Reservoir computing is a powerful framework for real-time information processing, characterized by its high computational ability and quick learning, with applications ranging from machine learning to biological systems. In this paper, we investigate how the computational ability of reservoir recurrent neural networks (RNNs) scales with an increasing number of readout neurons. First, we demonstrate that the memory capacity of a reservoir RNN scales sublinearly with the number of readout neurons. To elucidate this observation, we develop a theoretical framework for analytically deriving memory capacity that incorporates the effect of neuronal correlations, which have been ignored in prior theoretical work for analytical simplicity. Our theory successfully relates the sublinear scaling of memory capacity to the strength of neuronal correlations. Furthermore, we show this principle holds across diverse types of RNNs, even those beyond the direct applicability of our theory. Next, we numerically investigate the scaling behavior of nonlinear computational ability, which, alongside memory capacity, is crucial for overall computational performance. Our numerical simulations reveal that as memory capacity growth becomes sublinear, increasing the number of readout neurons successively enables nonlinear processing at progressively higher polynomial orders. Our theoretical framework suggests that neuronal correlations govern not only memory capacity but also the sequential growth of nonlinear computational capabilities. Our findings establish a foundation for designing scalable and cost-effective reservoir computing, providing novel insights into the interplay among neuronal correlations, linear memory, and nonlinear processing.

The evolution of cooperation has been extensively studied using abstract mathematical models and simulations. Recent advances in Large Language Models (LLMs) and the rise of LLM agents have demonstrated their ability to perform social reasoning, thus providing an opportunity to test the emergence of norms in more realistic agent-based simulations with human-like reasoning using natural language. In this research, we investigate whether the cooperation dynamics presented in Boyd and Richerson's model persist in a more realistic simulation of the Diner's Dilemma using LLM agents compared to the abstract mathematical nature in the work of Boyd and Richerson. Our findings indicate that agents follow the strategies defined in the Boyd and Richerson model, and explicit punishment mechanisms drive norm emergence, reinforcing cooperative behaviour even when the agent strategy configuration varies. Our results suggest that LLM-based Multi-Agent System simulations, in fact, can replicate the evolution of cooperation predicted by the traditional mathematical models. Moreover, our simulations extend beyond the mathematical models by integrating natural language-driven reasoning and a pairwise imitation method for strategy adoption, making them a more realistic testbed for cooperative behaviour in MASs.

When applying reinforcement learning--typically through GRPO--to large vision-language model reasoning struggles to effectively scale reasoning length or generates verbose outputs across all tasks with only marginal gains in accuracy. To address this issue, we present FAST-GRPO, a variant of GRPO that dynamically adapts reasoning depth based on question characteristics. Through empirical analysis, we establish the feasibility of fast-slow thinking in LVLMs by investigating how response length and data distribution affect performance. Inspired by these observations, we introduce two complementary metrics to estimate the difficulty of the questions, guiding the model to determine when fast or slow thinking is more appropriate. Next, we incorporate adaptive length-based rewards and difficulty-aware KL divergence into the GRPO algorithm. Experiments across seven reasoning benchmarks demonstrate that FAST achieves state-of-the-art accuracy with over 10\% relative improvement compared to the base model, while reducing token usage by 32.7-67.3\% compared to previous slow-thinking approaches, effectively balancing reasoning length and accuracy.

Process reward models (PRMs) have proven effective for test-time scaling of Large Language Models (LLMs) on challenging reasoning tasks. However, reward hacking issues with PRMs limit their successful application in reinforcement fine-tuning. In this paper, we identify the main cause of PRM-induced reward hacking: the canonical summation-form credit assignment in reinforcement learning (RL), which defines the value as cumulative gamma-decayed future rewards, easily induces LLMs to hack steps with high rewards. To address this, we propose PURE: Process sUpervised Reinforcement lEarning. The key innovation of PURE is a min-form credit assignment that formulates the value function as the minimum of future rewards. This method significantly alleviates reward hacking by limiting the value function range and distributing advantages more reasonably. Through extensive experiments on 3 base models, we show that PRM-based approaches enabling min-form credit assignment achieve comparable reasoning performance to verifiable reward-based methods within only 30% steps. In contrast, the canonical sum-form credit assignment collapses training even at the beginning! Additionally, when we supplement PRM-based fine-tuning with just 10% verifiable rewards, we further alleviate reward hacking and produce the best fine-tuned model based on Qwen2.5-Math-7B in our experiments, achieving 82.5% accuracy on AMC23 and 53.3% average accuracy across 5 benchmarks. Moreover, we summarize the observed reward hacking cases and analyze the causes of training collapse. We release our code and model weights at https://github.com/CJReinforce/PURE.

The performance gap between training sparse neural networks from scratch (PaI) and dense-to-sparse training presents a major roadblock for efficient deep learning. According to the Lottery Ticket Hypothesis, PaI hinges on finding a problem specific parameter initialization. As we show, to this end, determining correct parameter signs is sufficient. Yet, they remain elusive to PaI. To address this issue, we propose Sign-In, which employs a dynamic reparameterization that provably induces sign flips. Such sign flips are complementary to the ones that dense-to-sparse training can accomplish, rendering Sign-In as an orthogonal method. While our experiments and theory suggest performance improvements of PaI, they also carve out the main open challenge to close the gap between PaI and dense-to-sparse training.

Text-attributed graphs (TAGs) present unique challenges in representation learning by requiring models to capture both the semantic richness of node-associated texts and the structural dependencies of the graph. While graph neural networks (GNNs) excel at modeling topological information, they lack the capacity to process unstructured text. Conversely, large language models (LLMs) are proficient in text understanding but are typically unaware of graph structure. In this work, we propose BiGTex (Bidirectional Graph Text), a novel architecture that tightly integrates GNNs and LLMs through stacked Graph-Text Fusion Units. Each unit allows for mutual attention between textual and structural representations, enabling information to flow in both directions, text influencing structure and structure guiding textual interpretation. The proposed architecture is trained using parameter-efficient fine-tuning (LoRA), keeping the LLM frozen while adapting to task-specific signals. Extensive experiments on five benchmark datasets demonstrate that BiGTex achieves state-of-the-art performance in node classification and generalizes effectively to link prediction. An ablation study further highlights the importance of soft prompting and bi-directional attention in the model's success.

It is commonly believed that optimizing the reverse KL divergence results in "mode seeking", while optimizing forward KL results in "mass covering", with the latter being preferred if the goal is to sample from multiple diverse modes. We show -- mathematically and empirically -- that this intuition does not necessarily transfer well to doing reinforcement learning with reverse/forward KL regularization (e.g. as commonly used with language models). Instead, the choice of reverse/forward KL determines the family of optimal target distributions, parameterized by the regularization coefficient. Mode coverage depends primarily on other factors, such as regularization strength, and relative scales between rewards and reference probabilities. Further, we show commonly used settings such as low regularization strength and equal verifiable rewards tend to specify unimodal target distributions, meaning the optimization objective is, by construction, non-diverse. We leverage these insights to construct a simple, scalable, and theoretically justified algorithm. It makes minimal changes to reward magnitudes, yet optimizes for a target distribution which puts high probability over all high-quality sampling modes. In experiments, this simple modification works to post-train both Large Language Models and Chemical Language Models to have higher solution quality and diversity, without any external signals of diversity, and works with both forward and reverse KL when using either naively fails.

With the widespread use of large language models (LLMs), many researchers have turned their attention to detecting text generated by them. However, there is no consistent or precise definition of their target, namely "LLM-generated text". Differences in usage scenarios and the diversity of LLMs further increase the difficulty of detection. What is commonly regarded as the detecting target usually represents only a subset of the text that LLMs can potentially produce. Human edits to LLM outputs, together with the subtle influences that LLMs exert on their users, are blurring the line between LLM-generated and human-written text. Existing benchmarks and evaluation approaches do not adequately address the various conditions in real-world detector applications. Hence, the numerical results of detectors are often misunderstood, and their significance is diminishing. Therefore, detectors remain useful under specific conditions, but their results should be interpreted only as references rather than decisive indicators.

Personal use of this material is permitted. Abstract--Inspired by the performance and scalability of autoregressive large language models, transformer-based models have seen recent success in the visual domain. This study investigates a transformer adaptation for video prediction with a simple end-to-end approach, comparing various spatiotemporal self-attention layouts. Focusing on causal modelling of physical simulations over time; a common shortcoming of existing video-generative approaches, we attempt to isolate spatiotemporal reasoning via physical object tracking metrics and unsupervised training on physical simulation datasets. We introduce a simple yet effective pure transformer model for autoregressive video prediction, utilising continuous pixel-space representations for video prediction. Without the need for complex training strategies or latent feature-learning components, our approach significantly extends the time horizon for physically accurate predictions by up to 50% when compared with existing latent-space approaches, while maintaining comparable performance on common video quality metrics. Additionally, we conduct interpretability experiments to identify network regions that encode information useful to perform accurate estimations of PDE simulation parameters via probing models, and find this generalises to the estimation of out-of-distribution simulation parameters. This work serves as a platform for further attention-based spatiotemporal modelling of videos via a simple, parameter-efficient, and interpretable approach. ECENT progress in the development of transformer [1] based generative models, particularly text-generative models in Natural Language Processing (NLP), have led to increased efforts to extend their application beyond the linguistic domain [2, 3, 4]. Building on the success of generative modelling in the image domain, such as V ariational Autoencoders (V AEs) [5] and Diffusion models [6], recent advances have extended to generative modelling of videos. This is becoming an area of increasing research, focusing on the development of novel architectures and techniques for model interpretability [7, 4, 8].

Recently, Sharma et al. suggested a method called Layer-SElective-Rank reduction (LASER) which demonstrated that pruning high-order components of carefully chosen LLM's weight matrices can boost downstream accuracy -- without any gradient-based fine-tuning. Yet LASER's exhaustive, per-matrix search (each requiring full-dataset forward passes) makes it impractical for rapid deployment. We demonstrate that this overhead can be removed and find that: (i) Only a small, carefully chosen subset of matrices needs to be inspected -- eliminating the layer-by-layer sweep, (ii) The gradient of each matrix's singular values pinpoints which matrices merit reduction, (iii) Increasing the factorization search space by allowing matrices rows to cluster around multiple subspaces and then decomposing each cluster separately further reduces overfitting on the original training data and further lifts accuracy by up to 24.6 percentage points, and finally, (iv) we discover that evaluating on just 100 samples rather than the full training data -- both for computing the indicative gradients and for measuring the final accuracy -- suffices to further reduce the search time; we explain that as adaptation to downstream tasks is dominated by prompting style, not dataset size. As a result, we show that combining these findings yields a fast and robust adaptation algorithm for downstream tasks. Overall, with a single gradient step on 100 examples and a quick scan of the top candidate layers and factorization techniques, we can adapt LLMs to new datasets -- entirely without fine-tuning.