Parameter-efficient fine-tuning (PEFT) for cross-task generalization consists in pre-training adapters on a multi-task training set before few-shot adaptation to test tasks. Polytropon [Ponti et al., 2023] ($\texttt{Poly}$) jointly learns an inventory of adapters and a *routing* function that selects a (variable-size) subset of adapters for each task during both pre-training and few-shot adaptation. In this paper, we investigate the role that adapter routing plays in its success and design new variants based on our findings.First, we build on the intuition that finer-grained routing provides more expressivity. Hence,we propose $\texttt{MHR}$ (Multi-Head Routing) which combines *subsets* of adapter parameters and outperforms $\texttt{Poly}$ under a comparable parameter budget; by only fine-tuning the routing function and not the adapters ($\texttt{MHR}$-$z$) we achieve competitive performance with extreme parameter efficiency. Second, we find that $\texttt{Poly}$/$\texttt{MHR}$ performance is a result of better multi-task optimization, rather than modular inductive biases that facilitate adapter recombination and local adaptation, as previously hypothesized.

Neural algorithmic reasoning is an emerging area of machine learning that focuses on building neural networks capable of solving complex algorithmic tasks. Recent advancements predominantly follow the standard supervised learning paradigm -- feeding an individual problem instance into the network each time and training it to approximate the execution steps of a classical algorithm. We challenge this mode and propose a novel open-book learning framework. In this framework, whether during training or testing, the network can access and utilize all instances in the training dataset when reasoning for a given instance.Empirical evaluation is conducted on the challenging CLRS Algorithmic Reasoning Benchmark, which consists of 30 diverse algorithmic tasks. Our open-book learning framework exhibits a significant enhancement in neural reasoning capabilities. Further, we notice that there is recent literature suggesting that multi-task training on CLRS can improve the reasoning accuracy of certain tasks, implying intrinsic connections between different algorithmic tasks.

Empirical evaluation is conducted on the challenging CLRS Algorithmic Reasoning Benchmark, which consists of 30 diverse algorithmic tasks.

Low-Rank Adaptation (LoRA) is widely adopted for downstream fine-tuning of foundation models due to its efficiency and zero additional inference cost. Many real-world applications require foundation models to specialize in several specific tasks simultaneously, motivating the need for efficient multi-task downstream adaptation. To address this need, existing studies have primarily explored two directions: Model Merging with LoRA, which shows advantages in training-free scenarios but still lags behind multi-task training in overall performance; and MoE-based LoRA approaches, which improve multi-task learning performance but introduce routers that hinder the mergeability of LoRA parameters and incur considerable inference overhead, thereby limiting real-world deployment practicality. To this end, we propose ThanoRA, a Task Heterogeneity-Aware Multi-Task Low-Rank Adaptation framework that enables effective, efficient and unified multi-task downstream adaptation without introducing additional structure. ThanoRA performs multi-task learning by tailoring subspace allocation at initialization and enforcing diversity preservation throughout training: it allocates varying dimensions to construct task-specific low-rank subspaces driven by inter-task heterogeneity, enabling fine-grained knowledge injection, while diversity-preserving regularization mitigates task interference and subspace collapse, thereby fully exploiting the low-rank capacity. Extensive experiments across multimodal and text-only benchmarks under varying multi-task mixtures demonstrate that ThanoRA consistently outperforms strong baselines, surpassing even separate task-specific fine-tuning, while introducing no additional structures or inference overhead. Our code will be publicly available at: https://github.com/LiangJian24/ThanoRA.

Deep reinforcement learning (RL) is a powerful approach to complex decision making. However, one issue that limits its practical application is its brittleness, sometimes failing to train in the presence of small changes in the environment.

Neural algorithmic reasoning is an emerging area of machine learning that focuses on building neural networks capable of solving complex algorithmic tasks. Recent advancements predominantly follow the standard supervised learning paradigm -- feeding an individual problem instance into the network each time and training it to approximate the execution steps of a classical algorithm. We challenge this mode and propose a novel open-book learning framework. In this framework, whether during training or testing, the network can access and utilize all instances in the training dataset when reasoning for a given instance.Empirical evaluation is conducted on the challenging CLRS Algorithmic Reasoning Benchmark, which consists of 30 diverse algorithmic tasks. Our open-book learning framework exhibits a significant enhancement in neural reasoning capabilities.

Parameter-efficient fine-tuning (PEFT) for cross-task generalization consists in pre-training adapters on a multi-task training set before few-shot adaptation to test tasks. Polytropon [Ponti et al., 2023] ( \texttt{Poly}) jointly learns an inventory of adapters and a *routing* function that selects a (variable-size) subset of adapters for each task during both pre-training and few-shot adaptation. In this paper, we investigate the role that adapter routing plays in its success and design new variants based on our findings.First, we build on the intuition that finer-grained routing provides more expressivity. Hence,we propose \texttt{MHR} (Multi-Head Routing) which combines *subsets* of adapter parameters and outperforms \texttt{Poly} under a comparable parameter budget; by only fine-tuning the routing function and not the adapters ( \texttt{MHR} - z) we achieve competitive performance with extreme parameter efficiency. Second, we find that \texttt{Poly} / \texttt{MHR} performance is a result of better multi-task optimization, rather than modular inductive biases that facilitate adapter recombination and local adaptation, as previously hypothesized.

Neural algorithmic reasoning is an emerging area of machine learning that focuses on building neural networks capable of solving complex algorithmic tasks. Recent advancements predominantly follow the standard supervised learning paradigm -- feeding an individual problem instance into the network each time and training it to approximate the execution steps of a classical algorithm. We challenge this mode and propose a novel open-book learning framework. In this framework, whether during training or testing, the network can access and utilize all instances in the training dataset when reasoning for a given instance. Empirical evaluation is conducted on the challenging CLRS Algorithmic Reasoning Benchmark, which consists of 30 diverse algorithmic tasks. Our open-book learning framework exhibits a significant enhancement in neural reasoning capabilities. Further, we notice that there is recent literature suggesting that multi-task training on CLRS can improve the reasoning accuracy of certain tasks, implying intrinsic connections between different algorithmic tasks. We delve into this direction via the open-book framework. When the network reasons for a specific task, we enable it to aggregate information from training instances of other tasks in an attention-based manner. We show that this open-book attention mechanism offers insights into the inherent relationships among various tasks in the benchmark and provides a robust tool for interpretable multi-task training.