Merge Models by What They Represent

Model merging has a dirty secret: it usually works by averaging weights and hoping. Task Arithmetic, TIES, DARE — the whole family combines fine-tuned models by operating on parameters, with heuristics for resolving sign conflicts and dropping redundant deltas. RECALL starts from a different premise: what a model knows lives in its representations, not its weights. Two models can implement similar knowledge with different parameters; two models with similar parameters can behave differently. If you want to merge knowledge without destroying it, align what the models represent — layer by layer — and let the merging weights follow from that.

The mechanism: merge by representation, hierarchically

RECALL (REpresentation-aligned Catastrophic-forgetting ALLeviation), from Wang et al., works in three steps:

1. Find typical samples. For each domain, cluster the data (K-means) and take cluster centers as "typical samples" — a compact, representative probe set. No historical training data is needed at merge time; the typical samples are the only data involved, which makes the method effectively data-free with respect to the original corpora.
2. Measure representational similarity. Feed the typical samples through each model and collect layer-wise hidden representations. Compute similarity between models with an RBF kernel over these representations, then softmax into merging weights. Models whose representations agree get merged more strongly; models that diverge get downweighted — per layer, not globally.
3. Fuse hierarchically. The merging is hierarchical across depth, reflecting a structural prior about transformers: shallow layers encode domain-general features worth preserving, deep layers encode task-specific adaptations worth updating. The fusion respects this gradient, preserving shared structure early while allowing specialization late.

The RBF-then-softmax step is doing the real work. A fixed merging coefficient (as in naive averaging) assumes all models contribute equally everywhere; RECALL lets the data decide, per layer, whose representations are trustworthy. If two domain models learned compatible shallow representations but divergent deep ones, the merge preserves the shared foundation and negotiates the divergence — rather than averaging parameters and corrupting both.

Why representations instead of parameters

This is the paper's conceptual bet, and it's worth examining. Parameter-space merging assumes that models fine-tuned from the same base live in a shared, well-behaved basin where interpolation is meaningful. That assumption is fragile: permutation symmetries, scale differences, and divergent optimization paths all break it, which is why merging methods need sign-election and sparsification hacks. Representation space is better behaved for this purpose because it's functional — hidden states are what the model actually computes with, and similarity there means similarity in behavior on the probe set. The abstract's opening claim is strong: internal representations serve as "reliable proxies of learned knowledge." If you believe that — and a decade of probing and steering work suggests you should — then merging should be representation-guided by construction.

The hierarchical prior (preserve shallow, adapt deep) also encodes genuine knowledge about transformer organization rather than treating all layers symmetrically. It's the same depth-gradient intuition behind layer-freezing heuristics in transfer learning and the "shallow layers are general" finding from the progressive networks' transfer analysis — here operationalized as a merging schedule.

Results and limits

Across five NLP tasks and multiple continual learning scenarios, RECALL outperforms baselines on both knowledge retention and generalization, per the authors' report — as a data-free, task-label-free method. The "no task labels" property is significant: most continual learning methods (EWC, GEM, SI) need to know when tasks begin and end. RECALL sidesteps the boundary problem entirely by operating post-hoc on finished models. And unlike regularization methods, it never constrains learning itself — each domain model trains freely, and the continual-learning problem is solved at merge time, not training time.

The limitations are where the interesting questions live. First, the method needs a model per domain — it's continual learning by accumulating models, which is progressive networks' growth problem in a new costume. The merge compresses them into one, but you still trained and stored K models to get there. Second, "typical samples" via K-means is a heuristic; if the clusters miss modes of the domain, the similarity estimates are biased, and the paper's robustness to probe-set quality is the thing I'd probe first. Third, the RBF kernel's bandwidth and the softmax temperature are hyperparameters that control how aggressively models are weighted — the method replaces the "fixed coefficient" assumption with a "similarity metric" assumption, and metrics have their own fragility. Finally, five NLP tasks is a reasonable demonstration but not a stress test; the representation-similarity prior should be tested where domains genuinely conflict, not just where they differ.

Don't average weights and hope. Measure what each model represents, layer by layer, and let the merge follow the representations: preserve what's shared in the shallows, negotiate what's specialized in the depths.

The arc

RECALL belongs to the merging branch of continual learning, which is really the field's quietest admission: maybe sequential training is the wrong primitive, and the right one is train freely, combine wisely. That idea runs from distillation through model soups to the current merging renaissance. RECALL's contribution is making the combination representation-aware and hierarchical rather than parameter-heuristic. It also closes a loop with the oldest idea in this series: McCloskey and Cohen showed interleaved (concurrent) training avoids forgetting; merging is concurrent training after the fact — you train separately, then combine as if you'd trained together. For my credit-assignment research, the representation-first move resonates: credit, like knowledge, may be more faithfully assigned in the space of what the network computes than in the space of its parameters. The Fisher, the path integral, the RBF similarity — they're all trying to answer "what matters," and the trend is unmistakable: away from weights, toward functions.

Paper: RECALL: REpresentation-aligned Catastrophic-forgetting ALLeviation via Hierarchical Model Merging — Wang, Wan, Shi, Yang, He, Ma, Han, Li, Tan, Li, Liu, Gong & Zhang, 2025.