Existing reinforcement learning methods for Chain-of-Thought reasoning suffer from two critical limitations. First, they operate as monolithic black boxes that provide undifferentiated reward signals, obscuring individual step contributions and hindering error diagnosis. Second, sequential decoding has O(n) time complexity. This makes real-time deployment impractical for complex reasoning tasks. We present DeCoRL (Decoupled Reasoning Chains via Coordinated Reinforcement Learning), a novel framework that transforms reasoning from sequential processing into collaborative modular orchestration. DeCoRL trains lightweight specialized models to generate reasoning sub-steps concurrently, eliminating sequential bottlenecks through parallel processing. To enable precise error attribution, the framework designs modular reward functions that score each sub-step independently. Cascaded DRPO optimization then coordinates these rewards while preserving inter-step dependencies. Comprehensive evaluation demonstrates state-of-the-art results across RM-Bench, RMB, and RewardBench, outperforming existing methods including large-scale models. DeCoRL delivers 3.8 times faster inference while maintaining superior solution quality and offers a 22.7% improvement in interpretability through explicit reward attribution. These advancements, combined with a 72.4% reduction in energy consumption and a 68% increase in throughput, make real-time deployment of complex reasoning systems a reality.

Medical image segmentation requires large annotated datasets, creating a significant bottleneck for clinical applications. While few-shot segmentation methods can learn from minimal examples, existing approaches demonstrate suboptimal performance in precise boundary delineation for medical images, particularly when anatomically similar regions appear without sufficient spatial context. We propose AGENet (Adaptive Geodesic Edge-aware Network), a novel framework that incorporates spatial relationships through edge-aware geodesic distance learning. Our key insight is that medical structures follow predictable geometric patterns that can guide prototype extraction even with limited training data. Unlike methods relying on complex architectural components or heavy neural networks, our approach leverages computationally lightweight geometric modeling. The framework combines three main components: (1) An edge-aware geodesic distance learning module that respects anatomical boundaries through iterative Fast Marching refinement, (2) adaptive prototype extraction that captures both global structure and local boundary details via spatially-weighted aggregation, and (3) adaptive parameter learning that automatically adjusts to different organ characteristics. Extensive experiments across diverse medical imaging datasets demonstrate improvements over state-of-the-art methods. Notably, our method reduces boundary errors compared to existing approaches while maintaining computational efficiency, making it highly suitable for clinical applications requiring precise segmentation with limited annotated data.

Medical vision-language segmentation models suffer from catastrophic forgetting when adapting to new anatomical structures, requiring complete retraining that limits their clinical deployment. Although continual learning approaches have been studied for various applications, targeted research on continual learning approaches specifically designed for medical vision-language tasks remains underexplored. We propose MedPEFT-CL, a parameter-efficient continual learning framework that addresses both efficient learning of new tasks and preservation of previous knowledge through a dual-phase architecture based on CLIPSeg. Our dual-phase architecture features an adaptive learning phase that employs semantic similarity-based adapter allocation and parameter-efficient fine-tuning for medical tasks through prompt similarity analysis, and a knowledge consolidation phase employing bi-directional Fisher-memory coordination. This creates a reinforcing cycle: consolidation directs replay priorities while new tasks provide challenging samples that improve retention strategies. Our key contributions are: (1) a semantic-driven adapter allocation mechanism that enables efficient learning of new medical tasks, (2) a bi-modal LoRA adaptation that significantly reduces trainable parameters while maintaining cross-modal learning, and (3) bidirectional Fisher-memory coordination that prevents catastrophic forgetting from previous medical tasks. Extensive experiments across diverse medical datasets demonstrate superior forgetting mitigation and performance retention with minimal parameter overhead, making the framework effective for continual learning in medical vision-language scenarios.

This paper studies the recursion-theoretic aspects of large-scale geometries of infinite strings, a subject initiated by Khoussainov and Takisaka (2017). We investigate several notions of quasi-isometric reductions between recursive infinite strings and prove various results on the equivalence classes of such reductions. The main result is the construction of two infinite recursive strings $α$ and $β$ such that $α$ is strictly quasi-isometrically reducible to $β$, but the reduction cannot be made recursive. This answers an open problem posed by Khoussainov and Takisaka.

This paper introduces and studies a notion of \emph{algorithmic randomness} for subgroups of rationals. Given a randomly generated additive subgroup $(G,+)$ of rationals, two main questions are addressed: first, what are the model-theoretic and recursion-theoretic properties of $(G,+)$; second, what learnability properties can one extract from $G$ and its subclass of finitely generated subgroups? For the first question, it is shown that the theory of $(G,+)$ coincides with that of the additive group of integers and is therefore decidable; furthermore, while the word problem for $G$ with respect to any generating sequence for $G$ is not even semi-decidable, one can build a generating sequence $β$ such that the word problem for $G$ with respect to $β$ is co-recursively enumerable (assuming that the set of generators of $G$ is limit-recursive). In regard to the second question, it is proven that there is a generating sequence $β$ for $G$ such that every non-trivial finitely generated subgroup of $G$ is recursively enumerable and the class of all such subgroups of $G$ is behaviourally correctly learnable, that is, every non-trivial finitely generated subgroup can be semantically identified in the limit (again assuming that the set of generators of $G$ is limit-recursive). On the other hand, the class of non-trivial finitely generated subgroups of $G$ cannot be syntactically identified in the limit with respect to any generating sequence for $G$. The present work thus contributes to a recent line of research studying algorithmically random infinite structures and uncovers an interesting connection between the arithmetical complexity of the set of generators of a randomly generated subgroup of rationals and the learnability of its finitely generated subgroups.

The present paper deals with the inductive inference of recursively enumerable languages from positive data (also called text). It introduces the learning models of \emph{verifiability} and \emph{comparability}. The input to a verifier is an index $e$ and a text of the target language $L$, and the learner has to \emph{verify} whether or not the index $e$ input is correct for the target language $L$. A comparator receives two indices of languages from the target class $\cL$ as input and has to decide in the limit whether or not these indices generate the same language. Furthermore, \emph{standardisability} is studied, where a \emph{standardiser} receives an index $j$ of some target language $L$ from the class $\cL$, and for every $L∈\cL$ there must be an index $e$ such that $e$ generates $L$ and the standardiser has to map every index $j$ for $L$ to $e$. Additionally, the common learning models of \emph{explanatory learning}, \emph{conservative explanatory learning}, and \emph{behaviourally correct learning} are considered. For almost all learning models mentioned above it is also appropriate to consider the number of times a learner changes its mind. In particular, if no mind change occurs then we obtain the \emph{finite} variant of the models considered. Occasionally, also learning with the help of an oracle is taken into consideration. The main goal of this paper is to figure out to what extent verifiability, comparability, and standardisability are helpful for the inductive inference of classes of recursively enumerable languages. Here we also distinguish between \emph{indexed families}, \emph{one-one enumerable classes}, and \emph{recursively enumerable classes}. Our results are manyfold, and an almost complete picture is obtained. In particular, for indexed families and recursively enumerable classes finite comparability, finite standardisability, and finite verifiability always imply finite learnability. If at least one mind change is allowed, then there are differences, i.e., for indexed families, comparability or verifiability imply conservative explanatory learning, but standardisability does not; still explanatory learning can be achieved.

Pattern languages have been an object of study in various subfields of computer science for decades. This paper introduces and studies a decision problem on patterns called the finite distinguishability problem: given a pattern $\pi$, are there finite sets $T^+$ and $T^-$ of strings such that the only pattern language containing all strings in $T^+$ and none of the strings in $T^-$ is the language generated by $\pi$? This problem is related to the complexity of teacher-directed learning, as studied in computational learning theory, as well as to the long-standing open question whether the equivalence of two patterns is decidable. We show that finite distinguishability is decidable if the underlying alphabet is of size other than $2$ or $3$, and provide a number of related results, such as (i) partial solutions for alphabet sizes $2$ and $3$, and (ii) decidability proofs for variants of the problem for special subclasses of patterns, namely, regular, 1-variable, and non-cross patterns. For the same subclasses, we further determine the values of two complexity parameters in teacher-directed learning, namely the teaching dimension and the recursive teaching dimension.

This paper studies exact learning of unions of non-discretized geometric concepts in the model of preference-based teaching. In particular, it focuses on upper and lower bounds of the corresponding sample complexity parameter, the preference-based teaching dimension (PBTD), when learning disjoint unions of a bounded number of geometric concepts of various types -- for instance balls, axis-aligned cubes, or axis-aligned boxes -- in arbitrary dimensions. It is shown that the PBTD of disjoint unions of some such types of concepts grows linearly with the number of concepts in the union, independent of the dimensionality. Teaching the union of potentially overlapping objects turns out to be more involved and is hence considered here only for unions of up to two objects.

We introduce a new model of teaching named preference-based teaching and a corresponding complexity parameter---the preference-based teaching dimension (PBTD)---representing the worst-case number of examples needed to teach any concept in a given concept class. Although the PBTD coincides with the well- known recursive teaching dimension (RTD) on finite classes, it is radically different on infinite ones: the RTD becomes infinite already for trivial infinite classes (such as half- intervals) whereas the PBTD evaluates to reasonably small values for a wide collection of infinite classes including classes consisting of so-called closed sets w.r.t. a given closure operator, including various classes related to linear sets over $\mathbb{N}_0$ (whose RTD had been studied quite recently) and including the class of Euclidean half-spaces. On top of presenting these concrete results, we provide the reader with a theoretical framework (of a combinatorial flavor) which helps to derive bounds on the PBTD.

We introduce a new model of teaching named “preference-based teaching” and a corresponding complexity parameter—the preference-based teaching dimension (PBTD)—representing the worst-case number of examples needed to teach any concept in a given concept class. Although the PBTD coincides with the well-known recursive teaching dimension (RTD) on finite classes, it is radically different on infinite ones: the RTD becomes infinite already for trivial infinite classes (such as half-intervals) whereas the PBTD evaluates to reasonably small values for a wide collection of infinite classes including classes consisting of so-called closed sets w.r.t. a given closure operator, including various classes related to linear sets over \mathbbN_0 (whose RTD had been studied quite recently) and including the class of Euclidean half-spaces (and some other geometric classes). On top of presenting these concrete results, we provide the reader with a theoretical framework (of a combinatorial flavor) which helps to derive bounds on the PBTD.