NAApr 25, 2023
Efficient Bayesian inference using physics-informed invertible neural networks for inverse problemsXiaofei Guan, Xintong Wang, Hao Wu et al.
In this paper, we introduce an innovative approach for addressing Bayesian inverse problems through the utilization of physics-informed invertible neural networks (PI-INN). The PI-INN framework encompasses two sub-networks: an invertible neural network (INN) and a neural basis network (NB-Net). The primary role of the NB-Net lies in modeling the spatial basis functions characterizing the solution to the forward problem dictated by the underlying partial differential equation. Simultaneously, the INN is designed to partition the parameter vector linked to the input physical field into two distinct components: the expansion coefficients representing the forward problem solution and the Gaussian latent noise. If the forward mapping is precisely estimated, and the statistical independence between expansion coefficients and latent noise is well-maintained, the PI-INN offers a precise and efficient generative model for Bayesian inverse problems, yielding tractable posterior density estimates. As a particular physics-informed deep learning model, the primary training challenge for PI-INN centers on enforcing the independence constraint, which we tackle by introducing a novel independence loss based on estimated density. We support the efficacy and precision of the proposed PI-INN through a series of numerical experiments, including inverse kinematics, 1-dimensional and 2-dimensional diffusion equations, and seismic traveltime tomography. Specifically, our experimental results showcase the superior performance of the proposed independence loss in comparison to the commonly used but computationally demanding kernel-based maximum mean discrepancy loss.
AIOct 17, 2023Code
Leveraging Large Language Model for Automatic Evolving of Industrial Data-Centric R&D CycleXu Yang, Xiao Yang, Weiqing Liu et al.
In the wake of relentless digital transformation, data-driven solutions are emerging as powerful tools to address multifarious industrial tasks such as forecasting, anomaly detection, planning, and even complex decision-making. Although data-centric R&D has been pivotal in harnessing these solutions, it often comes with significant costs in terms of human, computational, and time resources. This paper delves into the potential of large language models (LLMs) to expedite the evolution cycle of data-centric R&D. Assessing the foundational elements of data-centric R&D, including heterogeneous task-related data, multi-facet domain knowledge, and diverse computing-functional tools, we explore how well LLMs can understand domain-specific requirements, generate professional ideas, utilize domain-specific tools to conduct experiments, interpret results, and incorporate knowledge from past endeavors to tackle new challenges. We take quantitative investment research as a typical example of industrial data-centric R&D scenario and verified our proposed framework upon our full-stack open-sourced quantitative research platform Qlib and obtained promising results which shed light on our vision of automatic evolving of industrial data-centric R&D cycle.
LGSep 16, 2022
Linear TreeShapPeng Yu, Chao Xu, Albert Bifet et al.
Decision trees are well-known due to their ease of interpretability. To improve accuracy, we need to grow deep trees or ensembles of trees. These are hard to interpret, offsetting their original benefits. Shapley values have recently become a popular way to explain the predictions of tree-based machine learning models. It provides a linear weighting to features independent of the tree structure. The rise in popularity is mainly due to TreeShap, which solves a general exponential complexity problem in polynomial time. Following extensive adoption in the industry, more efficient algorithms are required. This paper presents a more efficient and straightforward algorithm: Linear TreeShap. Like TreeShap, Linear TreeShap is exact and requires the same amount of memory.
NAApr 16, 2018
Isogeometric analysis with local adaptivity based on a posterior error estimation for elastodynamicsPeng Yu, Cosmin Anitescu, Satyendra Tomar et al.
This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner-Mindlin plates. The adaptive discretization is based on the recently developed Geometry Independent Field approximaTion (GIFT) framework, which may be seen as a generalisation of the Iso-Geometric Analysis (IGA). Within the GIFT framework, we describe the geometry of the structure exactly with NURBS (Non-Uniform Rational B-Splines), whilst independently employing Polynomial splines over Hierarchical T-meshes (PHT)-splines to represent the solution field. The proposed strategy of local adaptivity, wherein a posteriori error estimators are computed based on inexpensive hierarchical $h-$refinement, aims to control the discretisation error within a frequency band. The approach sweeps from lower to higher frequencies, refining the mesh appropriately so that each of the free vibration mode within the targeted frequency band is sufficiently resolved. Through several numerical examples, we show that the GIFT framework is a powerful and versatile tool to perform local adaptivity in structural dynamics. We also show that the proposed adaptive local $h-$refinement scheme allows us to achieve significantly faster convergence rates than when using a uniform $h-$refinement.
LGNov 11, 2025
Binary Split Categorical feature with Mean Absolute Error Criteria in CARTPeng Yu, Yike Chen, Chao Xu et al.
In the context of the Classification and Regression Trees (CART) algorithm, the efficient splitting of categorical features using standard criteria like GINI and Entropy is well-established. However, using the Mean Absolute Error (MAE) criterion for categorical features has traditionally relied on various numerical encoding methods. This paper demonstrates that unsupervised numerical encoding methods are not viable for the MAE criteria. Furthermore, we present a novel and efficient splitting algorithm that addresses the challenges of handling categorical features with the MAE criterion. Our findings underscore the limitations of existing approaches and offer a promising solution to enhance the handling of categorical data in CART algorithms.
44.4LGMay 6
Quadrature-TreeSHAP: Depth-Independent TreeSHAP and Shapley InteractionsRon Wettenstein, Rory Mitchell, Peng Yu
Shapley values are a standard tool for explaining predictions of tree ensembles, with Path-Dependent SHAP being the most widely used variant. Despite substantial progress, existing methods still exhibit trade-offs between depth-dependent runtime, numerical stability, and support for higher-order interactions. To address these challenges, we introduce Quadrature-TreeSHAP, a quadrature-based reformulation of Path-Dependent TreeSHAP that is numerically stable, naturally extends to any-order Shapley interaction values and is practically insensitive to tree depth. Our implementation supports both CPU and GPU and is integrated into XGBoost. Our method is based on a weighted-Banzhaf interaction polynomial, which expresses Banzhaf interaction values as expectations under a feature participation probability $p$. Shapley values and any-order interaction values are then recovered by integrating these polynomials over $p$ from 0 to 1. We evaluate these integrals using Gauss-Legendre quadrature, and show that, in practice, only 8 fixed quadrature points are sufficient to reach machine precision. In fact, Quadrature-TreeSHAP with 8 fixed points achieves greater numerical stability than TreeSHAP. This fixed-point formulation removes depth dependence from the inner computation and enables efficient SIMD execution. We confirm these advantages empirically. On 12 XGBoost benchmarks, Quadrature-TreeSHAP computes Shapley values 1.06x-10.59x faster than TreeSHAP on CPU and 1.84x-6.95x faster than GPUTreeSHAP on GPU. Shapley pairwise interactions are 3.80x-58.11x faster on CPU, with higher-order interactions achieving speedups of up to 1200x compared to TreeSHAP-IQ.
82.5AIMay 9Code
Not All Turns Matter: Credit Assignment for Multi-Turn JailbreakingZhida He, Xiaoyu Wen, Han Qi et al.
Deploying LLMs in multi-turn dialogues facilitates jailbreak attacks that distribute harmful intent across seemingly benign turns. Recent training-based multi-turn jailbreak methods learn long-horizon attack strategies from interaction feedback, but often rely on coarse trajectory-level outcome signals that broadcast uniformly to every turn. However, we find that turn-level contributions in multi-turn jailbreaking are non-uniform, phase-dependent, and target-specific. Such coarse outcome supervision induces a credit assignment problem, leading to over-rewarding redundant turns in successful trajectories and under-crediting useful intermediate turns in failed ones. To address this, we propose TRACE, a turn-aware credit assignment framework for reinforcement learning (RL)-based multi-turn jailbreaking. For successful trajectories, TRACE estimates turn-level contributions via leave-one-turn-out semantic masking; for failed ones, TRACE assigns penalties based on prompt harmfulness and semantic relevance, with an additional local refusal-aware penalty. Furthermore, we reuse the attack-side credit signal for multi-turn defense alignment. Extensive experiments on open-source and closed-source targets show that TRACE achieves strong overall performance in effectiveness, transferability, and efficiency, yielding about a 25% relative improvement in attack success rate over the strongest RL baseline while also improving the safety-utility balance when reused for defense alignment.
15.4CLApr 24
STEM: Structure-Tracing Evidence Mining for Knowledge Graphs-Driven Retrieval-Augmented GenerationPeng Yu, En Xu, Bin Chen et al.
Knowledge Graph-based Question Answering (KGQA) plays a pivotal role in complex reasoning tasks but remains constrained by two persistent challenges: the structural heterogeneity of Knowledge Graphs(KGs) often leads to semantic mismatch during retrieval, while existing reasoning path retrieval methods lack a global structural perspective. To address these issues, we propose Structure-Tracing Evidence Mining (STEM), a novel framework that reframes multi-hop reasoning as a schema-guided graph search task. First, we design a Semantic-to-Structural Projection pipeline that leverages KG structural priors to decompose queries into atomic relational assertions and construct an adaptive query schema graph. Subsequently, we execute globally-aware node anchoring and subgraph retrieval to obtain the final evidence reasoning graph from KG. To more effectively integrate global structural information during the graph construction process, we design a Triple-Dependent GNN (Triple-GNN) to generate a Global Guidance Subgraph (Guidance Graph) that guides the construction. STEM significantly improves both the accuracy and evidence completeness of multi-hop reasoning graph retrieval, and achieves State-of-the-Art performance on multiple multi-hop benchmarks.
IRDec 21, 2024Code
Large Language Model Can Be a Foundation for Hidden Rationale-Based RetrievalLuo Ji, Feixiang Guo, Teng Chen et al.
Despite the recent advancement in Retrieval-Augmented Generation (RAG) systems, most retrieval methodologies are often developed for factual retrieval, which assumes query and positive documents are semantically similar. In this paper, we instead propose and study a more challenging type of retrieval task, called hidden rationale retrieval, in which query and document are not similar but can be inferred by reasoning chains, logic relationships, or empirical experiences. To address such problems, an instruction-tuned Large language model (LLM) with a cross-encoder architecture could be a reasonable choice. To further strengthen pioneering LLM-based retrievers, we design a special instruction that transforms the retrieval task into a generative task by prompting LLM to answer a binary-choice question. The model can be fine-tuned with direct preference optimization (DPO). The framework is also optimized for computational efficiency with no performance degradation. We name this retrieval framework by RaHoRe and verify its zero-shot and fine-tuned performance superiority on Emotional Support Conversation (ESC), compared with previous retrieval works. Our study suggests the potential to employ LLM as a foundation for a wider scope of retrieval tasks. Our codes, models, and datasets are available on https://github.com/flyfree5/LaHoRe.
ROMar 2
Shape-Interpretable Visual Self-Modeling Enables Geometry-Aware Continuum Robot ControlPeng Yu, Xin Wang, Ning Tan
Continuum robots possess high flexibility and redundancy, making them well suited for safe interaction in complex environments, yet their continuous deformation and nonlinear dynamics pose fundamental challenges to perception, modeling, and control. Existing vision-based control approaches often rely on end-to-end learning, achieving shape regulation without explicit awareness of robot geometry or its interaction with the environment. Here, we introduce a shape-interpretable visual self-modeling framework for continuum robots that enables geometry-aware control. Robot shapes are encoded from multi-view planar images using a Bezier-curve representation, transforming visual observations into a compact and physically meaningful shape space that uniquely characterizes the robot's three-dimensional configuration. Based on this representation, neural ordinary differential equations are employed to self-model both shape and end-effector dynamics directly from data, enabling hybrid shape-position control without analytical models or dense body markers. The explicit geometric structure of the learned shape space allows the robot to reason about its body and surroundings, supporting environment-aware behaviors such as obstacle avoidance and self-motion while maintaining end-effector objectives. Experiments on a cable-driven continuum robot demonstrate accurate shape-position regulation and tracking, with shape errors within 1.56% of image resolution and end-effector errors within 2% of robot length, as well as robust performance in constrained environments. By elevating visual shape representations from two-dimensional observations to an interpretable three-dimensional self-model, this work establishes a principled alternative to vision-based end-to-end control and advances autonomous, geometry-aware manipulation for continuum robots.
CLApr 8, 2024
LTNER: Large Language Model Tagging for Named Entity Recognition with Contextualized Entity MarkingFaren Yan, Peng Yu, Xin Chen
The use of LLMs for natural language processing has become a popular trend in the past two years, driven by their formidable capacity for context comprehension and learning, which has inspired a wave of research from academics and industry professionals. However, for certain NLP tasks, such as NER, the performance of LLMs still falls short when compared to supervised learning methods. In our research, we developed a NER processing framework called LTNER that incorporates a revolutionary Contextualized Entity Marking Gen Method. By leveraging the cost-effective GPT-3.5 coupled with context learning that does not require additional training, we significantly improved the accuracy of LLMs in handling NER tasks. The F1 score on the CoNLL03 dataset increased from the initial 85.9% to 91.9%, approaching the performance of supervised fine-tuning. This outcome has led to a deeper understanding of the potential of LLMs.
CLJul 31, 2025
A Novel Evaluation Benchmark for Medical LLMs: Illuminating Safety and Effectiveness in Clinical DomainsShirui Wang, Zhihui Tang, Huaxia Yang et al.
Large language models (LLMs) hold promise in clinical decision support but face major challenges in safety evaluation and effectiveness validation. We developed the Clinical Safety-Effectiveness Dual-Track Benchmark (CSEDB), a multidimensional framework built on clinical expert consensus, encompassing 30 criteria covering critical areas like critical illness recognition, guideline adherence, and medication safety, with weighted consequence measures. Thirty-two specialist physicians developed and reviewed 2,069 open-ended Q&A items aligned with these criteria, spanning 26 clinical departments to simulate real-world scenarios. Benchmark testing of six LLMs revealed moderate overall performance (average total score 57.2%, safety 54.7%, effectiveness 62.3%), with a significant 13.3% performance drop in high-risk scenarios (p < 0.0001). Domain-specific medical LLMs showed consistent performance advantages over general-purpose models, with relatively higher top scores in safety (0.912) and effectiveness (0.861). The findings of this study not only provide a standardized metric for evaluating the clinical application of medical LLMs, facilitating comparative analyses, risk exposure identification, and improvement directions across different scenarios, but also hold the potential to promote safer and more effective deployment of large language models in healthcare environments.
CLAug 29, 2025
QZhou-Embedding Technical ReportPeng Yu, En Xu, Bin Chen et al.
We present QZhou-Embedding, a general-purpose contextual text embedding model with exceptional text representation capabilities. Built upon the Qwen2.5-7B-Instruct foundation model, we designed a unified multi-task framework comprising specialized data transformation and training strategies. The data transformation scheme enables the incorporation of more diverse textual training datasets, while the task-specific training strategies enhance model learning efficiency. We developed a data synthesis pipeline leveraging LLM API, incorporating techniques such as paraphrasing, augmentation, and hard negative example generation to improve the semantic richness and sample difficulty of the training set. Additionally, we employ a two-stage training strategy, comprising initial retrieval-focused pretraining followed by full-task fine-tuning, enabling the embedding model to extend its capabilities based on robust retrieval performance. Our model achieves state-of-the-art results on the MTEB and CMTEB benchmarks, ranking first on both leaderboards (August 27 2025), and simultaneously achieves state-of-the-art performance on tasks including reranking, clustering, etc. Our findings demonstrate that higher-quality, more diverse data is crucial for advancing retrieval model performance, and that leveraging LLMs generative capabilities can further optimize data quality for embedding model breakthroughs. Our model weights are released on HuggingFace under Apache 2.0 license. For reproducibility, we provide evaluation code and instructions on GitHub.
IRDec 22, 2024
Towards a Unified Paradigm: Integrating Recommendation Systems as a New Language in Large ModelsKai Zheng, Qingfeng Sun, Can Xu et al. · microsoft-research
This paper explores the use of Large Language Models (LLMs) for sequential recommendation, which predicts users' future interactions based on their past behavior. We introduce a new concept, "Integrating Recommendation Systems as a New Language in Large Models" (RSLLM), which combines the strengths of traditional recommenders and LLMs. RSLLM uses a unique prompting method that combines ID-based item embeddings from conventional recommendation models with textual item features. It treats users' sequential behaviors as a distinct language and aligns the ID embeddings with the LLM's input space using a projector. We also propose a two-stage LLM fine-tuning framework that refines a pretrained LLM using a combination of two contrastive losses and a language modeling loss. The LLM is first fine-tuned using text-only prompts, followed by target domain fine-tuning with unified prompts. This trains the model to incorporate behavioral knowledge from the traditional sequential recommender into the LLM. Our empirical results validate the effectiveness of our proposed framework.
CLDec 6, 2024
KaLM: Knowledge-aligned Autoregressive Language Modeling via Dual-view Knowledge Graph Contrastive LearningPeng Yu, Cheng Deng, Beiya Dai et al.
Autoregressive large language models (LLMs) pre-trained by next token prediction are inherently proficient in generative tasks. However, their performance on knowledge-driven tasks such as factual knowledge querying remains unsatisfactory. Knowledge graphs (KGs), as high-quality structured knowledge bases, can provide reliable knowledge for LLMs, potentially compensating for their knowledge deficiencies. Aligning LLMs with explicit, structured knowledge from KGs has been a challenge; previous attempts either failed to effectively align knowledge representations or compromised the generative capabilities of LLMs, leading to less-than-optimal outcomes. This paper proposes \textbf{KaLM}, a \textit{Knowledge-aligned Language Modeling} approach, which fine-tunes autoregressive LLMs to align with KG knowledge via the joint objective of explicit knowledge alignment and implicit knowledge alignment. The explicit knowledge alignment objective aims to directly optimize the knowledge representation of LLMs through dual-view knowledge graph contrastive learning. The implicit knowledge alignment objective focuses on incorporating textual patterns of knowledge into LLMs through triple completion language modeling. Notably, our method achieves a significant performance boost in evaluations of knowledge-driven tasks, specifically embedding-based knowledge graph completion and generation-based knowledge graph question answering.
CLSep 27, 2025
Learning to Reason in Structured In-context Environments with Reinforcement LearningPeng Yu, Zeyuan Zhao, Shao Zhang et al.
Large language models (LLMs) have achieved significant advancements in reasoning capabilities through reinforcement learning (RL) via environmental exploration. As the intrinsic properties of the environment determine the abilities that LLMs can learn, the environment plays a important role in the RL finetuning process. An ideal LLM reasoning environment should possess three core characteristics: scalability, generalizable reasoning, and verifiability. However, existing mathematical and coding environments are difficult to scale due to heavy reliance on expert annotation, while the skills learned in game-based environments are too specialized to generalize. To bridge this gap, we introduce the \textbf{S}tructured \textbf{I}n-context \textbf{E}nvironment (SIE) framework. SIE achieves scalability by automatically constructing reasoning environments from large-scale structured data, where the rich compositional patterns naturally support generalizable reasoning. Moreover, the explicit schemas and reasoning chains in structured data provide a foundation for rule-based verifiability. Experimental results show that SIE framework not only achieves substantial improvements in in-domain structured reasoning, but also enables the learned compositional reasoning skills to generalize effectively to out-of-domain mathematical and logical reasoning tasks. We further explored learning in information-limited partial SIEs and found that LLMs can infer the missing information through exploring the environment, leading to robust reasoning improvements and generalization performance.
CVAug 6, 2025
RotatedMVPS: Multi-view Photometric Stereo with Rotated Natural LightSongyun Yang, Yufei Han, Jilong Zhang et al.
Multiview photometric stereo (MVPS) seeks to recover high-fidelity surface shapes and reflectances from images captured under varying views and illuminations. However, existing MVPS methods often require controlled darkroom settings for varying illuminations or overlook the recovery of reflectances and illuminations properties, limiting their applicability in natural illumination scenarios and downstream inverse rendering tasks. In this paper, we propose RotatedMVPS to solve shape and reflectance recovery under rotated natural light, achievable with a practical rotation stage. By ensuring light consistency across different camera and object poses, our method reduces the unknowns associated with complex environment light. Furthermore, we integrate data priors from off-the-shelf learning-based single-view photometric stereo methods into our MVPS framework, significantly enhancing the accuracy of shape and reflectance recovery. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of our approach.
AIJun 14, 2025
DinoCompanion: An Attachment-Theory Informed Multimodal Robot for Emotionally Responsive Child-AI InteractionBoyang Wang, Yuhao Song, Jinyuan Cao et al.
Children's emotional development fundamentally relies on secure attachment relationships, yet current AI companions lack the theoretical foundation to provide developmentally appropriate emotional support. We introduce DinoCompanion, the first attachment-theory-grounded multimodal robot for emotionally responsive child-AI interaction. We address three critical challenges in child-AI systems: the absence of developmentally-informed AI architectures, the need to balance engagement with safety, and the lack of standardized evaluation frameworks for attachment-based capabilities. Our contributions include: (i) a multimodal dataset of 128 caregiver-child dyads containing 125,382 annotated clips with paired preference-risk labels, (ii) CARPO (Child-Aware Risk-calibrated Preference Optimization), a novel training objective that maximizes engagement while applying epistemic-uncertainty-weighted risk penalties, and (iii) AttachSecure-Bench, a comprehensive evaluation benchmark covering ten attachment-centric competencies with strong expert consensus (\k{appa}=0.81). DinoCompanion achieves state-of-the-art performance (57.15%), outperforming GPT-4o (50.29%) and Claude-3.7-Sonnet (53.43%), with exceptional secure base behaviors (72.99%, approaching human expert levels of 78.4%) and superior attachment risk detection (69.73%). Ablations validate the critical importance of multimodal fusion, uncertainty-aware risk modeling, and hierarchical memory for coherent, emotionally attuned interactions.
ROMar 7, 2025
Learning High-Fidelity Robot Self-Model with Articulated 3D Gaussian SplattingKejun Hu, Peng Yu, Ning Tan
Self-modeling enables robots to build task-agnostic models of their morphology and kinematics based on data that can be automatically collected, with minimal human intervention and prior information, thereby enhancing machine intelligence. Recent research has highlighted the potential of data-driven technology in modeling the morphology and kinematics of robots. However, existing self-modeling methods suffer from either low modeling quality or excessive data acquisition costs. Beyond morphology and kinematics, texture is also a crucial component of robots, which is challenging to model and remains unexplored. In this work, a high-quality, texture-aware, and link-level method is proposed for robot self-modeling. We utilize three-dimensional (3D) Gaussians to represent the static morphology and texture of robots, and cluster the 3D Gaussians to construct neural ellipsoid bones, whose deformations are controlled by the transformation matrices generated by a kinematic neural network. The 3D Gaussians and kinematic neural network are trained using data pairs composed of joint angles, camera parameters and multi-view images without depth information. By feeding the kinematic neural network with joint angles, we can utilize the well-trained model to describe the corresponding morphology, kinematics and texture of robots at the link level, and render robot images from different perspectives with the aid of 3D Gaussian splatting. Furthermore, we demonstrate that the established model can be exploited to perform downstream tasks such as motion planning and inverse kinematics.
IRMay 27, 2019
On a scalable problem transformation method for multi-label learningDora Jambor, Peng Yu
Binary relevance is a simple approach to solve multi-label learning problems where an independent binary classifier is built per each label. A common challenge with this in real-world applications is that the label space can be very large, making it difficult to use binary relevance to larger scale problems. In this paper, we propose a scalable alternative to this, via transforming the multi-label problem into a single binary classification. We experiment with a few variations of our method and show that our method achieves higher precision than binary relevance and faster execution times on a top-K recommender system task.
LGApr 27, 2018
Negative Log Likelihood Ratio Loss for Deep Neural Network ClassificationDonglai Zhu, Hengshuai Yao, Bei Jiang et al.
In deep neural network, the cross-entropy loss function is commonly used for classification. Minimizing cross-entropy is equivalent to maximizing likelihood under assumptions of uniform feature and class distributions. It belongs to generative training criteria which does not directly discriminate correct class from competing classes. We propose a discriminative loss function with negative log likelihood ratio between correct and competing classes. It significantly outperforms the cross-entropy loss on the CIFAR-10 image classification task.
AIFeb 9, 2016
Time Resource NetworksSzymon Sidor, Peng Yu, Cheng Fang et al.
The problem of scheduling under resource constraints is widely applicable. One prominent example is power management, in which we have a limited continuous supply of power but must schedule a number of power-consuming tasks. Such problems feature tightly coupled continuous resource constraints and continuous temporal constraints. We address such problems by introducing the Time Resource Network (TRN), an encoding for resource-constrained scheduling problems. The definition allows temporal specifications using a general family of representations derived from the Simple Temporal network, including the Simple Temporal Network with Uncertainty, and the probabilistic Simple Temporal Network (Fang et al. (2014)). We propose two algorithms for determining the consistency of a TRN: one based on Mixed Integer Programing and the other one based on Constraint Programming, which we evaluate on scheduling problems with Simple Temporal Constraints and Probabilistic Temporal Constraints.