Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks

Fractional-order differentiation has many characteristics different from integer-order differentiation. These characteristics can be applied to the optimization algorithms of artificial neural networks to obtain better results. However, due to insufficient theoretical research, at present, there is no fractional-order matrix differentiation method that is perfectly compatible with automatic differentiation (Autograd) technology. Therefore, we propose a fractional-order matrix differentiation calculation method. This method is introduced by the definition of the integer-order Jacobian matrix. We denote it as fractional-order Jacobian matrix differentiation (${{\bf{J}}^\alpha }$). Through ${{\bf{J}}^\alpha }$, we can carry out the matrix-based fractional-order chain rule. Based on the Linear module and the fractional-order differentiation, we design the fractional-order Autograd technology to enable the use of fractional-order differentiation in hidden layers, thereby enhancing the practicality of fractional-order differentiation in deep learning. In the experiment, according to the PyTorch framework, we design fractional-order Linear (FLinear) and replace nn.Linear in the multilayer perceptron with FLinear. Through the qualitative analysis of the training set and validation set $Loss$, the quantitative analysis of the test set indicators, and the analysis of time consumption and GPU memory usage during model training, we verify the superior performance of ${{\bf{J}}^\alpha }$ and prove that it is an excellent fractional-order gradient descent method in the field of deep learning.

A Multi-Dimensional Constraint Framework for Evaluating and Improving Instruction Following in Large Language Models

Instruction following evaluates large language models (LLMs) on their ability to generate outputs that adhere to user-defined constraints. However, existing benchmarks often rely on templated constraint prompts, which lack the diversity of real-world usage and limit fine-grained performance assessment. To fill this gap, we propose a multi-dimensional constraint framework encompassing three constraint patterns, four constraint categories, and four difficulty levels. Building on this framework, we develop an automated instruction generation pipeline that performs constraint expansion, conflict detection, and instruction rewriting, yielding 1,200 code-verifiable instruction-following test samples. We evaluate 19 LLMs across seven model families and uncover substantial variation in performance across constraint forms. For instance, average performance drops from 77.67% at Level I to 32.96% at Level IV. Furthermore, we demonstrate the utility of our approach by using it to generate data for reinforcement learning, achieving substantial gains in instruction following without degrading general performance. In-depth analysis indicates that these gains stem primarily from modifications in the model's attention modules parameters, which enhance constraint recognition and adherence. Code and data are available in https://github.com/Junjie-Ye/MulDimIF.

Measuring Data Diversity for Instruction Tuning: A Systematic Analysis and A Reliable Metric

Data diversity is crucial for the instruction tuning of large language models. Existing studies have explored various diversity-aware data selection methods to construct high-quality datasets and enhance model performance. However, the fundamental problem of precisely defining and measuring data diversity remains underexplored, limiting clear guidance for data engineering. To address this, we systematically analyze 11 existing diversity measurement methods by evaluating their correlation with model performance through extensive fine-tuning experiments. Our results indicate that a reliable diversity measure should properly account for both inter-sample differences and the information distribution in the sample space. Building on this, we propose NovelSum, a new diversity metric based on sample-level "novelty." Experiments on both simulated and real-world data show that NovelSum accurately captures diversity variations and achieves a 0.97 correlation with instruction-tuned model performance, highlighting its value in guiding data engineering practices. With NovelSum as an optimization objective, we further develop a greedy, diversity-oriented data selection strategy that outperforms existing approaches, validating both the effectiveness and practical significance of our metric.

Predicting Large Language Model Capabilities on Closed-Book QA Tasks Using Only Information Available Prior to Training

The GPT-4 technical report from OpenAI suggests that model performance on specific tasks can be predicted prior to training, though methodologies remain unspecified. This approach is crucial for optimizing resource allocation and ensuring data alignment with target tasks. To achieve this vision, we focus on predicting performance on Closed-book Question Answering (CBQA) tasks, which are closely tied to pre-training data and knowledge retention. We address three major challenges: 1) mastering the entire pre-training process, especially data construction; 2) evaluating a model's knowledge retention; and 3) predicting task-specific knowledge retention using only information available prior to training. To tackle these challenges, we pre-train three large language models (i.e., 1.6B, 7B, and 13B) using 560k dollars and 520k GPU hours. We analyze the pre-training data with knowledge triples and assess knowledge retention using established methods. Additionally, we introduce the SMI metric, an information-theoretic measure that quantifies the relationship between pre-training data, model size, and task-specific knowledge retention. Our experiments reveal a strong linear correlation ($\text{R}^2 > 0.84$) between the SMI metric and the model's accuracy on CBQA tasks across models of varying sizes (i.e., 1.1B, 1.6B, 7B, and 13B). The dataset, model, and code are available at https://github.com/yuhui1038/SMI.

SMART: Advancing Scalable Map Priors for Driving Topology Reasoning

Topology reasoning is crucial for autonomous driving as it enables comprehensive understanding of connectivity and relationships between lanes and traffic elements. While recent approaches have shown success in perceiving driving topology using vehicle-mounted sensors, their scalability is hindered by the reliance on training data captured by consistent sensor configurations. We identify that the key factor in scalable lane perception and topology reasoning is the elimination of this sensor-dependent feature. To address this, we propose SMART, a scalable solution that leverages easily available standard-definition (SD) and satellite maps to learn a map prior model, supervised by large-scale geo-referenced high-definition (HD) maps independent of sensor settings. Attributed to scaled training, SMART alone achieves superior offline lane topology understanding using only SD and satellite inputs. Extensive experiments further demonstrate that SMART can be seamlessly integrated into any online topology reasoning methods, yielding significant improvements of up to 28% on the OpenLane-V2 benchmark.

Agent-R: Training Language Model Agents to Reflect via Iterative Self-Training

Large Language Models (LLMs) agents are increasingly pivotal for addressing complex tasks in interactive environments. Existing work mainly focuses on enhancing performance through behavior cloning from stronger experts, yet such approaches often falter in real-world applications, mainly due to the inability to recover from errors. However, step-level critique data is difficult and expensive to collect. Automating and dynamically constructing self-critique datasets is thus crucial to empowering models with intelligent agent capabilities. In this work, we propose an iterative self-training framework, Agent-R, that enables language Agent to Reflect on the fly. Unlike traditional methods that reward or penalize actions based on correctness, Agent-R leverages MCTS to construct training data that recover correct trajectories from erroneous ones. A key challenge of agent reflection lies in the necessity for timely revision rather than waiting until the end of a rollout. To address this, we introduce a model-guided critique construction mechanism: the actor model identifies the first error step (within its current capability) in a failed trajectory. Starting from it, we splice it with the adjacent correct path, which shares the same parent node in the tree. This strategy enables the model to learn reflection based on its current policy, therefore yielding better learning efficiency. To further explore the scalability of this self-improvement paradigm, we investigate iterative refinement of both error correction capabilities and dataset construction. Our findings demonstrate that Agent-R continuously improves the model's ability to recover from errors and enables timely error correction. Experiments on three interactive environments show that Agent-R effectively equips agents to correct erroneous actions while avoiding loops, achieving superior performance compared to baseline methods (+5.59%).

Joint Antenna Selection and Beamforming Design for Active RIS-aided ISAC Systems

Active reconfigurable intelligent surface (A-RIS) aided integrated sensing and communications (ISAC) system has been considered as a promising paradigm to improve spectrum efficiency. However, massive energy-hungry radio frequency (RF) chains hinder its large-scale deployment. To address this issue, an A-RIS-aided ISAC system with antenna selection (AS) is proposed in this work, where a target is sensed while multiple communication users are served with specifically selected antennas. Specifically, a cuckoo search-based scheme is first utilized to select the antennas associated with high-gain channels. Subsequently, with the properly selected antennas, the weighted sum-rate (WSR) of the system is optimized under the condition of radar probing power level, power budget for the A-RIS and transmitter. To solve the highly non-convex optimization problem, we develop an efficient algorithm based on weighted minimum mean square error (WMMSE) and fractional programming (FP). Simulation results show that the proposed AS scheme and the algorithm are effective, which reduce the number of RF chains without significant performance degradation.

ToolHop: A Query-Driven Benchmark for Evaluating Large Language Models in Multi-Hop Tool Use

Effective evaluation of multi-hop tool use is critical for analyzing the understanding, reasoning, and function-calling capabilities of large language models (LLMs). However, progress has been hindered by a lack of reliable evaluation datasets. To address this, we present ToolHop, a dataset comprising 995 user queries and 3,912 associated tools, specifically designed for rigorous evaluation of multi-hop tool use. ToolHop ensures diverse queries, meaningful interdependencies, locally executable tools, detailed feedback, and verifiable answers through a novel query-driven data construction approach that includes tool creation, document refinement, and code generation. We evaluate 14 LLMs across five model families (i.e., LLaMA3.1, Qwen2.5, Gemini1.5, Claude3.5, and GPT), uncovering significant challenges in handling multi-hop tool-use scenarios. The leading model, GPT-4o, achieves an accuracy of 49.04%, underscoring substantial room for improvement. Further analysis reveals variations in tool-use strategies for various families, offering actionable insights to guide the development of more effective approaches. Code and data can be found in https://huggingface.co/datasets/bytedance-research/ToolHop.

TL-Training: A Task-Feature-Based Framework for Training Large Language Models in Tool Use

Large language models (LLMs) achieve remarkable advancements by leveraging tools to interact with external environments, a critical step toward generalized AI. However, the standard supervised fine-tuning (SFT) approach, which relies on large-scale datasets, often overlooks task-specific characteristics in tool use, leading to performance bottlenecks. To address this issue, we analyze three existing LLMs and uncover key insights: training data can inadvertently impede tool-use behavior, token importance is distributed unevenly, and errors in tool calls fall into a small set of distinct categories. Building on these findings, we propose TL-Training, a task-feature-based framework that mitigates the effects of suboptimal training data, dynamically adjusts token weights to prioritize key tokens during SFT, and incorporates a robust reward mechanism tailored to error categories, optimized through proximal policy optimization. We validate TL-Training by training CodeLLaMA-2-7B and evaluating it on four diverse open-source test sets. Our results demonstrate that the LLM trained by our method matches or surpasses both open- and closed-source LLMs in tool-use performance using only 1,217 training data points. Additionally, our method enhances robustness in noisy environments and improves general task performance, offering a scalable and efficient paradigm for tool-use training in LLMs. The code and data are available at https://github.com/Junjie-Ye/TL-Training.

Learning from Massive Human Videos for Universal Humanoid Pose Control

Scalable learning of humanoid robots is crucial for their deployment in real-world applications. While traditional approaches primarily rely on reinforcement learning or teleoperation to achieve whole-body control, they are often limited by the diversity of simulated environments and the high costs of demonstration collection. In contrast, human videos are ubiquitous and present an untapped source of semantic and motion information that could significantly enhance the generalization capabilities of humanoid robots. This paper introduces Humanoid-X, a large-scale dataset of over 20 million humanoid robot poses with corresponding text-based motion descriptions, designed to leverage this abundant data. Humanoid-X is curated through a comprehensive pipeline: data mining from the Internet, video caption generation, motion retargeting of humans to humanoid robots, and policy learning for real-world deployment. With Humanoid-X, we further train a large humanoid model, UH-1, which takes text instructions as input and outputs corresponding actions to control a humanoid robot. Extensive simulated and real-world experiments validate that our scalable training approach leads to superior generalization in text-based humanoid control, marking a significant step toward adaptable, real-world-ready humanoid robots.