# Paged attention This page documents the paged attention forward function used in [continuous batching](./continuous_batching). It wraps two versions of the flash attention kernel to handle different batch configurations efficiently. ## Varlen path The `flash_attn_varlen_func` kernel handles variable length batches. This path is recommended for batches with a large number of requests in prefill. ### Cache behavior This kernel has no mechanism to interact with the paged cache directly, so the cache is manually read and written using the [`~PagedAttentionCache.update`] method. This can become a bottleneck when sequence length grows large. ### Indexing mechanism The kernel uses maximum sequence length (`max_seqlen_q`, `max_seqlen_k`) and cumulative sequence lengths (`cu_seq_lens_q`, `cu_seq_lens_k`) to compute attention for each sequence. ### Example Consider a batch of 3 sequences with query lengths `[10, 3, 1]` and key lengths `[0, 1, 7]`: ``` cu_seq_lens_q = [0, 10, 13, 14] cu_seq_lens_k = [0, 0, 1, 8] max_seqlen_q = 10 max_seqlen_k = 7 ``` Input shapes: ``` Q: [1, 10+3+1, num_heads, head_dim] = [1, 14, num_heads, head_dim] K or V: [1, 0+1+7, num_kv_heads, head_dim] = [1, 8, num_kv_heads, head_dim] ``` The kernel assigns each query and key/value token to a sequence using the cumulative sequence lengths: ``` Q request index: [r0, r0, r0, r0, r0, r0, r0, r0, r0, r0, r1, r1, r1, r2] cu_seq_lens_q: 0____________________________________10__________13__14 K request index: [r1, r2, r2, r2, r2, r2, r2, r2] (r0 has 0 K tokens) cu_seq_lens_k: 0,0_1_______________________8 ``` ## Decode path The `flash_attn_with_kvcache` kernel handles decode-only batches where each sequence has exactly one query token. This is more efficient than the varlen path but cannot handle batches with prefilling requests. ### Cache behavior This kernel interacts with the paged cache using a `block_table` to index into the cache and update it in-place. The block table has shape `(batch_size, max_blocks_per_seq)`, where each row contains the physical locations of a request's cache blocks in the KV cache tensor. ### Indexing mechanism The kernel uses `cache_seqlens` to retrieve the cache length for each sequence. It assumes each query token belongs to a different sequence (one token per sequence). ### Example Consider a batch of 3 sequences with query lengths `[1, 1, 1]` and key lengths `[30, 32, 70]`. The cache block size is 32 and the maximum number of blocks per sequence is 4. The cache sequence lengths are simply the key lengths: ``` cache_seqlens = [30, 32, 70] ``` The block table shape is `(3, 4)`. Using example addresses: ``` block_table = [[2, -1, -1, -1], [0, 1, -1, -1], [3, 5, 6, -1]] ``` Values of `-1` indicate unallocated blocks. - **Sequence 0** (30 cached tokens): cache in `KV_cache[2]`. The new token fits (30 + 1 = 31 < 32). - **Sequence 1** (32 cached tokens): cache in `KV_cache[0]` and `KV_cache[1]`. A second block is needed since 32 + 1 > 32. - **Sequence 2** (70 cached tokens): cache in `KV_cache[3]`, `KV_cache[5]`, and `KV_cache[6]`. Note that blocks are not necessarily contiguous, which is the key advantage of paged cache. The new token fits in the third block.