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Miscellaneous Aspects of Machine Learning/Representation Learning

Sophia Sanborn, Nina Miolane

We introduce a general method for achieving robust group-invariance in group-equivariant convolutional neural networks ($G$-CNNs), which we call the $G$-triple-correlation ($G$-TC) layer. The approach leverages the theory of the triple-correlation on groups, which is the unique, lowest-degree polynomial invariant map that is also \textit{complete}. Many commonly used invariant maps\textemdash such as the \texttt{max}\textemdash are incomplete: they remove both group and signal structure. A complete invariant, by contrast, removes only the variation due to the actions of the group, while preserving all information about the structure of the signal. The completeness of the triple correlation endows the $G$-TC layer with strong robustness, which can be observed in its resistance to invariance-based adversarial attacks. In addition, we observe that it yields measurable improvements in classification accuracy over standard Max $G$-Pooling in $G$-CNN architectures. We provide a general and efficient implementation of the method for any discretized group, which requires only a table defining the group's product structure. We demonstrate the benefits of this method for $G$-CNNs defined on both commutative and non-commutative groups\textemdash $SO(2)$, $O(2)$, $SO(3)$, and $O(3)$ (discretized as the cyclic $C8$, dihedral $D16$, chiral octahedral $O$ and full octahedral $O_h$ groups)\textemdash acting on $\mathbb{R}^2$ and $\mathbb{R}^3$ on both $G$-MNIST and $G$-ModelNet10 datasets.

Miscellaneous Aspects of Machine Learning/Unsupervised and Semi-supervised Learning

Vinay Shukla, Zhe Zeng, Kareem Ahmed, Guy Van den Broeck

High-quality labels are often very scarce, whereas unlabeled data with inferred weak labels occurs more naturally. In many cases, these weak labels dictate the frequency of each respective class over a set of instances. In this paper, we develop a unified approach to learning from such weakly-labeled data, which we call *count-based weakly-supervised learning*. At the heart of our approach is the ability to compute the probability of exactly $k$ out of $n$ outputs being set to true. This computation is differentiable, exact, and efficient. Building upon the previous computation, we derive a *count loss* penalizing the model for deviations in its distribution from an arithmetic constraint defined over label counts.

Miscellaneous Aspects of Machine Learning/Online Learning, Active Learning and Bandits

Juan M. Cardenas, Ben Adcock, Nick Dexter

We introduce a general framework for active learning in regression problems. Our framework extends the standard setup by allowing for general types of data, rather than merely pointwise samples of the target function. This generalization covers many cases of practical interest, such as data acquired in transform domains (e.g., Fourier data), vector-valued data (e.g., gradient-augmented data), data acquired along continuous curves, and, multimodal data (i.e., combinations of different types of measurements). Our framework considers random sampling according to a finite number of sampling measures and arbitrary nonlinear approximation spaces (model classes). We introduce the concept of \textit{generalized Christoffel functions} and show how these can be used to optimize the sampling measures. We prove that this leads to near-optimal sample complexity in various important cases. This paper focuses on applications in scientific computing, where active learning is often desirable, since it is usually expensive to generate data. We demonstrate the efficacy of our framework for gradient-augmented learning with polynomials, Magnetic Resonance Imaging (MRI) using generative models and adaptive sampling for solving PDEs using Physics-Informed Neural Networks (PINNs).

Social Aspects/Trustworthy Machine Learning

Yuzhou Cao, Hussein Mozannar, Lei Feng, Hongxin Wei, Bo An

Enabling machine learning classifiers to defer their decision to a downstream expert when the expert is more accurate will ensure improved safety and performance. This objective can be achieved with the learning-to-defer framework which aims to jointly learn how to classify and how to defer to the expert. In recent studies, it has been theoretically shown that popular estimators for learning to defer parameterized with softmax provide unbounded estimates for the likelihood of deferring which makes them uncalibrated. However, it remains unknown whether this is due to the widely used softmax parameterization and if we can find a softmax-based estimator that is both statistically consistent and possesses a valid probability estimator. In this work, we first show that the cause of the miscalibrated and unbounded estimator in prior literature is due to the symmetric nature of the surrogate losses used and not due to softmax. We then propose a novel statistically consistent asymmetric softmax-based surrogate loss that can produce valid estimates without the issue of unboundedness. We further analyze the non-asymptotic properties of our proposed method and empirically validate its performance and calibration on benchmark datasets.

Miscellaneous Aspects of Machine Learning/General Machine Learning Techniques

Samantha Chen, Yusu Wang

Learning distance functions between complex objects, such as the Wasserstein distance to compare point sets, is a common goal in machine learning applications. However, functions on such complex objects (e.g., point sets and graphs) are often required to be invariant to a wide variety of group actions e.g. permutation or rigid transformation. Therefore, continuous and symmetric *product* functions (such as distance functions) on such complex objects must also be invariant to the *product* of such group actions. We call these functions symmetric and factor-wise group invariant functions (or SGFI functions} in short).In this paper, we first present a general neural network architecture for approximating SFGI functions. The main contribution of this paper combines this general NN with a sketching idea in order to develop a specific and efficient neural network which can approximate the $p$-th Wasserstein distance between point sets.Very importantly, the required model complexity is *independent* of the sizes of input point sets. On the theoretical front, to the best of our knowledge, this is the first result showing that there exists a neural network with the capacity to approximate Wasserstein distance with bounded model complexity. Our work provides an interesting integration of sketching ideas for geometric problems with universal approximation of symmetric functions. On the empirical front, we present a range of results showing that our newly proposed neural network architecture performs comparatively or better than other models (including a SOTA Siamese Autoencoder based approach). In particular, our NN generalizes significantly better and trains much faster than the SOTA Siamese AE.Finally, this line of investigation could be useful in exploring effective neural network design for solving a broad range of geometric optimization problems (e.g., $k$-means in a metric space).

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Weiwei Kong, Andres Munoz Medina

A well-known numerical bottleneck in the differentially-private stochastic gradient descent (DP-SGD) algorithm is the computation of the gradient norm for each example in a large input batch. When the loss function in DP-SGD is consists of an intermediate linear operation, existing methods in the literature have proposed decompositions of gradients that are amenable to fast norm computations. In this paper, we present a framework that generalizes the above approach to arbitrary (possibly nonlinear) intermediate operations. Moreover, we show that for certain operations, such as fully-connected and embedding layer computations, further improvements to the runtime and storage costs of existing decompositions can be deduced using certain components of our framework. Finally, preliminary numerical experiments are given to demonstrate the substantial effects of the aforementioned improvements.

Miscellaneous Aspects of Machine Learning/Kernel methods

Diego Martinez Taboada, Aaditya Ramdas, Edward Kennedy

The average treatment effect, which is the difference in expectation of the counterfactuals, is probably the most popular target effect in causal inference with binary treatments. However, treatments may have effects beyond the mean, for instance decreasing or increasing the variance. We propose a new kernel-based test for distributional effects of the treatment. It is, to the best of our knowledge, the first kernel-based, doubly-robust test with provably valid type-I error. Furthermore, our proposed algorithm is computationally efficient, avoiding the use of permutations.

Miscellaneous Aspects of Machine Learning/Causality

Jiaqi Zhang, Kristjan Greenewald, Chandler Squires, Akash Srivastava, Karthikeyan Shanmugam, Caroline Uhler

Causal disentanglement aims to uncover a representation of data using latent variables that are interrelated through a causal model. Such a representation is identifiable if the latent model that explains the data is unique. In this paper, we focus on the scenario where unpaired observational and interventional data are available, with each intervention changing the mechanism of a latent variable. When the causal variables are fully observed, statistically consistent algorithms have been developed to identify the causal model under faithfulness assumptions. We here show that identifiability can still be achieved with unobserved causal variables, given a generalized notion of faithfulness. Our results guarantee that we can recover the latent causal model up to an equivalence class and predict the effect of unseen combinations of interventions, in the limit of infinite data. We implement our causal disentanglement framework by developing an autoencoding variational Bayes algorithm and apply it to the problem of predicting combinatorial perturbation effects in genomics.

Miscellaneous Aspects of Machine Learning/Causality

Fateme Jamshidi, Sina Akbari, Negar Kiyavash

Drawbacks of ignoring the causal mechanisms when performing imitation learning have recently been acknowledged. Several approaches both to assess the feasibility of imitation and to circumvent causal confounding and causal misspecifications have been proposed in the literature.However, the potential benefits of the incorporation of additional information about the underlying causal structure are left unexplored.An example of such overlooked information is context-specific independence (CSI), i.e., independence that holds only in certain contexts.We consider the problem of causal imitation learning when CSI relations are known.We prove that the decision problem pertaining to the feasibility of imitation in this setting is NP-hard.Further, we provide a necessary graphical criterion for imitation learning under CSI and show that under a structural assumption, this criterion is also sufficient.Finally, we propose a sound algorithmic approach for causal imitation learning which takes both CSI relations and data into account.

Miscellaneous Aspects of Machine Learning/Representation Learning

João Carvalho, Mengtao Zhang, Robin Geyer, Carlos Cotrini, Joachim M Buhmann

Anomaly detection (AD) is the machine learning task of identifying highly discrepant abnormal samples by solely relying on the consistency of the normal training samples. Under the constraints of a distribution shift, the assumption that training samples and test samples are drawn from the same distribution breaks down. In this work, by leveraging tools from causal inference we attempt to increase the resilience of anomaly detection models to different kinds of distribution shifts. We begin by elucidating a simple yet necessary statistical property that ensures invariant representations, which is critical for robust AD under both domain and covariate shifts. From this property, we derive a regularization term which, when minimized, leads to partial distribution invariance across environments. Through extensive experimental evaluation on both synthetic and real-world tasks, covering a range of six different AD methods, we demonstrated significant improvements in out-of-distribution performance. Under both covariate and domain shift, models regularized with our proposed term showed marked increased robustness. Code is available at: https://github.com/JoaoCarv/invariant-anomaly-detection

Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Dami Choi, Derrick Xin, Hamid Dadkhahi, Justin Gilmer, Ankush Garg, Orhan Firat, Chih-Kuan Yeh, Andrew Dai, Behrooz Ghorbani

In this paper, we empirically study the optimization dynamics of multi-task learning, particularly focusing on those that govern a collection of tasks with significant data imbalance. We present a simple yet effective method of pre-training on high-resource tasks, followed by fine-tuning on a mixture of high/low-resource tasks. We provide a thorough empirical study and analysis of this method's benefits showing that it achieves consistent improvements relative to the performance trade-off profile of standard static weighting. We analyze under what data regimes this method is applicable and show its improvements empirically in neural machine translation (NMT) and multi-lingual language modeling.

Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Yonatan Dukler, Alessandro Achille, Hao Yang, Varsha Vivek, Luca Zancato, Benjamin Bowman, Avinash Ravichandran, Charless Fowlkes, Ashwin Swaminathan, Stefano Soatto

We present a framework for transfer learning that efficiently adapts a large base-model by learning lightweight cross-attention modules attached to its intermediate activations.We name our approach InCA (Introspective-Cross-Attention) and show that it can efficiently survey a network’s representations and identify strong performing adapter models for a downstream task.During training, InCA enables training numerous adapters efficiently and in parallel, isolated from the frozen base model. On the ViT-L/16 architecture, our experiments show that a single adapter, 1.3% of the full model, is able to reach full fine-tuning accuracy on average across 11 challenging downstream classification tasks.Compared with other forms of parameter-efficient adaptation, the isolated nature of the InCA adaptation is computationally desirable for large-scale models. For instance, we adapt ViT-G/14 (1.8B+ parameters) quickly with 20+ adapters in parallel on a single V100 GPU (76% GPU memory reduction) and exhaustively identify its most useful representations.We further demonstrate how the adapters learned by InCA can be incrementally modified or combined for flexible learning scenarios and our approach achieves state of the art performance on the ImageNet-to-Sketch multi-task benchmark.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Jerry Chee, Yaohui Cai, Volodymyr Kuleshov, Christopher De Sa

This work studies post-training parameter quantization in large language models (LLMs). We introduce quantization with incoherence processing (QuIP), a new method based on the insight that quantization benefits from incoherent weight and Hessian matrices, i.e., from the weights being even in magnitude and the directions in which it is important to round them accurately being unaligned with the coordinate axes. QuIP consists of two steps: (1) an adaptive rounding procedure minimizing a quadratic proxy objective; (2) efficient pre- and post-processing that ensures weight and Hessian incoherence via multiplication by random orthogonal matrices. We complement QuIP with the first theoretical analysis for an LLM-scale quantization algorithm, and show that our theory also applies to an existing method, OPTQ. Empirically, we find that our incoherence preprocessing improves several existing quantization algorithms and yields the first LLM quantization methods that produce viable results using only two bits per weight. Our code can be found at https://github.com/Cornell-RelaxML/QuIP.

Miscellaneous Aspects of Machine Learning/Causality

Abhin Shah, Karthikeyan Shanmugam, Murat Kocaoglu

Causal effect estimation from data typically requires assumptions about the cause-effect relations either explicitly in the form of a causal graph structure within the Pearlian framework, or implicitly in terms of (conditional) independence statements between counterfactual variables within the potential outcomes framework. When the treatment variable and the outcome variable are confounded, front-door adjustment is an important special case where, given the graph, causal effect of the treatment on the target can be estimated using post-treatment variables. However, the exact formula for front-door adjustment depends on the structure of the graph, which is difficult to learn in practice. In this work, we provide testable conditional independence statements to compute the causal effect using front-door-like adjustment without knowing the graph under limited structural side information. We show that our method is applicable in scenarios where knowing the Markov equivalence class is not sufficient for causal effect estimation. We demonstrate the effectiveness of our method on a class of random graphs as well as real causal fairness benchmarks.

Theory/Learning Theory

Surbhi Goel, Steve Hanneke, Shay Moran, Abhishek Shetty

We study the problem of sequential prediction in the stochastic setting with an adversary that is allowed to inject clean-label adversarial (or out-of-distribution) examples. Algorithms designed to handle purely stochastic data tend to fail in the presence of such adversarial examples, often leading to erroneous predictions. This is undesirable in many high-stakes applications such as medical recommendations, where abstaining from predictions on adversarial examples is preferable to misclassification. On the other hand, assuming fully adversarial data leads to very pessimistic bounds that are often vacuous in practice. To move away from these pessimistic guarantees, we propose a new model of sequential prediction that sits between the purely stochastic and fully adversarial settings by allowing the learner to abstain from making a prediction at no cost on adversarial examples, thereby asking the learner to make predictions with certainty. Assuming access to the marginal distribution on the non-adversarial examples, we design a learner whose error scales with the VC dimension (mirroring the stochastic setting) of the hypothesis class, as opposed to the Littlestone dimension which characterizes the fully adversarial setting. Furthermore, we design learners for VC dimension~1 classes and the class of axis-aligned rectangles, which work even in the absence of access to the marginal distribution. Our key technical contribution is a novel measure for quantifying uncertainty for learning VC classes, which may be of independent interest.

Theory/Learning Theory

Ilias Diakonikolas, Daniel Kane, Vasilis Kontonis, Sihan Liu, Nikos Zarifis

We give the first polynomial-time algorithm for the testable learning of halfspaces in the presence of adversarial label noise under the Gaussian distribution. In the recently introduced testable learning model, one is required to produce a tester-learner such that if the data passes the tester, then one can trust the output of the robust learner on the data. Our tester-learner runs in time $\text{poly}(d/\epsilon)$ and outputs a halfspace with misclassification error $O(\text{opt})+\epsilon$, where $\text{opt}$ is the 0-1 error of the best fitting halfspace. At a technical level, our algorithm employs an iterative soft localization technique enhanced with appropriate testers to ensure that the data distribution is sufficiently similar to a Gaussian. Finally, our algorithm can be readily adapted to yield an efficient and testable active learner requiring only $d ~ \text{polylog}(1/\epsilon)$ labeled examples.

Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Wei Dong, Dawei Yan, Zhijun Lin, Peng Wang

The advent of high-capacity pre-trained models has revolutionized problem-solving in computer vision, shifting the focus from training task-specific models to adapting pre-trained models. Consequently, effectively adapting large pre-trained models to downstream tasks in an efficient manner has become a prominent research area. Existing solutions primarily concentrate on designing lightweight adapters and their interaction with pre-trained models, with the goal of minimizing the number of parameters requiring updates. In this study, we propose a novel Adapter Re-Composing (ARC) strategy that addresses efficient pre-trained model adaptation from a fresh perspective. Our approach considers the reusability of adaptation parameters and introduces a parameter-sharing scheme. Specifically, we leverage symmetric down-/up-projections to construct bottleneck operations, which are shared across layers. By learning low-dimensional re-scaling coefficients, we can effectively re-compose layer-adaptive adapters. This parameter-sharing strategy in adapter design allows us to further reduce the number of new parameters while maintaining satisfactory performance, thereby offering a promising approach to compress the adaptation cost. We conduct experiments on 24 downstream image classification tasks using various Vision Transformer variants to evaluate our method. The results demonstrate that our approach achieves compelling transfer learning performance with a reduced parameter count. Our code is available at https://github.com/DavidYanAnDe/ARC.

Connor Toups, Rishi Bommasani, Kathleen Creel, Sarah Bana, Dan Jurafsky, Percy Liang

Machine learning is traditionally studied at the model level: researchers measure and improve the accuracy, robustness, bias, efficiency, and other dimensions of specific models. In practice, however, the societal impact of any machine learning model is partially determined by the context into which it is deployed. To capture this, we introduce *ecosystem-level analysis:* rather than analyzing a single model, we consider the collection of models that are deployed in a given context. For example, ecosystem-level analysis in hiring recognizes that a job candidate’s outcomes are determined not only by a single hiring algorithm or firm but instead by the collective decisions of all the firms to which the candidate applied. Across three modalities (text, images, speech) and 11 datasets, we establish a clear trend: deployed machine learning is prone to systemic failure, meaning some users are exclusively misclassified by all models available. Even when individual models improve at the population level over time, we find these improvements rarely reduce the prevalence of systemic failure. Instead, the benefits of these improvements predominantly accrue to individuals who are already correctly classified by other models. In light of these trends, we analyze medical imaging for dermatology, a setting where the costs of systemic failure are especially high. While traditional analyses reveal that both models and humans exhibit racial performance disparities, ecosystem-level analysis reveals new forms of racial disparity in model predictions that do not present in human predictions. These examples demonstrate that ecosystem-level analysis has unique strengths in characterizing the societal impact of machine learning.

Miscellaneous Aspects of Machine Learning/Unsupervised and Semi-supervised Learning

Sangwoo Mo, Minkyu Kim, Kyungmin Lee, Jinwoo Shin

Vision-language models, such as contrastive language-image pre-training (CLIP), have demonstrated impressive results in natural image domains. However, these models often struggle when applied to specialized domains like remote sensing, and adapting to such domains is challenging due to the limited number of image-text pairs available for training. To address this, we propose S-CLIP, a semi-supervised learning method for training CLIP that utilizes additional unpaired images. S-CLIP employs two pseudo-labeling strategies specifically designed for contrastive learning and the language modality. The caption-level pseudo-label is given by a combination of captions of paired images, obtained by solving an optimal transport problem between unpaired and paired images. The keyword-level pseudo-label is given by a keyword in the caption of the nearest paired image, trained through partial label learning that assumes a candidate set of labels for supervision instead of the exact one. By combining these objectives, S-CLIP significantly enhances the training of CLIP using only a few image-text pairs, as demonstrated in various specialist domains, including remote sensing, fashion, scientific figures, and comics. For instance, S-CLIP improves CLIP by 10% for zero-shot classification and 4% for image-text retrieval on the remote sensing benchmark, matching the performance of supervised CLIP while using three times fewer image-text pairs.

Miscellaneous Aspects of Machine Learning/Unsupervised and Semi-supervised Learning

Dong Qiao, Chris Ding, Jicong Fan

Federated learning has a significant advantage in protecting information privacy. Many scholars proposed various secure learning methods within the framework of federated learning but the study on secure federated unsupervised learning especially clustering is limited. We in this work propose a secure kernelized factorization method for federated spectral clustering on distributed dataset. The method is non-trivial because the kernel or similarity matrix for spectral clustering is computed by data pairs, which violates the principle of privacy protection. Our method implicitly constructs an approximation for the kernel matrix on distributed data such that we can perform spectral clustering under the constraint of privacy protection. We provide a convergence guarantee of the optimization algorithm, reconstruction error bounds of the Gaussian kernel matrix, and the sufficient condition of correct clustering of our method. We also present some results of differential privacy. Numerical results on synthetic and real datasets demonstrate that the proposed method is efficient and accurate in comparison to the baselines.