June 12, 2023
By Natasha Ali
Vector Faculty Members and Faculty Affiliates had a number of papers accepted at the 2023 proceedings of the International Conference on Learning Representations (ICLR). The annual event was held from May 1 to May 5 and featured presentations and workshops from deep learning researchers around the world.
Among the 21 papers from Vector Faculty and Faculty Affiliates was new work and novel approaches in the areas of automated language processing, predictive AI, and reinforcement learning.
Vector Faculty Member Jimmy Ba, co-authored “Large Language Models are Human-Level Prompt Engineers,” which proposes a novel algorithm that automatically generates instructions using natural language input. Called Automatic Prompt Engineering, it lets researchers program large language models (LLMs) to process human commands, create a list of potentially relevant instructions, and choose the most compatible instruction model. This method allows LLMs to process human language more precisely and execute the desired instructions. Their ultimate goal is to facilitate human-machine interaction and achieve human-level performance with text generation models.
Also accepted to this year’s conference was Pascal Poupart’s paper “Benchmarking Constraint Inference in Inverse Reinforcement Learning.” This paper highlights the importance of gathering experimental data to develop machine learning models that mimic human behaviour. To create accurate depictions of real-life scenarios, researchers created a human run simulator that included realistic components and obstacles. Exploring the prospects of AI in automated driving, they developed a highway driving simulation and recruited human agents to perform controlled demonstrations. By observing human response to constraints and obstacles in real-world driving conditions, they collected practical data to develop a machine learning algorithm. Through Inverse Constrained Reinforcement Learning (ICRL), the algorithm was trained to recognize patterns in human behaviour and avoid environmental constraints accordingly. By rewarding behaviour that mimics experimental data, they reinforced human-like behaviour and developed effective ICRL models.
Below are abstracts for each of the papers co-authored by Vector Faculty and Faculty Affiliates accepted at this year’s ICLR.
Benchmarking Constraint Inference in Inverse Reinforcement Learning
Guiliang Liu, Yudong Luo, Ashish Gaurav, Kasra Rezaee, Pascal Poupart
When deploying Reinforcement Learning (RL) agents into a physical system, we must ensure that these agents are well aware of the underlying constraints. In many real-world problems, however, the constraints are often hard to specify mathematically and unknown to the RL agents. To tackle these issues, Inverse Constrained Reinforcement Learning (ICRL) empirically estimates constraints from expert demonstrations. As an emerging research topic, ICRL does not have common benchmarks, and previous works tested algorithms under hand-crafted environments with manually-generated expert demonstrations. In this paper, we construct an ICRL benchmark in the context of RL application domains, including robot control, and autonomous driving. For each environment, we design relevant constraints and train expert agents to generate demonstration data. Besides, unlike existing baselines that learn a deterministic constraint, we propose a variational ICRL method to model a posterior distribution of candidate constraints. We conduct extensive experiments on these algorithms under our benchmark and show how they can facilitate studying important research challenges for ICRL.
Casual Balancing for Domain Generalization
Xinyi Wang, Michael Saxon, Jiachen Li, Hongyang Zhang, Kun Zhang, William Yang Wang
While machine learning models rapidly advance the state-of-the-art on various real-world tasks, out-of-domain (OOD) generalization remains a challenging problem given the vulnerability of these models to spurious correlations. We propose a balanced mini-batch sampling strategy to transform a biased data distribution into a spurious-free balanced distribution, based on the invariance of the underlying causal mechanisms for the data generation process. We argue that the Bayes optimal classifiers trained on such balanced distribution are minimax optimal across a diverse enough environment space. We also provide an identifiability guarantee of the latent variable model of the proposed data generation process, when utilizing enough train environments. Experiments are conducted on DomainBed, demonstrating empirically that our method obtains the best performance across 20 baselines reported on the benchmark.
Confidential-PROFITT: Confidential PROof of FaIr Training of Trees
Ali Shahin Shamsabadi, Sierra Calanda Wyllie, Nicholas Franzese, Natalie Dullerud, Sébastien Gambs, Nicolas Papernot, Xiao Wang, Adrian Weller
Post hoc auditing of model fairness suffers from potential drawbacks: (1) auditing may be highly sensitive to the test samples chosen; (2) the model and/or its training data may need to be shared with an auditor thereby breaking confidentiality. We address these issues by instead providing a certificate that demonstrates that the learning algorithm itself is fair, and hence, as a consequence, so too is the trained model. We introduce a method to provide a confidential proof of fairness for training, in the context of widely used decision trees, which we term Confidential-PROFITT. We propose novel fair decision tree learning algorithms along with customized zero-knowledge proof protocols to obtain a proof of fairness that can be audited by a third party. Using zero-knowledge proofs enables us to guarantee confidentiality of both the model and its training data. We show empirically that bounding the information gain of each node with respect to the sensitive attributes reduces the unfairness of the final tree. In extensive experiments on the COMPAS, Communities and Crime, Default Credit, and Adult datasets, we demonstrate that a company can use Confidential-PROFITT to certify the fairness of their decision tree to an auditor in less than 2 minutes, thus indicating the applicability of our approach. This is true for both the demographic parity and equalized odds definitions of fairness. Finally, we extend Confidential-PROFITT to apply to ensembles of trees.
Conservative Bayesian Model-Based Value Expansion for Offline
Jihwan Jeong, Xiaoyu Wang, Michael Gimelfarb, Hyunwoo Kim, Baher abdulhai, Scott Sanner
Offline reinforcement learning (RL) addresses the problem of learning a performant policy from a fixed batch of data collected by following some behavior policy. Model-based approaches are particularly appealing in the offline setting since they can extract more learning signals from the logged dataset by learning a model of the environment. However, the performance of existing model-based approaches falls short of model-free counterparts, due to the compounding of estimation errors in the learned model. Driven by this observation, we argue that it is critical for a model-based method to understand when to trust the model and when to rely on model-free estimates, and how to act conservatively w.r.t. both. To this end, we derive an elegant and simple methodology called conservative Bayesian model-based value expansion for offline policy optimization (CBOP), that trades off model-free and model-based estimates during the policy evaluation step according to their epistemic uncertainties, and facilitates conservatism by taking a lower bound on the Bayesian posterior value estimate. On the standard D4RL continuous control tasks, we find that our method significantly outperforms previous model-based approaches: e.g., MOPO by 116.4%, MOReL by 23.2% and COMBO by 23.7%. Further, CBOP achieves state-of-the-art performance on 11 out of 18 benchmark datasets while doing on par on the remaining datasets.
Contrastive Learning Can Find An Optimal Basis For Approximately
Daniel D. Johnson, Ayoub El Hanchi, Chris J. Maddison
Contrastive learning is a powerful framework for learning self-supervised representations that generalize well to downstream supervised tasks. We show that multiple existing contrastive learning methods can be reinterpreted as learning a positive-definite kernel that approximates a particular *contrastive kernel* defined by the positive pairs. The principal components of the data under this kernel exactly correspond to the eigenfunctions of a positive-pair Markov chain, and these eigenfunctions can be used to build a representation that provably minimizes the worst-case approximation error of linear predictors under the assumption that positive pairs have similar labels. We give generalization bounds for downstream linear prediction using this optimal representation, and show how to approximate this representation using kernel PCA. We also explore kernel-based representations on a noisy MNIST task for which the positive pair distribution has a closed form, and compare the properties of the true eigenfunctions with their learned approximations.
Instance-wise Batch Label Restoration via Gradients in Federated
Kailang Ma, Yu Sun, Jian Cui, Dawei Li, Zhenyu Guan, Jianwei Liu
Gradient inversion attacks have posed a serious threat to the privacy of federated learning. The attacks search for the optimal pair of input and label best matching the shared gradients and the search space of the attacks can be reduced by pre-restoring labels. Recently, label restoration technique allows for the extraction of labels from gradients analytically, but even the state-of-the-art remains limited to identify the presence of categories (i.e., the class-wise label restoration). This work considers the more real-world settings, where there are multiple instances of each class in a training batch. An analytic method is proposed to perform instance-wise batch label restoration from only the gradient of the final layer. On the basis of the approximate recovered class-wise embeddings and post-softmax probabilities, we establish linear equations of the gradients, probabilities and labels to derive the Number of Instances (NoI) per class by the Moore-Penrose pseudoinverse algorithm. Our experimental evaluations reach over 99% Label existence Accuracy (LeAcc) and exceed 96% Label number Accuracy (LnAcc) in most cases on three image datasets and four classification models. The two metrics are used to evaluate class-wise and instance-wise label restoration accuracy, respectively. And the recovery is made feasible even with a batch size of 4096 and partially negative activations (e.g., Leaky ReLU and Swish). Furthermore, we demonstrate that our method facilitates the existing gradient inversion attacks by exploiting the recovered labels, with an increase of 6-7 in PSNR on both MNIST and CIFAR100.
Large Language Models are Human-Level Prompt Engineers
Yongchao Zhou, Andrei Ioan Muresanu, Ziwen Han, Keiran Paster, Silviu Pitis, Harris Chan, Jimmy Ba
By conditioning on natural language instructions, large language models (LLMs) have displayed impressive capabilities as general-purpose computers. However, task performance depends significantly on the quality of the prompt used to steer the model, and most effective prompts have been handcrafted by humans. Inspired by classical program synthesis and the human approach to prompt engineering, we propose Automatic Prompt Engineer (APE) for automatic instruction generation and selection. In our method, we treat the instruction as the “program,” optimized by searching over a pool of instruction candidates proposed by an LLM in order to maximize a chosen score function. To evaluate the quality of the selected instruction, we evaluate the zero-shot performance of another LLM following the selected instruction. Experiments on 24 NLP tasks show that our automatically generated instructions outperform the prior LLM baseline by a large margin and achieve better or comparable performance to the instructions generated by human annotators on 21/24 tasks. We conduct extensive qualitative and quantitative analyses to explore the performance of APE. We show that APE-engineered prompts can be applied to steer models toward truthfulness and/or informativeness, as well as to improve few-shot learning performance by simply prepending them to standard in-context learning prompts.
Learning Achievement Structure for Structured Exploration in
Zihan Zhou, Animesh Garg
We propose Structured Exploration with Achievements (SEA), a multi-stage reinforcement learning algorithm designed for achievement-based environments, a particular type of environment with an internal achievement set. SEA first uses offline data to learn a representation of the known achievements with a determinant loss function, then recovers the dependency graph of the learned achievements with a heuristic algorithm, and finally interacts with the environment online to learn policies that master known achievements and explore new ones with a controller built with the recovered dependency graph. We empirically demonstrate that SEA can recover the achievement structure accurately and improve exploration in hard domains such as Crafter that are procedurally generated with high-dimensional observations like images.
Learning Soft Constraints From Constrained Expert Demonstrations
Ashish Gaurav, Kasra Rezaee, Guiliang Liu, Pascal Poupart
Inverse reinforcement learning (IRL) methods assume that the expert data is generated by an agent optimizing some reward function. However, in many settings, the agent may optimize a reward function subject to some constraints, where the constraints induce behaviors that may be otherwise difficult to express with just a reward function. We consider the setting where the reward function is given, and the constraints are unknown, and propose a method that is able to recover these constraints satisfactorily from the expert data. While previous work has focused on recovering hard constraints, our method can recover cumulative soft constraints that the agent satisfies on average per episode. In IRL fashion, our method solves this problem by adjusting the constraint function iteratively through a constrained optimization procedure, until the agent behavior matches the expert behavior. We demonstrate our approach on synthetic environments, robotics environments and real world highway driving scenarios.
Measuring Forgetting of Memorized Training Examples
Matthew Jagielski, Om Thakkar, Florian Tramer, Daphne Ippolito, Katherine Lee, Nicholas Carlini, Eric Wallace, Shuang Song, Abhradeep Guha Thakurta, Nicolas Papernot, Chiyuan Zhang
Machine learning models exhibit two seemingly contradictory phenomena: training data memorization and various forms of forgetting. In memorization, models overfit specific training examples and become susceptible to privacy attacks. In forgetting, examples which appeared early in training are forgotten by the end. In this work, we connect these phenomena. We propose a technique to measure to what extent models “forget” the specifics of training examples, becoming less susceptible to privacy attacks on examples they have not seen recently. We show that, while non-convexity can prevent forgetting from happening in the worst-case, standard image,speech, and language models empirically do forget examples over time. We identify nondeterminism as a potential explanation, showing that deterministically trained models do not forget. Our results suggest that examples seen early when training with extremely large datasets—for instance those examples used to pre-train a model—may observe privacy benefits at the expense of examples seen later.
Metadata Archaeology: Unearthing Data Subsets by Leveraging
Shoaib Ahmed Siddiqui, Nitarshan Rajkumar, Tegan Maharaj, David Krueger, Sara Hooker
Modern machine learning research relies on relatively few carefully curated datasets. Even in these datasets, and typically in `untidy’ or raw data, practitioners are faced with significant issues of data quality and diversity which can be prohibitively labor intensive to address. Existing methods for dealing with these challenges tend to make strong assumptions about the particular issues at play, and often require a priori knowledge or metadata such as domain labels. Our work is orthogonal to these methods: we instead focus on providing a unified and efficient framework for Metadata Archaeology — uncovering and inferring metadata of examples in a dataset. We curate different subsets of data that might exist in a dataset (e.g. mislabeled, atypical, or out-of-distribution examples) using simple transformations, and leverage differences in learning dynamics between these probe suites to infer metadata of interest. Our method is on par with far more sophisticated mitigation methods across different tasks: identifying and correcting mislabeled examples, classifying minority-group samples, prioritizing points relevant for training and enabling scalable human auditing of relevant examples.
Multi-Objective Reinforcement Learning: Convexity, Stationarity
Haoye Lu, Daniel Herman, Yaoliang Yu
In recent years, single-objective reinforcement learning (SORL) algorithms have received a significant amount of attention and seen some strong results. However, it is generally recognized that many practical problems have intrinsic multi-objective properties that cannot be easily handled by SORL algorithms. Although there have been many multi-objective reinforcement learning (MORL) algorithms proposed, there has been little recent exploration of the fundamental properties of the spaces we are learning in. In this paper, we perform a rigorous analysis of policy induced value functions and use the insights to distinguish three views of Pareto optimality. The results imply the convexity of the induced value function’s range for stationary policies and suggest that any point of its Pareto front can be achieved by training a policy using linear scalarization (LS). We show the problem that leads to the suboptimal performance of LS can be solved by adding strongly concave terms to the immediate rewards, which motivates us to propose a new vector reward-based Q-learning algorithm, CAPQL. Combined with an actor-critic formulation, our algorithm achieves state-of-the-art performance on multiple MuJoCo tasks in the preference agnostic setting. Furthermore, we empirically show that, in contrast to other LS-based algorithms, our approach is significantly more stable, achieving similar results across various random seeds.
Multi-Rate VAE: Train Once, Get the Full Rate-Distortion Curve
Juhan Bae, Michael R. Zhang, Michael Ruan, Eric Wang, So Hasegawa, Jimmy Ba, Roger Baker Grosse
Variational autoencoders (VAEs) are powerful tools for learning latent representations of data used in a wide range of applications. In practice, VAEs usually require multiple training rounds to choose the amount of information the latent variable should retain. This trade-off between the reconstruction error (distortion) and the KL divergence (rate) is typically parameterized by a hyperparameter β. In this paper, we introduce Multi-Rate VAE (MR-VAE), a computationally efficient framework for learning optimal parameters corresponding to various β in a single training run. The key idea is to explicitly formulate a response function using hypernetworks that maps β to the optimal parameters. MR-VAEs construct a compact response hypernetwork where the pre-activations are conditionally gated based on β. We justify the proposed architecture by analyzing linear VAEs and showing that it can represent response functions exactly for linear VAEs. With the learned hypernetwork, MR-VAEs can construct the rate-distortion curve without additional training and can be deployed with significantly less hyperparameter tuning. Empirically, our approach is competitive and often exceeds the performance of multiple β-VAEs training with minimal computation and memory overheads.
Quantile Risk Control: A Flexible Framework for Bounding the
Probability of High-Loss Predictions
Jake Snell, Thomas P Zollo, Zhun Deng, Toniann Pitassi, Richard Zemel
Rigorous guarantees about the performance of predictive algorithms are necessary in order to ensure their responsible use. Previous work has largely focused on bounding the expected loss of a predictor, but this is not sufficient in many risk sensitive applications where the distribution of errors is important. In this work, we propose a flexible framework to produce a family of bounds on quantiles of the loss distribution incurred by a predictor. Our method takes advantage of the order statistics of the observed loss values rather than relying on the sample mean alone. We show that a quantile is an informative way of quantifying predictive performance, and that our framework applies to a variety of quantile-based metrics, each targeting important subsets of the data distribution. We analyze the theoretical properties of our proposed method and demonstrate its ability to rigorously control loss quantiles on several real-world datasets.
Re-Imagen: Retrieval-Augmented Text-to-Image Generator
Wenhu Chen, Hexiang Hu, Chitwan Saharia, William W. Cohen
Research on text-to-image generation has witnessed significant progress in generating diverse and photo-realistic images, driven by diffusion and auto-regressive models trained on large-scale image-text data. Though state-of-the-art models can generate high-quality images of common entities, they often have difficulty generating images of uncommon entities, such as ‘Chortai (dog)’ or ‘Picarones (food)’. To tackle this issue, we present the Retrieval-Augmented Text-to-Image Generator (Re-Imagen), a generative model that uses retrieved information to produce high-fidelity and faithful images, even for rare or unseen entities. Given a text prompt, Re-Imagen accesses an external multi-modal knowledge base to retrieve relevant (image, text) pairs and uses them as references to generate the image. With this retrieval step, Re-Imagen is augmented with the knowledge of highlevel semantics and low-level visual details of the mentioned entities, and thus improves its accuracy in generating the entities’ visual appearances. We train ReImagen on a constructed dataset containing (image, text, retrieval) triples to teach the model to ground on both text prompt and retrieval. Furthermore, we develop a new sampling strategy to interleave the classifier-free guidance for text and retrieval conditions to balance the text and retrieval alignment. Re-Imagen achieves significant gain on FID score over COCO and WikiImage. To further evaluate the capabilities of the model, we introduce EntityDrawBench, a new benchmark that evaluates image generation for diverse entities, from frequent to rare, across multiple object categories including dogs, foods, landmarks, birds, and characters. Human evaluation on EntityDrawBench shows that Re-Imagen can significantly improve the fidelity of generated images, especially on less frequent entities.
Self-supervision through Random Segments with Autoregressive
Tianyu Hua, Yonglong Tian, Sucheng Ren, Michalis Raptis, Hang Zhao, Leonid Sigal
Inspired by the success of self-supervised autoregressive representation learning in natural language (GPT and its variants), and advances in recent visual architecture design with Vision Transformers (ViTs), in this paper, we explore the effect various design choices have on the success of applying such training strategies for visual feature learning. Specifically, we introduce a novel strategy that we call Random Segments with Autoregressive Coding (RandSAC). In RandSAC, we group patch representations (image tokens) into hierarchically arranged segments; within each segment, tokens are predicted in parallel, similar to BERT, while across segment predictions are sequential, similar to GPT. We illustrate that randomized serialization of the segments significantly improves the performance and results in distribution over spatially-long (across-segments) and -short (within-segment) predictions which are effective for feature learning. We illustrate the pertinence of these design choices and explore alternatives on a number of datasets (e.g., CIFAR10, CIFAR100, ImageNet). While our pre-training strategy works with vanilla Transformer, we also propose a conceptually simple, but highly effective, addition to the decoder that allows learnable skip-connections to encoder’s feature layers, which further improves the performance.
The Tilted Variational Autoencoder: Improving Out-of-Distribution
Griffin Floto, Stefan Kremer, Mihai Nica
A problem with using the Gaussian distribution as a prior for a variational autoencoder (VAE) is that the set on which Gaussians have high probability density is small as the latent dimension increases. This is an issue because VAEs aim to achieve both a high likelihood with respect to a prior distribution and at the same time, separation between points for better reconstruction. Therefore, a small volume in the high-density region of the prior is problematic because it restricts the separation of latent points. To address this, we propose a simple generalization of the Gaussian distribution, the tilted Gaussian, whose maximum probability density occurs on a sphere instead of a single point. The tilted Gaussian has exponentially more volume in high-density regions than the standard Gaussian as a function of the distribution dimension. We empirically demonstrate that this simple change in the prior distribution improves VAE performance on the task of detecting unsupervised out-of-distribution (OOD) samples. We also introduce a new OOD testing procedure, called the Will-It-Move test, where the tilted Gaussian achieves remarkable OOD performance.
When Source-Free Domain Adaptation Meets Learning with Noisy Labels
Li Yi, Gezheng Xu, Pengcheng Xu, Jiaqi Li, Ruizhi Pu, Charles Ling, Ian McLeod, Boyu Wang
Recent state-of-the-art source-free domain adaptation (SFDA) methods have focused on learning meaningful cluster structures in the feature space, which have succeeded in adapting the knowledge from source domain to unlabeled target domain without accessing the private source data. However, existing methods rely on the pseudo-labels generated by source models that can be noisy due to domain shift. In this paper, we study SFDA from the perspective of learning with label noise (LLN). Unlike the label noise in the conventional LLN scenario, we prove that the label noise in SFDA follows a different distribution assumption. We also prove that such a difference makes existing LLN methods that rely on their distribution assumptions unable to address the label noise in SFDA. Empirical evidence suggests that only marginal improvements are achieved when applying the existing LLN methods to solve the SFDA problem. On the other hand, although there exists a fundamental difference between the label noise in the two scenarios, we demonstrate theoretically that the early-time training phenomenon (ETP), which has been previously observed in conventional label noise settings, can also be observed in the SFDA problem. Extensive experiments demonstrate significant improvements to existing SFDA algorithms by leveraging ETP to address the label noise in SFDA.
SlotFormer: Unsupervised Visual Dynamics Simulation with
Ziyi Wu, Nikita Dvornik, Klaus Greff, Thomas Kipf, Animesh Garg
Understanding dynamics from visual observations is a challenging problem that requires disentangling individual objects from the scene and learning their interactions. While recent object-centric models can successfully decompose a scene into objects, modeling their dynamics effectively still remains a challenge. We address this problem by introducing SlotFormer – a Transformer-based autoregressive model operating on learned object-centric representations. Given a video clip, our approach reasons over object features to model spatio-temporal relationships and predicts accurate future object states. In this paper, we successfully apply SlotFormer to perform video prediction on datasets with complex object interactions. Moreover, the unsupervised SlotFormer’s dynamics model can be used to improve the performance on supervised downstream tasks, such as Visual Question Answering (VQA), and goal-conditioned planning. Compared to past works on dynamics modeling, our method achieves significantly better long-term synthesis of object dynamics, while retaining high quality visual generation. Besides, SlotFormer enables VQA models to reason about the future without objectlevel labels, even outperforming counterparts that use ground-truth annotations. Finally, we show its ability to serve as a world model for model-based planning, which is competitive with methods designed specifically for such tasks.
Mutual Partial Label Learning with Competitive Label Noise
Yan Yan, Yuhong Guo
Partial label learning (PLL) is an important weakly supervised learning problem, where each training instance is associated with a set of candidate labels that include both the true label and additional noisy labels. Most existing PLL methods assume the candidate noisy labels are randomly chosen, which hardly holds in real-world learning scenarios. In this paper, we consider a more realistic PLL scenario with competitive label noise that is more difficult to distinguish from the true label than the random label noise. We propose a novel Mutual Learning based PLL approach named ML-PLL to address this challenging problem. ML-PLL learns a prediction network based classifier and a class-prototype based classifier cooperatively through interactive mutual learning and label correction. Moreover, we use a transformation network to model the association relationships between the true label and candidate labels, and learn it together with the prediction network to match the observed candidate labels in the training data and enhance label correction. Extensive experiments are conducted on several benchmark PLL datasets, and the proposed ML-PLL approach demonstrates state-of-the-art performance for partial label learning.
Partial Label Unsupervised Domain Adaptation with Class-Prototype Alignment
Yan Yan, Yuhong Guo
Partial label learning (PLL) tackles the problem where each instance is associated with a set of candidate labels, only one of which is the ground-truth label. Most existing PLL approaches assume that both the training and test sets share an identical data distribution. However, this assumption does not hold in many realworld scenarios where the training and test data come from different distributions. In this paper, we formalize this learning scenario as a new problem called partial label unsupervised domain adaptation (PLUDA). To address this challenging PLUDA problem, we propose a novel Prototype Alignment based PLUDA method named PAPLUDA, which dynamically refines the pseudo-labels of instances from both the source and target domains by consulting the outputs of a teacher-student model in a moving-average manner, and bridges the cross-domain discrepancy through inter-domain class-prototype alignment. In addition, a teacher-student model based contrastive regularization is deployed to enhance prediction stability and hence improve the class-prototypes in both domains for PLUDA. Comprehensive experimental results demonstrate that PAPLUDA achieves state-of-the-art performance on the widely used benchmark datasets.
