papers/zen/zen-embeddings-retrieval.tex

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\title{\textbf{Zen Embeddings: Dense Retrieval and Semantic Search}\\
\large Technical Report v2025.06}
\author{Antje Worring, Zach Kelling, Zen LM Research Team\\
\texttt{[email protected]}}
\date{June 2025}

\begin{document}
\maketitle

\begin{abstract}
We present Zen Embed, a family of text embedding models derived from the Zen MoDE (Mixture of Distilled Experts) backbone, optimized for dense retrieval, semantic search, and cross-lingual understanding. Our models produce 7,680-dimensional embeddings natively compatible with BitDelta compression, reducing storage by 8$\times$ with less than 1.2\% NDCG@10 degradation. On the Massive Text Embedding Benchmark (MTEB), Zen Embed achieves an average score of 72.4 across 56 tasks. On BEIR zero-shot retrieval, we achieve 54.8 NDCG@10. On MIRACL multilingual retrieval covering 18 languages, we achieve 68.3 nDCG@10. We detail our bi-encoder training methodology, hard negative mining strategy, and cross-lingual alignment techniques.
\end{abstract}

\section{Introduction}

Dense retrieval has become foundational to modern AI systems: retrieval-augmented generation (RAG), semantic search, question answering, and recommendation systems all depend on high-quality embeddings that capture semantic meaning across diverse content types.

The core challenge in embedding model development is the tension between three objectives:
\begin{enumerate}
  \item \textbf{Semantic fidelity}: Embeddings must capture nuanced meaning, distinguishing semantically similar from dissimilar pairs.
  \item \textbf{Efficiency}: Production retrieval over billion-scale corpora demands compact representations and efficient search.
  \item \textbf{Generalization}: Models must transfer to unseen domains, languages, and task types without fine-tuning.
\end{enumerate}

Zen Embed addresses all three through a combination of Zen MoDE backbone fine-tuning, novel hard negative mining, BitDelta-compatible dimensionality, and a cross-lingual pre-alignment stage.

\section{Model Architecture}

\subsection{Backbone and Pooling}

Zen Embed uses the Zen MoDE encoder as its backbone. Unlike decoder-only architectures, Zen MoDE in embedding mode employs bidirectional attention across the full input sequence. We extract sentence embeddings via weighted mean pooling:

\begin{equation}
\mathbf{e} = \frac{\sum_{i=1}^{L} w_i \cdot \mathbf{h}_i}{\sum_{i=1}^{L} w_i}
\end{equation}

where $\mathbf{h}_i$ is the hidden state at position $i$ and $w_i$ is a learned scalar weight. The weights $w_i$ are produced by a two-layer attention head over the final layer representations, allowing the model to emphasize semantically important tokens.

The final embedding dimension is 7,680, matching the Zen MoDE hidden dimension. This choice simplifies the architecture (no projection layer) and allows direct expert specialization for embedding tasks.

\subsection{Instruction-Following Embedding}

Zen Embed supports task-specific instruction prefixes following the Instructor pattern. For retrieval, the query encoder receives a prefix such as ``Represent this query for searching relevant documents:'' while the document encoder receives ``Represent this document for retrieval:''. This single-model approach handles diverse embedding tasks:

\begin{itemize}
  \item Semantic textual similarity (STS)
  \item Asymmetric retrieval (query vs. document)
  \item Classification via embedding
  \item Clustering
  \item Reranking
\end{itemize}

\section{Training Methodology}

\subsection{Contrastive Objective}

We train Zen Embed with the InfoNCE contrastive objective. Given a batch of $N$ query-document pairs $\{(q_i, d_i^+)\}_{i=1}^N$ with in-batch negatives and $K$ mined hard negatives $\{d_i^{(k)-}\}$:

\begin{equation}
\mathcal{L} = -\frac{1}{N} \sum_{i=1}^{N} \log \frac{e^{\text{sim}(q_i, d_i^+)/\tau}}{e^{\text{sim}(q_i, d_i^+)/\tau} + \sum_{j \neq i} e^{\text{sim}(q_i, d_j^+)/\tau} + \sum_k e^{\text{sim}(q_i, d_i^{(k)-})/\tau}}
\end{equation}

where $\text{sim}(\mathbf{u}, \mathbf{v}) = \mathbf{u}^\top \mathbf{v} / (\|\mathbf{u}\| \|\mathbf{v}\|)$ is cosine similarity and $\tau = 0.02$ is the temperature.

\subsection{Hard Negative Mining}

Effective contrastive learning requires hard negatives—documents that are superficially similar to the query but semantically incorrect. We employ a three-stage mining pipeline:

\paragraph{Stage 1: BM25 Retrieval.} For each query, retrieve the top-100 candidates by BM25. Documents not in the relevant set serve as hard negatives.

\paragraph{Stage 2: Embedding-based Re-mining.} After initial training (1 epoch), use the current model to retrieve top-50 candidates. Negatives are sampled from positions 5--50 (avoiding the top-4 which may contain false negatives).

\paragraph{Stage 3: Cross-encoder Scoring.} A fine-tuned cross-encoder assigns relevance scores to all candidates. We select negatives with cross-encoder score $>$ 0.3 but $<$ 0.7 as ``hard but not false'' negatives.

\begin{table}[H]
\centering
\caption{Impact of hard negative mining on BEIR NDCG@10}
\label{tab:hard_neg}
\begin{tabular}{lccc}
\toprule
Negative Source & BEIR Avg & MS-MARCO Dev & FIQA \\
\midrule
In-batch only & 48.2 & 38.4 & 44.1 \\
+ BM25 negatives & 51.4 & 40.2 & 47.8 \\
+ Embedding re-mining & 53.6 & 41.8 & 49.2 \\
+ Cross-encoder filtering & \textbf{54.8} & \textbf{42.6} & \textbf{51.4} \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Training Data}

We curate a training corpus of 2.1 billion query-document pairs from diverse sources:

\begin{table}[H]
\centering
\caption{Training data composition}
\label{tab:training_data}
\begin{tabular}{lcc}
\toprule
Source & Pairs (millions) & Weight \\
\midrule
MS-MARCO passages & 532 & 0.18 \\
Common Crawl pairs & 812 & 0.24 \\
Academic QA (NQ, TQA, HotpotQA) & 124 & 0.12 \\
Code search (GitHub) & 98 & 0.08 \\
Multilingual parallel corpora & 418 & 0.28 \\
Synthetic DSO pairs & 116 & 0.10 \\
\bottomrule
\end{tabular}
\end{table}

Synthetic DSO (Decentralized Semantic Optimization) pairs are generated by the Zen MoDE generative model using constitutional prompts, then filtered by cross-encoder quality scoring.

\section{BitDelta-Compatible Embedding Compression}

\subsection{Problem and Approach}

Storing 7,680-dimensional float32 embeddings for a 1-billion-document corpus requires $1 \times 10^9 \times 7680 \times 4 \approx 28.7$ TB of storage and comparable index memory. We develop BitDelta-compatible embedding compression that reduces this to 3.6 TB at negligible quality loss.

The key insight is that production embedding corpora exhibit strong structure: most embeddings lie near the convex hull of a low-rank manifold. We exploit this via:

\begin{equation}
\tilde{\mathbf{e}} = \mathbf{e}_0 + \text{sign}(\mathbf{e} - \mathbf{e}_0) \cdot s
\end{equation}

where $\mathbf{e}_0$ is a learned centroid vector (per-cluster), $\text{sign}(\cdot)$ is the bitwise sign quantization, and $s$ is a learned scalar. This is the embedding analog of BitDelta weight quantization.

\subsection{Reconstruction Quality}

\begin{table}[H]
\centering
\caption{Embedding compression: retrieval quality vs. storage}
\label{tab:compression}
\begin{tabular}{lcccc}
\toprule
Method & Storage & BEIR Avg & MTEB Avg & MS-MARCO \\
\midrule
Full float32 (7680-d) & 28.7 TB & 54.8 & 72.4 & 42.6 \\
float16 (7680-d) & 14.4 TB & 54.7 & 72.3 & 42.5 \\
PQ-64 & 2.4 TB & 52.1 & 69.8 & 40.1 \\
BitDelta-Embed & 3.6 TB & 54.1 & 71.7 & 42.1 \\
BitDelta-Embed (2048-d MRL) & 0.96 TB & 53.4 & 71.0 & 41.6 \\
\bottomrule
\end{tabular}
\end{table}

Matryoshka Representation Learning (MRL) at 2048 dimensions reduces storage to 0.96 TB with only 1.4 MTEB points degradation—an 30$\times$ reduction from full float32.

\section{Cross-Lingual Alignment}

\subsection{Alignment Pre-training}

Before task-specific fine-tuning, we apply a cross-lingual alignment stage that ensures semantically equivalent sentences in different languages map to nearby embedding spaces. Given a parallel corpus $\{(s_i^{L_1}, s_i^{L_2})\}$, we minimize:

\begin{equation}
\mathcal{L}_{\text{align}} = \sum_i \left\|\mathbf{e}(s_i^{L_1}) - \mathbf{e}(s_i^{L_2})\right\|_2^2
\end{equation}

Combined with contrastive objectives over multilingual batches, this produces embeddings where the same concept in any of the 100+ supported languages maps to a consistent region of the embedding space.

\subsection{Language Coverage}

\begin{table}[H]
\centering
\caption{MIRACL retrieval NDCG@10 by language family}
\label{tab:miracl}
\begin{tabular}{lcc}
\toprule
Language Family & Languages & NDCG@10 \\
\midrule
Germanic & en, de, sv, nl, da & 71.4 \\
Romance & fr, es, it, pt, ro & 69.8 \\
CJK & zh, ja, ko & 67.2 \\
Slavic & ru, pl, cs, uk & 65.8 \\
Arabic & ar & 64.1 \\
South Asian & hi, bn, ta, te & 62.4 \\
Southeast Asian & id, th, vi, ms & 63.7 \\
Other & sw, yo, fi, hu + 80 more & 58.9 \\
\midrule
\textbf{Overall (18 MIRACL)} & \textbf{18} & \textbf{68.3} \\
\bottomrule
\end{tabular}
\end{table}

\section{MTEB Benchmark Results}

\begin{table}[H]
\centering
\caption{MTEB benchmark results across task categories (56 tasks)}
\label{tab:mteb}
\begin{tabular}{lcccc}
\toprule
Task Category & Tasks & Zen Embed & Prev. Best & $\Delta$ \\
\midrule
Classification & 12 & 76.8 & 74.2 & +2.6 \\
Clustering & 11 & 54.1 & 51.8 & +2.3 \\
Pair Classification & 3 & 86.2 & 85.1 & +1.1 \\
Reranking & 4 & 60.4 & 58.9 & +1.5 \\
Retrieval & 15 & 58.3 & 55.8 & +2.5 \\
STS & 10 & 83.4 & 81.9 & +1.5 \\
Summarization & 1 & 31.8 & 30.4 & +1.4 \\
\midrule
\textbf{Average} & \textbf{56} & \textbf{72.4} & \textbf{70.2} & \textbf{+2.2} \\
\bottomrule
\end{tabular}
\end{table}

\section{BEIR Zero-Shot Retrieval}

BEIR evaluates retrieval across 18 heterogeneous datasets spanning diverse domains without any fine-tuning on target domains.

\begin{table}[H]
\centering
\caption{BEIR zero-shot NDCG@10 on selected datasets}
\label{tab:beir}
\begin{tabular}{lccc}
\toprule
Dataset & Domain & Zen Embed & $\Delta$ vs. BM25 \\
\midrule
MS-MARCO & Web & 42.6 & +14.2 \\
TREC-COVID & Biomedical & 77.4 & +14.8 \\
NFCorpus & Medical & 36.8 & +3.2 \\
NQ & Wikipedia & 62.4 & +29.8 \\
HotpotQA & Wikipedia & 71.2 & +34.8 \\
FiQA-2018 & Finance & 51.4 & +20.4 \\
ArguAna & Counter-argument & 59.8 & +12.4 \\
CQAdupstack & Forum & 37.4 & +10.8 \\
DBPedia & Entity & 41.2 & +8.4 \\
SciFact & Scientific & 72.8 & +16.2 \\
\midrule
\textbf{BEIR Average (18 datasets)} & — & \textbf{54.8} & \textbf{+16.2} \\
\bottomrule
\end{tabular}
\end{table}

\section{MS-MARCO Leaderboard}

On the MS-MARCO passage retrieval development set (MRR@10), Zen Embed achieves 42.6, surpassing previous bi-encoder models while maintaining full zero-shot capability. Full-pipeline with cross-encoder reranking achieves 44.1 MRR@10.

\begin{table}[H]
\centering
\caption{MS-MARCO passage ranking development MRR@10}
\label{tab:msmarco}
\begin{tabular}{lcc}
\toprule
System & MRR@10 & Recall@1000 \\
\midrule
BM25 & 18.4 & 85.7 \\
Zen Embed (bi-encoder) & 42.6 & 97.8 \\
Zen Embed + cross-encoder & 44.1 & 97.8 \\
\bottomrule
\end{tabular}
\end{table}

\section{Practical Deployment}

\subsection{Embedding Throughput}

\begin{table}[H]
\centering
\caption{Embedding throughput (sentences/second) on different hardware}
\label{tab:throughput}
\begin{tabular}{lccc}
\toprule
Hardware & Batch Size & Avg Seq Len & Sentences/s \\
\midrule
A100 80GB (fp16) & 512 & 128 & 24,800 \\
A100 80GB (fp16) & 512 & 512 & 8,200 \\
H100 80GB (fp16) & 512 & 128 & 41,200 \\
H100 80GB (fp16) & 512 & 512 & 13,800 \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Indexing at Scale}

For billion-scale document corpora, we recommend hierarchical navigable small world (HNSW) indexing with:
\begin{itemize}
  \item Dimension 2048 (MRL-compressed) for memory efficiency
  \item $M=32$ connections, $ef_\text{construction}=200$
  \item Approximate recall@10 of 98.4\% at 5ms P95 latency
\end{itemize}

\section{Conclusion}

Zen Embed delivers state-of-the-art dense retrieval quality across English and multilingual benchmarks while remaining practically deployable through BitDelta-compatible compression. The 7,680-dimensional embeddings achieve 72.4 MTEB average and 54.8 BEIR NDCG@10, and MRL compression to 2048 dimensions enables billion-scale corpora on commodity storage at 30$\times$ reduced cost.

\begin{thebibliography}{99}
\bibitem{mteb} Muennighoff, N. et al. MTEB: Massive Text Embedding Benchmark. \textit{EACL}, 2023.
\bibitem{beir} Thakur, N. et al. BEIR: A Heterogeneous Benchmark for Zero-shot Evaluation of Information Retrieval Models. \textit{NeurIPS}, 2021.
\bibitem{miracl} Zhang, X. et al. MIRACL: A Multilingual Retrieval Dataset Covering 18 Diverse Languages. \textit{TACL}, 2023.
\bibitem{mrl} Kusupati, A. et al. Matryoshka Representation Learning. \textit{NeurIPS}, 2022.
\bibitem{instructor} Su, H. et al. One Embedder, Any Task: Instruction-Finetuned Text Embeddings. \textit{ACL Findings}, 2023.
\end{thebibliography}

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