LARA: Lightweight Adapters in the Residual Stream for Composable Adaptation and Alignment

We present LARA (Lightweight Additive Residual Adaptation), a method for efficient adaptation that operates in the residual stream of a frozen model rather than in its weights. Where LoRA adds an update of low rank to weight matrices, LARA reads the hidden state at a small set of layers and adds a correction of low rank back to the residual stream, leaving all base weights untouched. On a code fine-tuning task and on preference optimization (DPO), LARA matches LoRA at equal parameter counts. Because adaptation is a frozen base plus a residual, LARA exposes a scale γ, applied at inference, that interpolates smoothly between base and adapted behavior, a form of graded control that adaptation in weight space does not offer. Finally, because each behavior is a small residual module over a shared frozen base, many behaviors can be held resident at once and routed automatically per token. We place seven behaviors, six fine-tuned and one optimized for preference, on one frozen 1.5B model for roughly 33 MB of overhead, against one full model for each behavior. Because the base is untouched, behaviors are trained separately and selected per token rather than loaded on demand, which suits hosting many behaviors, and adding new ones, on a single model on a device.

Learning to Select, Not Relearn: Hard-Routed Mixtures of Reasoning LoRAs

Composing independently trained LoRA adapters into a single large language model is useful for multi-domain adaptation, especially when the original training data cannot be shared. A common approach is to use MoE-style routing over LoRA experts, but for frozen pretrained adapters, soft weighted combinations can change the unit-scale additive update under which each LoRA module was originally trained. We propose \textbf{Hard-Routed MoR-LoRA}, a two-stage framework for composing frozen reasoning LoRA experts through unit-scale hard selection. First, domain-specific LoRA adapters are trained independently using reinforcement learning from verifiable feedback to obtain reasoning experts. Then, all experts are frozen, reasoning traces are distilled from them, and only a lightweight shared router together with a small attention LoRA is trained for integration. The router selects exactly one expert per token using hard top-1 routing, while a straight-through estimator enables gradient-based training. Experiments across five benchmarks, multiple model scales, and additional model families show that Hard-Routed MoR-LoRA preserves expert behavior while requiring substantially fewer trainable parameters than soft-routing mixture baselines. Our analysis further shows that normalized soft mixtures often concentrate most routing mass on a single expert, suggesting that hard unit-scale routing provides a simple and efficient abstraction for frozen LoRA expert composition.

Divide-and-Denoise: A Game-Theoretic Method for Fairly Composing Diffusion Models

The abundance of pre-trained diffusion models provides an opportunity for composition. Combining several models, however, runs the risk of one model dominating or models disagreeing with each other. Here, we propose Divide-and-Denoise, a method for coordinating multiple pre-trained diffusion models during sampling. Much like managing a specialized workforce, our method creates a fair but efficient division of labor across models. Central to our method is the notion of an allocation which defines the responsibility of each model to every region of the noisy sample. At every timestep, we then denoise by (i) updating the allocation by solving a fair division game, where we divide the sample into regions that maximize total utility under fairness constraints, and (ii) aligning the models with this allocation, where we guide each model to denoise within its assigned region. This leads to a new composite denoising process that evolves in tandem with a division process. We evaluate Divide-and-Denoise on conditional image generation. Across several quality metrics, including the GenEval benchmark, our method outperforms baselines and resolves common failures including missing objects and mismatched attributes. Experiments show that Divide-and-Denoise utilizes each model's expertise without neglecting any other model.