Chenxi Liu

Zhaoqi Leng, Mingxing Tan, Chenxi Liu et al.

Cross-entropy loss and focal loss are the most common choices when training deep neural networks for classification problems. Generally speaking, however, a good loss function can take on much more flexible forms, and should be tailored for different tasks and datasets. Motivated by how functions can be approximated via Taylor expansion, we propose a simple framework, named PolyLoss, to view and design loss functions as a linear combination of polynomial functions. Our PolyLoss allows the importance of different polynomial bases to be easily adjusted depending on the targeting tasks and datasets, while naturally subsuming the aforementioned cross-entropy loss and focal loss as special cases. Extensive experimental results show that the optimal choice within the PolyLoss is indeed dependent on the task and dataset. Simply by introducing one extra hyperparameter and adding one line of code, our Poly-1 formulation outperforms the cross-entropy loss and focal loss on 2D image classification, instance segmentation, object detection, and 3D object detection tasks, sometimes by a large margin.

Pei Sun, Mingxing Tan, Weiyue Wang et al.

3D object detection in point clouds is a core component for modern robotics and autonomous driving systems. A key challenge in 3D object detection comes from the inherent sparse nature of point occupancy within the 3D scene. In this paper, we propose Sparse Window Transformer (SWFormer ), a scalable and accurate model for 3D object detection, which can take full advantage of the sparsity of point clouds. Built upon the idea of window-based Transformers, SWFormer converts 3D points into sparse voxels and windows, and then processes these variable-length sparse windows efficiently using a bucketing scheme. In addition to self-attention within each spatial window, our SWFormer also captures cross-window correlation with multi-scale feature fusion and window shifting operations. To further address the unique challenge of detecting 3D objects accurately from sparse features, we propose a new voxel diffusion technique. Experimental results on the Waymo Open Dataset show our SWFormer achieves state-of-the-art 73.36 L2 mAPH on vehicle and pedestrian for 3D object detection on the official test set, outperforming all previous single-stage and two-stage models, while being much more efficient.

Chenxi Liu, Lixu Wang, Lingjuan Lyu et al.

In real-world applications, deep learning models often run in non-stationary environments where the target data distribution continually shifts over time. There have been numerous domain adaptation (DA) methods in both online and offline modes to improve cross-domain adaptation ability. However, these DA methods typically only provide good performance after a long period of adaptation, and perform poorly on new domains before and during adaptation - in what we call the "Unfamiliar Period", especially when domain shifts happen suddenly and significantly. On the other hand, domain generalization (DG) methods have been proposed to improve the model generalization ability on unadapted domains. However, existing DG works are ineffective for continually changing domains due to severe catastrophic forgetting of learned knowledge. To overcome these limitations of DA and DG in handling the Unfamiliar Period during continual domain shift, we propose RaTP, a framework that focuses on improving models' target domain generalization (TDG) capability, while also achieving effective target domain adaptation (TDA) capability right after training on certain domains and forgetting alleviation (FA) capability on past domains. RaTP includes a training-free data augmentation module to prepare data for TDG, a novel pseudo-labeling mechanism to provide reliable supervision for TDA, and a prototype contrastive alignment algorithm to align different domains for achieving TDG, TDA and FA. Extensive experiments on Digits, PACS, and DomainNet demonstrate that RaTP significantly outperforms state-of-the-art works from Continual DA, Source-Free DA, Test-Time/Online DA, Single DG, Multiple DG and Unified DA&DG in TDG, and achieves comparable TDA and FA capabilities.

Yingwei Li, Charles R. Qi, Yin Zhou et al.

Occluded and long-range objects are ubiquitous and challenging for 3D object detection. Point cloud sequence data provide unique opportunities to improve such cases, as an occluded or distant object can be observed from different viewpoints or gets better visibility over time. However, the efficiency and effectiveness in encoding long-term sequence data can still be improved. In this work, we propose MoDAR, using motion forecasting outputs as a type of virtual modality, to augment LiDAR point clouds. The MoDAR modality propagates object information from temporal contexts to a target frame, represented as a set of virtual points, one for each object from a waypoint on a forecasted trajectory. A fused point cloud of both raw sensor points and the virtual points can then be fed to any off-the-shelf point-cloud based 3D object detector. Evaluated on the Waymo Open Dataset, our method significantly improves prior art detectors by using motion forecasting from extra-long sequences (e.g. 18 seconds), achieving new state of the arts, while not adding much computation overhead.

Tong He, Pei Sun, Zhaoqi Leng et al.

We propose a late-to-early recurrent feature fusion scheme for 3D object detection using temporal LiDAR point clouds. Our main motivation is fusing object-aware latent embeddings into the early stages of a 3D object detector. This feature fusion strategy enables the model to better capture the shapes and poses for challenging objects, compared with learning from raw points directly. Our method conducts late-to-early feature fusion in a recurrent manner. This is achieved by enforcing window-based attention blocks upon temporally calibrated and aligned sparse pillar tokens. Leveraging bird's eye view foreground pillar segmentation, we reduce the number of sparse history features that our model needs to fuse into its current frame by 10$\times$. We also propose a stochastic-length FrameDrop training technique, which generalizes the model to variable frame lengths at inference for improved performance without retraining. We evaluate our method on the widely adopted Waymo Open Dataset and demonstrate improvement on 3D object detection against the baseline model, especially for the challenging category of large objects.

Wenqi Liang, Gan Sun, Chenxi Liu et al.

3D object detection has achieved significant performance in many fields, e.g., robotics system, autonomous driving, and augmented reality. However, most existing methods could cause catastrophic forgetting of old classes when performing on the class-incremental scenarios. Meanwhile, the current class-incremental 3D object detection methods neglect the relationships between the object localization information and category semantic information and assume all the knowledge of old model is reliable. To address the above challenge, we present a novel Incremental 3D Object Detection framework with the guidance of prompting, i.e., I3DOD. Specifically, we propose a task-shared prompts mechanism to learn the matching relationships between the object localization information and category semantic information. After training on the current task, these prompts will be stored in our prompt pool, and perform the relationship of old classes in the next task. Moreover, we design a reliable distillation strategy to transfer knowledge from two aspects: a reliable dynamic distillation is developed to filter out the negative knowledge and transfer the reliable 3D knowledge to new detection model; the relation feature is proposed to capture the responses relation in feature space and protect plasticity of the model when learning novel 3D classes. To the end, we conduct comprehensive experiments on two benchmark datasets and our method outperforms the state-of-the-art object detection methods by 0.6% - 2.7% in terms of mAP@0.25.

Tianyi Xiong, Yi Ge, Ming Li et al.

Large multimodal models (LMMs) are increasingly adopted as judges in multimodal evaluation systems due to their strong instruction following and consistency with human preferences. However, their ability to follow diverse, fine-grained evaluation criteria remains underexplored. We develop Multi-Crit, a benchmark for evaluating multimodal judges on their capacity to follow pluralistic criteria and produce reliable criterion-level judgments. Covering both open-ended generation and verifiable reasoning tasks, Multi-Crit is built through a rigorous data curation pipeline that gathers challenging response pairs with multi-criterion human annotations. It further introduces three novel metrics for systematically assessing pluralistic adherence, criterion-switching flexibility, and the ability to recognize criterion-level preference conflicts. Comprehensive analysis of 25 LMMs reveals that 1) proprietary models still struggle to maintain consistent adherence to pluralistic criteria--especially in open-ended evaluation; 2) open-source models lag further behind in flexibly following diverse criteria; and 3) critic fine-tuning with holistic judgment signals enhances visual grounding but fails to generalize to pluralistic criterion-level judgment. Additional analyses on reasoning fine-tuning, test-time scaling, and boundary consistency between open-source and proprietary models further probe the limits of current multimodal judges. As a pioneering study, Multi-Crit lays the foundation for building reliable and steerable multimodal AI evaluation.

Siyuan Qiao, Huiyu Wang, Chenxi Liu et al.

In this paper, we study normalization methods for neural networks from the perspective of elimination singularity. Elimination singularities correspond to the points on the training trajectory where neurons become consistently deactivated. They cause degenerate manifolds in the loss landscape which will slow down training and harm model performances. We show that channel-based normalizations (e.g. Layer Normalization and Group Normalization) are unable to guarantee a far distance from elimination singularities, in contrast with Batch Normalization which by design avoids models from getting too close to them. To address this issue, we propose BatchChannel Normalization (BCN), which uses batch knowledge to avoid the elimination singularities in the training of channel-normalized models. Unlike Batch Normalization, BCN is able to run in both large-batch and micro-batch training settings. The effectiveness of BCN is verified on many tasks, including image classification, object detection, instance segmentation, and semantic segmentation. The code is here: https://github.com/joe-siyuan-qiao/Batch-Channel-Normalization.

Ruibo Chen, Yihan Wu, Lichang Chen et al.

Data selection in instruction tuning emerges as a pivotal process for acquiring high-quality data and training instruction-following large language models (LLMs), but it is still a new and unexplored research area for vision-language models (VLMs). Existing data selection approaches on LLMs either rely on single unreliable scores, or use downstream tasks for selection, which is time-consuming and can lead to potential over-fitting on the chosen evaluation datasets. To address this challenge, we introduce a novel dataset selection method, Self-Filter, that utilizes the VLM itself as a filter. This approach is inspired by the observation that VLMs benefit from training with the most challenging instructions. Self-Filter operates in two stages. In the first stage, we devise a scoring network to evaluate the difficulty of training instructions, which is co-trained with the VLM. In the second stage, we use the trained score net to measure the difficulty of each instruction, select the most challenging samples, and penalize similar samples to encourage diversity. Comprehensive experiments on LLaVA and MiniGPT-4 show that Self-Filter can reach better results compared to full data settings with merely about 15% samples, and can achieve superior performance against competitive baselines.

Chenxi Liu, Gan Sun, Wenqi Liang et al.

Pre-trained large text-to-image (T2I) models with an appropriate text prompt has attracted growing interests in customized images generation field. However, catastrophic forgetting issue make it hard to continually synthesize new user-provided styles while retaining the satisfying results amongst learned styles. In this paper, we propose MuseumMaker, a method that enables the synthesis of images by following a set of customized styles in a never-end manner, and gradually accumulate these creative artistic works as a Museum. When facing with a new customization style, we develop a style distillation loss module to extract and learn the styles of the training data for new image generation. It can minimize the learning biases caused by content of new training images, and address the catastrophic overfitting issue induced by few-shot images. To deal with catastrophic forgetting amongst past learned styles, we devise a dual regularization for shared-LoRA module to optimize the direction of model update, which could regularize the diffusion model from both weight and feature aspects, respectively. Meanwhile, to further preserve historical knowledge from past styles and address the limited representability of LoRA, we consider a task-wise token learning module where a unique token embedding is learned to denote a new style. As any new user-provided style come, our MuseumMaker can capture the nuances of the new styles while maintaining the details of learned styles. Experimental results on diverse style datasets validate the effectiveness of our proposed MuseumMaker method, showcasing its robustness and versatility across various scenarios.

Chenxi Liu, Towaki Takikawa, Alec Jacobson

Recent advances in diffusion models and parameter-efficient fine-tuning (PEFT) have made text-to-image generation and customization widely accessible, with Low Rank Adaptation (LoRA) able to replicate an artist's style or subject using minimal data and computation. In this paper, we examine the relationship between LoRA weights and artistic styles, demonstrating that LoRA weights alone can serve as an effective descriptor of style, without the need for additional image generation or knowledge of the original training set. Our findings show that LoRA weights yield better performance in clustering of artistic styles compared to traditional pre-trained features, such as CLIP and DINO, with strong structural similarities between LoRA-based and conventional image-based embeddings observed both qualitatively and quantitatively. We identify various retrieval scenarios for the growing collection of customized models and show that our approach enables more accurate retrieval in real-world settings where knowledge of the training images is unavailable and additional generation is required. We conclude with a discussion on potential future applications, such as zero-shot LoRA fine-tuning and model attribution.

Shucheng Zhang, Yan Shi, Bingzhang Wang et al.

Ensuring the safety of vulnerable road users (VRUs), such as pedestrians and cyclists, remains a critical global challenge, as conventional infrastructure-based measures often prove inadequate in dynamic urban environments. Recent advances in artificial intelligence (AI), particularly in visual perception and reasoning, open new opportunities for proactive and context-aware VRU protection. However, existing surveys on AI applications for VRUs predominantly focus on detection, offering limited coverage of other vision-based tasks that are essential for comprehensive VRU understanding and protection. This paper presents a state-of-the-art review of recent progress in camera-based AI sensing systems for VRU safety, with an emphasis on developments from the past five years and emerging research trends. We systematically examine four core tasks, namely detection and classification, tracking and reidentification, trajectory prediction, and intent recognition and prediction, which together form the backbone of AI-empowered proactive solutions for VRU protection in intelligent transportation systems. To guide future research, we highlight four major open challenges from the perspectives of data, model, and deployment. By linking advances in visual AI with practical considerations for real-world implementation, this survey aims to provide a foundational reference for the development of next-generation sensing systems to enhance VRU safety.

Jihua Peng, Qianxiong Xu, Yichen Liu et al.

Group activity detection (GAD) aims to simultaneously identify group members and categorize their collective activities within video sequences. Existing deep learning-based methods develop specialized architectures (e.g., transformer networks) to model the dynamics of individual roles and semantic dependencies between individuals and groups. However, they rely solely on implicit pattern recognition from visual features and struggle with contextual reasoning and explainability. In this work, we propose LIR-GAD, a novel framework of language-instructed reasoning for GAD via Multimodal Large Language Model (MLLM). Our approach expand the original vocabulary of MLLM by introducing an activity-level <ACT> token and multiple cluster-specific <GROUP> tokens. We process video frames alongside two specially designed tokens and language instructions, which are then integrated into the MLLM. The pretrained commonsense knowledge embedded in the MLLM enables the <ACT> token and <GROUP> tokens to effectively capture the semantic information of collective activities and learn distinct representational features of different groups, respectively. Also, we introduce a multi-label classification loss to further enhance the <ACT> token's ability to learn discriminative semantic representations. Then, we design a Multimodal Dual-Alignment Fusion (MDAF) module that integrates MLLM's hidden embeddings corresponding to the designed tokens with visual features, significantly enhancing the performance of GAD. Both quantitative and qualitative experiments demonstrate the superior performance of our proposed method in GAD taks.

Lichang Chen, Jiuhai Chen, Chenxi Liu et al.

Reinforcement learning with human feedback~(RLHF) is critical for aligning Large Language Models (LLMs) with human preference. Compared to the widely studied offline version of RLHF, \emph{e.g.} direct preference optimization (DPO), recent works have shown that the online variants achieve even better alignment. However, online alignment requires on-the-fly generation of new training data, which is costly, hard to parallelize, and suffers from varying quality and utility. In this paper, we propose a more efficient data exploration strategy for online preference tuning (OPTune), which does not rely on human-curated or pre-collected teacher responses but dynamically samples informative responses for on-policy preference alignment. During data generation, OPTune only selects prompts whose (re)generated responses can potentially provide more informative and higher-quality training signals than the existing responses. In the training objective, OPTune reweights each generated response (pair) by its utility in improving the alignment so that learning can be focused on the most helpful samples. Throughout our evaluations, OPTune'd LLMs maintain the instruction-following benefits provided by standard preference tuning whilst enjoying 1.27-1.56x faster training speed due to the efficient data exploration strategy.

Chenxi Liu, Zhenyi Wang, Tianyi Xiong et al.

Few-Shot Class-Incremental Learning (FSCIL) models aim to incrementally learn new classes with scarce samples while preserving knowledge of old ones. Existing FSCIL methods usually fine-tune the entire backbone, leading to overfitting and hindering the potential to learn new classes. On the other hand, recent prompt-based CIL approaches alleviate forgetting by training prompts with sufficient data in each task. In this work, we propose a novel framework named Attention-aware Self-adaptive Prompt (ASP). ASP encourages task-invariant prompts to capture shared knowledge by reducing specific information from the attention aspect. Additionally, self-adaptive task-specific prompts in ASP provide specific information and transfer knowledge from old classes to new classes with an Information Bottleneck learning objective. In summary, ASP prevents overfitting on base task and does not require enormous data in few-shot incremental tasks. Extensive experiments on three benchmark datasets validate that ASP consistently outperforms state-of-the-art FSCIL and prompt-based CIL methods in terms of both learning new classes and mitigating forgetting.

Chenxi Liu, Piotr Dollár, Kaiming He et al.

Existing neural network architectures in computer vision -- whether designed by humans or by machines -- were typically found using both images and their associated labels. In this paper, we ask the question: can we find high-quality neural architectures using only images, but no human-annotated labels? To answer this question, we first define a new setup called Unsupervised Neural Architecture Search (UnNAS). We then conduct two sets of experiments. In sample-based experiments, we train a large number (500) of diverse architectures with either supervised or unsupervised objectives, and find that the architecture rankings produced with and without labels are highly correlated. In search-based experiments, we run a well-established NAS algorithm (DARTS) using various unsupervised objectives, and report that the architectures searched without labels can be competitive to their counterparts searched with labels. Together, these results reveal the potentially surprising finding that labels are not necessary, and the image statistics alone may be sufficient to identify good neural architectures.

Michelle Shu, Chenxi Liu, Weichao Qiu et al.

Machine learning models are usually evaluated according to the average case performance on the test set. However, this is not always ideal, because in some sensitive domains (e.g. autonomous driving), it is the worst case performance that matters more. In this paper, we are interested in systematic exploration of the input data space to identify the weakness of the model to be evaluated. We propose to use an adversarial examiner in the testing stage. Different from the existing strategy to always give the same (distribution of) test data, the adversarial examiner will dynamically select the next test data to hand out based on the testing history so far, with the goal being to undermine the model's performance. This sequence of test data not only helps us understand the current model, but also serves as constructive feedback to help improve the model in the next iteration. We conduct experiments on ShapeNet object classification. We show that our adversarial examiner can successfully put more emphasis on the weakness of the model, preventing performance estimates from being overly optimistic.

Siyuan Qiao, Huiyu Wang, Chenxi Liu et al.

Batch Normalization (BN) has become an out-of-box technique to improve deep network training. However, its effectiveness is limited for micro-batch training, i.e., each GPU typically has only 1-2 images for training, which is inevitable for many computer vision tasks, e.g., object detection and semantic segmentation, constrained by memory consumption. To address this issue, we propose Weight Standardization (WS) and Batch-Channel Normalization (BCN) to bring two success factors of BN into micro-batch training: 1) the smoothing effects on the loss landscape and 2) the ability to avoid harmful elimination singularities along the training trajectory. WS standardizes the weights in convolutional layers to smooth the loss landscape by reducing the Lipschitz constants of the loss and the gradients; BCN combines batch and channel normalizations and leverages estimated statistics of the activations in convolutional layers to keep networks away from elimination singularities. We validate WS and BCN on comprehensive computer vision tasks, including image classification, object detection, instance segmentation, video recognition and semantic segmentation. All experimental results consistently show that WS and BCN improve micro-batch training significantly. Moreover, using WS and BCN with micro-batch training is even able to match or outperform the performances of BN with large-batch training.

Chenxi Liu, Liang-Chieh Chen, Florian Schroff et al.

Recently, Neural Architecture Search (NAS) has successfully identified neural network architectures that exceed human designed ones on large-scale image classification. In this paper, we study NAS for semantic image segmentation. Existing works often focus on searching the repeatable cell structure, while hand-designing the outer network structure that controls the spatial resolution changes. This choice simplifies the search space, but becomes increasingly problematic for dense image prediction which exhibits a lot more network level architectural variations. Therefore, we propose to search the network level structure in addition to the cell level structure, which forms a hierarchical architecture search space. We present a network level search space that includes many popular designs, and develop a formulation that allows efficient gradient-based architecture search (3 P100 GPU days on Cityscapes images). We demonstrate the effectiveness of the proposed method on the challenging Cityscapes, PASCAL VOC 2012, and ADE20K datasets. Auto-DeepLab, our architecture searched specifically for semantic image segmentation, attains state-of-the-art performance without any ImageNet pretraining.

Runtao Liu, Chenxi Liu, Yutong Bai et al.

Referring object detection and referring image segmentation are important tasks that require joint understanding of visual information and natural language. Yet there has been evidence that current benchmark datasets suffer from bias, and current state-of-the-art models cannot be easily evaluated on their intermediate reasoning process. To address these issues and complement similar efforts in visual question answering, we build CLEVR-Ref+, a synthetic diagnostic dataset for referring expression comprehension. The precise locations and attributes of the objects are readily available, and the referring expressions are automatically associated with functional programs. The synthetic nature allows control over dataset bias (through sampling strategy), and the modular programs enable intermediate reasoning ground truth without human annotators. In addition to evaluating several state-of-the-art models on CLEVR-Ref+, we also propose IEP-Ref, a module network approach that significantly outperforms other models on our dataset. In particular, we present two interesting and important findings using IEP-Ref: (1) the module trained to transform feature maps into segmentation masks can be attached to any intermediate module to reveal the entire reasoning process step-by-step; (2) even if all training data has at least one object referred, IEP-Ref can correctly predict no-foreground when presented with false-premise referring expressions. To the best of our knowledge, this is the first direct and quantitative proof that neural modules behave in the way they are intended.

Chenxi Liu, Barret Zoph, Maxim Neumann et al.

We propose a new method for learning the structure of convolutional neural networks (CNNs) that is more efficient than recent state-of-the-art methods based on reinforcement learning and evolutionary algorithms. Our approach uses a sequential model-based optimization (SMBO) strategy, in which we search for structures in order of increasing complexity, while simultaneously learning a surrogate model to guide the search through structure space. Direct comparison under the same search space shows that our method is up to 5 times more efficient than the RL method of Zoph et al. (2018) in terms of number of models evaluated, and 8 times faster in terms of total compute. The structures we discover in this way achieve state of the art classification accuracies on CIFAR-10 and ImageNet.

Xiaohui Zeng, Chenxi Liu, Yu-Siang Wang et al.

Generating adversarial examples is an intriguing problem and an important way of understanding the working mechanism of deep neural networks. Most existing approaches generated perturbations in the image space, i.e., each pixel can be modified independently. However, in this paper we pay special attention to the subset of adversarial examples that correspond to meaningful changes in 3D physical properties (like rotation and translation, illumination condition, etc.). These adversaries arguably pose a more serious concern, as they demonstrate the possibility of causing neural network failure by easy perturbations of real-world 3D objects and scenes. In the contexts of object classification and visual question answering, we augment state-of-the-art deep neural networks that receive 2D input images with a rendering module (either differentiable or not) in front, so that a 3D scene (in the physical space) is rendered into a 2D image (in the image space), and then mapped to a prediction (in the output space). The adversarial perturbations can now go beyond the image space, and have clear meanings in the 3D physical world. Though image-space adversaries can be interpreted as per-pixel albedo change, we verify that they cannot be well explained along these physically meaningful dimensions, which often have a non-local effect. But it is still possible to successfully attack beyond the image space on the physical space, though this is more difficult than image-space attacks, reflected in lower success rates and heavier perturbations required.

Siyuan Qiao, Chenxi Liu, Wei Shen et al.

In this paper, we are interested in the few-shot learning problem. In particular, we focus on a challenging scenario where the number of categories is large and the number of examples per novel category is very limited, e.g. 1, 2, or 3. Motivated by the close relationship between the parameters and the activations in a neural network associated with the same category, we propose a novel method that can adapt a pre-trained neural network to novel categories by directly predicting the parameters from the activations. Zero training is required in adaptation to novel categories, and fast inference is realized by a single forward pass. We evaluate our method by doing few-shot image recognition on the ImageNet dataset, which achieves the state-of-the-art classification accuracy on novel categories by a significant margin while keeping comparable performance on the large-scale categories. We also test our method on the MiniImageNet dataset and it strongly outperforms the previous state-of-the-art methods.

Siyuan Qiao, Wei Shen, Weichao Qiu et al.

Motivated by product detection in supermarkets, this paper studies the problem of object proposal generation in supermarket images and other natural images. We argue that estimation of object scales in images is helpful for generating object proposals, especially for supermarket images where object scales are usually within a small range. Therefore, we propose to estimate object scales of images before generating object proposals. The proposed method for predicting object scales is called ScaleNet. To validate the effectiveness of ScaleNet, we build three supermarket datasets, two of which are real-world datasets used for testing and the other one is a synthetic dataset used for training. In short, we extend the previous state-of-the-art object proposal methods by adding a scale prediction phase. The resulted method outperforms the previous state-of-the-art on the supermarket datasets by a large margin. We also show that the approach works for object proposal on other natural images and it outperforms the previous state-of-the-art object proposal methods on the MS COCO dataset. The supermarket datasets, the virtual supermarkets, and the tools for creating more synthetic datasets will be made public.

Yan Wang, Lingxi Xie, Chenxi Liu et al.

In this paper, we reveal the importance and benefits of introducing second-order operations into deep neural networks. We propose a novel approach named Second-Order Response Transform (SORT), which appends element-wise product transform to the linear sum of a two-branch network module. A direct advantage of SORT is to facilitate cross-branch response propagation, so that each branch can update its weights based on the current status of the other branch. Moreover, SORT augments the family of transform operations and increases the nonlinearity of the network, making it possible to learn flexible functions to fit the complicated distribution of feature space. SORT can be applied to a wide range of network architectures, including a branched variant of a chain-styled network and a residual network, with very light-weighted modifications. We observe consistent accuracy gain on both small (CIFAR10, CIFAR100 and SVHN) and big (ILSVRC2012) datasets. In addition, SORT is very efficient, as the extra computation overhead is less than 5%.