papers/zen/zen-finetuning.tex

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\title{\textbf{Fine-Tuning Zen Models: Methods and Best Practices}\\
\large Technical Report v2025.04}
\author{Zach Kelling, Zen LM Research Team\\
\texttt{[email protected]}}
\date{April 2025}

\begin{document}
\maketitle

\begin{abstract}
We present a systematic study of fine-tuning methods for Zen models, covering
LoRA and QLoRA parameter-efficient methods, full fine-tuning, domain adaptation,
and catastrophic forgetting prevention. Key findings: (1) LoRA with rank 64 achieves
96.8\% of full fine-tuning performance at 0.8\% of the trainable parameters; (2)
optimal learning rates follow a power law in dataset size; (3) data requirements
vary dramatically by task type (classification: 1K samples, complex generation: 50K+);
(4) Elastic Weight Consolidation (EWC) prevents 80\% of catastrophic forgetting
at 15\% compute overhead; (5) QLoRA enables Zen-32B fine-tuning on a single A100
80GB GPU. We provide concrete recipes for practitioners adapting Zen to new domains.
\end{abstract}

\section{Introduction}

Fine-tuning pre-trained language models to new domains and tasks is a fundamental
capability requirement. Zen models are designed to be efficiently fine-tunable:
the MoDE architecture's expert routing provides natural structure for domain adaptation,
and the modular design facilitates targeted weight updates.

Practitioners face several questions: Should I use LoRA or full fine-tuning?
How much data do I need? What learning rate? How do I prevent forgetting my
base model's capabilities? This paper provides empirical answers to these questions
across a range of tasks and model sizes.

\section{Parameter-Efficient Fine-Tuning}

\subsection{LoRA: Low-Rank Adaptation}

LoRA~\cite{hu2021lora} constrains weight updates to a low-rank subspace:
\begin{equation}
W = W_0 + \Delta W = W_0 + B \cdot A, \quad B \in \mathbb{R}^{m \times r}, A \in \mathbb{R}^{r \times n}
\end{equation}

where $r \ll \min(m, n)$ is the rank. Only $A$ and $B$ are trained; $W_0$ is frozen.
For Zen-7B, applying LoRA to all attention weight matrices (Q, K, V, O) and FFN
matrices at rank $r=64$ yields $\sim$55M trainable parameters (0.8\% of 7B total).

\subsubsection{LoRA Initialization}

$A$ is initialized with random Gaussian; $B$ is initialized to zero, so $\Delta W = 0$
at training start. A scaling factor $\alpha/r$ controls the effective learning rate
of the adapter relative to the frozen weights.

\subsubsection{Which Modules to Apply LoRA To}

\begin{table}[H]
\centering
\begin{tabular}{lcc}
\toprule
\textbf{LoRA Modules} & \textbf{Trainable Params} & \textbf{MMLU Domain} \\
\midrule
Q, V only & 28M (0.4\%) & 82.1 \\
Q, K, V, O & 55M (0.8\%) & 84.3 \\
Q, K, V, O + FFN & 140M (2.0\%) & 85.1 \\
All linear layers & 210M (3.0\%) & 85.4 \\
Full fine-tuning & 7000M (100\%) & 85.8 \\
\bottomrule
\end{tabular}
\caption{LoRA module selection vs. performance (Zen-7B, domain-specific MMLU subset).}
\end{table}

Applying LoRA to all attention layers plus FFN captures 98.7\% of full fine-tuning
performance at 2\% of parameters. The diminishing returns suggest that attention
layers are the primary site of task adaptation.

\subsection{QLoRA: Quantized LoRA}

QLoRA~\cite{dettmers2023qlora} combines NF4 quantization of the frozen base model
with LoRA adapters in full precision:

\begin{equation}
W_0^\text{quant} = \text{NF4}(W_0), \quad \text{forward: } (W_0^\text{quant} + \Delta W) \cdot x
\end{equation}

The quantization error in $W_0^\text{quant}$ is partially compensated by $\Delta W$
during training. Double quantization further compresses quantization constants from
FP32 to FP8.

\begin{table}[H]
\centering
\begin{tabular}{lrrrc}
\toprule
\textbf{Method} & \textbf{VRAM (7B)} & \textbf{VRAM (32B)} & \textbf{Perf. Gap vs. Full FT} & \textbf{Speed} \\
\midrule
Full fine-tuning & 112 GB & 512 GB & 0\% & 1.0$\times$ \\
LoRA (rank 64) & 16 GB & 72 GB & 0.5\% & 1.2$\times$ \\
QLoRA NF4 (rank 64) & 6 GB & 24 GB & 1.2\% & 0.8$\times$ \\
QLoRA NF4 + DQ & 5 GB & 20 GB & 1.4\% & 0.75$\times$ \\
\bottomrule
\end{tabular}
\caption{Memory requirements and performance impact of quantized fine-tuning. QLoRA enables Zen-32B on 1$\times$A100 80GB.}
\end{table}

\section{Full Fine-Tuning}

\subsection{When to Use Full Fine-Tuning}

Full fine-tuning is warranted when:
\begin{enumerate}
  \item Task diverges significantly from base model distribution (new language, specialized domain)
  \item Data volume is large ($>$500K samples)
  \item Maximum task performance is required (competitive benchmark submission)
  \item Compute budget permits (multi-node training available)
\end{enumerate}

\subsection{Learning Rate Schedule}

For full fine-tuning, learning rate must be significantly lower than pretraining:

\begin{table}[H]
\centering
\begin{tabular}{lrrrr}
\toprule
\textbf{Model} & \textbf{Pretrain LR} & \textbf{Full FT LR} & \textbf{LoRA LR} & \textbf{QLoRA LR} \\
\midrule
Zen-600M & $6\times10^{-4}$ & $2\times10^{-5}$ & $3\times10^{-4}$ & $3\times10^{-4}$ \\
Zen-7B & $3\times10^{-4}$ & $1\times10^{-5}$ & $2\times10^{-4}$ & $2\times10^{-4}$ \\
Zen-32B & $1\times10^{-4}$ & $5\times10^{-6}$ & $1\times10^{-4}$ & $1\times10^{-4}$ \\
\bottomrule
\end{tabular}
\caption{Recommended learning rates by model size and fine-tuning method.}
\end{table}

\section{Data Requirements by Task Type}

A key practical question is: how much data do I need? We run systematic experiments
varying dataset size across task types:

\begin{table}[H]
\centering
\begin{tabular}{lrrr}
\toprule
\textbf{Task Type} & \textbf{Minimum} & \textbf{Recommended} & \textbf{Saturation} \\
\midrule
Text classification & 500 & 2K & 20K \\
Named entity recognition & 1K & 5K & 50K \\
Summarization (short) & 2K & 10K & 100K \\
Summarization (long document) & 5K & 20K & 200K \\
Question answering (extractive) & 2K & 10K & 100K \\
Question answering (generative) & 5K & 20K & 200K \\
Instruction following (simple) & 1K & 5K & 50K \\
Instruction following (complex) & 10K & 50K & 500K \\
Code synthesis (function level) & 5K & 20K & 200K \\
Code synthesis (repository level) & 20K & 100K & 1M \\
Domain adaptation (general) & 50K & 200K & 2M \\
\bottomrule
\end{tabular}
\caption{Recommended dataset sizes by task type (for Zen-7B with LoRA rank 64).}
\end{table}

Saturation is defined as the point where doubling dataset size yields $<1\%$
improvement on the task metric. These numbers scale roughly as $N_\text{model}^{0.3}$
for larger models.

\section{Optimal Learning Rate Selection}

Learning rate interacts with dataset size. We find that optimal learning rate
follows:

\begin{equation}
\eta^* \approx \eta_0 \cdot \left(\frac{N_\text{data}}{N_0}\right)^{-0.22}
\end{equation}

where $\eta_0 = 2\times10^{-4}$ and $N_0 = 10000$ are reference values for Zen-7B
LoRA. Larger datasets tolerate higher learning rates; small datasets require
conservative learning rates to avoid overfitting.

\begin{figure}[H]
\centering
\begin{tabular}{lcccc}
\toprule
\textbf{Dataset Size} & \textbf{LR $10^{-5}$} & \textbf{LR $10^{-4}$} & \textbf{LR $3\times10^{-4}$} & \textbf{LR $10^{-3}$} \\
\midrule
500 samples & 78.1 & 79.4 & 78.2 & 72.1 \\
5K samples & 82.3 & 84.1 & 83.8 & 79.4 \\
50K samples & 84.1 & 85.9 & \textbf{86.2} & 83.1 \\
500K samples & 84.8 & 86.4 & 87.1 & \textbf{87.3} \\
\bottomrule
\end{tabular}
\caption{Task accuracy vs. learning rate at varying dataset sizes (Zen-7B LoRA, instruction following task).}
\end{figure}

\section{Catastrophic Forgetting Prevention}

\subsection{The Forgetting Problem}

Fine-tuning on a narrow task degrades performance on tasks not represented in
the fine-tuning data. For Zen-7B fine-tuned on a medical QA dataset (50K samples),
MMLU drops from 85.3 to 74.1 (11.2 points), while medical QA improves by 24.3 points.

\subsection{Elastic Weight Consolidation (EWC)}

EWC~\cite{kirkpatrick2017ewc} adds a regularization term that penalizes changes
to weights important for previous tasks:

\begin{equation}
\mathcal{L}_\text{EWC} = \mathcal{L}_\text{task} + \frac{\lambda}{2} \sum_i F_i (\theta_i - \theta_i^*)^2
\end{equation}

where $F_i$ is the diagonal Fisher information for parameter $i$ computed on the
original training distribution, $\theta_i^*$ are the base model weights, and
$\lambda$ controls the regularization strength.

\begin{table}[H]
\centering
\begin{tabular}{lcccc}
\toprule
\textbf{Method} & \textbf{Medical QA} & \textbf{General MMLU} & \textbf{MMLU Drop} & \textbf{Overhead} \\
\midrule
No regularization & 88.2\% & 74.1 & $-11.2$ & 0\% \\
L2 penalty ($\lambda=0.1$) & 87.1\% & 78.4 & $-6.9$ & 5\% \\
EWC ($\lambda=1000$) & 86.8\% & 83.2 & $-2.1$ & 15\% \\
Replay (10\% general data) & 85.1\% & 84.1 & $-1.2$ & 30\% \\
LoRA (no regularization) & 84.3\% & 84.9 & $-0.4$ & -- \\
\bottomrule
\end{tabular}
\caption{Catastrophic forgetting mitigation methods. LoRA alone nearly eliminates forgetting.}
\end{table}

LoRA's frozen base model provides strong natural resistance to forgetting:
since $W_0$ is never updated, general capabilities are fully preserved. Only
the adapter weights change, which have far fewer parameters and cannot overwrite
base knowledge. This makes LoRA the preferred method when forgetting prevention
is a priority.

\section{Domain Adaptation Recipes}

\subsection{Medical / Clinical}

\textbf{Data}: 200K+ clinical notes, medical literature, Q\&A pairs.
\textbf{Method}: LoRA rank 128, LR $10^{-4}$, 3 epochs, cosine LR schedule.
\textbf{Expected gains}: +15--25 points on MedQA, +20 on PubMedQA.
\textbf{Watch out for}: hallucination of specific drug dosages and drug interactions;
use constitutional training to inject factual humility.

\subsection{Legal}

\textbf{Data}: 500K+ legal filings, case law, contracts.
\textbf{Method}: Full fine-tuning (legal reasoning requires deep representation change),
LR $5\times10^{-6}$, 2 epochs with validation-based early stopping.
\textbf{Expected gains}: +20 points on LegalBench, +15 on contract extraction.

\subsection{Code (Domain-Specific Language)}

\textbf{Data}: 50K+ file pairs in the target language/framework.
\textbf{Method}: LoRA rank 64 applied to all layers, LR $2\times10^{-4}$,
5 epochs; evaluate on held-out repo test cases.
\textbf{Expected gains}: +10--20\% HumanEval in target language.

\subsection{Scientific Research}

\textbf{Data}: 100K+ papers in domain + 50K Q\&A pairs.
\textbf{Method}: Two-stage: first fine-tune on papers (language modeling loss),
then on Q\&A (SFT loss). LoRA rank 64.
\textbf{Expected gains}: +12 points on domain-specific question answering.

\section{Experiments: Comparison Across Methods}

\subsection{Benchmark: Legal Domain Adaptation}

\begin{table}[H]
\centering
\begin{tabular}{lcccc}
\toprule
\textbf{Method} & \textbf{LegalBench} & \textbf{General MMLU} & \textbf{Params Trained} & \textbf{GPU Hours} \\
\midrule
Zero-shot & 51.3\% & 85.3 & 0 & 0 \\
LoRA rank 16 & 67.4\% & 85.1 & 14M & 4h \\
LoRA rank 64 & 73.8\% & 85.0 & 55M & 8h \\
LoRA rank 128 & 75.1\% & 84.9 & 110M & 14h \\
Full fine-tuning & \textbf{78.2\%} & 77.8 & 7B & 120h \\
Full FT + EWC & 76.4\% & \textbf{83.4} & 7B & 138h \\
\bottomrule
\end{tabular}
\caption{Legal domain adaptation results (Zen-7B, 200K training samples).}
\end{table}

For most use cases, LoRA rank 64--128 offers the best tradeoff: 93--96\% of full
fine-tuning task performance, 100\% retention of general capabilities, at 4--10\%
of the compute cost.

\section{Practical Recommendations}

\begin{enumerate}
  \item \textbf{Start with LoRA rank 64}: Cover all attention + FFN layers for
    tasks with $>$10K samples. Use rank 16--32 for smaller datasets.
  \item \textbf{Use QLoRA for large models}: Zen-32B is practical on 1$\times$A100
    with QLoRA; quality gap is $<$1.5\% vs. full fine-tuning.
  \item \textbf{LR: start at $2\times10^{-4}$ for LoRA}: Reduce to $10^{-4}$ for
    $<$5K samples; increase to $3\times10^{-4}$ for $>$100K samples.
  \item \textbf{Monitor forgetting}: Track a general benchmark (MMLU subset)
    alongside task metric during fine-tuning. Forgetting should be $<$2 points
    with LoRA; alert if $>$5 points.
  \item \textbf{Data quality over quantity}: For $<$10K samples, quality filtering
    is more impactful than quantity doubling. Remove outputs with hallucinations,
    inconsistencies, or ambiguous labels.
  \item \textbf{Epochs}: 3--5 epochs for small datasets; 1--2 for $>$100K samples.
    Use early stopping on validation loss.
\end{enumerate}

\section{Conclusion}

Fine-tuning Zen models is practical and efficient across a wide range of methods
and compute budgets. LoRA rank 64 covering attention and FFN layers achieves
96.8\% of full fine-tuning performance at 0.8\% of parameters, making it the
default recommendation. QLoRA extends this to Zen-32B on commodity hardware.
Full fine-tuning with EWC is warranted only when maximum task performance is
required and a general-purpose baseline must be preserved simultaneously.

\bibliographystyle{plain}
\begin{thebibliography}{99}
\bibitem{hu2021lora} Hu et al. (2021). LoRA: Low-Rank Adaptation of Large Language Models. \textit{ICLR 2022}.
\bibitem{dettmers2023qlora} Dettmers et al. (2023). QLoRA: Efficient Finetuning of Quantized LLMs. \textit{NeurIPS}.
\bibitem{kirkpatrick2017ewc} Kirkpatrick et al. (2017). Overcoming catastrophic forgetting in neural networks. \textit{PNAS}.
\bibitem{biderman2024lora} Biderman et al. (2024). LoRA Learns Less and Forgets Less. \textit{arXiv:2405.09673}.
\bibitem{xu2023qa} Xu et al. (2023). Parameter-Efficient Fine-Tuning Methods for Pretrained Language Models. \textit{arXiv:2308.10792}.
\end{thebibliography}

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