This appendix outlines the algorithms and data structures used for memory management in the context of LLM inference on mid-range GPUs. We focus on the key techniques discussed in the main text: dynamic memory allocation, paged memory management, and the copy-on-write mechanism.
Dynamic Memory Allocation Algorithm
Dynamic memory allocation is crucial for handling variable-length sequences in LLMs. The algorithm allocates memory based on the actual sequence length rather than a fixed maximum size.
Algorithm: DynamicMemoryAllocation
Input: SequenceLength L, MaximumMemoryBlock B, MemoryAllocator A
Output: AllocatedMemory M
1. M ← A.Allocate(Min(L * MemoryPerToken, B))
2. if M is NULL then
3. M ← A.Allocate(B) // Attempt to allocate maximum block if minimum fails
4. if M is NULL then
5. A.FreeAll() // Free all memory and retry allocation
6. M ← A.Allocate(Min(L * MemoryPerToken, B))
7. return M
Paged Memory Management
Paged memory management involves dividing the memory into fixed-size pages and managing these pages to optimize usage.
Algorithm: PagedMemoryManagement
Input: MemoryRequest R, PageTable T, PageSize S
Output: MemoryBlock B
1. B ← T.Lookup(R)
2. if B is NULL then
3. B ← AllocateNewPage(S)
4. T.Insert(R, B)
5. return B
Function AllocateNewPage(PageSize S)
1. if NoFreePagesAvailable() then
2. CoalesceFreePages() // Merge adjacent free pages
3. if NoFreePagesAvailable() then
4. return NULL // No free pages available
5. page ← GetFreePage(S)
6. return page
Copy-on-Write Mechanism
The copy-on-write (COW) mechanism defers the duplication of memory until a write operation occurs.
Algorithm: CopyOnWrite
Input: MemoryBlock B to be modified, ReferenceCount C for B
Output: Modified MemoryBlock B'
1. if C > 1 then // Check if B is shared
2. B' ← A.Allocate(SameSizeAs(B))
3. Copy(B, B') // Duplicate the contents of B to B'
4. C ← C - 1 // Decrement the reference count of the old block
6. return B' // Return the new block B'
Swapping Mechanism
Swapping involves moving data between the GPU memory and a slower, auxiliary memory to free up space in the GPU memory.
Algorithm: SwappingMechanism
Input: MemoryBlock B to be swapped out, AuxiliaryMemory M
Output: SwappedOut MemoryBlock B
1. if GPUMemoryFull() then
2. B ← SelectVictimBlock() // Choose a block to swap out
3. Write(B, M) // Write the contents of B to auxiliary memory M
4. GPU.Free(B) // Free the GPU memory occupied by B
5. return B
Recomputation Mechanism
Recomputation is an alternative to swapping where data is recalculated instead of being stored in memory.
Algorithm: RecomputationMechanism
Input: ComputationDependencies D, RecomputationFunction R
Output: Recomputed Data B
1. if GPUMemoryFull() then
2. foreach Dependency ∈ D do
3. if NotInGPUMemory(Dependency) then
4. Dependency ← R(Dependency) // Recompute the dependency
5. return R(B) // Recompute the data B using its dependencies
These algorithms are central to the efficient management of memory resources during LLM inference on mid-range GPUs. They provide a foundation for the development of more sophisticated memory management systems tailored to the needs of LLMs.