Hy Dang, Tianyi Liu, Zhuofeng Wu, Jingfeng Yang, Haoming Jiang, Tao Yang, Pei Chen, Zhengyang Wang, Helen Wang, Huasheng Li, Bing Yin, Meng Jiang. Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing. 2025.

Supervised fine-tuning (SFT) has become a crucial step for aligning pretrained large language models (LLMs) using supervised datasets of input-output pairs. However, despite being supervised, SFT is inherently limited by its generative training objective. To address its limitations, the existing common strategy is to follow SFT with a separate phase of preference optimization (PO), which relies on either human-labeled preference data or a strong reward model to guide the learning process. In this paper, we address the limitations of SFT by exploring one of the most successful techniques in conventional supervised learning: discriminative learning. We introduce Discriminative Fine-Tuning (DFT), an improved variant of SFT, which mitigates the burden of collecting human-labeled preference data or training strong reward models. Unlike SFT that employs a generative approach and overlooks negative data, DFT adopts a discriminative paradigm that increases the probability of positive answers while suppressing potentially negative ones, aiming for data prediction instead of token prediction. Our contributions include: (i) a discriminative probabilistic framework for fine-tuning LLMs by explicitly modeling the discriminative likelihood of an answer among all possible outputs given an input; (ii) efficient algorithms to optimize this discriminative likelihood; and (iii) extensive experiments demonstrating DFT’s effectiveness, achieving performance better than SFT and comparable to if not better than SFT$\rightarrow$PO. The code can be found at https://github.com/Optimization-AI/DFT.

Zhihan Zhang, Shiyang Li, Zixuan Zhang, Xin Liu, Haoming Jiang, Xianfeng Tang, Yifan Gao, Zheng Li, Haodong Wang, Zhaoxuan Tan, Yichuan Li, Qingyu Yin, Bing Yin, Meng Jiang. Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2025.

Yuchen Zhuang, Jingfeng Yang, Haoming Jiang, Xin Liu, Kewei Cheng, Sanket Lokegaonkar, Yifan Gao, Qing Ping, Tianyi Liu, Binxuan Huang, Zheng Li, Zhengyang Wang, Pei Chen, Ruijie Wang, Rongzhi Zhang, Nasser Zalmout, Priyanka Nigam, Bing Yin, Chao Zhang. Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2025.

Reinforcement learning from human feedback (RLHF) has become a powerful post-training paradigm for aligning large language models with human preferences. A core challenge in RLHF is constructing accurate reward signals, where the conventional Bradley-Terry reward models (BT RMs) often suffer from sensitivity to data size and coverage, as well as vulnerability to reward hacking. Generative reward models (GenRMs) offer a more robust alternative by generating chain-of-thought (CoT) rationales followed by a final verdict. However, existing GenRMs rely on shallow, vertically scaled reasoning, limiting their capacity to handle nuanced or complex tasks. Moreover, their pairwise preference outputs are incompatible with standard RLHF algorithms that require pointwise reward signals. In this work, we introduce Think-RM, a training framework that enables long-horizon reasoning in GenRMs by modeling an internal thinking process. Rather than producing structured, externally provided rationales, Think-RM generates flexible, self-guided reasoning traces that support advanced capabilities such as self-reflection, hypothetical reasoning, and divergent reasoning. To elicit these reasoning abilities, we first warm-up the models by supervised fine-tuning (SFT) over long CoT data. We then further improve the model's long-horizon abilities by rule-based reinforcement learning (RL). In addition, we propose a novel pairwise RLHF pipeline that directly optimizes policies from pairwise comparisons, eliminating the need for pointwise reward conversion. Experiments show that Think-RM outperforms baselines on both in-distribution and out-of-distribution tasks, with particularly strong gains on reasoning-heavy benchmarks: more than 10\% and 5\% on RewardBench's Chat Hard and Reasoning, and 12\% on RM-Bench's Math domain. When combined with our pairwise RLHF pipeline, it demonstrates superior end-policy performance compared to traditional approaches. This depth-oriented approach not only broadens the GenRM design space but also establishes a new paradigm for preference-based policy optimization in RLHF.

Reward model (RM) plays a pivotal role in reinforcement learning with human feedback (RLHF) for aligning large language models (LLMs). However, classical RMs trained on human preferences are vulnerable to reward hacking and generalize poorly to out-of-distribution (OOD) inputs. By contrast, strong LLM judges equipped with reasoning capabilities demonstrate superior generalization, even without additional training, but incur significantly higher inference costs, limiting their applicability in online RLHF. In this work, we propose an uncertainty-based routing framework that efficiently complements a fast RM with a strong but costly LLM judge. Our approach formulates advantage estimation in policy gradient (PG) methods as pairwise preference classification, enabling principled uncertainty quantification to guide routing. Uncertain pairs are forwarded to the LLM judge, while confident ones are evaluated by the RM. Experiments on RM benchmarks demonstrate that our uncertainty-based routing strategy significantly outperforms random judge calling at the same cost, and downstream alignment results showcase its effectiveness in improving online RLHF.

Fenglin Liu, Zheng Li, Hongjian Zhou, Qingyu Yin, Jingfeng Yang, Xianfeng Tang, Chen Luo, Ming Zeng, Haoming Jiang, Yifan Gao, Priyanka Nigam, Sreyashi Nag, Bing Yin, Yining Hua, Xuan Zhou, Omid Rohanian, Anshul Thakur, Lei Clifton, David A. Clifton. Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing. 2024.

Haoyu Wang, Ruirui Li, Haoming Jiang, Jinjin Tian, Zhengyang Wang, Chen Luo, Xianfeng Tang, Monica Xiao Cheng, Tuo Zhao, Jing Gao. Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing. 2024.

Existing Large Language Models (LLMs) usually remain static after deployment, which might make it hard to inject new knowledge into the model. We aim to build models containing a considerable portion of self-updatable parameters, enabling the model to integrate new knowledge effectively and efficiently. To this end, we introduce MEMORYLLM, a model that comprises a transformer and a fixed-size memory pool within the latent space of the transformer. MEMORYLLM can self-update with text knowledge and memorize the knowledge injected earlier. Our evaluations demonstrate the ability of MEMORYLLM to effectively incorporate new knowledge, as evidenced by its performance on model editing benchmarks. Meanwhile, the model exhibits long-term information retention capacity, which is validated through our custom-designed evaluations and long-context benchmarks. MEMORYLLM also shows operational integrity without any sign of performance degradation even after nearly a million memory updates. Our code and model are open-sourced at https://github.com/wangyu-ustc/MemoryLLM.

Reinforcement learning from human feedback (RLHF) provides a principled framework for aligning AI systems with human preference data. For various reasons, e.g., personal bias, context ambiguity, lack of training, etc, human annotators may give incorrect or inconsistent preference labels. To tackle this challenge, we propose a robust RLHF approach -- $R^3M$, which models the potentially corrupted preference label as sparse outliers. Accordingly, we formulate the robust reward learning as an $\ell_1$-regularized maximum likelihood estimation problem. Computationally, we develop an efficient alternating optimization algorithm, which only incurs negligible computational overhead compared with the standard RLHF approach. Theoretically, we prove that under proper regularity conditions, $R^3M$ can consistently learn the underlying reward and identify outliers, provided that the number of outlier labels scales sublinearly with the preference sample size. Furthermore, we remark that $R^3M$ is versatile and can be extended to various preference optimization methods, including direct preference optimization (DPO). Our experiments on robotic control and natural language generation with large language models (LLMs) show that $R^3M$ improves robustness of the reward against several types of perturbations to the preference data.

Reinforcement learning from human feedback (RLHF) is a prevalent approach to align AI systems with human values by learning rewards from human preference data. Due to various reasons, however, such data typically takes the form of rankings over pairs of trajectory segments, which fails to capture the varying strengths of preferences across different pairs. In this paper, we propose a novel adaptive preference loss, underpinned by distributionally robust optimization (DRO), designed to address this uncertainty in preference strength. By incorporating an adaptive scaling parameter into the loss for each pair, our method increases the flexibility of the reward function. Specifically, it assigns small scaling parameters to pairs with ambiguous preferences, leading to more comparable rewards, and large scaling parameters to those with clear preferences for more distinct rewards. Computationally, our proposed loss function is strictly convex and univariate with respect to each scaling parameter, enabling its efficient optimization through a simple second-order algorithm. Our method is versatile and can be readily adapted to various preference optimization frameworks, including direct preference optimization (DPO). Our experiments with robotic control and natural language generation with large language models (LLMs) show that our method not only improves policy performance but also aligns reward function selection more closely with policy optimization, simplifying the hyperparameter tuning process.

This article presents a comprehensive and practical guide for practitioners and end-users working with Large Language Models (LLMs) in their downstream Natural Language Processing (NLP) tasks. We provide discussions and insights into the usage of LLMs from the perspectives of models, data, and downstream tasks. First, we offer an introduction and brief summary of current language models. Then, we discuss the influence of pre-training data, training data, and test data. Most importantly, we provide a detailed discussion about the use and non-use cases of large language models for various natural language processing tasks, such as knowledge-intensive tasks, traditional natural language understanding tasks, generation tasks, emergent abilities, and considerations for specific tasks. We present various use cases and non-use cases to illustrate the practical applications and limitations of LLMs in real-world scenarios. We also try to understand the importance of data and the specific challenges associated with each NLP task. Furthermore, we explore the impact of spurious biases on LLMs and delve into other essential considerations, such as efficiency, cost, and latency, to ensure a comprehensive understanding of deploying LLMs in practice. This comprehensive guide aims to provide researchers and practitioners with valuable insights and best practices for working with LLMs, thereby enabling the successful implementation of these models in a wide range of NLP tasks. A curated list of practical guide resources of LLMs, regularly updated, can be found at https://github.com/Mooler0410/LLMsPracticalGuide . An LLMs evolutionary tree, editable yet regularly updated, can be found at llmtree.ai .

Hierarchies are common structures used to organize data, such as e-commerce hierarchies associated with product data. With these product hierarchies, we aim to learn hierarchy-aware product text embeddings to improve fine-tuning performance on a variety of downstream e-commerce tasks. Existing methods leverage hierarchies by either aligning the text embeddings to separate hierarchical embeddings or by aligning the hierarchical information implicitly within a unified text Transformer. Although these models optimize to predict hierarchy information, performing further fine-tuning on new tasks is non-trivial. To bridge this gap, we propose a pre-training architecture to implicitly encode the hierarchy within the product text and then directly leverage a sub-set of the pre-training model during fine-tuning. Pre-training is done through Semantic and Structural Transformers (SST) where the Semantic-Transformer first encodes the product text into a contextual embedding, which is then used by the Structural-Transformer to infer the product’s path in the hierarchy. Fine-tuning is done using only the initial Semantic-Transformer, now that hierarchy-aware text embeddings are learned. With this design, we eliminate the need of linking each fine-tuning dataset with corresponding hierarchies. This leads to fine-tuning performance improvements on critical e-commerce downstream tasks over the existing state-of-the-art hierarchy models, even when hierarchy data $is$ available during fine-tuning. Moreover, this improvement is consistent even after augmenting our baseline models to support fine-tuning. We conclude by discussing how such implicit structural encodings can be leveraged beyond the e-commerce domain.

Transformer Hawkes process models have shown to be successful in modeling event sequence data. However, most of the existing training methods rely on maximizing the likelihood of event sequences, which involves calculating some intractable integral. Moreover, the existing methods fail to provide uncertainty quantification for model predictions, e.g., confidence interval for the predicted event’s arrival time. To address these issues, we propose SMURF-THP, a score-based method for learning Transformer Hawkes process and quantifying prediction uncertainty. Specifically, SMURF-THP learns the score function of the event’s arrival time based on a score-matching objective that avoids the intractable computation. With such a learnt score function, we can sample arrival time of events from the predictive distribution. This naturally allows for the quantification of uncertainty by computing confidence intervals over the generated samples. We conduct extensive experiments in both event type prediction and uncertainty quantification on time of arrival. In all the experiments, SMURF-THP outperforms existing likelihood-based methods in confidence calibration while exhibiting comparable prediction accuracy.

Modeling customer shopping intentions is a crucial task for e-commerce, as it directly impacts user experience and engagement. Thus, accurately understanding customer preferences is essential for providing personalized recommendations. Session-based recommendation, which utilizes customer session data to predict their next interaction, has become increasingly popular. However, existing session datasets have limitations in terms of item attributes, user diversity, and dataset scale. As a result, they cannot comprehensively capture the spectrum of user behaviors and preferences.To bridge this gap, we present the Amazon Multilingual Multi-locale Shopping Session Dataset, namely Amazon-M2. It is the first multilingual dataset consisting of millions of user sessions from six different locales, where the major languages of products are English, German, Japanese, French, Italian, and Spanish.Remarkably, the dataset can help us enhance personalization and understanding of user preferences, which can benefit various existing tasks as well as enable new tasks. To test the potential of the dataset, we introduce three tasks in this work:(1) next-product recommendation, (2) next-product recommendation with domain shifts, and (3) next-product title generation.With the above tasks, we benchmark a range of algorithms on our proposed dataset, drawing new insights for further research and practice. In addition, based on the proposed dataset and tasks, we hosted a competition in the KDD CUP 2023 https://www.aicrowd.com/challenges/amazon-kdd-cup-23-multilingual-recommendation-challenge and have attracted thousands of users and submissions. The winning solutions and the associated workshop can be accessed at our website~https://kddcup23.github.io/.

Zijie Huang, Zheng Li, Haoming Jiang, Tianyu Cao, Hanqing Lu, Bing Yin, Karthik Subbian, Yizhou Sun, Wei Wang. Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2022.

As training deep learning models on large dataset takes a lot of time and resources, it is desired to construct a small synthetic dataset with which we can train deep learning models sufficiently. There are recent works that have explored solutions on condensing image datasets through complex bi-level optimization. For instance, dataset condensation (DC) matches network gradients w.r.t. large-real data and small-synthetic data, where the network weights are optimized for multiple steps at each outer iteration. However, existing approaches have their inherent limitations: (1) they are not directly applicable to graphs where the data is discrete; and (2) the condensation process is computationally expensive due to the involved nested optimization. To bridge the gap, we investigate efficient dataset condensation tailored for graph datasets where we model the discrete graph structure as a probabilistic model. We further propose a one-step gradient matching scheme, which performs gradient matching for only one single step without training the network weights. Our theoretical analysis shows this strategy can generate synthetic graphs that lead to lower classification loss on real graphs. Extensive experiments on various graph datasets demonstrate the effectiveness and efficiency of the proposed method. In particular, we are able to reduce the dataset size by 90% while approximating up to 98% of the original performance and our method is significantly faster than multi-step gradient matching (e.g. $15$× in CIFAR10 for synthesizing 500 graphs).

Query understanding models extract attributes from search queries, like color, product type, brand, etc. Search engines rely on these attributes for ranking, advertising, and recommendation, etc. However, product search queries are usually short, three or four words on average. This information shortage limits the search engine’s power to provide high-quality services.

Haoming Jiang, Danqing Zhang, Tianyu Cao, Bing Yin, Tuo Zhao. Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2021.

Chen Liang, Simiao Zuo, Minshuo Chen, Haoming Jiang, Xiaodong Liu, Pengcheng He, Tuo Zhao, Weizhu Chen. Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2021.

Adversarial training provides a principled approach for training robust neural networks. From an optimization perspective, adversarial training is essentially solving a bilevel optimization problem. The leader problem is trying to learn a robust classifier, while the follower maximization is trying to generate adversarial samples. Unfortunately, such a bilevel problem is difficult to solve due to its highly complicated structure. This work proposes a new adversarial training method based on a generic learning-to-learn (L2L) framework. Specifically, instead of applying existing hand-designed algorithms for the inner problem, we learn an optimizer, which is parametrized as a convolutional neural network. At the same time, a robust classifier is learned to defense the adversarial attack generated by the learned optimizer. Experiments over CIFAR-10 and CIFAR-100 datasets demonstrate that L2L outperforms existing adversarial training methods in both classification accuracy and computational efficiency. Moreover, our L2L framework can be extended to generative adversarial imitation learning and stabilize the training.

Reliable automatic evaluation of dialogue systems under an interactive environment has long been overdue.An ideal environment for evaluating dialog systems, also known as the Turing test, needs to involve human interaction, which is usually not affordable for large scale experiments.Though researchers have attempted to use metrics for language generation tasks (e.g., perplexity, BLEU) or some model-based reinforcement learning methods (e.g., self-play evaluation) for automatic evaluation, these methods only show very weak correlation with the actual human evaluation in practice.To bridge such a gap, we propose a new framework named ENIGMA for estimating human evaluation scores based on recent advances of off-policy evaluation in reinforcement learning.ENIGMA only requires a handful of pre-collected experience data, and therefore does not involve human interaction with the target policy during the evaluation, making automatic evaluations feasible.More importantly, ENIGMA is model-free and agnostic to the behavior policies for collecting the experience data (see details in Section 2), which significantly alleviates the technical difficulties of modeling complex dialogue environments and human behaviors.Our experiments show that ENIGMA significantly outperforms existing methods in terms of correlation with human evaluation scores.

Adversarial regularization has been shown to improve the generalization performance of deep learning models in various natural language processing tasks.Existing works usually formulate the method as a zero-sum game, which is solved by alternating gradient descent/ascent algorithms.Such a formulation treats the adversarial and the defending players equally, which is undesirable because only the defending player contributes to the generalization performance.To address this issue, we propose Stackelberg Adversarial Regularization (SALT), which formulates adversarial regularization as a Stackelberg game.This formulation induces a competition between a leader and a follower, where the follower generates perturbations, and the leader trains the model subject to the perturbations.Different from conventional approaches, in SALT, the leader is in an advantageous position.When the leader moves, it recognizes the strategy of the follower and takes the anticipated follower's outcomes into consideration.Such a leader's advantage enables us to improve the model fitting to the unperturbed data.The leader's strategic information is captured by the Stackelberg gradient, which is obtained using an unrolling algorithm.Our experimental results on a set of machine translation and natural language understanding tasks show that SALT outperforms existing adversarial regularization baselines across all tasks.Our code is publicly available.

Yue Yu, Simiao Zuo, Haoming Jiang, Wendi Ren, Tuo Zhao, Chao Zhang. Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2021.

Transfer learning has fundamentally changed the landscape of natural language processing (NLP).Many state-of-the-art models are first pre-trained on a large text corpus and then fine-tuned on downstream tasks.However, due to limited data resources from downstream tasks and the extremely high complexity of pre-trained models, aggressive fine-tuning often causes the fine-tuned model to overfit the training data of downstream tasks and fail to generalize to unseen data.To address such an issue in a principled manner, we propose a new learning framework for robust and efficient fine-tuning for pre-trained models to attain better generalization performance.The proposed framework contains two important ingredients: 1. Smoothness-inducing regularization, which effectively manages the complexity of the model; 2. Bregman proximal point optimization, which is an instance of trustregion methods and can prevent aggressive updating.Our experiments show that the proposed framework achieves new state-of-the-art performance on a number of NLP tasks including GLUE, SNLI, SciTail and ANLI.Moreover, it also outperforms the state-of-the-art T5 model, which is the largest pre-trained model containing 11 billion parameters, on GLUE. 1

Many multi-domain neural machine translation (NMT) models achieve knowledge transfer by enforcing one encoder to learn shared embedding across domains.However, this design lacks adaptation to individual domains.To overcome this limitation, we propose a novel multi-domain NMT model using individual modules for each domain, on which we apply word-level, adaptive and layer-wise domain mixing.We first observe that words in a sentence are often related to multiple domains.Hence, we assume each word has a domain proportion, which indicates its domain preference.Then word representations are obtained by mixing their embedding in individual domains based on their domain proportions.We show this can be achieved by carefully designing multi-head dot-product attention modules for different domains, and eventually taking weighted averages of their parameters by word-level layer-wise domain proportions.Through this, we can achieve effective domain knowledge sharing, and capture fine-grained domain-specific knowledge as well.Our experiments show that our proposed model outperforms existing ones in several NMT tasks.

Fine-tuned pre-trained language models can suffer from severe miscalibration for both in-distribution and out-of-distribution (OOD) data due to over-parameterization.To mitigate this issue, we propose a regularized fine-tuning method.Our method introduces two types of regularization for better calibration: (1) On-manifold regularization, which generates pseudo on-manifold samples through interpolation within the data manifold.Augmented training with these pseudo samples imposes a smoothness regularization to improve in-distribution calibration.(2) Off-manifold regularization, which encourages the model to output uniform distributions for pseudo off-manifold samples to address the over-confidence issue for OOD data.Our experiments demonstrate that the proposed method outperforms existing calibration methods for text classification in terms of expectation calibration error, misclassification detection, and OOD detection on six datasets.Our code can be found at https://github.com/Lingkai-Kong/ Calibrated-BERT-Fine-Tuning.

Deep reinforcement learning (RL) has achieved great empirical successes in various domains. However, the large search space of neural networks requires a large amount of data, which makes the current RL algorithms not sample efficient. Motivated by the fact that many environments with continuous state space have smooth transitions, we propose to learn a smooth policy that behaves smoothly with respect to states. We develop a new framework — \textbf{S}mooth \textbf{R}egularized \textbf{R}einforcement \textbf{L}earning ($\textbf{SR}^2\textbf{L}$), where the policy is trained with smoothness-inducing regularization. Such regularization effectively constrains the search space, and enforces smoothness in the learned policy. Moreover, our proposed framework can also improve the robustness of policy against measurement error in the state space, and can be naturally extended to distribubutionally robust setting. We apply the proposed framework to both on-policy (TRPO) and off-policy algorithm (DDPG). Through extensive experiments, we demonstrate that our method achieves improved sample efficiency and robustness.

Modern data acquisition routinely produce massive amounts of event sequence data in various domains, such as social media, healthcare, and financial markets. These data often exhibit complicated short-term and long-term temporal dependencies. However, most of the existing recurrent neural network based point process models fail to capture such dependencies, and yield unreliable prediction performance. To address this issue, we propose a Transformer Hawkes Process (THP) model, which leverages the self-attention mechanism to capture long-term dependencies and meanwhile enjoys computational efficiency. Numerical experiments on various datasets show that THP outperforms existing models in terms of both likelihood and event prediction accuracy by a notable margin. Moreover, THP is quite general and can incorporate additional structural knowledge. We provide a concrete example, where THP achieves improved prediction performance for learning multiple point processes when incorporating their relational information.

We study the open-domain named entity recognition (NER) problem under distant supervision. The distant supervision, though does not require large amounts of manual annotations, yields highly incomplete and noisy distant labels via external knowledge bases. To address this challenge, we propose a new computational framework -- BOND, which leverages the power of pre-trained language models (e.g., BERT and RoBERTa) to improve the prediction performance of NER models. Specifically, we propose a two-stage training algorithm: In the first stage, we adapt the pre-trained language model to the NER tasks using the distant labels, which can significantly improve the recall and precision; In the second stage, we drop the distant labels, and propose a self-training approach to further improve the model performance. Thorough experiments on 5 benchmark datasets demonstrate the superiority of BOND over existing distantly supervised NER methods. The code and distantly labeled data have been released in https://github.com/cliang1453/BOND.

Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework called SPOT (Scalable Push-forward of Optimal Transport). Specifically, we approximate the optimal transport plan by a pushforward of a reference distribution, and cast the optimal transport problem into a minimax problem. We then can solve OT problems efficiently using primal dual stochastic gradient-type algorithms. We also show that we can recover the density of the optimal transport plan using neural ordinary differential equations. Numerical experiments on both synthetic and real datasets illustrate that SPOT is robust and has favorable convergence behavior. SPOT also allows us to efficiently sample from the optimal transport plan, which benefits downstream applications such as domain adaptation.

Deep neural networks have revolutionized many real world applications, due to their flexibility in data fitting and accurate predictions for unseen data. A line of research reveals that neural networks can approximate certain classes of functions with an arbitrary accuracy, while the size of the network scales exponentially with respect to the data dimension. Empirical results, however, suggest that networks of moderate size already yield appealing performance. To explain such a gap, a common belief is that many data sets exhibit low dimensional structures, and can be modeled as samples near a low dimensional manifold. In this paper, we prove that neural networks can efficiently approximate functions supported on low dimensional manifolds. The network size scales exponentially in the approximation error, with an exponent depending on the intrinsic dimension of the data and the smoothness of the function. Our result shows that exploiting low dimensional data structures can greatly enhance the efficiency in function approximation by neural networks. We also implement a sub-network that assigns input data to their corresponding local neighborhoods, which may be of independent interest.

This paper proposes a new meta-learning method -- named HARMLESS (HAwkes Relational Meta Learning method for Short Sequences) for learning heterogeneous point process models from a collection of short event sequence data along with a relational network. Specifically, we propose a hierarchical Bayesian mixture Hawkes process model, which naturally incorporates the relational information among sequences into point process modeling. Compared with existing methods, our model can capture the underlying mixed-community patterns of the relational network, which simultaneously encourages knowledge sharing among sequences and facilitates adaptively learning for each individual sequence. We further propose an efficient stochastic variational meta-EM algorithm, which can scale to large problems. Numerical experiments on both synthetic and real data show that HARMLESS outperforms existing methods in terms of predicting the future events.

We describe a new library named picasso, which implements a unified framework of pathwise coordinate optimization for a variety of sparse learning problems (e.g., sparse linear regression, sparse logistic regression, sparse Poisson regression and scaled sparse linear regression) combined with efficient active set selection strategies. Besides, the library allows users to choose different sparsity-inducing regularizers, including the convex $\ell_1$, nonvoncex MCP and SCAD regularizers. The library is coded in \texttt{C++} and has user-friendly R and Python wrappers. Numerical experiments demonstrate that picasso can scale up to large problems efficiently.

Abstract Scissor structures, which transform from a compact state to an expanded state, are widely used in various fields, ranging from architectural design to aerospace applications. We focus on a challenging problem that breaks through the restriction of planarity: to design scissor structures that expand from one given 3D shape to another 3D shape. To achieve this purpose, we propose a three‐step algorithm to construct a 3D scissor structure that realizes non‐uniform concentration between two different 3D curves. First, the input shapes are divided into scissor segments, which are composed of a sequence of planar scissor units based on the shape correspondence. Secondly, we compute the scissor unit geometry of each segment in a suggestive manner. Finally, the ball‐and‐socket joints with parameterized guide slits are integrated in order to connect the scissor segments, thereby completing the 3D deployment. Judging from a series of simulation and fabrication results, we demonstrate that our approach generates deployable structures for a wide range of 3D shape pairs.