Bidirectional Maxsim Score (BiMax)

• Bidirectional Maxsim Score (BiMax) is a cross-lingual document alignment metric that computes bidirectional maximum cosine similarities using multilingual sentence embeddings.
• BiMax segments documents and applies max pooling from source to target and vice versa, streamlining similarity computations for enhanced scalability.
• Evaluations show that BiMax maintains high alignment accuracy while achieving up to 100-fold speed improvements over traditional methods.

The Bidirectional Maxsim Score (BiMax) is a cross-lingual document alignment metric designed to efficiently and accurately measure similarity between documents using multilingual sentence embeddings. It is motivated by the need for scalable, robust document-level mining across vast web data, outperforming traditional methods like Optimal Transport (OT) in computational efficiency while maintaining comparable accuracy. BiMax operates by evaluating the maximal inter-segment similarity in both source-to-target and target-to-source directions and combining these scores, making it an effective filtering and re-ranking tool in parallel corpus mining and related large-scale data curation tasks.

1. Foundations and Motivation

BiMax was developed in response to the challenges imposed by large-scale web mining, where both alignment accuracy and computation speed are critical. Existing methods—such as TK-PERT (Thompson and Koehn, 2020), OT (Clark et al., 2019; El-Kishky and Guzman, 2020), and simple Mean-Pool approaches—attain high precision but often suffer from substantial runtime and scalability constraints. BiMax’s foundational concept is “bidirectional maxsim”—evaluating the maximum similarity from source to target and vice versa, ensuring that document pairing leverages the strongest segment correspondences. This approach addresses the limitations of averaging-based metrics, which tend to dilute discriminative signals, thus enhancing document alignment robustness, especially within hierarchical mining pipelines (Wang et al., 17 Oct 2025).

2. Methodology

BiMax utilizes multilingual sentence embeddings, leveraging models such as LaBSE, LASER-2, distiluse-base-multilingual-cased-v2, BGE M3, and jina-embeddings-v3. The primary methodological steps are as follows:

1. Document segmentation: Documents are partitioned into segments using strategies like Mean-Pool, TK-PERT, SBS, or Overlapping Fixed-Length Segmentation (OFLS).
2. Embedding extraction: Each segment is mapped to a vector representation via a pre-trained multilingual encoder.
3. Similarity matrix computation: For segments $S$ in the source document and $T$ in the target document, compute all pairwise cosine similarities.
4. Max-pooling: For each direction, select the maximum segment-to-segment similarity:
   • $$MaxSim(S, T) = \max_{s \in S} \max_{t \in T} \cos(\text{embedding}(s), \text{embedding}(t))$$
   • $MaxSim(T, S)$ analogously.
5. Aggregation: Combine the directional maxima, typically via mean:
   • $$BiMax(S, T) = \frac{1}{2} [MaxSim(S, T) + MaxSim(T, S)]$$

This procedure minimizes computational overhead—requiring only one similarity matrix and two max-pooling operations—thereby facilitating rapid batched computation and scalability.

3. Comparative Analysis with Alignment Methods

Evaluations on benchmarks such as WMT16 demonstrate that BiMax consistently achieves F1 scores competitive with OT and superior to Mean-Pool in many settings. The accuracy of BiMax approaches or modestly exceeds that of OT and TK-PERT, with recall improvements in the range of 0.3%–2.4% relative to SBS with OT. Crucially, BiMax attains approximately 100-fold speed increases over OT on typical document alignment tasks. The OT algorithm involves iterative optimization over the similarity matrix, incurring substantial runtime per document pair, whereas BiMax’s computational simplicity enables the alignment of thousands of document pairs per second. TK-PERT, though more resistant to noise and capable with longer documents, requires additional preprocessing steps, which increase its runtime relative to BiMax (Wang et al., 17 Oct 2025).

Method	Accuracy	Computation Time
OT	High	Very High
TK-PERT	Moderate	High
Mean-Pool	Lower	Low
BiMax	High	Extremely Low

4. Performance on WMT16 Document Alignment

In experiments on the WMT16 bilingual document alignment task, BiMax achieves recall and F1 metrics similar to or surpassing OT and TK-PERT under identical segmentation (notably OFLS). Quantitative tables illustrate recall parity, while log-scale runtime charts document BiMax’s dramatic computational advantage—processing thousands of document pairs per second versus the few dozen pairs managed by OT. This renders BiMax particularly suitable for web-scale application, where throughput is vital. The capacity for batched computations further enhances practical usability in automated mining pipelines (Wang et al., 17 Oct 2025).

5. Role of Multilingual Sentence Embeddings

BiMax’s efficacy is inherently linked to the quality of underlying cross-lingual sentence embeddings. The paper provides a systematic analysis of several state-of-the-art models, revealing that the performance ceiling for alignment tasks is set by the embedding model and segmentation combination. LaBSE and OFLS emerge as optimal pairings. When deployed with weaker or less expressive models, BiMax mitigates the drop in accuracy by reliably matching representative segments, thereby maintaining robust performance. The shared embedding space introduced by these multilingual encoders is thus a critical enabler for BiMax’s effectiveness.

6. Practical Integration and Tooling

BiMax is implemented in the publicly available EmbDA toolkit, which automates the identification of parallel document pairs from web-mined data. EmbDA supports modular selection of embedding models and segmentation strategies, allowing adaptation to diverse language pairs and domains. The workflow typically involves initial candidate retrieval using a fast method (e.g., Mean-Pool), followed by precise filtering and re-ranking via BiMax. This design supports end-to-end parallel corpus construction for downstream tasks including machine translation, cross-lingual retrieval, and bilingual knowledge base augmentation (Wang et al., 17 Oct 2025).

7. Implications, Limitations, and Future Directions

BiMax’s scalable, accurate alignment capacity meets the demands of large-scale, low-resource cross-lingual data mining. The authors identify further research opportunities, including:

• Adaptive segmentation strategies tailored to document complexity.
• Integration of advanced embedding models for broader linguistic coverage.
• Extension of BiMax’s methodology to document-level machine translation evaluation.

A plausible implication is that BiMax’s efficiency and modularity will facilitate wider adoption in web mining and automated corpus generation. The method’s capacity to handle scale and heterogeneous data sources suggests relevance beyond current benchmarks, with ongoing innovation anticipated in segmentation and embedding methodology.

In summary, BiMax unites a robust bidirectional max-similarity approach with high-performance multilingual encoding to deliver state-of-the-art document alignment, serving both research and operational needs in mining parallel data at scale.