HybridProver: Augmenting Theorem Proving with LLM-Driven Proof Synthesis and Refinement

Formal methods is pivotal for verifying the reliability of critical systems through rigorous mathematical proofs. However, its adoption is hindered by labor-intensive manual proofs and the expertise required to use theorem provers. Recent advancements in large language models (LLMs) offer new opportunities for automated theorem proving. Two promising approaches are generating tactics step by step and generating a whole proof directly with an LLM. However, existing work makes no attempt to combine the two approaches. In this work, we introduce HybridProver, a dual-model proof synthesis framework that combines tactic-based generation and whole-proof synthesis to harness the benefits of both approaches. HybridProver generates whole proof candidates for evaluation directly, then extracts proof sketches from those candidates. It then uses a tactic-based generation model that integrates automated tools to complete the sketches via stepwise refinement. We implement HybridProver for the Isabelle theorem prover and fine-tune LLMs on our optimized Isabelle datasets. Evaluation on the miniF2F dataset illustrates HybridProver's effectiveness. We achieve a 59.4% success rate on miniF2F, where the previous SOTA is 56.1%. Our ablation studies show that this SOTA result is attributable to combining whole-proof and tactic-based generation. Additionally, we show how the dataset quality, training parameters, and sampling diversity affect the final result during automated theorem proving with LLMs. All of our code, datasets, and LLMs are open source.

TransferTraj: A Vehicle Trajectory Learning Model for Region and Task Transferability

Vehicle GPS trajectories provide valuable movement information that supports various downstream tasks and applications. A desirable trajectory learning model should be able to transfer across regions and tasks without retraining, avoiding the need to maintain multiple specialized models and subpar performance with limited training data. However, each region has its unique spatial features and contexts, which are reflected in vehicle movement patterns and difficult to generalize. Additionally, transferring across different tasks faces technical challenges due to the varying input-output structures required for each task. Existing efforts towards transferability primarily involve learning embedding vectors for trajectories, which perform poorly in region transfer and require retraining of prediction modules for task transfer. To address these challenges, we propose TransferTraj, a vehicle GPS trajectory learning model that excels in both region and task transferability. For region transferability, we introduce RTTE as the main learnable module within TransferTraj. It integrates spatial, temporal, POI, and road network modalities of trajectories to effectively manage variations in spatial context distribution across regions. It also introduces a TRIE module for incorporating relative information of spatial features and a spatial context MoE module for handling movement patterns in diverse contexts. For task transferability, we propose a task-transferable input-output scheme that unifies the input-output structure of different tasks into the masking and recovery of modalities and trajectory points. This approach allows TransferTraj to be pre-trained once and transferred to different tasks without retraining. Extensive experiments on three real-world vehicle trajectory datasets under task transfer, zero-shot, and few-shot region transfer, validating TransferTraj's effectiveness.

Rethinking Irregular Time Series Forecasting: A Simple yet Effective Baseline

The forecasting of irregular multivariate time series (IMTS) is crucial in key areas such as healthcare, biomechanics, climate science, and astronomy. However, achieving accurate and practical predictions is challenging due to two main factors. First, the inherent irregularity and data missingness in irregular time series make modeling difficult. Second, most existing methods are typically complex and resource-intensive. In this study, we propose a general framework called APN to address these challenges. Specifically, we design a novel Time-Aware Patch Aggregation (TAPA) module that achieves adaptive patching. By learning dynamically adjustable patch boundaries and a time-aware weighted averaging strategy, TAPA transforms the original irregular sequences into high-quality, regularized representations in a channel-independent manner. Additionally, we use a simple query module to effectively integrate historical information while maintaining the model's efficiency. Finally, predictions are made by a shallow MLP. Experimental results on multiple real-world datasets show that APN outperforms existing state-of-the-art methods in both efficiency and accuracy.

NeuroLoc: Encoding Navigation Cells for 6-DOF Camera Localization

Recently, camera localization has been widely adopted in autonomous robotic navigation due to its efficiency and convenience. However, autonomous navigation in unknown environments often suffers from scene ambiguity, environmental disturbances, and dynamic object transformation in camera localization. To address this problem, inspired by the biological brain navigation mechanism (such as grid cells, place cells, and head direction cells), we propose a novel neurobiological camera location method, namely NeuroLoc. Firstly, we designed a Hebbian learning module driven by place cells to save and replay historical information, aiming to restore the details of historical representations and solve the issue of scene fuzziness. Secondly, we utilized the head direction cell-inspired internal direction learning as multi-head attention embedding to help restore the true orientation in similar scenes. Finally, we added a 3D grid center prediction in the pose regression module to reduce the final wrong prediction. We evaluate the proposed NeuroLoc on commonly used benchmark indoor and outdoor datasets. The experimental results show that our NeuroLoc can enhance the robustness in complex environments and improve the performance of pose regression by using only a single image.

Psychometric-Based Evaluation for Theorem Proving with Large Language Models

Large language models (LLMs) for formal theorem proving have become a prominent research focus. At present, the proving ability of these LLMs is mainly evaluated through proof pass rates on datasets such as miniF2F. However, this evaluation method overlooks the varying importance of theorems. As a result, it fails to highlight the real performance disparities between LLMs and leads to high evaluation costs. This study proposes a psychometric-based evaluation method for theorem proving with LLMs, comprising two main components: Dataset Annotation and Adaptive Evaluation. First, we propose a metric calculation method to annotate the dataset with difficulty and discrimination metrics. Specifically, we annotate each theorem in the miniF2F dataset and grade them into varying difficulty levels according to the performance of LLMs, resulting in an enhanced dataset: miniF2F-Graded. Experimental results show that the difficulty grading in miniF2F-Graded better reflects the theorem difficulty perceived by LLMs. Secondly, we design an adaptive evaluation method to dynamically select the most suitable theorems for testing based on the annotated metrics and the real-time performance of LLMs. We apply this method to evaluate 10 LLMs. The results show that our method finely highlights the performance disparities between LLMs. It also reduces evaluation costs by using only 23% of the theorems in the dataset.

EasyTime: Time Series Forecasting Made Easy

Time series forecasting has important applications across diverse domains. EasyTime, the system we demonstrate, facilitates easy use of time-series forecasting methods by researchers and practitioners alike. First, EasyTime enables one-click evaluation, enabling researchers to evaluate new forecasting methods using the suite of diverse time series datasets collected in the preexisting time series forecasting benchmark (TFB). This is achieved by leveraging TFB's flexible and consistent evaluation pipeline. Second, when practitioners must perform forecasting on a new dataset, a nontrivial first step is often to find an appropriate forecasting method. EasyTime provides an Automated Ensemble module that combines the promising forecasting methods to yield superior forecasting accuracy compared to individual methods. Third, EasyTime offers a natural language Q&A module leveraging large language models. Given a question like "Which method is best for long term forecasting on time series with strong seasonality?", EasyTime converts the question into SQL queries on the database of results obtained by TFB and then returns an answer in natural language and charts. By demonstrating EasyTime, we intend to show how it is possible to simplify the use of time series forecasting and to offer better support for the development of new generations of time series forecasting methods.

DUET: Dual Clustering Enhanced Multivariate Time Series Forecasting

Multivariate time series forecasting is crucial for various applications, such as financial investment, energy management, weather forecasting, and traffic optimization. However, accurate forecasting is challenging due to two main factors. First, real-world time series often show heterogeneous temporal patterns caused by distribution shifts over time. Second, correlations among channels are complex and intertwined, making it hard to model the interactions among channels precisely and flexibly. In this study, we address these challenges by proposing a general framework called \textbf{DUET}, which introduces \underline{DU}al clustering on the temporal and channel dimensions to \underline{E}nhance multivariate \underline{T}ime series forecasting. First, we design a Temporal Clustering Module (TCM) that clusters time series into fine-grained distributions to handle heterogeneous temporal patterns. For different distribution clusters, we design various pattern extractors to capture their intrinsic temporal patterns, thus modeling the heterogeneity. Second, we introduce a novel Channel-Soft-Clustering strategy and design a Channel Clustering Module (CCM), which captures the relationships among channels in the frequency domain through metric learning and applies sparsification to mitigate the adverse effects of noisy channels. Finally, DUET combines TCM and CCM to incorporate both the temporal and channel dimensions. Extensive experiments on 25 real-world datasets from 10 application domains, demonstrate the state-of-the-art performance of DUET.

MM-Path: Multi-modal, Multi-granularity Path Representation Learning -- Extended Version

Developing effective path representations has become increasingly essential across various fields within intelligent transportation. Although pre-trained path representation learning models have shown improved performance, they predominantly focus on the topological structures from single modality data, i.e., road networks, overlooking the geometric and contextual features associated with path-related images, e.g., remote sensing images. Similar to human understanding, integrating information from multiple modalities can provide a more comprehensive view, enhancing both representation accuracy and generalization. However, variations in information granularity impede the semantic alignment of road network-based paths (road paths) and image-based paths (image paths), while the heterogeneity of multi-modal data poses substantial challenges for effective fusion and utilization. In this paper, we propose a novel Multi-modal, Multi-granularity Path Representation Learning Framework (MM-Path), which can learn a generic path representation by integrating modalities from both road paths and image paths. To enhance the alignment of multi-modal data, we develop a multi-granularity alignment strategy that systematically associates nodes, road sub-paths, and road paths with their corresponding image patches, ensuring the synchronization of both detailed local information and broader global contexts. To address the heterogeneity of multi-modal data effectively, we introduce a graph-based cross-modal residual fusion component designed to comprehensively fuse information across different modalities and granularities. Finally, we conduct extensive experiments on two large-scale real-world datasets under two downstream tasks, validating the effectiveness of the proposed MM-Path. The code is available at: https://github.com/decisionintelligence/MM-Path.

MultiRC: Joint Learning for Time Series Anomaly Prediction and Detection with Multi-scale Reconstructive Contrast

Many methods have been proposed for unsupervised time series anomaly detection. Despite some progress, research on predicting future anomalies is still relatively scarce. Predicting anomalies is particularly challenging due to the diverse reaction time and the lack of labeled data. To address these challenges, we propose MultiRC to integrate reconstructive and contrastive learning for joint learning of anomaly prediction and detection, with multi-scale structure and adaptive dominant period mask to deal with the diverse reaction time. MultiRC also generates negative samples to provide essential training momentum for the anomaly prediction tasks and prevent model degradation. We evaluate seven benchmark datasets from different fields. For both anomaly prediction and detection tasks, MultiRC outperforms existing state-of-the-art methods.

PTR: A Pre-trained Language Model for Trajectory Recovery

Spatiotemporal trajectory data is vital for web-of-things services and is extensively collected and analyzed by web-based hardware and platforms. However, issues such as service interruptions and network instability often lead to sparsely recorded trajectories, resulting in a loss of detailed movement data. As a result, recovering these trajectories to restore missing information becomes essential. Despite progress, several challenges remain unresolved. First, the lack of large-scale dense trajectory data hampers the performance of existing deep learning methods, which rely heavily on abundant data for supervised training. Second, current methods struggle to generalize across sparse trajectories with varying sampling intervals, necessitating separate re-training for each interval and increasing computational costs. Third, external factors crucial for the recovery of missing points are not fully incorporated. To address these challenges, we propose a framework called PTR. This framework mitigates the issue of limited dense trajectory data by leveraging the capabilities of pre-trained language models (PLMs). PTR incorporates an explicit trajectory prompt and is trained on datasets with multiple sampling intervals, enabling it to generalize effectively across different intervals in sparse trajectories. To capture external factors, we introduce an implicit trajectory prompt that models road conditions, providing richer information for recovering missing points. Additionally, we present a trajectory embedder that encodes trajectory points and transforms the embeddings of both observed and missing points into a format comprehensible to PLMs. Experimental results on two public trajectory datasets with three sampling intervals demonstrate the efficacy and scalability of PTR.