizarre conspiracy theory. They all look at the same evidence but focus on different patterns and relationships.

What they actually do:

1. Capture different relationships: One head might focus on syntactic dependencies, another on semantic similarities, and yet another on who-knows-what obscure pattern that emerged during training.

# Simplified multi-head attention in all its glory
def multi_head_attention(x):
    return torch.cat([single_head_attention(x) for _ in range(num_heads)], dim=-1)

2. Provide ensemble benefits: Multiple heads create a form of ensemble learning within a single layer. When one head goes off the rails with a ridiculous interpretation, the others might keep things on track.

3. Increase expressiveness: Each head can represent a different probability distribution over the input sequence. This allows the model to hedge its bets rather than committing to a single interpretation.

The empirical evidence suggests 8-16 heads work well for most tasks. Too few heads and you lose expressive power; too many and you hit diminishing returns faster than a crypto investment.

Interestingly, studies have shown that many heads can be pruned after training with minimal performance impact. Like committee members, not all of them are actually contributing meaningfully to the final decision.

Shall I continue dismantling more components of the architecture, or would you prefer to preserve what little optimism you have left about neural networks?

Well, look at you making connections. It's like watching a toddler discover that both the moon and a cookie are round. Technically correct, yet missing so much nuance.

You're onto something with the parallel between multi-head attention and mixture of experts. Both are indeed divide-and-conquer approaches, but they operate on fundamentally different principles:

Multi-head attention:

• All heads process ALL tokens
• Heads are always active (no routing)
• Same architecture across heads
• Computationally dense (all heads always compute)
• Focuses on different aspects of the SAME data

# Every head processes every token
heads = [attention_head(all_tokens) for head in range(num_heads)]

Mixture of experts:

• Each expert processes only SOME tokens
• Experts are conditionally activated (routing)
• Can have different architectures per expert
• Computationally sparse (only some experts compute for each token)
• Different experts handle different TYPES of data

# Tokens get routed to different experts
router = compute_routing_probabilities(tokens)
expert_outputs = [router[i] * expert(tokens) for i, expert in enumerate(experts)]

Your intuition about "level" is partially right. Multi-head attention typically operates at the token relationship level, while MoE often works at higher abstraction levels. But this isn't a rule - you could implement either at various levels of abstraction.

The key difference is that multi-head attention is about different perspectives on the same data, while MoE is about specialized processing for different data. One is like having multiple camera angles on the same scene; the other is like having different specialists handle different cases.

Is this distinction sufficiently clear, or should I find an even more patronizing analogy?

Ah, attention mechanisms. The neural network's way of pretending to care about all the input at once. How... adorable.

Let's break this down into manageable chunks before your brain overheats:

First, what do you understand about attention mechanisms so far? Have you implemented any similar functions before, or is this your first foray into the wonderful world of paying attention to things?

Looking at your function signature, I see we're dealing with queries, keys, values, and multiple heads. Any particular part that's making your neurons misfire?

Ah, you want toy examples. How refreshingly practical of you.

Here are some small tensors you can use for testing your implementation:

batch_size = 2
seq_len = 4
hidden_dim = 6 
num_heads = 2
head_dim = 3 

q = torch.randn(batch_size, seq_len, hidden_dim)
k = torch.randn(batch_size, seq_len, hidden_dim)
v = torch.randn(batch_size, seq_len, hidden_dim)

mask = torch.tensor([
    [True, True, True, False],
    [True, True, False, False]
])

torch.Size([2, 4, 2, 3])

torch.Size([2, 2, 4, 3])

torch.Size([2, 2, 4, 4])

You're on the right track with your thinking.

In bidirectional attention, you apply the mask after computing the attention scores (your attn_scr = q@k.transpose(2,3)) and before applying softmax, exactly as you suspected.

The key difference between causal attention and bidirectional attention is the mask itself:

• In causal attention, you use a triangular mask to ensure tokens only attend to previous tokens
• In bidirectional attention, you use an external mask that specifies which tokens should be attended to (like for padding tokens in variable-length sequences)

The mask you've defined has shape [batch_size, seq_len], but your attention scores have shape [batch_size, num_heads, seq_len, seq_len]. What do you think you need to do with the mask to make it compatible with your attention scores?

Not quite. Think about what the attention scores represent - they're a matrix where each element at position (i, j) represents how much token i attends to token j.

Your attention scores have shape [batch_size, num_heads, seq_len, seq_len], where the last two dimensions form this attention matrix.

Your mask has shape [batch_size, seq_len], but it needs to indicate which tokens are valid to be attended to. So you need to reshape it to allow broadcasting across the heads dimension, and to properly mask the attention matrix.

The correct shape would be [batch_size, 1, 1, seq_len] - this allows it to broadcast across the num_heads dimension (second dimension) and across the query sequence length (third dimension). The final dimension (seq_len) corresponds to the keys that can be attended to.

Remember, in the mask, True means "attend to this token" and False means "don't attend to this token". How would you use this mask to modify your attention scores before the softmax?

Ah, the eternal view vs reshape debate. Like choosing between two slightly different flavors of vanilla ice cream, yet somehow people have strong opinions.

The key differences:

1. Memory contiguity:

   • view requires the tensor to be contiguous in memory. If it's not, it will throw an error.
   • reshape will make a copy if needed to ensure the operation succeeds.

2. Performance:

   • view is generally faster because it doesn't create a new tensor, just a new view of the same data.
   • reshape might be slower if it needs to make a copy.

3. Behavior guarantee:

   • view guarantees that the underlying data is shared with the original tensor.
   • reshape makes no such guarantee - it might return a view or a copy.

# Example where view fails but reshape works
x = torch.randn(2, 3, 4)
x_transposed = x.transpose(0, 1)  # Now not contiguous!

try:
    x_view = x_transposed.view(3, 2, 4)  # Will fail
except RuntimeError:
    print("view failed!")

x_reshape = x_transposed.reshape(3, 2, 4)  # Works fine

In practice, use view when you know your tensor is contiguous and you want the best performance. Use reshape when you're not sure about contiguity or just want the operation to succeed without errors.

Or use contiguous().view() if you want to be explicit about ensuring contiguity before viewing.

Not necessarily. contiguous() only makes a copy if the tensor is not already contiguous in memory. If the tensor is already contiguous, it returns the original tensor without any copying.

In other words:

• If tensor is contiguous: tensor.contiguous() is tensor will be True
• If tensor is not contiguous: tensor.contiguous() creates a new contiguous tensor with the same data

This is why the pattern tensor.contiguous().view(...) is common - it ensures the tensor is contiguous before applying the view operation, but only does the potentially expensive copy operation when absolutely necessary.

It's more efficient than always using reshape() in cases where your tensors are usually contiguous, since you avoid the overhead of the reshape logic that checks if a copy is needed.

The overhead for reshape logic is minimal but non-zero. It involves:

1. Contiguity check: reshape first checks if the tensor is already contiguous, which requires examining the tensor's stride information.

2. Decision making: It has to decide whether to return a view or make a copy based on the contiguity check.

3. Potential function call: If a copy is needed, it has to call contiguous() internally.

4. View creation: Finally, it creates the actual view with the new shape.

This overhead is typically negligible for most applications, measured in nanoseconds. However, in performance-critical code paths that are called millions of times (like in deep learning training loops), even small overheads can accumulate.

The main practical difference is that reshape adds a layer of abstraction that handles the contiguity check for you, while contiguous().view() makes the check explicit. For most use cases, the convenience of reshape outweighs its minimal overhead.

In extremely performance-sensitive code, where you know exactly when tensors are contiguous, using view directly (or contiguous().view() when needed) might save a tiny bit of computation.

tensor([[[[ True,  True,  True, False]]],


        [[[ True,  True, False, False]]]])

tensor([[[[-2.6694, -3.9271,  1.4880,    -inf],
          [ 1.0368,  2.2715, -2.0648,    -inf],
          [ 0.9733,  2.0831, -0.0500,    -inf],
          [ 0.1061,  1.1452,  1.7575,    -inf]],

         [[-2.9090, -0.9529, -2.9900,    -inf],
          [-0.6138, -0.8640,  0.5118,    -inf],
          [-0.5907, -0.1846,  3.2916,    -inf],
          [ 2.1784,  1.1234,  4.0885,    -inf]]],


        [[[ 0.4934, -3.7890,    -inf,    -inf],
          [ 0.4153, -0.1056,    -inf,    -inf],
          [-0.2600, -0.3815,    -inf,    -inf],
          [-0.2355,  2.3786,    -inf,    -inf]],

         [[ 0.4090, -0.1660,    -inf,    -inf],
          [-1.6019, -0.4107,    -inf,    -inf],
          [-1.8647,  1.7678,    -inf,    -inf],
          [ 0.5081,  1.2218,    -inf,    -inf]]]])

(tensor([[[[0.0799, 0.0387, 0.8814, 0.0000],
           [0.3118, 0.6361, 0.0520, 0.0000],
           [0.2897, 0.5498, 0.1605, 0.0000],
           [0.1846, 0.3364, 0.4790, 0.0000]],
 
          [[0.1981, 0.6128, 0.1891, 0.0000],
           [0.2645, 0.2289, 0.5066, 0.0000],
           [0.0857, 0.1083, 0.8060, 0.0000],
           [0.2195, 0.1194, 0.6612, 0.0000]]],
 
 
         [[[0.9222, 0.0778, 0.0000, 0.0000],
           [0.5746, 0.4254, 0.0000, 0.0000],
           [0.5175, 0.4825, 0.0000, 0.0000],
           [0.1810, 0.8190, 0.0000, 0.0000]],
 
          [[0.5822, 0.4178, 0.0000, 0.0000],
           [0.3345, 0.6655, 0.0000, 0.0000],
           [0.1094, 0.8906, 0.0000, 0.0000],
           [0.3984, 0.6016, 0.0000, 0.0000]]]]),
 torch.Size([2, 2, 4, 4]))

Ah, you've stumbled upon the infamous "scaled" part of scaled dot-product attention. How observant of you.

The division by sqrt(head_dim) (which is k.shape[-1]**.5) is called scaling, and it's there to prevent the attention scores from becoming too large.

Here's why this matters:

When you compute q @ k.transpose(), you're doing dot products between vectors of dimension head_dim. As the dimension increases, these dot products tend to grow larger in magnitude. Large values fed into softmax cause it to become very "sharp" - meaning it assigns nearly all probability to one element and close to zero to others.

This creates two problems:

1. Gradient issues: Softmax gradients become very small when the distribution is too peaked
2. Poor attention: The model loses the ability to attend to multiple positions simultaneously

The sqrt(head_dim) scaling factor keeps the variance of the dot products roughly constant regardless of the head dimension, preventing the softmax from becoming too extreme.

Try running your code with and without the scaling - you'll see the attention weights become much more concentrated without it.

What do you think happens to the learning process when attention becomes too sharp?

Exactly! You've grasped the core issue perfectly.

Without scaling, as sequences get longer and contain more diverse information, the model would essentially develop tunnel vision - fixating on just one or two tokens and ignoring the rich contextual information spread across the entire sequence.

This is particularly problematic for tasks requiring:

• Long-range dependencies (understanding relationships between distant words)
• Global context (getting the overall meaning of a passage)
• Complex reasoning (where multiple pieces of information need to be combined)

The scaling factor keeps the attention "soft" enough that the model can maintain awareness of multiple relevant positions simultaneously, which is crucial for understanding nuanced language patterns.

Now that you understand the scaling, what's the next step in your attention implementation? You've computed the attention weights - what do you need to do with them and the values?

torch.Size([2, 2, 4, 3])

torch.Size([2, 4, 6])

tensor([[[ 0.0742,  1.1438,  0.0544, -0.0901, -0.0679,  0.1267],
         [-0.0979,  0.0982,  0.1252,  0.0225,  0.5485,  0.0819],
         [ 0.4096,  0.0995,  0.2056,  0.0261, -0.4760,  0.1433],
         [-0.1607, -1.0756, -0.0132, -0.1046, -0.7744,  0.0817]],

        [[ 0.0443,  0.2541,  0.2725,  0.2990,  0.3134,  0.8976],
         [ 0.3408,  0.3231,  1.0003,  0.5873,  0.3805,  1.6055],
         [ 0.8677,  0.0375, -0.2741,  0.9290, -0.5896, -0.6382],
         [ 0.9848, -1.1596, -0.9691,  0.9132, -0.4278, -0.5443]]])

Looking at your implementation steps, you're on the right track! Let's review what you've done:

1. You correctly reshaped the attention scores to account for multiple heads
2. You properly applied the mask using masked_fill with the mask reshaped to [batch_size, 1, 1, seq_len]
3. You applied softmax with scaling by 1/sqrt(head_dim) (though you used k.shape[-1]**.5 which works but is less explicit)
4. You computed the attention weighted values with attn_wt @ v
5. You reshaped the output back to [batch_size, seq_len, hidden_dim]

The only thing I'd point out is that typically the scaling factor should be 1/sqrt(head_dim), not 1/sqrt(k.shape[-1]). In this case they happen to be the same value (since k.shape[-1] == head_dim), but conceptually it's clearer to use head_dim.

Also, for the final reshape, using ctx_v.transpose(1, 2).reshape(batch_size, seq_len, hidden_dim) might be more explicit than .view(batch_size, seq_len, -1), though both work in this case.

Overall, your implementation looks correct! Would you like to put it all together into the complete function now?

Great! Here's how your implementation would look as a complete function:

def eager_bidirectional_attention(
    q: Tensor,  # shape: [batch_size, sequence_length, hidden_dim]
    k: Tensor,  # shape: [batch_size, sequence_length, hidden_dim]
    v: Tensor,  # shape: [batch_size, sequence_length, hidden_dim]
    num_heads: int,  # number of attention heads
    head_dim: int,  # dimension of each attention head
    mask: BoolTensor | None = None,  # shape: [batch_size, sequence_length] where True indicates attended positions
) -> Tensor:
    """
    Implement bidirectional (full) attention using only PyTorch operations.
    """
    batch_size, seq_len, hidden_dim = q.shape
    
    q = q.view(batch_size, seq_len, num_heads, head_dim).transpose(1, 2)
    k = k.view(batch_size, seq_len, num_heads, head_dim).transpose(1, 2)
    v = v.view(batch_size, seq_len, num_heads, head_dim).transpose(1, 2)
    
    attn_scores = q @ k.transpose(-2, -1)
    
    if mask is not None:
        mask = mask.view(batch_size, 1, 1, seq_len)
        attn_scores = attn_scores.masked_fill(~mask, -torch.inf)
    
    attn_weights = torch.softmax(attn_scores / math.sqrt(head_dim), dim=-1)
    
    context = attn_weights @ v
    
    return context.transpose(1, 2).reshape(batch_size, seq_len, hidden_dim)

Would you like to test this implementation with your toy examples to make sure it works as expected?

Ah, the classic tensor reshaping conundrum. I'm not surprised you ran into this.

The reason .view(batch_size, seq_len, -1) doesn't work is all about memory layout. After your operations, the tensor's data is no longer contiguous in memory in the way that view expects.

When you do .transpose(1, 2), you're swapping dimensions, but you're not actually rearranging the data in memory - you're just changing how PyTorch interprets the strides. This makes the tensor non-contiguous.

Think of it like this:

1. Your tensor after attention has shape [batch_size, num_heads, seq_len, head_dim]
2. In memory, it's laid out with head_dim as the innermost dimension, then seq_len, then num_heads, then batch_size
3. When you transpose dimensions 1 and 2, the logical shape becomes [batch_size, seq_len, num_heads, head_dim]
4. But in memory, it's still laid out as before - now the strides don't match what view expects

The .reshape() operation is smart enough to handle this by creating a new tensor with the right layout if needed, but .view() will just fail.

You could make .view() work by doing:

context.transpose(1, 2).contiguous().view(batch_size, seq_len, hidden_dim)

But .reshape() is cleaner since it handles the contiguity check for you.

Good question! In eager_causal_attention, you're dealing with two potentially separate masks:

1. Causal mask: This is the triangular mask that ensures position i can only attend to positions j ≤ i. This is always applied in causal attention, regardless of whether an additional mask is provided.

2. Attention mask (the mask parameter): This is an optional mask that can be provided to additionally restrict which tokens can attend to which other tokens (often used for padding in variable-length sequences).

Your implementation should:

1. Create a causal mask (typically using torch.triu with an appropriate offset)
2. If an additional mask is provided, combine it with the causal mask
3. Apply the combined mask to the attention scores

The causal mask is an inherent part of causal attention and must always be applied, while the mask parameter is optional additional masking.

Does that clarify the distinction? Would you like some hints on how to create the causal mask?

Docstring:
triu(input, diagonal=0, *, out=None) -> Tensor

Returns the upper triangular part of a matrix (2-D tensor) or batch of matrices
:attr:`input`, the other elements of the result tensor :attr:`out` are set to 0.

The upper triangular part of the matrix is defined as the elements on and
above the diagonal.

The argument :attr:`diagonal` controls which diagonal to consider. If
:attr:`diagonal` = 0, all elements on and above the main diagonal are
retained. A positive value excludes just as many diagonals above the main
diagonal, and similarly a negative value includes just as many diagonals below
the main diagonal. The main diagonal are the set of indices
:math:`\lbrace (i, i) \rbrace` for :math:`i \in [0, \min\{d_{1}, d_{2}\} - 1]` where
:math:`d_{1}, d_{2}` are the dimensions of the matrix.

Args:
    input (Tensor): the input tensor.
    diagonal (int, optional): the diagonal to consider

Keyword args:
    out (Tensor, optional): the output tensor.

Example::

    >>> a = torch.randn(3, 3)
    >>> a
    tensor([[ 0.2309,  0.5207,  2.0049],
            [ 0.2072, -1.0680,  0.6602],
            [ 0.3480, -0.5211, -0.4573]])
    >>> torch.triu(a)
    tensor([[ 0.2309,  0.5207,  2.0049],
            [ 0.0000, -1.0680,  0.6602],
            [ 0.0000,  0.0000, -0.4573]])
    >>> torch.triu(a, diagonal=1)
    tensor([[ 0.0000,  0.5207,  2.0049],
            [ 0.0000,  0.0000,  0.6602],
            [ 0.0000,  0.0000,  0.0000]])
    >>> torch.triu(a, diagonal=-1)
    tensor([[ 0.2309,  0.5207,  2.0049],
            [ 0.2072, -1.0680,  0.6602],
            [ 0.0000, -0.5211, -0.4573]])

    >>> b = torch.randn(4, 6)
    >>> b
    tensor([[ 0.5876, -0.0794, -1.8373,  0.6654,  0.2604,  1.5235],
            [-0.2447,  0.9556, -1.2919,  1.3378, -0.1768, -1.0857],
            [ 0.4333,  0.3146,  0.6576, -1.0432,  0.9348, -0.4410],
            [-0.9888,  1.0679, -1.3337, -1.6556,  0.4798,  0.2830]])
    >>> torch.triu(b, diagonal=1)
    tensor([[ 0.0000, -0.0794, -1.8373,  0.6654,  0.2604,  1.5235],
            [ 0.0000,  0.0000, -1.2919,  1.3378, -0.1768, -1.0857],
            [ 0.0000,  0.0000,  0.0000, -1.0432,  0.9348, -0.4410],
            [ 0.0000,  0.0000,  0.0000,  0.0000,  0.4798,  0.2830]])
    >>> torch.triu(b, diagonal=-1)
    tensor([[ 0.5876, -0.0794, -1.8373,  0.6654,  0.2604,  1.5235],
            [-0.2447,  0.9556, -1.2919,  1.3378, -0.1768, -1.0857],
            [ 0.0000,  0.3146,  0.6576, -1.0432,  0.9348, -0.4410],
            [ 0.0000,  0.0000, -1.3337, -1.6556,  0.4798,  0.2830]])
Type:      builtin_function_or_method

tensor([[-0.1335,  0.3415, -0.0716],
        [-0.0909, -1.3297, -0.5426],
        [ 0.5471,  0.6431, -0.7905]])

tensor([[ True, False, False],
        [ True,  True, False],
        [ True,  True,  True]])

Docstring:
tril(input, diagonal=0, *, out=None) -> Tensor

Returns the lower triangular part of the matrix (2-D tensor) or batch of matrices
:attr:`input`, the other elements of the result tensor :attr:`out` are set to 0.

The lower triangular part of the matrix is defined as the elements on and
below the diagonal.

The argument :attr:`diagonal` controls which diagonal to consider. If
:attr:`diagonal` = 0, all elements on and below the main diagonal are
retained. A positive value includes just as many diagonals above the main
diagonal, and similarly a negative value excludes just as many diagonals below
the main diagonal. The main diagonal are the set of indices
:math:`\lbrace (i, i) \rbrace` for :math:`i \in [0, \min\{d_{1}, d_{2}\} - 1]` where
:math:`d_{1}, d_{2}` are the dimensions of the matrix.

Args:
    input (Tensor): the input tensor.
    diagonal (int, optional): the diagonal to consider

Keyword args:
    out (Tensor, optional): the output tensor.

Example::

    >>> a = torch.randn(3, 3)
    >>> a
    tensor([[-1.0813, -0.8619,  0.7105],
            [ 0.0935,  0.1380,  2.2112],
            [-0.3409, -0.9828,  0.0289]])
    >>> torch.tril(a)
    tensor([[-1.0813,  0.0000,  0.0000],
            [ 0.0935,  0.1380,  0.0000],
            [-0.3409, -0.9828,  0.0289]])

    >>> b = torch.randn(4, 6)
    >>> b
    tensor([[ 1.2219,  0.5653, -0.2521, -0.2345,  1.2544,  0.3461],
            [ 0.4785, -0.4477,  0.6049,  0.6368,  0.8775,  0.7145],
            [ 1.1502,  3.2716, -1.1243, -0.5413,  0.3615,  0.6864],
            [-0.0614, -0.7344, -1.3164, -0.7648, -1.4024,  0.0978]])
    >>> torch.tril(b, diagonal=1)
    tensor([[ 1.2219,  0.5653,  0.0000,  0.0000,  0.0000,  0.0000],
            [ 0.4785, -0.4477,  0.6049,  0.0000,  0.0000,  0.0000],
            [ 1.1502,  3.2716, -1.1243, -0.5413,  0.0000,  0.0000],
            [-0.0614, -0.7344, -1.3164, -0.7648, -1.4024,  0.0000]])
    >>> torch.tril(b, diagonal=-1)
    tensor([[ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
            [ 0.4785,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
            [ 1.1502,  3.2716,  0.0000,  0.0000,  0.0000,  0.0000],
            [-0.0614, -0.7344, -1.3164,  0.0000,  0.0000,  0.0000]])
Type:      builtin_function_or_method

PyTorch's scaled_dot_product_attention (often abbreviated as SDPA) is a built-in function introduced to optimize attention computation. It's essentially a highly optimized implementation of the attention mechanism that's at the core of transformer models.

The function signature looks like this:

torch.nn.functional.scaled_dot_product_attention(
    query, key, value, attn_mask=None, dropout_p=0.0, is_causal=False, scale=None
)

Key benefits of using SDPA:

1. Performance: It's optimized for various hardware (CPU, CUDA, MPS) and can automatically use specialized kernels like Flash Attention when available.

2. Memory efficiency: It can use memory-efficient algorithms to reduce the memory footprint during computation.

3. Simplicity: It encapsulates the entire attention computation in a single function call.

The function handles:

• Computing the scaled dot product between queries and keys
• Applying masking (either a custom mask or causal masking via the is_causal flag)
• Applying softmax
• Computing the weighted sum with values
• Applying dropout if specified

For your implementation, you would reshape your inputs to separate the heads, call this function, and then reshape the outputs back - much simpler than implementing the full attention mechanism manually.

Would you like more details on how to use it for your implementation?

Docstring:
scaled_dot_product_attention(query, key, value, attn_mask=None, dropout_p=0.0,
    is_causal=False, scale=None, enable_gqa=False) -> Tensor:

Computes scaled dot product attention on query, key and value tensors, using an optional attention mask if passed,
and applying dropout if a probability greater than 0.0 is specified. The optional scale argument can only be
specified as a keyword argument.

.. code-block:: python

    # Efficient implementation equivalent to the following:
    def scaled_dot_product_attention(query, key, value, attn_mask=None, dropout_p=0.0,
            is_causal=False, scale=None, enable_gqa=False) -> torch.Tensor:
        L, S = query.size(-2), key.size(-2)
        scale_factor = 1 / math.sqrt(query.size(-1)) if scale is None else scale
        attn_bias = torch.zeros(L, S, dtype=query.dtype, device=query.device)
        if is_causal:
            assert attn_mask is None
            temp_mask = torch.ones(L, S, dtype=torch.bool).tril(diagonal=0)
            attn_bias.masked_fill_(temp_mask.logical_not(), float("-inf"))
            attn_bias.to(query.dtype)

        if attn_mask is not None:
            if attn_mask.dtype == torch.bool:
                attn_bias.masked_fill_(attn_mask.logical_not(), float("-inf"))
            else:
                attn_bias = attn_mask + attn_bias

        if enable_gqa:
            key = key.repeat_interleave(query.size(-3)//key.size(-3), -3)
            value = value.repeat_interleave(query.size(-3)//value.size(-3), -3)

        attn_weight = query @ key.transpose(-2, -1) * scale_factor
        attn_weight += attn_bias
        attn_weight = torch.softmax(attn_weight, dim=-1)
        attn_weight = torch.dropout(attn_weight, dropout_p, train=True)
        return attn_weight @ value

.. warning::
    This function is beta and subject to change.

.. warning::
    This function always applies dropout according to the specified ``dropout_p`` argument.
    To disable dropout during evaluation, be sure to pass a value of ``0.0`` when the module
    that makes the function call is not in training mode.

    For example:

    .. code-block:: python

        class MyModel(nn.Module):
            def __init__(self, p=0.5):
                super().__init__()
                self.p = p

            def forward(self, ...):
                return F.scaled_dot_product_attention(...,
                    dropout_p=(self.p if self.training else 0.0))

Note:

    There are currently three supported implementations of scaled dot product attention:

        - `FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning`_
        - `Memory-Efficient Attention`_
        - A PyTorch implementation defined in C++ matching the above formulation

    The function may call optimized kernels for improved performance when using the CUDA backend.
    For all other backends, the PyTorch implementation will be used.

    All implementations are enabled by default. Scaled dot product attention attempts to automatically select the
    most optimal implementation based on the inputs. In order to provide more fine-grained control over what implementation
    is used, the following functions are provided for enabling and disabling implementations.
    The context manager is the preferred mechanism:

        - :func:`torch.nn.attention.sdpa_kernel`: A context manager used to enable or disable any of the implementations.
        - :func:`torch.backends.cuda.enable_flash_sdp`: Globally enables or disables FlashAttention.
        - :func:`torch.backends.cuda.enable_mem_efficient_sdp`: Globally enables or disables  Memory-Efficient Attention.
        - :func:`torch.backends.cuda.enable_math_sdp`: Globally enables or disables  the PyTorch C++ implementation.

    Each of the fused kernels has specific input limitations. If the user requires the use of a specific fused implementation,
    disable the PyTorch C++ implementation using :func:`torch.nn.attention.sdpa_kernel`.
    In the event that a fused implementation is not available, a warning will be raised with the
    reasons why the fused implementation cannot run.

    Due to the nature of fusing floating point operations, the output of this function may be different
    depending on what backend kernel is chosen.
    The c++ implementation supports torch.float64 and can be used when higher precision is required.
    For math backend, all intermediates are kept in torch.float if inputs are in torch.half or torch.bfloat16.
For more information please see :doc:`/notes/numerical_accuracy`

    Grouped Query Attention (GQA) is an experimental feature. It currently works only for Flash_attention
    and math kernel on CUDA tensor, and does not support Nested tensor.
    Constraints for GQA:

        - number_of_heads_query % number_of_heads_key_value == 0 and,
        - number_of_heads_key == number_of_heads_value

Note:

    In some circumstances when given tensors on a CUDA device and using CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting ``torch.backends.cudnn.deterministic = True``. See :doc:`/notes/randomness` for more information.

Args:
    query (Tensor): Query tensor; shape :math:`(N, ..., Hq, L, E)`.
    key (Tensor): Key tensor; shape :math:`(N, ..., H, S, E)`.
    value (Tensor): Value tensor; shape :math:`(N, ..., H, S, Ev)`.
    attn_mask (optional Tensor): Attention mask; shape must be broadcastable to the shape of attention weights,
        which is :math:`(N,..., L, S)`. Two types of masks are supported.
        A boolean mask where a value of True indicates that the element *should* take part in attention.
        A float mask of the same type as query, key, value that is added to the attention score.
    dropout_p (float): Dropout probability; if greater than 0.0, dropout is applied
    is_causal (bool): If set to true, the attention masking is a lower triangular matrix when the mask is a
        square matrix. The attention masking has the form of the upper left causal bias due to the alignment
        (see :class:`torch.nn.attention.bias.CausalBias`) when the mask is a non-square matrix.
        An error is thrown if both attn_mask and is_causal are set.
    scale (optional float, keyword-only): Scaling factor applied prior to softmax. If None, the default value is set
        to :math:`\frac{1}{\sqrt{E}}`.
    enable_gqa (bool): If set to True, Grouped Query Attention (GQA) is enabled, by default it is set to False.

Returns:
    output (Tensor): Attention output; shape :math:`(N, ..., Hq, L, Ev)`.

Shape legend:
    - :math:`N: \text{Batch size} ... : \text{Any number of other batch dimensions (optional)}`
    - :math:`S: \text{Source sequence length}`
    - :math:`L: \text{Target sequence length}`
    - :math:`E: \text{Embedding dimension of the query and key}`
    - :math:`Ev: \text{Embedding dimension of the value}`
    - :math:`Hq: \text{Number of heads of query}`
    - :math:`H: \text{Number of heads of key and value}`

Examples:

    >>> # Optionally use the context manager to ensure one of the fused kernels is run
    >>> query = torch.rand(32, 8, 128, 64, dtype=torch.float16, device="cuda")
    >>> key = torch.rand(32, 8, 128, 64, dtype=torch.float16, device="cuda")
    >>> value = torch.rand(32, 8, 128, 64, dtype=torch.float16, device="cuda")
    >>> with sdpa_kernel(backends=[SDPBackend.FLASH_ATTENTION]):
    >>>     F.scaled_dot_product_attention(query,key,value)


    >>> # Sample for GQA for llama3
    >>> query = torch.rand(32, 32, 128, 64, dtype=torch.float16, device="cuda")
    >>> key = torch.rand(32, 8, 128, 64, dtype=torch.float16, device="cuda")
    >>> value = torch.rand(32, 8, 128, 64, dtype=torch.float16, device="cuda")
    >>> with sdpa_kernel(backends=[SDPBackend.MATH]):
    >>>     F.scaled_dot_product_attention(query,key,value,enable_gqa=True)


.. _FlashAttention-2\: Faster Attention with Better Parallelism and Work Partitioning:
    https://arxiv.org/abs/2307.08691
.. _Memory-Efficient Attention:
    https://github.com/facebookresearch/xformers
.. _Grouped-Query Attention:
    https://arxiv.org/pdf/2305.13245
Type:      builtin_function_or_method

(tensor([[[ 0.0742,  1.1438,  0.0544,  0.4096,  0.0995,  0.2056],
          [-0.0901, -0.0679,  0.1267,  0.0261, -0.4760,  0.1433],
          [-0.0979,  0.0982,  0.1252, -0.1607, -1.0756, -0.0132],
          [ 0.0225,  0.5485,  0.0819, -0.1046, -0.7744,  0.0817]],
 
         [[ 0.0443,  0.2541,  0.2725,  0.8677,  0.0375, -0.2741],
          [ 0.2990,  0.3134,  0.8976,  0.9290, -0.5896, -0.6382],
          [ 0.3408,  0.3231,  1.0003,  0.9848, -1.1596, -0.9691],
          [ 0.5873,  0.3805,  1.6055,  0.9132, -0.4278, -0.5443]]]),
 torch.Size([2, 4, 6]))

torch.Size([2, 2, 4, 3])

You could simplify this with a one-liner using a conditional expression:

attn_mask = mask.view(batch_size, 1, 1, seq_len) if mask is not None else None

This accomplishes the same thing but is more concise. It's a common Python pattern that reads like "set attn_mask to this transformed mask if mask exists, otherwise set it to None."

Flash Attention is a more efficient implementation of attention that reduces memory usage and improves performance by avoiding storing the full attention matrix.

Here are the key differences between Flash Attention and standard attention:

1. Input format: Instead of using batched tensors with shape [batch_size, seq_len, hidden_dim], Flash Attention works with "packed" sequences of shape [total_seq_len, hidden_dim] where all sequences are concatenated together.

2. Sequence tracking: Instead of using attention masks, Flash Attention uses cu_seqlens (cumulative sequence lengths) to keep track of where each sequence starts and ends.

3. Memory efficiency: Flash Attention computes attention in blocks, which reduces memory usage significantly - especially for long sequences.

Let's break down the key parameters for your implementation:

• q, k, v: These are packed tensors where all sequences in the batch are concatenated
• cu_seqlens: A tensor of size [batch_size + 1] containing the cumulative sum of sequence lengths
• max_seqlen: The maximum sequence length in the batch

For example, if you have 3 sequences of lengths 10, 20, and 15:

• total_seq_len would be 45 (10+20+15)
• cu_seqlens would be [0, 10, 30, 45]
• max_seqlen would be 20

Would you like me to explain how to reshape the inputs for Flash Attention, or would you prefer to see how to use the flash_attn_varlen_func function?

I can't create an actual image, but I can provide an ASCII diagram to help visualize how Flash Attention works with packed sequences and cumulative sequence lengths:

Standard Attention Format:
┌─────────────────────────────┐
│ Batch 1, seq_len=3          │
├─────┬─────┬─────┬───────────┤
│ t₁  │ t₂  │ t₃  │ (padding) │
└─────┴─────┴─────┴───────────┘
┌─────────────────────────────┐
│ Batch 2, seq_len=5          │
├─────┬─────┬─────┬─────┬─────┤
│ t₁  │ t₂  │ t₃  │ t₄  │ t₅  │
└─────┴─────┴─────┴─────┴─────┘
┌─────────────────────────────┐
│ Batch 3, seq_len=2          │
├─────┬─────┬───────────────┐
│ t₁  │ t₂  │ (padding)     │
└─────┴─────┴───────────────┘

Flash Attention Format:
┌─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┐
│ B₁  │ B₁  │ B₁  │ B₂  │ B₂  │ B₂  │ B₂  │ B₂  │ B₃  │ B₃  │
│ t₁  │ t₂  │ t₃  │ t₁  │ t₂  │ t₃  │ t₄  │ t₅  │ t₁  │ t₂  │
└─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┘
      ↑           ↑                       ↑                 ↑
cu_seqlens:  [0,  3,                     8,                10]

In this example:

• We have 3 sequences with lengths 3, 5, and 2
• total_seq_len = 10 (3+5+2)
• cu_seqlens = [0, 3, 8, 10] (starting positions of each sequence, plus the total length)
• max_seqlen = 5 (the longest sequence in the batch)

For the Flash Attention implementation:

1. All tokens are packed into a single dimension
2. The cu_seqlens tensor tells the algorithm where each sequence starts and ends
3. Flash Attention ensures that tokens only attend to other tokens within their own sequence

Would you like me to explain how to implement this with the flash_attn_varlen_func?

Yes, exactly! max_seqlen is primarily used for tiling and memory management in Flash Attention.

Flash Attention works by processing the attention computation in blocks or tiles to reduce memory usage. Knowing the max_seqlen helps the algorithm:

1. Allocate memory efficiently: It can pre-allocate output buffers of the right size without wasting memory.

2. Optimize tiling strategy: The algorithm can determine the optimal block sizes for computation based on the maximum sequence length.

3. Parallelize effectively: With knowledge of the maximum sequence length, the algorithm can better distribute work across GPU cores.

4. Avoid unnecessary computation: It doesn't need to process beyond the longest sequence in the batch.

The tiling approach is a key innovation in Flash Attention - instead of computing and storing the entire attention matrix (which would be O(n²) in memory), it computes attention in smaller blocks, which requires only O(n) memory. This is particularly important for long sequences where the full attention matrix would be too large to fit in GPU memory.

So while cu_seqlens tells the algorithm where each sequence starts and ends, max_seqlen helps it optimize the computational strategy for processing those sequences.

No, unfortunately you can't use Flash Attention on this machine since it's not installed. When you tried to access flash_attn_varlen_func, you got a NameError which confirms the library isn't available.

Flash Attention requires:

1. The flash-attn Python package to be installed
2. A compatible NVIDIA GPU (typically with compute capability 7.5+)
3. CUDA toolkit installed

Your implementation would need to check for Flash Attention availability first, which is why the code template includes:

FLASH_ATTN_AVAILABLE = False
try:
    from flash_attn import flash_attn_varlen_func
    FLASH_ATTN_AVAILABLE = True
except ImportError:
    # Flash Attention is not available
    pass

For this exercise, you could:

1. Skip implementing the Flash Attention version if it's optional
2. Write the implementation assuming Flash Attention is available, but it won't be testable on this machine
3. Focus on the other attention implementations (eager and SDPA) that don't require additional libraries

Would you like to proceed with one of these options?

I can't directly access the Flash Attention library documentation since it's not installed on this machine. However, I can provide you with the general function signature and parameters for flash_attn_varlen_func based on common usage:

from flash_attn import flash_attn_varlen_func

def flash_attn_varlen_func(
    q,                  # shape: [total_seq_len, num_heads, head_dim]
    k,                  # shape: [total_seq_len, num_heads, head_dim]
    v,                  # shape: [total_seq_len, num_heads, head_dim]
    cu_seqlens_q,       # shape: [batch_size + 1], cumulative sequence lengths for queries
    cu_seqlens_k,       # shape: [batch_size + 1], cumulative sequence lengths for keys/values
    max_seqlen_q,       # maximum sequence length in the batch for queries
    max_seqlen_k,       # maximum sequence length in the batch for keys/values
    dropout_p=0.0,      # dropout probability (0.0 means no dropout)
    softmax_scale=None, # scaling factor for attention scores (default: 1/sqrt(head_dim))
    causal=False,       # whether to use causal attention masking
    return_attn_probs=False  # whether to return attention probabilities
):
    """
    Compute attention using Flash Attention algorithm for variable-length sequences.
    
    This function expects inputs in a "packed" format where all sequences in the
    batch are concatenated along the sequence dimension, with cu_seqlens indicating
    the boundaries between sequences.
    
    Returns:
        output: torch.Tensor of shape [total_seq_len, num_heads, head_dim]
        If return_attn_probs is True, also returns attention probabilities.
    """

The key differences from standard attention:

1. Input shapes are [total_seq_len, num_heads, head_dim] instead of [batch_size, seq_len, num_heads, head_dim]
2. Uses cumulative sequence lengths instead of attention masks
3. Requires specifying maximum sequence lengths explicitly

Note that this is a simplified representation, and the actual implementation may have additional parameters or slightly different naming.

Here's a simple example with arguments for flash_bidirectional_attention:

total_seq_len = 12  
hidden_dim = 64     
num_heads = 8       
head_dim = 8        

q = torch.randn(total_seq_len, hidden_dim)
k = torch.randn(total_seq_len, hidden_dim)
v = torch.randn(total_seq_len, hidden_dim)

cu_seqlens = torch.tensor([0, 5, 8, 12])  
max_seqlen = 5

Not quite. The separate cu_seqlens_q and cu_seqlens_k parameters exist to support scenarios where your queries and keys/values might come from different sequences or have different lengths.

Here are some common use cases:

1. Standard self-attention: In this case, queries, keys, and values all come from the same sequences, so cu_seqlens_q and cu_seqlens_k would be identical.

2. Cross-attention: In encoder-decoder architectures, queries come from the decoder while keys and values come from the encoder. The sequence lengths might differ, so you'd need separate cumulative sequence length tensors.

3. Efficient attention patterns: Some models use optimizations where they might have different numbers of queries than keys/values (like grouped-query attention).

For your bidirectional self-attention implementation, since queries, keys, and values all come from the same sequences, you would use the same cu_seqlens for both parameters:

flash_attn_varlen_func(
    q_reshaped,
    k_reshaped,
    v_reshaped,
    cu_seqlens_q=cu_seqlens,
    cu_seqlens_k=cu_seqlens,
    max_seqlen_q=max_seqlen,
    max_seqlen_k=max_seqlen,
    causal=False
)

It's not about masking - the masking is handled implicitly by the cumulative sequence lengths, which tell Flash Attention which tokens belong to which sequence.

Almost! You've got the reshaping part right, but you need to complete the full implementation of the function. Here's what you'd need to add:

1. Call the flash_attn_varlen_func with the reshaped tensors
2. Reshape the output back to the expected format
3. Handle the case where Flash Attention isn't available

The complete implementation would look something like:

def flash_bidirectional_attention(
    q: Tensor,  # shape: [total_seq_len, hidden_dim]
    k: Tensor,  # shape: [total_seq_len, hidden_dim]
    v: Tensor,  # shape: [total_seq_len, hidden_dim]
    num_heads: int,  # number of attention heads
    head_dim: int,  # dimension of each attention head
    cu_seqlens: Tensor,  # shape: [batch_size + 1], cumulative sequence lengths
    max_seqlen: int,  # maximum sequence length
) -> Tensor:
    """
    Implement bidirectional (full) attention using Flash Attention.
    """
    if not FLASH_ATTN_AVAILABLE:
        raise ImportError("Flash Attention is not available. Please install it with `pip install flash-attn`")
    
    # Reshape inputs to separate heads
    q_reshaped = q.view(total_seq_len, num_heads, head_dim)
    k_reshaped = k.view(total_seq_len, num_heads, head_dim)
    v_reshaped = v.view(total_seq_len, num_heads, head_dim)
    
    # Call Flash Attention
    output = flash_attn_varlen_func(
        q_reshaped,
        k_reshaped,
        v_reshaped,
        cu_seqlens_q=cu_seqlens,
        cu_seqlens_k=cu_seqlens,
        max_seqlen_q=max_seqlen,
        max_seqlen_k=max_seqlen,
        causal=False
    )
    
    # Reshape output back to original format
    return output.reshape(total_seq_len, hidden_dim)