In this paper, we consider the problem of iterative machine teaching, where a teacher provides examples sequentially based on the current iterative learner. In contrast to previous methods that have to scan over the entire pool and select teaching examples from it in each iteration, we propose a label synthesis teaching framework where the teacher randomly selects input teaching examples (e.g., images) and then synthesizes suitable outputs (e.g., labels) for them. We show that this framework can avoid costly example selection while still provably achieving exponential teachability. We propose multiple novel teaching algorithms in this framework. Finally, we empirically demonstrate the value of our framework.
We propose a new class of random feature methods for linearizing softmax and Gaussian kernels called hybrid random features (HRFs) that automatically adapt the quality of kernel estimation to provide most accurate approximation in the defined regions of interest. Special instantiations of HRFs lead to well-known methods such as trigonometric (Rahimi and Recht, 2007) or (recently introduced in the context of linear-attention Transformers) positive random features (Choromanski et al., 2021). By generalizing Bochner's Theorem for softmax/Gaussian kernels and leveraging random features for compositional kernels, the HRF-mechanism provides strong theoretical guarantees - unbiased approximation and strictly smaller worst-case relative errors than its counterparts. We conduct exhaustive empirical evaluation of HRF ranging from pointwise kernel estimation experiments, through tests on data admitting clustering structure to benchmarking implicit-attention Transformers (also for downstream Robotics applications), demonstrating its quality in a wide spectrum of machine learning problems.
This paper addresses the deep face recognition problem under an open-set protocol, where ideal face features are expected to have smaller maximal intra-class distance than minimal inter-class distance under a suitably chosen metric space. To this end, hyperspherical face recognition, as a promising line of research, has attracted increasing attention and gradually become a major focus in face recognition research. As one of the earliest works in hyperspherical face recognition, SphereFace explicitly proposed to learn face embeddings with large inter-class angular margin. However, SphereFace still suffers from severe training instability which limits its application in practice. In order to address this problem, we introduce a unified framework to understand large angular margin in hyperspherical face recognition. Under this framework, we extend the study of SphereFace and propose an improved variant with substantially better training stability -- SphereFace-R. Specifically, we propose two novel ways to implement the multiplicative margin, and study SphereFace-R under three different feature normalization schemes (no feature normalization, hard feature normalization and soft feature normalization). We also propose an implementation strategy -- "characteristic gradient detachment" -- to stabilize training. Extensive experiments on SphereFace-R show that it is consistently better than or competitive with state-of-the-art methods.
State-of-the-art deep face recognition methods are mostly trained with a softmax-based multi-class classification framework. Despite being popular and effective, these methods still have a few shortcomings that limit empirical performance. In this paper, we first identify the discrepancy between training and evaluation in the existing multi-class classification framework and then discuss the potential limitations caused by the "competitive" nature of softmax normalization. Motivated by these limitations, we propose a novel binary classification training framework, termed SphereFace2. In contrast to existing methods, SphereFace2 circumvents the softmax normalization, as well as the corresponding closed-set assumption. This effectively bridges the gap between training and evaluation, enabling the representations to be improved individually by each binary classification task. Besides designing a specific well-performing loss function, we summarize a few general principles for this "one-vs-all" binary classification framework so that it can outperform current competitive methods. We conduct comprehensive experiments on popular benchmarks to demonstrate that SphereFace2 can consistently outperform current state-of-the-art deep face recognition methods.
As the complexity of machine learning (ML) models increases, resulting in a lack of prediction explainability, several methods have been developed to explain a model's behavior in terms of the training data points that most influence the model. However, these methods tend to mark outliers as highly influential points, limiting the insights that practitioners can draw from points that are not representative of the training data. In this work, we take a step towards finding influential training points that also represent the training data well. We first review methods for assigning importance scores to training points. Given importance scores, we propose a method to select a set of DIVerse INfluEntial (DIVINE) training points as a useful explanation of model behavior. As practitioners might not only be interested in finding data points influential with respect to model accuracy, but also with respect to other important metrics, we show how to evaluate training data points on the basis of group fairness. Our method can identify unfairness-inducing training points, which can be removed to improve fairness outcomes. Our quantitative experiments and user studies show that visualizing DIVINE points helps practitioners understand and explain model behavior better than earlier approaches.
Approximate bi-level optimization (ABLO) consists of (outer-level) optimization problems, involving numerical (inner-level) optimization loops. While ABLO has many applications across deep learning, it suffers from time and memory complexity proportional to the length $r$ of its inner optimization loop. To address this complexity, an earlier first-order method (FOM) was proposed as a heuristic that omits second derivative terms, yielding significant speed gains and requiring only constant memory. Despite FOM's popularity, there is a lack of theoretical understanding of its convergence properties. We contribute by theoretically characterizing FOM's gradient bias under mild assumptions. We further demonstrate a rich family of examples where FOM-based SGD does not converge to a stationary point of the ABLO objective. We address this concern by proposing an unbiased FOM (UFOM) enjoying constant memory complexity as a function of $r$. We characterize the introduced time-variance tradeoff, demonstrate convergence bounds, and find an optimal UFOM for a given ABLO problem. Finally, we propose an efficient adaptive UFOM scheme.
Transformer networks are able to capture patterns in data coming from many domains (text, images, videos, proteins, etc.) with little or no change to architecture components. We perform a theoretical analysis of the core component responsible for signal propagation between elements, i.e. the self-attention matrix. In practice, this matrix typically exhibits two properties: (1) it is sparse, meaning that each token only attends to a small subset of other tokens; and (2) it changes dynamically depending on the input to the module. With these considerations in mind, we ask the following question: Can a fixed self-attention module approximate arbitrary sparse patterns depending on the input? How small is the hidden size $d$ required for such approximation? We make progress in answering this question and show that the self-attention matrix can provably approximate sparse matrices, where sparsity is in terms of a bounded number of nonzero elements in each row and column. While the parameters of self-attention are fixed, various sparse matrices can be approximated by only modifying the inputs. Our proof is based on the random projection technique and uses the seminal Johnson-Lindenstrauss lemma. Our proof is constructive, enabling us to propose an algorithm for finding adaptive inputs and fixed self-attention parameters in order to approximate a given matrix. In particular, we show that, in order to approximate any sparse matrix up to a given precision defined in terms of preserving matrix element ratios, $d$ grows only logarithmically with the sequence length $L$ (i.e. $d = O(\log L)$).
Concept bottleneck models map from raw inputs to concepts, and then from concepts to targets. Such models aim to incorporate pre-specified, high-level concepts into the learning procedure, and have been motivated to meet three desiderata: interpretability, predictability, and intervenability. However, we find that concept bottleneck models struggle to meet these goals. Using post hoc interpretability methods, we demonstrate that concepts do not correspond to anything semantically meaningful in input space, thus calling into question the usefulness of concept bottleneck models in their current form.