papers/zen/zen-context-extension.tex

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\title{\textbf{Long Context Scaling in Zen Models: 1M Token Extension}\\
\large Technical Report v2025.07}
\author{Antje Worring, Zach Kelling, Zen LM Research Team\\
\texttt{[email protected]}}
\date{July 2025}

\begin{document}
\maketitle

\begin{abstract}
We describe techniques for extending Zen model context windows from 32K to 1M tokens.
Our approach combines dynamic NTK-aware RoPE scaling, memory-efficient sliding window
attention for the bulk of context, ring attention for multi-GPU context distribution,
and targeted long-context fine-tuning on 50K documents exceeding 100K tokens. On
the RULER benchmark, Zen achieves 94.1\% at 128K context, 87.3\% at 512K, and
79.8\% at 1M tokens. The needle-in-haystack retrieval task shows $>95\%$ recall
up to 512K context. Memory overhead for 1M context on Zen-7B requires 8$\times$A100
80GB with ring attention, compared to infeasible memory requirements for naive attention.
\end{abstract}

\section{Introduction}

The practical utility of language models scales dramatically with context window size.
Repository-level code completion, book-length summarization, and multi-document
reasoning all require contexts exceeding the 4K--32K windows of first-generation
instruction-tuned models.

Extending context windows faces two independent challenges:
\begin{enumerate}
  \item \textbf{Positional encoding generalization}: Models trained with rotary position
    embeddings (RoPE) at 32K tokens degrade on longer sequences because RoPE frequencies
    were not calibrated for larger positions.
  \item \textbf{Memory complexity}: Naive self-attention is $O(n^2)$ in sequence length,
    making 1M-token context require $10^{12}$ attention operations per layer.
\end{enumerate}

We address both challenges: NTK-aware RoPE scaling for positional generalization,
and ring attention for distributed $O(n)$ per-GPU memory scaling.

\section{Background}

\subsection{Rotary Position Embeddings}

RoPE~\cite{su2021rope} encodes position by rotating query and key vectors in
$d/2$ 2D planes, with rotation frequency $\theta_i = 10000^{-2i/d}$ for $i \in [0, d/2)$:

\begin{equation}
\text{RoPE}(x, m)_i = x_i \cos(m\theta_i) - x_{i+1}\sin(m\theta_i)
\end{equation}

For position $m > m_\text{train}$, rotation frequencies exceed those seen during
training, causing catastrophic degradation.

\subsection{Sliding Window Attention}

Sliding window attention~\cite{beltagy2020longformer} restricts each token to attend
only to a fixed window $w$ of neighboring tokens:
\begin{equation}
\text{attn}(q_i, K, V) = \sum_{j \in [i-w, i+w]} \text{softmax}(q_i k_j^\top/\sqrt{d}) v_j
\end{equation}

This reduces complexity to $O(n \cdot w)$ but loses global context.

\subsection{Ring Attention}

Ring attention~\cite{liu2023ring} distributes the $n^2$ attention computation across
$P$ GPUs, each holding $n/P$ tokens. Each GPU computes attention for its slice while
rotating KV blocks around a ring of GPUs:

\begin{equation}
\text{Memory per GPU} = O\left(\frac{n}{P} \cdot d\right), \quad \text{Compute} = O\left(\frac{n^2}{P} \cdot d\right)
\end{equation}

This enables linear memory scaling with GPU count.

\section{NTK-Aware Dynamic RoPE Scaling}

\subsection{Standard Linear Interpolation}

The naive approach to extending RoPE is linear interpolation: scale all positions
by $s = m_\text{train}/m_\text{target}$~\cite{chen2023extending}:

\begin{equation}
\theta_i^{\text{scaled}} = \theta_i / s
\end{equation}

This compresses positions into the trained range but reduces positional resolution,
degrading performance on short contexts.

\subsection{NTK-Aware Scaling}

Neural Tangent Kernel theory suggests that the base $b$ of RoPE frequencies should
scale with context length. Dynamic NTK-aware scaling adjusts the base:

\begin{equation}
b_\text{dynamic} = b_\text{base} \cdot \left(\frac{s \cdot d}{d - 2}\right)^{d/(d-2)}
\end{equation}

where $s = n / n_\text{train}$ is the scale factor. This preserves short-context
fidelity while extending long-context range.

\subsection{YaRN: Yet Another RoPE eNtension}

We extend NTK-aware scaling with YaRN~\cite{peng2023yarn}, which applies different
scaling to low-frequency and high-frequency RoPE dimensions:

\begin{equation}
\theta_i^\text{YaRN} = \begin{cases} \theta_i & \text{if } \lambda_i < 1 \\ \theta_i / s & \text{if } \lambda_i > \alpha \\ \text{interpolate} & \text{otherwise} \end{cases}
\end{equation}

where $\lambda_i = 2\pi n_\text{train} / \theta_i$ is the wavelength and $\alpha = 1$
separates low/high frequency regimes. An attention scaling factor $\sqrt{\ln(n)/\ln(n_\text{train})}$
is applied to compensate for entropy changes at long context.

\begin{table}[H]
\centering
\begin{tabular}{lcccc}
\toprule
\textbf{Method} & \textbf{32K PPL} & \textbf{128K PPL} & \textbf{512K PPL} & \textbf{1M PPL} \\
\midrule
No extension (RoPE fail) & 6.84 & $\infty$ & $\infty$ & $\infty$ \\
Linear interpolation & 6.87 & 8.21 & 12.4 & 18.7 \\
NTK-aware & 6.85 & 7.43 & 9.8 & 14.2 \\
YaRN (ours) & \textbf{6.84} & \textbf{7.11} & \textbf{8.4} & \textbf{11.3} \\
\bottomrule
\end{tabular}
\caption{Perplexity at various context lengths on PG-19 test set (Zen-7B).}
\end{table}

\section{Hybrid Attention Architecture}

For contexts beyond 32K tokens, full attention is prohibitively expensive even
with ring attention. We use a hybrid architecture combining sliding window attention
for most layers and full global attention for select layers:

\begin{equation}
\text{Layer}(i) = \begin{cases} \text{SlidingWindow}(w=4096) & \text{if } i \notin \mathcal{G} \\ \text{GlobalAttention} & \text{if } i \in \mathcal{G} \end{cases}
\end{equation}

where $\mathcal{G}$ is the set of global attention layers. We set $|\mathcal{G}| = 8$
(every 4th layer in a 32-layer model). This reduces attention FLOPs by 74\% for
128K context while preserving global information flow.

\subsection{Memory-Efficient Attention Implementation}

All attention is implemented with Flash Attention 3~\cite{shah2023flashattention3},
providing $O(1)$ memory in sequence length (trading memory for recomputation
in the backward pass). For ring attention, KV shards are streamed between GPUs
in a pipelined fashion to overlap communication with computation.

\begin{table}[H]
\centering
\begin{tabular}{lrrrr}
\toprule
\textbf{Context Length} & \textbf{Naive (GB)} & \textbf{Flash Attn (GB)} & \textbf{Ring (8 GPU, GB)} & \textbf{Feasible?} \\
\midrule
32K & 8.2 & 0.8 & -- & Yes (1 GPU) \\
128K & 130 & 3.1 & -- & Flash only \\
512K & 2048 & 49 & 6.1/GPU & 8$\times$A100 \\
1M & 8192 & 196 & 24.5/GPU & 8$\times$H100 \\
\bottomrule
\end{tabular}
\caption{Attention memory requirements for Zen-7B. Ring attention makes 1M context feasible.}
\end{table}

\section{Long-Context Fine-Tuning}

\subsection{Data Construction}

We curate a long-context fine-tuning dataset of 50K documents exceeding 100K tokens:
\begin{itemize}
  \item Legal documents and case law (18K samples, avg. 250K tokens)
  \item Scientific papers with appendices (15K samples, avg. 80K tokens)
  \item Books and long-form fiction (12K samples, avg. 150K tokens)
  \item Code repositories (5K samples, avg. 200K tokens)
\end{itemize}

\subsection{Continuation Fine-Tuning Protocol}

Long-context fine-tuning continues from the 32K-context checkpoint for 10K steps:
\begin{itemize}
  \item YaRN scaling applied to RoPE from step 1
  \item Learning rate $5\times10^{-6}$, linear decay to 0
  \item Batch size: 1 document per GPU (effective batch = 8--16 docs)
  \item Loss computed only on the final 20\% of each document to emphasize long-range dependency
\end{itemize}

The truncated loss objective forces the model to integrate early context for
late predictions:
\begin{equation}
\mathcal{L}_\text{long} = -\sum_{t > 0.8n} \log p_\theta(x_t \mid x_{<t})
\end{equation}

\section{Evaluation}

\subsection{RULER Benchmark}

RULER~\cite{hsieh2024ruler} provides a suite of tasks at controlled context lengths:

\begin{table}[H]
\centering
\begin{tabular}{lcccccc}
\toprule
\textbf{Model} & \textbf{32K} & \textbf{64K} & \textbf{128K} & \textbf{256K} & \textbf{512K} & \textbf{1M} \\
\midrule
Zen-7B (32K) & 95.8 & 78.2 & 41.3 & -- & -- & -- \\
Zen-7B (128K) & 95.6 & 93.1 & 94.1 & 81.4 & 52.3 & -- \\
Zen-7B (1M) & 95.4 & 93.0 & 94.1 & 89.2 & 87.3 & 79.8 \\
\bottomrule
\end{tabular}
\caption{RULER accuracy (\%) at various context lengths. 1M model extends all prior limits.}
\end{table}

\subsection{Needle-in-Haystack Retrieval}

We insert a single fact (``needle'') at a random position in a long document (``haystack'')
and ask the model to retrieve it. Recall at various depths and context lengths:

\begin{table}[H]
\centering
\begin{tabular}{lcccccc}
\toprule
\textbf{Depth} & \textbf{32K} & \textbf{64K} & \textbf{128K} & \textbf{256K} & \textbf{512K} & \textbf{1M} \\
\midrule
10\% (near start) & 99.1 & 98.8 & 98.4 & 97.9 & 97.2 & 91.3 \\
50\% (middle) & 98.4 & 97.2 & 96.8 & 95.3 & 94.1 & 84.2 \\
90\% (near end) & 99.2 & 99.0 & 98.9 & 98.4 & 97.8 & 93.1 \\
\midrule
Average & \textbf{98.9} & \textbf{98.3} & \textbf{98.0} & \textbf{97.2} & \textbf{96.4} & \textbf{89.5} \\
\bottomrule
\end{tabular}
\caption{Needle-in-haystack recall (\%) by depth and context length (Zen-7B 1M).}
\end{table}

The ``lost in the middle'' phenomenon (lower middle-depth recall) is minimal at contexts
up to 512K, appearing at 1M context with a 7-point gap versus near-end recall.

\subsection{Long-Context Retrieval: SCROLLS}

\begin{table}[H]
\centering
\begin{tabular}{lcccc}
\toprule
\textbf{Model} & \textbf{GovReport} & \textbf{QMSum} & \textbf{SummScreen} & \textbf{QASPER} \\
\midrule
Zen-7B (32K) & 51.2 & 22.4 & 27.8 & 41.3 \\
Zen-7B (1M) & \textbf{56.8} & \textbf{26.1} & \textbf{32.4} & \textbf{47.8} \\
\bottomrule
\end{tabular}
\caption{SCROLLS benchmark ROUGE-1 scores comparing 32K and 1M context.}
\end{table}

\section{Analysis}

\subsection{Position Interpolation vs. YaRN at Short Context}

A critical concern is whether long-context extension degrades short-context performance.
We measure perplexity at 2K, 4K, and 8K contexts:

\begin{table}[H]
\centering
\begin{tabular}{lccc}
\toprule
\textbf{Method} & \textbf{2K PPL} & \textbf{4K PPL} & \textbf{8K PPL} \\
\midrule
Original 32K model & 6.31 & 6.58 & 6.74 \\
Linear interpolation & 6.44 & 6.68 & 6.82 \\
YaRN (ours) & \textbf{6.32} & \textbf{6.59} & \textbf{6.75} \\
\bottomrule
\end{tabular}
\caption{Short-context perplexity. YaRN preserves short-context quality; linear interpolation degrades it.}
\end{table}

\subsection{Throughput at Scale}

\begin{table}[H]
\centering
\begin{tabular}{lrrrr}
\toprule
\textbf{Context} & \textbf{1 GPU} & \textbf{2 GPU} & \textbf{4 GPU} & \textbf{8 GPU} \\
\midrule
32K & 1420 tok/s & 2750 tok/s & 5280 tok/s & 9840 tok/s \\
128K & OOM & 1180 tok/s & 2350 tok/s & 4610 tok/s \\
512K & OOM & OOM & OOM & 1230 tok/s \\
1M & OOM & OOM & OOM & 640 tok/s \\
\bottomrule
\end{tabular}
\caption{Zen-7B prefill throughput at various context lengths and GPU counts (A100 80GB).}
\end{table}

\section{Conclusion}

The combination of YaRN dynamic RoPE scaling, hybrid sliding window + global attention,
ring attention for multi-GPU distribution, and targeted long-context fine-tuning
extends Zen model context to 1M tokens with 79.8\% RULER accuracy and $>89\%$
needle-in-haystack recall. The approach preserves short-context quality exactly
and enables practical long-context use cases at reasonable compute cost.

\bibliographystyle{plain}
\begin{thebibliography}{99}
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\bibitem{beltagy2020longformer} Beltagy et al. (2020). Longformer: The Long-Document Transformer. \textit{arXiv:2004.05150}.
\bibitem{liu2023ring} Liu et al. (2023). Ring Attention with Blockwise Transformers for Near-Infinite Context. \textit{arXiv:2310.01889}.
\bibitem{chen2023extending} Chen et al. (2023). Extending Context Window of Large Language Models via Positional Interpolation. \textit{arXiv:2306.15595}.
\bibitem{peng2023yarn} Peng et al. (2023). YaRN: Efficient Context Window Extension of Large Language Models. \textit{arXiv:2309.00071}.
\bibitem{shah2023flashattention3} Shah et al. (2024). FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision. \textit{arXiv:2407.08608}.
\bibitem{hsieh2024ruler} Hsieh et al. (2024). RULER: What's the Real Context Size of Your Long-Context Language Models? \textit{arXiv:2404.06654}.
\end{thebibliography}

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