Leveraging our novel merging approach, we can seamlessly integrate instruction, reasoning, and code models into a single, high-performing unified model in just one step.

Model Highlights:

• merge method: cla-gm

• precision: dtype: bfloat16

• Context length: 262,144&1010000

Parameter Settings:

[!TIP] Temperature=0.7, TopP=0.8, TopK=20,MinP=0.

Geometric Median with CLA Initialization

Problem Setting

Objective: Merge 𝐾 fine-tuned models with identical tensor names and shapes into a single model whose parameters 𝜃⋆ lie at the robust center of the 𝐾 parameter sets.

Per-Tensor Formulation

For a given tensor name, each model provides a point 𝑥ᵢ ∈ ℝⁿ (flattened). We seek a robust center 𝜃⋆ ∈ ℝⁿ.

Mean and Median

Arithmetic Mean:

$$a = \frac{1}{K} \sum_{i=1}^{K} x_i$$

Efficient but sensitive to outliers.

Elementwise Median:

$$m = \text{median}({x_i})$$

Robust but ignores vector magnitude coupling; computed elementwise across coordinates.

CLA Initialization

Centered Linear Average:

$$\theta^{(0)} = \frac{a + m}{2}$$

This blends efficiency and robustness without tuning, offering a strong seed for iterative robust estimators.

Geometric Median Objective

Objective Function:

$$\theta^{\star} = \arg\min_{\theta \in \mathbb{R}^n} \sum_{i=1}^{K} |\theta - x_i|_2$$

This is the multivariate analogue of the median, robust to outliers in the Euclidean geometry of parameters.

Weiszfeld Algorithm

Update Rule: Given current 𝜃(𝑡), define weights:

$$w_i^{(t)} = \frac{1}{\max(|\theta^{(t)} - x_i|_2, \varepsilon)}$$

where 𝜀 = eps(float32) prevents division by zero.

Iteration Step:

$$\theta^{(t+1)} = \frac{\sum_{i=1}^{K} w_i^{(t)} x_i}{\sum_{i=1}^{K} w_i^{(t)}}$$

Convergence Criterion:

Stop when the relative change is below 𝜀:

$$\frac{|\theta^{(t+1)} - \theta^{(t)}|_2}{\max(|\theta^{(t)}|_2, 1)} \leq \varepsilon$$

where 𝜀 = eps(float32) ≈ 1.19×10⁻⁷.