SE-Merging: Dynamic Model & Map Integration

Updated 4 December 2025

SE-Merging is a dynamic, representation-aware method that fuses models, maps, and observational data without requiring additional training.
It employs per-sample coefficients and semantic alignment to preserve task-specific specialization while achieving robust multi-task generalization.
Empirical evaluations show SE-Merging outperforms static merging approaches, reducing representation bias and computational overhead across various applications.

SE-Merging encompasses a set of advanced methodologies for merging distinct models, maps, or observational data in machine learning, computer vision, and astrophysics. While the term frequently appears in recent literature to signify "Self-Enhanced Merging" in model fusion, it also arises in specialized contexts such as weak-lensing mapping in galaxy cluster studies and SE(3) (Special Euclidean group) transformations in structure-from-motion map integration. Across these domains, SE-Merging emphasizes dynamic, representation-aware, and training-free merging procedures that aim to preserve specialization and internal knowledge of constituent inputs, achieving robust multi-task or multi-source integration without retraining or prohibitive computational cost (Chen et al., 22 Jun 2025, Gu et al., 26 May 2025, Ahn et al., 5 Apr 2024, Flood et al., 2021).

1. Theoretical Foundations of SE-Merging

SE-Merging in machine learning exploits the empirical observation that standard linear interpolation of task-specific model parameters leads to multi-task-capable models. Formally, given $T$ expert models $\theta_1, ..., \theta_T$ fine-tuned on disjoint tasks and a pre-trained initialization $\theta_\text{PT}$ , conventional merging uses static convex combinations:

$\theta_\text{merged} = \sum_{i=1}^T \lambda_i \theta_i, \quad \sum_{i=1}^T \lambda_i = 1$

Empirically, $\theta_\text{merged}$ maintains performant behavior across all $T$ tasks; probe analyses reveal that the merged model distinguishes data from different sources and adapts its representation to match the expert corresponding to each sample, supporting efficient multi-task generalization (Chen et al., 22 Jun 2025). In structure-from-motion (SfM) map merging, merging is formulated as an optimization over SE(3) (or Sim(3)) transformations to produce globally consistent maps invariant to gauge and merge order, compressing submaps into a unified low-memory representation (Flood et al., 2021).

2. SE-Merging Algorithms: Dynamic and Representation-Aware Merging

The central innovation of SE-Merging is dynamic, representation-driven merging, as opposed to static interpolation. For $x \in \mathcal{X}$ , SE-Merging introduces per-sample coefficients $\alpha_i(x)$ :

$\theta_\text{SE}(x) = \theta_\text{PT} + \sum_{i=1}^T \alpha_i(x)\, (\theta_i - \theta_\text{PT})$

The coefficients $\alpha_i(x)$ are computed via a nonparametric router: for each sample, intermediate representations from both the merged model and each expert are compared using $\ell_2$ or cosine distance; similarities are normalized and transformed via softmax to produce sample-specific weights. This mechanism leverages implicit clustering in representation space—t-SNE visualizations confirm that merged representations cluster by task and that for input $x$ from task $i$ , the merged-model’s representations are closest to those of expert $i$ (Chen et al., 22 Jun 2025).

A layerwise pseudocode is as follows:

For each input sample x:
    For each expert i:
        Compute layer-ℓ representation r_i = f^{(ℓ)}(x; θ_PT + λτ_i)
    Compute merged representation r_merged = f^{(ℓ)}(x; θ_merged)
    Compute distances d_i = ||r_merged - r_i||_2
    Convert distances to similarities s_i, normalize via min-max
    Set coefficients α_i(x) ∝ exp(s_i)
    Merge model weights: θ_SE(x) = θ_PT + ∑ α_i(x) τ_i
    Predict ŷ with θ_SE(x)

No additional training or learned router is required; this process dynamically adjusts the weight combination per sample, enhancing task-specific behavior and reducing representation bias compared to static methods.

3. Semantic Alignment and Knowledge Preservation

SE-Merging is closely related to training-free, data-free semantic alignment approaches for large-scale model fusion. In SeMe (Semantic-based Merging), the merging objective is to align the latent semantics of each model via the pseudo-inverse of the model head, constructing semantic bases for the token vocabulary. At each layer, input weights from two models ( $A,B$ ) are projected into their respective semantic coordinate systems, and a closed-form ridge regression determines an alignment mapping before weights are merged:

$M_i^* = \arg\min_{M_i} \|\Phi_i^A M_i - \Phi_i^B\|_F^2 + \lambda \|M_i - I\|_F^2$

The final merged weights are formed by averaging in the aligned space:

$W_i^{\text{merge}} = \frac{1}{2}(W_i^A M_i^* + W_i^B)$

This procedure preserves both outward behavior and internal knowledge representations, outperforming naive averaging and data-guided baselines on a range of benchmarks (Gu et al., 26 May 2025). Theoretical analyses attribute SeMe’s efficacy to the approximate orthogonality (“semantic isotropy”) of vocabulary-defined latent bases and the superposition structure of hidden representations.

4. Empirical Evaluation and Performance

SE-Merging has been systematically evaluated on multi-task vision (e.g., CLIP ViT-B/32, ViT-L/14 on SUN397, Cars, SVHN, etc.) and language (e.g., GPT-2 on GLUE) benchmarks. In all cases, SE-Merging yields substantial performance improvements over static merging approaches:

Method	ViT-B/32 Avg.	ViT-L/14 Avg.	GPT-2/GLUE Avg.
Weight Averaging	65.8	79.6	56.1
Fisher-Merging	68.3	82.2	58.7
RegMean	71.8	83.7	68.8
Task Arithmetic	70.1	84.5	70.0
AdaMerging++	81.1	91.0	—
SE-Merging	84.96	91.57	76.86

SE-Merging also reduces representation bias between merged and expert models and is compatible with task arithmetic, Fisher, and PCB/TIES/DARE post-processing. Notably, these performance gains are achieved without further finetuning or external data (Chen et al., 22 Jun 2025).

5. SE-Merging in Other Domains: Astrophysics and SfM Map Merging

Outside deep learning, SE-Merging appears in astrophysics and computer vision. In weak-lensing mass reconstructions of galaxy clusters (e.g., Abell 514), “SE-Merging” refers to the reconstruction and substructure identification within the southeast (SE) subcluster. The methodology involves measuring background galaxy shape distortions to reconstruct two-dimensional mass maps, identifying bimodal mass substructures (SE_N and SE_S) via Kaiser–Squires inversion and NFW-profile fitting. These substructures are detected with high statistical significance (4.5σ and 4.8σ) and play a crucial role in understanding merger-driven cluster dynamics, shock heating, and subsequent evolution (Ahn et al., 5 Apr 2024).

In structure-from-motion, “SE-Merging” often refers to algorithms exploiting SE(3) or Sim(3) group structure to merge multiple 3D reconstructions. Such approaches optimize over per-map rigid-body transformations to achieve global coordinate/gauge invariance and recursion-friendly, low-memory summaries amenable to hierarchical or streaming merging. Loop closing and change detection are enabled statistically via the increase in the summed image-residuals post-merge, as analyzed under explicit probabilistic models (Flood et al., 2021).

6. Extensions, Limitations, and Open Challenges

SE-Merging’s generalization to heterogeneous architectures remains an open problem; current methods require aligned vocabularies and matching dimensions. Theoretical arguments often assume weight disentanglement and representation linearity, which are not fully proved for arbitrary deep networks. In structure-from-motion and weak-lensing, limitations may arise from non-rigid distortions, suboptimal gauge elimination, or insufficient data density. Proposed future extensions include more expressive (learned) gating for routing, integration with parameter conflict mitigation (e.g., sparse-masked or optimal transport-based merging), adaptation to generative modeling, and hierarchical routing for task ensembles with $T > 2$ (Chen et al., 22 Jun 2025, Gu et al., 26 May 2025).

7. Significance and Broader Impacts

SE-Merging systems demonstrate that specialized models can be compositionally merged with preservation of both external performance and internal specialization, without retraining or external data. In model fusion, this dramatically improves the efficiency and flexibility of multi-task and federated pipelines. In astrophysical and computational mapping, hierarchical SE-Merging supports scalable aggregation and change/loop detection across distributed data. These paradigms collectively point toward a unifying principle: leveraging implicit semantic or geometric structure—whether in parameter space, representation space, or physical correspondence—enables scalable, robust, and interpretable merging in modern computational science (Chen et al., 22 Jun 2025, Gu et al., 26 May 2025, Ahn et al., 5 Apr 2024, Flood et al., 2021).