docs: update llama-kv-cache.md

notes/llama-kv-cache.md

@@ -2085,27 +2085,183 @@ So as we can expect and have seen before the result of the Q and K matrix is a s
 matrix, and recall that this is par layer we are seeing.
 So what this is doing is it is caclulating the softmax of the logits in `kq` which like we
 said contains the dot product of the current token with all the cached Key values.
-In this case the first 6 tokens in the key cache belong to sequence 0, and the ones from 6-13 are
+In this case the first 6 tokens in the key cache belong to sequence 0, and the ones from 7-13 are
 the ones for sequence 1 which the current token belongs to:
 ```console
       kq                                 kq_mask
 z0                0     1    2    3    4    5   6     7    8    9    10  11    12   13   14  ... 31]
-   [0 ... 31]   [-inf -inf -inf -inf -inf -inf  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  -inf    -inf]
+   [0 ... 31]   [-inf -inf -inf -inf -inf -inf -inf  0.0  0.0  0.0  0.0  0.0  0.0  0.0  -inf    -inf]
                 [-inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf  -inf ...-inf]
                 ...
              31 [-inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf  -inf ...-inf]
 
 ...
 
 z31
-   [0 ... 31] 0 [-inf -inf -inf -inf -inf -inf  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  -inf    -inf]
+   [0 ... 31] 0 [-inf -inf -inf -inf -inf -inf -inf  0.0  0.0  0.0  0.0  0.0  0.0  0.0  -inf    -inf]
                 [-inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf  -inf ...-inf]
                 ...
              31 [-inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf  -inf ...-inf]
 ```
 So this will include only the logits that belong to the current token's sequence.
-So get a feel for how this works there is a standalone example in
+To get a feel for how this works there is a standalone example in
 [llama-att-softmax.c](../ggml/src/llama-att-softmax.c)
 
+### Connection/link between cells and cache tensors
+This might seem obvious but this was not clear to me initially which is why I'm adding this
+section. The `cells` member of `llama_kv_cache` is a vector of `llama_kv_cell`:
+```c++
+struct llama_kv_cache {
+    ...
+    std::vector<llama_kv_cell> cells;
+    ...
+}
+
+struct llama_kv_cell {
+    llama_pos pos   = -1;
+    llama_pos delta = 0;
+    int32_t   src   = -1; // used by recurrent state models to copy states
+    int32_t   tail  = -1;
+
+    std::set<llama_seq_id> seq_id;
+    ...
+};
+```
+As tokens are decoded they are added one by one to the cells vector. In the previous example when
+we had two prompts with different sequences 0, and 1, the would populate the first 12 positions
+in the cells vector. As we saw in the previous section `llama_set_inputs` iterated through the
+cells and checks if the current tokens sequence id is in that cell.
+
+If we inspect the cache we can see can see that the first 6 cells belong to sequence 0 and the
+next 7 belong to sequence 1:
+```console
+(lldb) p ctx->kv_self->cells
+(std::vector<llama_kv_cell>) size=1024 {
+  [0] = {
+    pos = 0
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 0
+    }
+  }
+  [1] = {
+    pos = 1
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 0
+    }
+  }
+  [2] = {
+    pos = 2
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 0
+    }
+  }
+  [3] = {
+    pos = 3
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 0
+    }
+  }
+  [4] = {
+    pos = 4
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 0
+    }
+  }
+  [5] = {
+    pos = 5
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 0
+    }
+  }
+  [6] = {
+    pos = 6
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 1
+    }
+  }
+  [7] = {
+    pos = 7
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 1
+    }
+  }
+  [8] = {
+    pos = 8
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 1
+    }
+  }
+  [9] = {
+    pos = 9
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 1
+    }
+  }
+  [10] = {
+    pos = 10
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 1
+    }
+  }
+  [11] = {
+    pos = 11
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 1
+    }
+  }
+  [12] = {
+    pos = 12
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=1 {
+      [0] = 1
+    }
+  }
+  [13] = {
+    pos = -1
+    delta = 0
+    src = -1
+    tail = -1
+    seq_id = size=0 {}
+  }
+```
+
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