Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to view a Bayesian network (a directed model) as a Markov network (an undirected model), whereas triangulation addresses the opposite direction. We present a categorical framework where these transformations are modelled as functors between a category of Bayesian networks and one of Markov networks. The two kinds of network (the objects of these categories) are themselves represented as functors from a `syntax' domain to a `semantics' codomain. Notably, moralisation and triangulation can be defined inductively on such syntax via functor pre-composition. Moreover, while moralisation is fully syntactic, triangulation relies on semantics. This leads to a discussion of the variable elimination algorithm, reinterpreted here as a functor in its own right, that splits the triangulation procedure in two: one purely syntactic, the other purely semantic. This approach introduces a functorial perspective into the theory of probabilistic graphical models, which highlights the distinctions between syntactic and semantic modifications.

Scaling language models unlocks impressive capabilities, but the accompanying computational and memory demands make both training and deployment expensive. Existing efficiency efforts typically target either parameter sharing or adaptive computation, leaving open the question of how to attain both simultaneously. We introduce Mixture-of-Recursions (MoR), a unified framework that combines the two axes of efficiency inside a single Recursive Transformer. MoR reuses a shared stack of layers across recursion steps to achieve parameter efficiency, while lightweight routers enable adaptive token-level thinking by dynamically assigning different recursion depths to individual tokens. This allows MoR to focus quadratic attention computation only among tokens still active at a given recursion depth, further improving memory access efficiency by selectively caching only their key-value pairs. Beyond these core mechanisms, we also propose a KV sharing variant that reuses KV pairs from the first recursion, specifically designed to further decrease memory footprint. Across model scales ranging from 135M to 1.7B parameters, MoR forms a new Pareto frontier: at equal training FLOPs and smaller model sizes, it significantly lowers validation perplexity and improves few-shot accuracy, while delivering higher throughput compared with vanilla and existing recursive baselines. These gains demonstrate that MoR is an effective path towards large-model quality without incurring large-model cost.

We focus on developing agents for knowledge-intensive tasks, where the agent completes users' information-seeking requests by interacting with specific knowledge bases [

Test-time scaling (TTS) has emerged as a promising, training-free approach for enhancing large language model (LLM) performance. However, the efficacy of existing methods, such as Best-of-N and Self-Consistency, is fundamentally constrained by the dominant single test-time scaling (STTS) paradigm, which relies on a single LLM agent interacting with a single reward model (SA-SR). Inspired by recent work showing that collective methods can surpass the performance ceiling of individual models, we introduce Collective T est-Time Scaling (CTTS). First, we systematically investigate three primary interaction paradigms of existing multiple models: single-agent-multi-reward (SA-MR), multi-agent-single-reward (MA-SR), and multi-agent-multi-reward (MA-MR). Extensive experiments reveal that the MA-MR paradigm is consistently superior. Based on this finding, we further propose CTTS-MM, a novel framework that operationalizes multi-agent and multi-reward collaboration. CTTS-MM integrates two key technical contributions: (1) for agent collaboration, an Agent Collaboration Search (ACS) that identifies the most effective combination of LLMs from a candidate pool; and (2) for reward model collaboration, a Mixture of Reward Models (MoR) strategy that leverages a Prior Reward model Ensemble Selection (PRES) algorithm to select the optimal ensemble. Evaluations across seven mainstream benchmarks demonstrate that CTTS-MM significantly outperforms leading STTS methods (+4.82% over Best-of-N) and surpasses even flagship proprietary LLMs (+7.06% over GPT - 4.1) and open-source LLMs. These results highlight the substantial potential of collective scaling to push the frontier of LLM inference. Recent advancements in large language models (LLMs) OpenAI (2025); Y ang et al. (2024b); Brown et al. (2020); DeepSeek-AI & et al. (2025); Touvron et al. (2023) have marked a significant milestone in natural language understanding and generation. LLMs are typically optimized through training-time scaling, where huge amounts of data and parameters are applied, facing growing limitations due to their resource-intensive nature and the endless hunger for human data. To avoid introducing an extra expensive training process, test-time scaling (TTS) has emerged as an orthogonal direction for fully stimulating the ability of pre-trained LLMs during inference.

Retrieval-augmented Generation (RAG) is powerful, but its effectiveness hinges on which retrievers we use and how. Different retrievers offer distinct, often complementary signals: BM25 captures lexical matches; dense retrievers, semantic similarity. Yet in practice, we typically fix a single retriever based on heuristics, which fails to generalize across diverse information needs. Can we dynamically select and integrate multiple retrievers for each individual query, without the need for manual selection? In our work, we validate this intuition with quantitative analysis and introduce mixture of retrievers: a zero-shot, weighted combination of heterogeneous retrievers. Extensive experiments show that such mixtures are effective and efficient: Despite totaling just 0.8B parameters, this mixture outperforms every individual retriever and even larger 7B models by +10.8% and +3.9% on average, respectively. Further analysis also shows that this mixture framework can help incorporate specialized non-oracle human information sources as retrievers to achieve good collaboration, with a 58.9% relative performance improvement over simulated humans alone.

Supervised fine-tuning (SFT) is a milestone in aligning large language models with human instructions and adapting them to downstream tasks. In particular, Low-Rank Adaptation (LoRA) has gained widespread attention due to its parameter efficiency. However, its impact on improving the performance of large models remains limited. Recent studies suggest that combining LoRA with Mixture-of-Experts (MoE) can significantly enhance fine-tuning performance. MoE adapts to the diversity and complexity of datasets by dynamically selecting the most suitable experts, thereby improving task accuracy and efficiency. Despite impressive results, recent studies reveal issues in the MoE routing mechanism, such as incorrect assignments and imbalanced expert allocation. Inspired by the principles of Redundancy and Fault Tolerance Theory. We innovatively integrate the concept of Mixture of Experts into the routing mechanism and propose an efficient fine-tuning method called Mixture of Routers (MoR). It employs multiple sub-routers for joint selection and uses a learnable main router to determine the weights of the sub-routers. The results show that MoR outperforms baseline models on most tasks, achieving an average performance improvement of 1%. MoR can serve as a plug-and-play, parameter-efficient fine-tuning method suitable for a wide range of applications. Our code is available here: https://anonymous.4open.science/r/MoR-DFC6.

In a clinical trial, the random allocation aims to balance prognostic factors between arms, preventing true confounders. However, residual differences due to chance may introduce near-confounders. Adjusting on prognostic factors is therefore recommended, especially because the related increase of the power. In this paper, we hypothesized that G-computation associated with machine learning could be a suitable method for randomized clinical trials even with small sample sizes. It allows for flexible estimation of the outcome model, even when the covariates' relationships with outcomes are complex. Through simulations, penalized regressions (Lasso, Elasticnet) and algorithm-based methods (neural network, support vector machine, super learner) were compared. Penalized regressions reduced variance but may introduce a slight increase in bias. The associated reductions in sample size ranged from 17\% to 54\%. In contrast, algorithm-based methods, while effective for larger and more complex data structures, underestimated the standard deviation, especially with small sample sizes. In conclusion, G-computation with penalized models, particularly Elasticnet with splines when appropriate, represents a relevant approach for increasing the power of RCTs and accounting for potential near-confounders.

Low-Rank Adaptation (LoRA) drives research to align its performance with full fine-tuning. However, significant challenges remain: (1) Simply increasing the rank size of LoRA does not effectively capture high-rank information, which leads to a performance bottleneck.(2) MoE-style LoRA methods substantially increase parameters and inference latency, contradicting the goals of efficient fine-tuning and ease of application. To address these challenges, we introduce Mixture of Ranks (MoR), which learns rank-specific information for different tasks based on input and efficiently integrates multi-rank information. We firstly propose a new framework that equates the integration of multiple LoRAs to expanding the rank of LoRA. Moreover, we hypothesize that low-rank LoRA already captures sufficient intrinsic information, and MoR can derive high-rank information through mathematical transformations of the low-rank components. Thus, MoR can reduces the learning difficulty of LoRA and enhances its multi-task capabilities. MoR achieves impressive results, with MoR delivering a 1.31\% performance improvement while using only 93.93\% of the parameters compared to baseline methods.

Zero-shot visual question answering (VQA) is a challenging task that requires reasoning across modalities. While some existing methods rely on a single rationale within the Chain of Thoughts (CoT) framework, they may fall short of capturing the complexity of the VQA problem. On the other hand, some other methods that use multiple rationales may still suffer from low diversity, poor modality alignment, and inefficient retrieval and fusion. In response to these challenges, we propose \emph{Mixture of Rationales (MoR)}, a novel multi-modal reasoning method that mixes multiple rationales for VQA. MoR uses a single frozen Vision-and-Language Pre-trained Models (VLPM) model to {dynamically generate, retrieve and fuse multi-modal thoughts}. We evaluate MoR on two challenging VQA datasets, i.e. NLVR2 and OKVQA, with two representative backbones OFA and VL-T5. MoR achieves a 12.43\% accuracy improvement on NLVR2, and a 2.45\% accuracy improvement on OKVQA-S( the science and technology category of OKVQA).