Weiyang Liu

Longhui Yu, Weisen Jiang, Han Shi et al. · cambridge

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (e.g., LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called MetaMathQA. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (i.e., GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves 66.4% on GSM8K and 19.4% on MATH, exceeding the state-of-the-art models of the same size by 11.5% and 8.7%. Particularly, MetaMath-70B achieves an accuracy of 82.3% on GSM8K, slightly better than GPT-3.5-Turbo. We release all the MetaMathQA dataset, the MetaMath models with different model sizes and the training code for public use.

Weiyang Liu, Longhui Yu, Adrian Weller et al. · cambridge

The neural collapse (NC) phenomenon describes an underlying geometric symmetry for deep neural networks, where both deeply learned features and classifiers converge to a simplex equiangular tight frame. It has been shown that both cross-entropy loss and mean square error can provably lead to NC. We remove NC's key assumption on the feature dimension and the number of classes, and then present a generalized neural collapse (GNC) hypothesis that effectively subsumes the original NC. Inspired by how NC characterizes the training target of neural networks, we decouple GNC into two objectives: minimal intra-class variability and maximal inter-class separability. We then use hyperspherical uniformity (which characterizes the degree of uniformity on the unit hypersphere) as a unified framework to quantify these two objectives. Finally, we propose a general objective -- hyperspherical uniformity gap (HUG), which is defined by the difference between inter-class and intra-class hyperspherical uniformity. HUG not only provably converges to GNC, but also decouples GNC into two separate objectives. Unlike cross-entropy loss that couples intra-class compactness and inter-class separability, HUG enjoys more flexibility and serves as a good alternative loss function. Empirical results show that HUG works well in terms of generalization and robustness.

Zhen Liu, Yao Feng, Michael J. Black et al.

We consider the task of generating realistic 3D shapes, which is useful for a variety of applications such as automatic scene generation and physical simulation. Compared to other 3D representations like voxels and point clouds, meshes are more desirable in practice, because (1) they enable easy and arbitrary manipulation of shapes for relighting and simulation, and (2) they can fully leverage the power of modern graphics pipelines which are mostly optimized for meshes. Previous scalable methods for generating meshes typically rely on sub-optimal post-processing, and they tend to produce overly-smooth or noisy surfaces without fine-grained geometric details. To overcome these shortcomings, we take advantage of the graph structure of meshes and use a simple yet very effective generative modeling method to generate 3D meshes. Specifically, we represent meshes with deformable tetrahedral grids, and then train a diffusion model on this direct parametrization. We demonstrate the effectiveness of our model on multiple generative tasks.

Longhui Yu, Tianyang Hu, Lanqing Hong et al. · cambridge

It has been observed that neural networks perform poorly when the data or tasks are presented sequentially. Unlike humans, neural networks suffer greatly from catastrophic forgetting, making it impossible to perform life-long learning. To address this issue, memory-based continual learning has been actively studied and stands out as one of the best-performing methods. We examine memory-based continual learning and identify that large variation in the representation space is crucial for avoiding catastrophic forgetting. Motivated by this, we propose to diversify representations by using two types of perturbations: model-agnostic variation (i.e., the variation is generated without the knowledge of the learned neural network) and model-based variation (i.e., the variation is conditioned on the learned neural network). We demonstrate that enlarging representational variation serves as a general principle to improve continual learning. Finally, we perform empirical studies which demonstrate that our method, as a simple plug-and-play component, can consistently improve a number of memory-based continual learning methods by a large margin.

Xiaofeng Cao, Weiyang Liu, Ivor W. Tsang

Deep learning on large-scale data is dominant nowadays. The unprecedented scale of data has been arguably one of the most important driving forces for the success of deep learning. However, there still exist scenarios where collecting data or labels could be extremely expensive, e.g., medical imaging and robotics. To fill up this gap, this paper considers the problem of data-efficient learning from scratch using a small amount of representative data. First, we characterize this problem by active learning on homeomorphic tubes of spherical manifolds. This naturally generates feasible hypothesis class. With homologous topological properties, we identify an important connection -- finding tube manifolds is equivalent to minimizing hyperspherical energy (MHE) in physical geometry. Inspired by this connection, we propose a MHE-based active learning (MHEAL) algorithm, and provide comprehensive theoretical guarantees for MHEAL, covering convergence and generalization analysis. Finally, we demonstrate the empirical performance of MHEAL in a wide range of applications on data-efficient learning, including deep clustering, distribution matching, version space sampling and deep active learning.

Chen Zhang, Xiaofeng Cao, Weiyang Liu et al.

In this paper, we consider the problem of Iterative Machine Teaching (IMT), where the teacher provides examples to the learner iteratively such that the learner can achieve fast convergence to a target model. However, existing IMT algorithms are solely based on parameterized families of target models. They mainly focus on convergence in the parameter space, resulting in difficulty when the target models are defined to be functions without dependency on parameters. To address such a limitation, we study a more general task -- Nonparametric Iterative Machine Teaching (NIMT), which aims to teach nonparametric target models to learners in an iterative fashion. Unlike parametric IMT that merely operates in the parameter space, we cast NIMT as a functional optimization problem in the function space. To solve it, we propose both random and greedy functional teaching algorithms. We obtain the iterative teaching dimension (ITD) of the random teaching algorithm under proper assumptions, which serves as a uniform upper bound of ITD in NIMT. Further, the greedy teaching algorithm has a significantly lower ITD, which reaches a tighter upper bound of ITD in NIMT. Finally, we verify the correctness of our theoretical findings with extensive experiments in nonparametric scenarios.

Weiyang Liu, Zeju Qiu, Yao Feng et al.

Large foundation models are becoming ubiquitous, but training them from scratch is prohibitively expensive. Thus, efficiently adapting these powerful models to downstream tasks is increasingly important. In this paper, we study a principled finetuning paradigm -- Orthogonal Finetuning (OFT) -- for downstream task adaptation. Despite demonstrating good generalizability, OFT still uses a fairly large number of trainable parameters due to the high dimensionality of orthogonal matrices. To address this, we start by examining OFT from an information transmission perspective, and then identify a few key desiderata that enable better parameter-efficiency. Inspired by how the Cooley-Tukey fast Fourier transform algorithm enables efficient information transmission, we propose an efficient orthogonal parameterization using butterfly structures. We apply this parameterization to OFT, creating a novel parameter-efficient finetuning method, called Orthogonal Butterfly (BOFT). By subsuming OFT as a special case, BOFT introduces a generalized orthogonal finetuning framework. Finally, we conduct an extensive empirical study of adapting large vision transformers, large language models, and text-to-image diffusion models to various downstream tasks in vision and language.

Yandong Wen, Weiyang Liu, Yao Feng et al.

In this paper, we focus on a general yet important learning problem, pairwise similarity learning (PSL). PSL subsumes a wide range of important applications, such as open-set face recognition, speaker verification, image retrieval and person re-identification. The goal of PSL is to learn a pairwise similarity function assigning a higher similarity score to positive pairs (i.e., a pair of samples with the same label) than to negative pairs (i.e., a pair of samples with different label). We start by identifying a key desideratum for PSL, and then discuss how existing methods can achieve this desideratum. We then propose a surprisingly simple proxy-free method, called SimPLE, which requires neither feature/proxy normalization nor angular margin and yet is able to generalize well in open-set recognition. We apply the proposed method to three challenging PSL tasks: open-set face recognition, image retrieval and speaker verification. Comprehensive experimental results on large-scale benchmarks show that our method performs significantly better than current state-of-the-art methods.

Chen Zhang, Xiaofeng Cao, Weiyang Liu et al.

We study the problem of teaching multiple learners simultaneously in the nonparametric iterative teaching setting, where the teacher iteratively provides examples to the learner for accelerating the acquisition of a target concept. This problem is motivated by the gap between current single-learner teaching setting and the real-world scenario of human instruction where a teacher typically imparts knowledge to multiple students. Under the new problem formulation, we introduce a novel framework -- Multi-learner Nonparametric Teaching (MINT). In MINT, the teacher aims to instruct multiple learners, with each learner focusing on learning a scalar-valued target model. To achieve this, we frame the problem as teaching a vector-valued target model and extend the target model space from a scalar-valued reproducing kernel Hilbert space used in single-learner scenarios to a vector-valued space. Furthermore, we demonstrate that MINT offers significant teaching speed-up over repeated single-learner teaching, particularly when the multiple learners can communicate with each other. Lastly, we conduct extensive experiments to validate the practicality and efficiency of MINT.

Andi Zhang, Tim Z. Xiao, Weiyang Liu et al.

We revisit the likelihood ratio between a pretrained large language model (LLM) and its finetuned variant as a criterion for out-of-distribution (OOD) detection. The intuition behind such a criterion is that, the pretrained LLM has the prior knowledge about OOD data due to its large amount of training data, and once finetuned with the in-distribution data, the LLM has sufficient knowledge to distinguish their difference. Leveraging the power of LLMs, we show that, the likelihood ratio can serve as an effective OOD detection criterion. Moreover, we apply the proposed LLM-based likelihood ratio to detect OOD questions in question-answering (QA) systems, which can be used to improve the performance of specialized LLMs for general questions. Given that likelihood can be easily obtained by the loss functions within contemporary neural network frameworks, it is straightforward to implement this approach in practice. Since both the pretrained LLMs and its various finetuned models are widely available from online platforms such as Hugging Face, our proposed criterion can be effortlessly incorporated for OOD detection without the need for further training. We conduct comprehensive evaluation across on multiple settings, including far OOD, near OOD, spam detection, and QA scenarios, to demonstrate the effectiveness of the method. Code can be found at https://github.com/andiac/LLMOODratio

Zhen Liu, Tim Z. Xiao, Weiyang Liu et al. · mila

While one commonly trains large diffusion models by collecting datasets on target downstream tasks, it is often desired to align and finetune pretrained diffusion models with some reward functions that are either designed by experts or learned from small-scale datasets. Existing post-training methods for reward finetuning of diffusion models typically suffer from lack of diversity in generated samples, lack of prior preservation, and/or slow convergence in finetuning. In response to this challenge, we take inspiration from recent successes in generative flow networks (GFlowNets) and propose a reinforcement learning method for diffusion model finetuning, dubbed Nabla-GFlowNet (abbreviated as $\nabla$-GFlowNet), that leverages the rich signal in reward gradients for probabilistic diffusion finetuning. We show that our proposed method achieves fast yet diversity- and prior-preserving finetuning of Stable Diffusion, a large-scale text-conditioned image diffusion model, on different realistic reward functions.

Muchao Ye, Weiyang Liu, Pan He

The rapid advancement of vision-language models (VLMs) has established a new paradigm in video anomaly detection (VAD): leveraging VLMs to simultaneously detect anomalies and provide comprehendible explanations for the decisions. Existing work in this direction often assumes the complex reasoning required for VAD exceeds the capabilities of pretrained VLMs. Consequently, these approaches either incorporate specialized reasoning modules during inference or rely on instruction tuning datasets through additional training to adapt VLMs for VAD. However, such strategies often incur substantial computational costs or data annotation overhead. To address these challenges in explainable VAD, we introduce a verbalized learning framework named VERA that enables VLMs to perform VAD without model parameter modifications. Specifically, VERA automatically decomposes the complex reasoning required for VAD into reflections on simpler, more focused guiding questions capturing distinct abnormal patterns. It treats these reflective questions as learnable parameters and optimizes them through data-driven verbal interactions between learner and optimizer VLMs, using coarsely labeled training data. During inference, VERA embeds the learned questions into model prompts to guide VLMs in generating segment-level anomaly scores, which are then refined into frame-level scores via the fusion of scene and temporal contexts. Experimental results on challenging benchmarks demonstrate that the learned questions of VERA are highly adaptable, significantly improving both detection performance and explainability of VLMs for VAD.

Zeju Qiu, Weiyang Liu, Adrian Weller et al.

Orthogonal finetuning (OFT) offers highly parameter-efficient adaptation while preventing catastrophic forgetting, but its high runtime and memory demands limit practical deployment. We identify the core computational bottleneck in OFT as its weight-centric implementation, which relies on costly matrix-matrix multiplications with cubic complexity. To overcome this, we propose OFTv2, an input-centric reformulation that instead uses matrix-vector multiplications (i.e., matrix-free computation), reducing the computational cost to quadratic. We further introduce the Cayley-Neumann parameterization, an efficient orthogonal parameterization that approximates the matrix inversion in the Cayley transform via a truncated Neumann series. These modifications allow OFTv2 to achieve up to 10x faster training and 3x lower GPU memory usage without compromising performance. In addition, we extend OFTv2 to support finetuning quantized foundation models and show that it outperforms the popular QLoRA in training stability, efficiency, and memory usage.

Tim Z. Xiao, Johannes Zenn, Zhen Liu et al.

Large language models (LLMs) can often accurately describe probability distributions using natural language, yet they still struggle to generate faithful samples from them. This mismatch limits their use in tasks requiring reliable stochasticity, such as Monte Carlo methods, agent-based simulations, and randomized decision-making. We investigate this gap between knowledge and sampling in the context of Bernoulli distributions. We introduce Verbalized Rejection Sampling (VRS), a natural-language adaptation of classical rejection sampling that prompts the LLM to reason about and accept or reject proposed samples. Despite relying on the same Bernoulli mechanism internally, VRS substantially reduces sampling bias across models. We provide theoretical analysis showing that, under mild assumptions, VRS improves over direct sampling, with gains attributable to both the algorithm and prompt design. More broadly, our results show how classical probabilistic tools can be verbalized and embedded into LLM workflows to improve reliability, without requiring access to model internals or heavy prompt engineering.

Tim Z. Xiao, Robert Bamler, Bernhard Schölkopf et al.

Motivated by the progress made by large language models (LLMs), we introduce the framework of verbalized machine learning (VML). In contrast to conventional machine learning (ML) models that are typically optimized over a continuous parameter space, VML constrains the parameter space to be human-interpretable natural language. Such a constraint leads to a new perspective of function approximation, where an LLM with a text prompt can be viewed as a function parameterized by the text prompt. Guided by this perspective, we revisit classical ML problems, such as regression and classification, and find that these problems can be solved by an LLM-parameterized learner and optimizer. The major advantages of VML include (1) easy encoding of inductive bias: prior knowledge about the problem and hypothesis class can be encoded in natural language and fed into the LLM-parameterized learner; (2) automatic model class selection: the optimizer can automatically select a model class based on data and verbalized prior knowledge, and it can update the model class during training; and (3) interpretable learner updates: the LLM-parameterized optimizer can provide explanations for why an update is performed. We empirically verify the effectiveness of VML, and hope that VML can serve as a stepping stone to stronger interpretability.

Ilia Sucholutsky, Katherine M. Collins, Maya Malaviya et al.

A good teacher should not only be knowledgeable, but should also be able to communicate in a way that the student understands -- to share the student's representation of the world. In this work, we introduce a new controlled experimental setting, GRADE, to study pedagogy and representational alignment. We use GRADE through a series of machine-machine and machine-human teaching experiments to characterize a utility curve defining a relationship between representational alignment, teacher expertise, and student learning outcomes. We find that improved representational alignment with a student improves student learning outcomes (i.e., task accuracy), but that this effect is moderated by the size and representational diversity of the class being taught. We use these insights to design a preliminary classroom matching procedure, GRADE-Match, that optimizes the assignment of students to teachers. When designing machine teachers, our results suggest that it is important to focus not only on accuracy, but also on representational alignment with human learners.

Hanlin Zhang, Yi-Fan Zhang, Weiyang Liu et al.

A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data, in part due to spurious correlations. To tackle this challenge, we first formalize the OOD generalization problem as constrained optimization, called Disentanglement-constrained Domain Generalization (DDG). We relax this non-trivial constrained optimization problem to a tractable form with finite-dimensional parameterization and empirical approximation. Then a theoretical analysis of the extent to which the above transformations deviates from the original problem is provided. Based on the transformation, we propose a primal-dual algorithm for joint representation disentanglement and domain generalization. In contrast to traditional approaches based on domain adversarial training and domain labels, DDG jointly learns semantic and variation encoders for disentanglement, enabling flexible manipulation and augmentation on training data. DDG aims to learn intrinsic representations of semantic concepts that are invariant to nuisance factors and generalizable across domains. Comprehensive experiments on popular benchmarks show that DDG can achieve competitive OOD performance and uncover interpretable salient structures within data.

Weiyang Liu, Zhen Liu, James M. Rehg et al.

Inner product-based convolution has been the founding stone of convolutional neural networks (CNNs), enabling end-to-end learning of visual representation. By generalizing inner product with a bilinear matrix, we propose the neural similarity which serves as a learnable parametric similarity measure for CNNs. Neural similarity naturally generalizes the convolution and enhances flexibility. Further, we consider the neural similarity learning (NSL) in order to learn the neural similarity adaptively from training data. Specifically, we propose two different ways of learning the neural similarity: static NSL and dynamic NSL. Interestingly, dynamic neural similarity makes the CNN become a dynamic inference network. By regularizing the bilinear matrix, NSL can be viewed as learning the shape of kernel and the similarity measure simultaneously. We further justify the effectiveness of NSL with a theoretical viewpoint. Most importantly, NSL shows promising performance in visual recognition and few-shot learning, validating the superiority of NSL over the inner product-based convolution counterparts.

Yisen Wang, Weiyang Liu, Xingjun Ma et al.

Large-scale datasets possessing clean label annotations are crucial for training Convolutional Neural Networks (CNNs). However, labeling large-scale data can be very costly and error-prone, and even high-quality datasets are likely to contain noisy (incorrect) labels. Existing works usually employ a closed-set assumption, whereby the samples associated with noisy labels possess a true class contained within the set of known classes in the training data. However, such an assumption is too restrictive for many applications, since samples associated with noisy labels might in fact possess a true class that is not present in the training data. We refer to this more complex scenario as the \textbf{open-set noisy label} problem and show that it is nontrivial in order to make accurate predictions. To address this problem, we propose a novel iterative learning framework for training CNNs on datasets with open-set noisy labels. Our approach detects noisy labels and learns deep discriminative features in an iterative fashion. To benefit from the noisy label detection, we design a Siamese network to encourage clean labels and noisy labels to be dissimilar. A reweighting module is also applied to simultaneously emphasize the learning from clean labels and reduce the effect caused by noisy labels. Experiments on CIFAR-10, ImageNet and real-world noisy (web-search) datasets demonstrate that our proposed model can robustly train CNNs in the presence of a high proportion of open-set as well as closed-set noisy labels.

Weiyang Liu, Yan-Ming Zhang, Xingguo Li et al.

Convolution as inner product has been the founding basis of convolutional neural networks (CNNs) and the key to end-to-end visual representation learning. Benefiting from deeper architectures, recent CNNs have demonstrated increasingly strong representation abilities. Despite such improvement, the increased depth and larger parameter space have also led to challenges in properly training a network. In light of such challenges, we propose hyperspherical convolution (SphereConv), a novel learning framework that gives angular representations on hyperspheres. We introduce SphereNet, deep hyperspherical convolution networks that are distinct from conventional inner product based convolutional networks. In particular, SphereNet adopts SphereConv as its basic convolution operator and is supervised by generalized angular softmax loss - a natural loss formulation under SphereConv. We show that SphereNet can effectively encode discriminative representation and alleviate training difficulty, leading to easier optimization, faster convergence and comparable (even better) classification accuracy over convolutional counterparts. We also provide some theoretical insights for the advantages of learning on hyperspheres. In addition, we introduce the learnable SphereConv, i.e., a natural improvement over prefixed SphereConv, and SphereNorm, i.e., hyperspherical learning as a normalization method. Experiments have verified our conclusions.

Weiyang Liu, Bo Dai, Xingguo Li et al.

In this paper, we make an important step towards the black-box machine teaching by considering the cross-space machine teaching, where the teacher and the learner use different feature representations and the teacher can not fully observe the learner's model. In such scenario, we study how the teacher is still able to teach the learner to achieve faster convergence rate than the traditional passive learning. We propose an active teacher model that can actively query the learner (i.e., make the learner take exams) for estimating the learner's status and provably guide the learner to achieve faster convergence. The sample complexities for both teaching and query are provided. In the experiments, we compare the proposed active teacher with the omniscient teacher and verify the effectiveness of the active teacher model.

Weiyang Liu, Bo Dai, Ahmad Humayun et al.

In this paper, we consider the problem of machine teaching, the inverse problem of machine learning. Different from traditional machine teaching which views the learners as batch algorithms, we study a new paradigm where the learner uses an iterative algorithm and a teacher can feed examples sequentially and intelligently based on the current performance of the learner. We show that the teaching complexity in the iterative case is very different from that in the batch case. Instead of constructing a minimal training set for learners, our iterative machine teaching focuses on achieving fast convergence in the learner model. Depending on the level of information the teacher has from the learner model, we design teaching algorithms which can provably reduce the number of teaching examples and achieve faster convergence than learning without teachers. We also validate our theoretical findings with extensive experiments on different data distribution and real image datasets.