Inverted list objects and scanners

This page introduces two low-level (ie. only C++) APIs to generalize the inverted list storage. This is useful eg. to store lists in a key-value database.

The InvertedLists abstract class defines how inverted lists are accessed from the search code. Any object that offers this interface can be used to store the lists.

The InvertedListsScanner offers even finer-grained access because the scanning function can be called on user-provided id and code tables.

Recap about IndexIVF

The IndexIVF class (and its children) is used for all large-scale applications of Faiss. It clusters all input vectors into nlist groups (nlist is a field of IndexIVF). At add time, a vector is assigned to a groups. At search time, the most similar groups to the query vector are identified and scanned exhaustively.

Thus, the IndexIVF has two components:

• the quantizer (aka coarse quantizer) index. Given a vector, the search function of the quantizer index returns the group the vector belongs to. When searched with nprobe>1 results, it returns the nprobe nearest groups to the query vector (nprobe is a field of IndexIVF).

• the InvertedLists object. This object maps a group id (in 0..nlist-1), to a sequence of (code, id) pairs.

The InvertedLists object

Codes are arbitrary byte strings of a constant size code_size. For example, an IndexIVFFlat in 36D has code_size = 36 * sizeof(float) = 144 bytes. Ids are arbitrary 64-bit integers (but negative values are reserved, so that's 63 useful bits).

In reality the codes and ids are returned in two separate arrays because some applications may need only one of them, and the memory alignement requirements are not the same.

Methods for search

The three relevant methods of the object are

/// get the size of a list
size_t list_size(size_t list_no);

/// @return codes    size list_size * code_size
const uint8_t * get_codes (size_t list_no);
void release_codes (const uint8_t *codes) const;

/// @return ids      size list_size
const idx_t * get_ids (size_t list_no);
void release_ids (const idx_t *ids) const;

Pointers obtained through get_codes (resp get_ids) should be released with release_codes (resp release_ids). The object InvertedLists::ScopedCodes (resp InvertedLists::ScopedIds) can be used if you prefer RAII.

There is an additional prefetch_lists method, that is used by the search method to inform the InvertedLists object that some inverted lists will be required in the near future.

Thus, the calling sequence of search looks like:

search(v) {
    list_nos = quantizer->search(v, nprobe)
    invlists->prefetch(list_nos)
    foreach no in list_nos {
        codes = invlists->get_codes(no)
        // linear scan of codes
        // select most similar codes 
        ids = invlists->get_ids(no)
        // convert list indexes to ids
        invlists->release_ids(ids)
        invlists->release_codes(codes)
    }
}

Methods for add()

Adding vectors requires read-write access to the InvertedLists object. This is provided by the add_entries method. Additional methods update_entries and resize are used for bulk operations like merging, splitting and removing elements.

Behavior of the InvertedLists object

Memory management

The InvertedLists object is deleted by the IndexIVF destructor if own_invlists is true. By default an ArrayInvertedLists object is constructed when the IndexIVF is instanciated, and own_invlists is set to true. The default invliststs can be replaced with replace_invlists, and the user has to decide about ownership.

Threading

Read-only multithreaded access is allowed. There are some comments about concurrent read-write access in the code.

I/O

The InvertedLists object needs not to be stored along with the index object. If this is not the case, the index object just contains the necessary information to handle external storage.

Built-in InvertedLists classes

The InvertedLists class is designed with extensibility in mind. However, there are two built-in InvertedLists classes in Faiss.

ArrayInvertedLists

This is basically a std::vector<std::vector<...> >. It is the simplest in-RAM inverted lists implementation, with very little overhead and fast add times. It has a special status because it is instantiated automatically when an IndexIVF is built, so that vectors can be added right away.

OnDiskInvertedLists

The inverted list data is stored on a memory-mapped file on disk. There is an indirection table that maps list ids to an offset in the file. Since the data is memory-mapped, there is no need to explicitly fetch the data from disk. However, the prefetch function is useful to exploit parallel reads on distributed file systems.

Interestingly, a "normal" IndexIVF can be loaded into an OnDiskInvertedLists by setting the IO_FLAG_MMAP flag to read_index. This makes it possible to load an arbitrary number of indexes without worrying about whether they fit in RAM.

See the chapter about this topic here

HStackInvertedLists and VStackInvertedLists

These are inverted list objects that combine several inverted list objects into one, so that they appear to be a single inverted lists object. The hstack/vstack name comes from the numpy functions of the same name. Indeed an inverted list object can be seen as a sparse matrix. HStack combines a set of inv lists together so that the search is performed in the combination of all the inverted lists. VStack combines k InvertedLists objects of size nlist1 assuming into an inverted lists object of size nlist1 * k.

The InvertedListScanner object

The inverted list scanning can be controlled outside of Faiss. This makes is unnecessary to implement the list access functions as callbacks, which is not always convenient.

To support this, Faiss offers:

• an encode_vector function that computes the inverted list codes into an array that can be used to populate inverted lists that are not managed by Faiss

• an InvertedListScanner object that can be obtained from an IndexIVF class. It can scan lists or compute a single query-to-code distance.

This access is at a very low level, but the user has total control over the scanning without having to implement callbacks as with the InvertedLists object.

Encoding vectors

To encode the vectors, the calling code should:

• quantize the vector to find the inverted list where it has to be stored

• call encode_vectors to actually encode it.

Both functions operate on batches for efficiency.

Here is a simplified code that adds nb vectors stored in xb to custom inverted lists:

// size nb
idx_t *list_nos = ... ; 
// find inverted list numbers 
index_ivf.quantizer->assign (nb, xb, list_nos);

// size index->code_size * nb
uint8_t *codes = ...; 
// compute the codes to store
index->encode_vectors (nb, xb, list_nos, codes);

// populate the custom inverted lists 
for (idx_t i = 0; i < nb; i++) {
      idx_t list_no = list_nos[i]; 
      // allocate a new entry in the inverted list list_no
      // get a pointer to the new entry's id and code
      idx_t * id_ptr = ... 
      uint8_t * code_ptr =  ...
      // assume the vectors are numbered sequentially
      *id_ptr = i; 
      memcpy (code_ptr, codes + i * index->code_size, index->code_size);
}

See here for an example: test_lowlevel_ivf.cpp (add)

Searching

To perform a search, there are several loop levels.

Here is a simplified code that performs the query. It queries nq vectors xq in index.

// size nprobe * nq
float * q_dis =  ...
idx_t *q_lists = ...
// perform quantization manually
index.quantizer->search (nq, xq, nprobe, q_dis, q_lists); 

// get a scanner object
scanner = index.get_InvertedListScanner();

// allocate result arrays (size k * nq), properly initialized
idx_t *I = ...
float *D = ...

// loop over queries
for (idx_t i = 0; i < nq; i++) {
    // set the current query
    scanner->set_query (xq + i * d);

    // loop over inverted lists for this query
    for (int j = 0; j < nprobe; j++) {
        // set the current inverted list
        int list_no = q_lists[i * nprobe + j];
        scanner->set_list (list_no, q_dis[i * nprobe + j]);

        // get the inverted list from somewhere
        long list_size = ...
        idx_t *ids = ....
        uint8_t *codes = ....
        // perform the scan, updating result lists
        scanner->scan_codes (list_size, codes, ids, D + i * k, I + i * k, k); 
   }
   // re-order heap in decreasing order
   maxheap_reorder (k, D + i * k, I + i * k);
}

See details here: test_lowlevel_ivf.cpp (search)

The scanner object is not thread-safe, but several of them can be used to process queries or inverted lists in parallel (see the same test for an example).