# LoRA

Model merging usually trains every expert at the same LoRA rank, yet each domain has its own best rank. Across 36 experts on mathematics, instruction following and multilingual data at four ranks and three model scales, six merge methods were compared at uniform ranks and at each domain's own best rank: simple averaging and loss-utility component selection are unaffected and gain up to 1.8 pp of multi-domain accuracy, while magnitude-based conflict-resolution methods such as TIES and KnOTS are inconsistent and can lose up to 4 pp. The cause is that selecting components by size discards the instruction adapter, whose singular values are smallest, almost entirely, and IFEval falls by 16 to 25 pp.

Model merging usually trains every expert at the same LoRA rank, yet each domain has its own best rank. Across 36 experts on mathematics, instruction following and multilingual data at four ranks and three model scales, six merge methods were compared at uniform ranks and at each domain's own best rank: simple averaging and loss-utility component selection are unaffected and gain up to 1.8 pp of multi-domain accuracy, while magnitude-based conflict-resolution methods such as TIES and KnOTS are inconsistent and can lose up to 4 pp. The cause is that selecting components by size discards the instruction adapter, whose singular values are smallest, almost entirely, and IFEval falls by 16 to 25 pp.

Planning and control of differentially flat systems rests on a flat output, yet no general procedure writes one down for arbitrary nonlinear dynamics. FlatSeek reverses the reconstruction relation in the definition of flatness: fix an output and its reconstruction maps, close the dynamics differentially, and obtain system–output pairs with known certificates at scale. A Qwen3.5-2B model fine-tuned with LoRA proposes candidates that a symbolic verifier accepts or rejects. FlatSeek solves 74 literature and 171 synthetic systems, against 58 and 127 for the strongest traditional symbolic method.

Planning and control of differentially flat systems rests on a flat output, yet no general procedure writes one down for arbitrary nonlinear dynamics. FlatSeek reverses the reconstruction relation in the definition of flatness: fix an output and its reconstruction maps, close the dynamics differentially, and obtain system–output pairs with known certificates at scale. A Qwen3.5-2B model fine-tuned with LoRA proposes candidates that a symbolic verifier accepts or rejects. FlatSeek solves 74 literature and 171 synthetic systems, against 58 and 127 for the strongest traditional symbolic method.

Majority-vote test-time reinforcement learning makes each question lock onto one answer during training, often a wrong one on hard questions, and until now which answer that is became known only after training. The work treats this as a short race driven by sampling noise between the answers that are close at the start, and gives a closed-form probability for how the network kernel shifts the gap of the two leaders through updates of the trailing answers. In LoRA training on MMLU-Pro multiple-choice questions with three models from two families, predictions from a frozen-kernel chain computed before training forecast which answer each question locks into better than a logistic model refitted on the outcomes, using no fitted constants.

Majority-vote test-time reinforcement learning makes each question lock onto one answer during training, often a wrong one on hard questions, and until now which answer that is became known only after training. The work treats this as a short race driven by sampling noise between the answers that are close at the start, and gives a closed-form probability for how the network kernel shifts the gap of the two leaders through updates of the trailing answers. In LoRA training on MMLU-Pro multiple-choice questions with three models from two families, predictions from a frozen-kernel chain computed before training forecast which answer each question locks into better than a logistic model refitted on the outcomes, using no fitted constants.

In aerial drone imagery, a referred target often covers only tens of pixels and sits among visually similar vehicles or people, so a generative editor can draw a plausible mask around the wrong instance. DroneSegEdit freezes the open-weight LongCat-Image-Edit, trains only a lightweight LoRA to render candidate regions, then uses a language-grounded spatial verifier to strip foreground inside that candidate that the referring expression does not support. On the complete official RIS-LAD test set it reaches 52.78 mIoU, 7.16 points above the previous best ReSaP-8B, and stays competitive overall on UAVid-RIS and VDD-RIS, with the clearest gains on compact vehicles and humans.

In aerial drone imagery, a referred target often covers only tens of pixels and sits among visually similar vehicles or people, so a generative editor can draw a plausible mask around the wrong instance. DroneSegEdit freezes the open-weight LongCat-Image-Edit, trains only a lightweight LoRA to render candidate regions, then uses a language-grounded spatial verifier to strip foreground inside that candidate that the referring expression does not support. On the complete official RIS-LAD test set it reaches 52.78 mIoU, 7.16 points above the previous best ReSaP-8B, and stays competitive overall on UAVid-RIS and VDD-RIS, with the clearest gains on compact vehicles and humans.

The information a fine-tune writes into its adapter is now measured not by parameter count or weight reconstruction error but as the smallest serialized size of a compressed adapter that, reloaded into the frozen model, keeps 90% of the held-out fine-tuning gain. The same dataset demands very different rates across frozen models: keeping 90% of the math gain takes 1.03 bits per value on Qwen2.5-Math-7B but 0.41 on Qwen2.5-7B, and on an adapter trained with deliberately mismatched reasoning supervision, compression lifts GSM8K accuracy from 23.7% to 82.9%, above the frozen Qwen2.5-7B's 77.6%.

The information a fine-tune writes into its adapter is now measured not by parameter count or weight reconstruction error but as the smallest serialized size of a compressed adapter that, reloaded into the frozen model, keeps 90% of the held-out fine-tuning gain. The same dataset demands very different rates across frozen models: keeping 90% of the math gain takes 1.03 bits per value on Qwen2.5-Math-7B but 0.41 on Qwen2.5-7B, and on an adapter trained with deliberately mismatched reasoning supervision, compression lifts GSM8K accuracy from 23.7% to 82.9%, above the frozen Qwen2.5-7B's 77.6%.

Forgetting in continual learning is usually fought with replay, regularization or architectural changes; STABLE instead works inside the optimizer, treating the distance from the previous task's solution as a budget that tightens the pullback when exceeded and relaxes it once drift returns inside. On the 100-task ImageNet-R stream the same LoRA goes from 0.66% average accuracy with Adam to 73.12%, with average forgetting falling from 60.22% to 10.17%, and CLIP zero-shot transfer stays near its pre-trained level.

Forgetting in continual learning is usually fought with replay, regularization or architectural changes; STABLE instead works inside the optimizer, treating the distance from the previous task's solution as a budget that tightens the pullback when exceeded and relaxes it once drift returns inside. On the 100-task ImageNet-R stream the same LoRA goes from 0.66% average accuracy with Adam to 73.12%, with average forgetting falling from 60.22% to 10.17%, and CLIP zero-shot transfer stays near its pre-trained level.

Biomedical ontologies need new textual definitions continuously, and a large language model can write definitions that read fluently and resemble curated text while still naming entities absent from the ontology or violating its logical constraints. A quality-control agentic workflow turns definition generation into an iterative process: draft a definition, extract predicate-object axioms, check whether entities resolve in the target ontology, and test logical consistency with a reasoner, then rewrite using the diagnostics. On Disease Ontology DO 2024, the Qwen2.5-14B base model's entity error rate fell from 67.0% to 37.8% after the existence-repair loop, while text-similarity scores stayed roughly level.

Biomedical ontologies need new textual definitions continuously, and a large language model can write definitions that read fluently and resemble curated text while still naming entities absent from the ontology or violating its logical constraints. A quality-control agentic workflow turns definition generation into an iterative process: draft a definition, extract predicate-object axioms, check whether entities resolve in the target ontology, and test logical consistency with a reasoner, then rewrite using the diagnostics. On Disease Ontology DO 2024, the Qwen2.5-14B base model's entity error rate fell from 67.0% to 37.8% after the existence-repair loop, while text-similarity scores stayed roughly level.

Reinforcement learning with verifiable rewards (RLVR) trains a language model on problems that may themselves be confidential, and the released weights can reveal which problems it saw. DP-GRPO aggregates all responses to one prompt into a single gradient, clips it once and adds Gaussian noise, so the privacy budget depends on neither the number of responses per prompt nor the clipping norm; the authors describe it as the first differential privacy guarantee for RLVR training. Training Qwen2.5-1.5B-Instruct with LoRA at a per-run budget of 8, the reward signal beats a control that removes only the reward by 2.65 points on MATH and 3.24 on GSM8K, positive in every seed.

Reinforcement learning with verifiable rewards (RLVR) trains a language model on problems that may themselves be confidential, and the released weights can reveal which problems it saw. DP-GRPO aggregates all responses to one prompt into a single gradient, clips it once and adds Gaussian noise, so the privacy budget depends on neither the number of responses per prompt nor the clipping norm; the authors describe it as the first differential privacy guarantee for RLVR training. Training Qwen2.5-1.5B-Instruct with LoRA at a per-run budget of 8, the reward signal beats a control that removes only the reward by 2.65 points on MATH and 3.24 on GSM8K, positive in every seed.