BATL: Learning Balanced Tree Indexes for Large-Scale Vector Retrieval

Описание: Paper: https://doi.org/10.1145/3580305.3599406

In a nutshell:
Model Definition: Encoder-decoder Transformer predicting branch-ID sequences (paths) on a balanced K-ary tree to locate nearest-neighbor buckets.

Reduced Complexity: Flattens massive multi-class bucket classification into small-vocabulary autoregressive routing, improving generalization and training efficiency.

Training Loop: Initialize random balanced tree - train seq2seq model - update tree structure by re-assigning data points layer-by-layer based on routing likelihood - repeat until convergence.

Training Signal: Query paired with the branch-ID sequence of its ground-truth nearest neighbors; neighbors identified via exhaustive search or subset sampling on large-scale databases.

Failure Modes & Fixes:
Lop-sided partitions - enforce branch capacity limit αN/K^h.
Collapse (vectors in few buckets) - check routing decision in descending order and assign to first branch satisfying balance constraints.
Error accumulation in deep trees - use low H (height) to minimize layer-wise prediction drift.

Inference-Time Safeguards: Beam search navigates the encoder-decoder to identify the top-M most likely candidate paths/buckets.

Boundary / Coverage Issues: Data near bucket boundary missed - ensemble multiple diversified trees and independent models to merge candidate set results.

Candidate Selection / Ranking: Merge points from top-M buckets - filter out points appearing only once to reduce scale - compute exact similarity - final ranking for top-k.

Key Parameters: α (load flexibility/balance factor), K (branching factor/vocabulary size), H (tree height), beam size (search breadth).

Efficiency Considerations: Sublinear query time; O(TN) memory usage; shared branch embeddings across layers significantly reduce model footprint versus flat MLP baselines.

Intuition: Breaking one massive "which bucket?" guess into a sequence of small "which branch?" decisions makes the index easier for neural nets to learn and much faster to navigate.


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