Plan and Budget: Effective and Efficient Test-Time Scaling on Large Language Model Reasoning

Large Language Models (LLMs) have achieved remarkable success in complex reasoning tasks, but their inference remains computationally inefficient. We observe a common failure mode in many prevalent LLMs, overthinking, where models generate verbose and tangential reasoning traces even for simple queries. Recent works have tried to mitigate this by enforcing fixed token budgets, however, this can lead to underthinking, especially on harder problems. Through empirical analysis, we identify that this inefficiency often stems from unclear problem-solving strategies. To formalize this, we develop a theoretical model, BBAM (Bayesian Budget Allocation Model), which models reasoning as a sequence of sub-questions with varying uncertainty, and introduce the $E^3$ metric to capture the trade-off between correctness and computation efficiency. Building on theoretical results from BBAM, we propose Plan-and-Budget, a model-agnostic, test-time framework that decomposes complex queries into sub-questions and allocates token budgets based on estimated complexity using adaptive scheduling. Plan-and-Budget improves reasoning efficiency across a range of tasks and models, achieving up to +70% accuracy gains, -39% token reduction, and +187.5% improvement in $E^3$. Notably, it elevates a smaller model (DS-Qwen-32B) to match the efficiency of a larger model (DS-LLaMA-70B)-demonstrating Plan-and-Budget's ability to close performance gaps without retraining. Our code is available at anonymous.4open.science/r/P-and-B-6513/.

LENSLLM: Unveiling Fine-Tuning Dynamics for LLM Selection

The proliferation of open-sourced Large Language Models (LLMs) and diverse downstream tasks necessitates efficient model selection, given the impracticality of fine-tuning all candidates due to computational constraints. Despite the recent advances in LLM selection, a fundamental research question largely remains nascent: how can we model the dynamic behaviors of LLMs during fine-tuning, thereby enhancing our understanding of their generalization performance across diverse downstream tasks? In this work, we propose a novel theoretical framework that provides a proper lens to assess the generalization capabilities of LLMs, thereby enabling accurate and efficient LLM selection for downstream applications. In particular, we first derive a Hessian-based PAC-Bayes generalization bound that unveils fine-tuning dynamics of LLMs and then introduce LENSLLM, a Neural Tangent Kernel(NTK)-based Rectified Scaling Model that enables accurate performance predictions across diverse tasks while maintaining computational efficiency. Extensive empirical results on 3 large-scale benchmarks demonstrate that our model achieves up to 91.1% accuracy and reduces up to 88.5% computational cost in LLM selection, outperforming 5 state-of-the-art methods. We open-source our proposed LENSLLM model and corresponding results at the Github link: https://github.com/Susan571/LENSLLM.git.

Reasoning of Large Language Models over Knowledge Graphs with Super-Relations

While large language models (LLMs) have made significant progress in processing and reasoning over knowledge graphs, current methods suffer from a high non-retrieval rate. This limitation reduces the accuracy of answering questions based on these graphs. Our analysis reveals that the combination of greedy search and forward reasoning is a major contributor to this issue. To overcome these challenges, we introduce the concept of super-relations, which enables both forward and backward reasoning by summarizing and connecting various relational paths within the graph. This holistic approach not only expands the search space, but also significantly improves retrieval efficiency. In this paper, we propose the ReKnoS framework, which aims to Reason over Knowledge Graphs with Super-Relations. Our framework's key advantages include the inclusion of multiple relation paths through super-relations, enhanced forward and backward reasoning capabilities, and increased efficiency in querying LLMs. These enhancements collectively lead to a substantial improvement in the successful retrieval rate and overall reasoning performance. We conduct extensive experiments on nine real-world datasets to evaluate ReKnoS, and the results demonstrate the superior performance of ReKnoS over existing state-of-the-art baselines, with an average accuracy gain of 2.92%.

Robust Domain Generalization for Multi-modal Object Recognition

In multi-label classification, machine learning encounters the challenge of domain generalization when handling tasks with distributions differing from the training data. Existing approaches primarily focus on vision object recognition and neglect the integration of natural language. Recent advancements in vision-language pre-training leverage supervision from extensive visual-language pairs, enabling learning across diverse domains and enhancing recognition in multi-modal scenarios. However, these approaches face limitations in loss function utilization, generality across backbones, and class-aware visual fusion. This paper proposes solutions to these limitations by inferring the actual loss, broadening evaluations to larger vision-language backbones, and introducing Mixup-CLIPood, which incorporates a novel mix-up loss for enhanced class-aware visual fusion. Our method demonstrates superior performance in domain generalization across multiple datasets.

When Heterophily Meets Heterogeneity: New Graph Benchmarks and Effective Methods

Many real-world graphs frequently present challenges for graph learning due to the presence of both heterophily and heterogeneity. However, existing benchmarks for graph learning often focus on heterogeneous graphs with homophily or homogeneous graphs with heterophily, leaving a gap in understanding how methods perform on graphs that are both heterogeneous and heterophilic. To bridge this gap, we introduce H2GB, a novel graph benchmark that brings together the complexities of both the heterophily and heterogeneity properties of graphs. Our benchmark encompasses 9 diverse real-world datasets across 5 domains, 28 baseline model implementations, and 26 benchmark results. In addition, we present a modular graph transformer framework UnifiedGT and a new model variant, H2G-former, that excels at this challenging benchmark. By integrating masked label embeddings, cross-type heterogeneous attention, and type-specific FFNs, H2G-former effectively tackles graph heterophily and heterogeneity. Extensive experiments across 26 baselines on H2GB reveal inadequacies of current models on heterogeneous heterophilic graph learning, and demonstrate the superiority of our H2G-former over existing solutions. Both the benchmark and the framework are available on GitHub (https://github.com/junhongmit/H2GB) and PyPI (https://pypi.org/project/H2GB), and documentation can be found at https://junhongmit.github.io/H2GB/.

Beyond Night Visibility: Adaptive Multi-Scale Fusion of Infrared and Visible Images

In addition to low light, night images suffer degradation from light effects (e.g., glare, floodlight, etc). However, existing nighttime visibility enhancement methods generally focus on low-light regions, which neglects, or even amplifies the light effects. To address this issue, we propose an Adaptive Multi-scale Fusion network (AMFusion) with infrared and visible images, which designs fusion rules according to different illumination regions. First, we separately fuse spatial and semantic features from infrared and visible images, where the former are used for the adjustment of light distribution and the latter are used for the improvement of detection accuracy. Thereby, we obtain an image free of low light and light effects, which improves the performance of nighttime object detection. Second, we utilize detection features extracted by a pre-trained backbone that guide the fusion of semantic features. Hereby, we design a Detection-guided Semantic Fusion Module (DSFM) to bridge the domain gap between detection and semantic features. Third, we propose a new illumination loss to constrain fusion image with normal light intensity. Experimental results demonstrate the superiority of AMFusion with better visual quality and detection accuracy. The source code will be released after the peer review process.

Revisiting Convergence of AdaGrad with Relaxed Assumptions

In this study, we revisit the convergence of AdaGrad with momentum (covering AdaGrad as a special case) on non-convex smooth optimization problems. We consider a general noise model where the noise magnitude is controlled by the function value gap together with the gradient magnitude. This model encompasses a broad range of noises including bounded noise, sub-Gaussian noise, affine variance noise and the expected smoothness, and it has been shown to be more realistic in many practical applications. Our analysis yields a probabilistic convergence rate which, under the general noise, could reach at (\tilde{\mathcal{O}}(1/\sqrt{T})). This rate does not rely on prior knowledge of problem-parameters and could accelerate to (\tilde{\mathcal{O}}(1/T)) where (T) denotes the total number iterations, when the noise parameters related to the function value gap and noise level are sufficiently small. The convergence rate thus matches the lower rate for stochastic first-order methods over non-convex smooth landscape up to logarithm terms [Arjevani et al., 2023]. We further derive a convergence bound for AdaGrad with mometum, considering the generalized smoothness where the local smoothness is controlled by a first-order function of the gradient norm.

Large Language Models for Forecasting and Anomaly Detection: A Systematic Literature Review

This systematic literature review comprehensively examines the application of Large Language Models (LLMs) in forecasting and anomaly detection, highlighting the current state of research, inherent challenges, and prospective future directions. LLMs have demonstrated significant potential in parsing and analyzing extensive datasets to identify patterns, predict future events, and detect anomalous behavior across various domains. However, this review identifies several critical challenges that impede their broader adoption and effectiveness, including the reliance on vast historical datasets, issues with generalizability across different contexts, the phenomenon of model hallucinations, limitations within the models' knowledge boundaries, and the substantial computational resources required. Through detailed analysis, this review discusses potential solutions and strategies to overcome these obstacles, such as integrating multimodal data, advancements in learning methodologies, and emphasizing model explainability and computational efficiency. Moreover, this review outlines critical trends that are likely to shape the evolution of LLMs in these fields, including the push toward real-time processing, the importance of sustainable modeling practices, and the value of interdisciplinary collaboration. Conclusively, this review underscores the transformative impact LLMs could have on forecasting and anomaly detection while emphasizing the need for continuous innovation, ethical considerations, and practical solutions to realize their full potential.

On Convergence of Adam for Stochastic Optimization under Relaxed Assumptions

The Adaptive Momentum Estimation (Adam) algorithm is highly effective in training various deep learning tasks. Despite this, there's limited theoretical understanding for Adam, especially when focusing on its vanilla form in non-convex smooth scenarios with potential unbounded gradients and affine variance noise. In this paper, we study vanilla Adam under these challenging conditions. We introduce a comprehensive noise model which governs affine variance noise, bounded noise and sub-Gaussian noise. We show that Adam can find a stationary point with a $\mathcal{O}(\text{poly}(\log T)/\sqrt{T})$ rate in high probability under this general noise model where $T$ denotes total number iterations, matching the lower rate of stochastic first-order algorithms up to logarithm factors. More importantly, we reveal that Adam is free of tuning step-sizes with any problem-parameters, yielding a better adaptation property than the Stochastic Gradient Descent under the same conditions. We also provide a probabilistic convergence result for Adam under a generalized smooth condition which allows unbounded smoothness parameters and has been illustrated empirically to more accurately capture the smooth property of many practical objective functions.

PAC-Bayesian Adversarially Robust Generalization Bounds for Graph Neural Network

Graph neural networks (GNNs) have gained popularity for various graph-related tasks. However, similar to deep neural networks, GNNs are also vulnerable to adversarial attacks. Empirical studies have shown that adversarially robust generalization has a pivotal role in establishing effective defense algorithms against adversarial attacks. In this paper, we contribute by providing adversarially robust generalization bounds for two kinds of popular GNNs, graph convolutional network (GCN) and message passing graph neural network, using the PAC-Bayesian framework. Our result reveals that spectral norm of the diffusion matrix on the graph and spectral norm of the weights as well as the perturbation factor govern the robust generalization bounds of both models. Our bounds are nontrivial generalizations of the results developed in (Liao et al., 2020) from the standard setting to adversarial setting while avoiding exponential dependence of the maximum node degree. As corollaries, we derive better PAC-Bayesian robust generalization bounds for GCN in the standard setting, which improve the bounds in (Liao et al., 2020) by avoiding exponential dependence on the maximum node degree.