GenAI4ELab/papercli-papers huggingface dataset:
Neural Network Approximations of PDEs Beyond Linearity: Representational Perspective
Authors: Tanya Marwah; Zachary Chase Lipton; Jianfeng Lu; Andrej Risteski
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: A burgeoning line of research has developed deep neural networks capable of approximating the solutions to high dimensional PDEs, opening related lines of theoretical inquiry focused on explaining how it is that these models appear to evade the curse of dimensionality. However, most theoretical analyses thus far have been limited to simple linear PDEs. In this work, we take a step towards studying the representational power of neural networks for approximating solutions to nonlinear PDEs. We focus on a class of PDEs known as nonlinear elliptic variational PDEs, whose solutions minimize an Euler-Lagrange energy functional $\mathcal{E}(u) = \int_\Omega L(\nabla u) dx$. We show that if composing a function with Barron norm $b$ with $L$ produces a function of Barron norm at most $B_L b^p$, the solution to the PDE can be $\epsilon$-approximated in the $L^2$ sense by a function with Barron norm $O\left(\left(dB_L\right)^{p^{\log(1/\epsilon)}}\right)$. By a classical result due to \cite{barron1993universal}, this correspondingly bounds the size of a 2-layer neural network needed to approximate the solution. Treating $p, \epsilon, B_L$ as constants, this quantity is polynomial in dimension, thus showing neural networks can evade the curse of dimensionality. Our proof technique involves neurally simulating (preconditioned) gradient in an appropriate Hilbert space, which converges exponentially fast to the solution of the PDE, and such that we can bound the increase of the Barron norm at each iterate. Our results subsume and substantially generalize analogous prior results for linear elliptic PDEs.
Accelerating spiking neural network training using the $d$-block model
Authors: Luke Taylor; Andrew J King; Nicol Spencer Harper
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: There is a growing interest in using spiking neural networks (SNNs) to study the brain \textit{in silico} and in emulating them on neuromorphic computers due to their lower energy consumption compared to artificial neural networks (ANNs). Significant progress has been made in directly training SNNs to perform on a par with ANNs in terms of accuracy. However, these methods are slow due to their sequential nature and require careful network regularisation to avoid overfitting. We propose a new SNN model, the $d$-block model, with stochastic absolute refractory periods and recurrent conductance latencies, which reduces the number of sequential computations using fast vectorised operations. Our model obtains accelerated training speeds and state-of-the-art performance across various neuromorphic datasets without the need for any regularisation and using fewer spikes compared to standard SNNs.
Parallel Deep Neural Networks Have Zero Duality Gap
Authors: Yifei Wang; Tolga Ergen; Mert Pilanci
Venue: ICLR 2023 (ICLR 2023 poster)

Abstract: Training deep neural networks is a challenging non-convex optimization problem. Recent work has proven that the strong duality holds (which means zero duality gap) for regularized finite-width two-layer ReLU networks and consequently provided an equivalent convex training problem. However, extending this result to deeper networks remains to be an open problem. In this paper, we prove that the duality gap for deeper linear networks with vector outputs is non-zero. In contrast, we show that the zero duality gap can be obtained by stacking standard deep networks in parallel, which we call a parallel architecture, and modifying the regularization. Therefore, we prove the strong duality and existence of equivalent convex problems that enable globally optimal training of deep networks. As a by-product of our analysis, we demonstrate that the weight decay regularization on the network parameters explicitly encourages low-rank solutions via closed-form expressions. In addition, we show that strong duality holds for three-layer standard ReLU networks given rank-1 data matrices.
The Ultimate Combo: Boosting Adversarial Example Transferability by Composing Data Augmentations
Authors: Zebin Yun; Achi-Or Weingarten; Eyal Ronen; Mahmood Sharif
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: Transferring adversarial examples from surrogate (ML) models to evade target models is a common method for evaluating adversarial robustness in black-box settings. Researchers have invested substantial efforts to enhance transferability. Chiefly, attacks leveraging data augmentation have been found to help adversarial examples generalize better from surrogate to target models. Still, prior work has explored a limited set of augmentation techniques and their composition. To fill the gap, we conducted a systematic, comprehensive study of how data augmentation affects transferability. Particularly, we explored ten augmentation techniques of six categories originally proposed to help ML models generalize to unseen benign samples, and assessed how they influence transferability, both when applied individually and when composed. Our extensive experiments with the ImageNet dataset showed that simple color-space augmentations (e.g., color to greyscale) outperform the state of the art when combined with standard augmentations, such as translation and scaling. Additionally, except for two methods that may harm transferability, we found that composing augmentation methods impacts transferability monotonically (i.e., more methods composed $\rightarrow$ $\ge$transferability)---the best composition we found significantly outperformed the state of the art (e.g., 95.6% vs. 90.9% average transferability from normally trained surrogates to other normally trained models). We provide intuitive, empirically supported explanations for why certain augmentations fail to improve transferability.
SGDA with shuffling: faster convergence for nonconvex-PŁ minimax optimization
Authors: Hanseul Cho; Chulhee Yun
Venue: ICLR 2023 (ICLR 2023 poster)

Abstract: Stochastic gradient descent-ascent (SGDA) is one of the main workhorses for solving finite-sum minimax optimization problems. Most practical implementations of SGDA randomly reshuffle components and sequentially use them (i.e., without-replacement sampling); however, there are few theoretical results on this approach for minimax algorithms, especially outside the easier-to-analyze (strongly-)monotone setups. To narrow this gap, we study the convergence bounds of SGDA with random reshuffling (SGDA-RR) for smooth nonconvex-nonconcave objectives with Polyak-{\L}ojasiewicz (P{\L}) geometry. We analyze both simultaneous and alternating SGDA-RR for nonconvex-P{\L} and primal-P{\L}-P{\L} objectives, and obtain convergence rates faster than with-replacement SGDA. Our rates extend to mini-batch SGDA-RR, recovering known rates for full-batch gradient descent-ascent (GDA). Lastly, we present a comprehensive lower bound for GDA with an arbitrary step-size ratio, which matches the full-batch upper bound for the primal-P{\L}-P{\L} case.
Beyond calibration: estimating the grouping loss of modern neural networks
Authors: Alexandre Perez-Lebel; Marine Le Morvan; Gael Varoquaux
Venue: ICLR 2023 (ICLR 2023 poster)

Abstract: The ability to ensure that a classifier gives reliable confidence scores is essential to ensure informed decision-making. To this end, recent work has focused on miscalibration, i.e., the over or under confidence of model scores. Yet calibration is not enough: even a perfectly calibrated classifier with the best possible accuracy can have confidence scores that are far from the true posterior probabilities. This is due to the grouping loss, created by samples with the same confidence scores but different true posterior probabilities. Proper scoring rule theory shows that given the calibration loss, the missing piece to characterize individual errors is the grouping loss. While there are many estimators of the calibration loss, none exists for the grouping loss in standard settings. Here, we propose an estimator to approximate the grouping loss. We show that modern neural network architectures in vision and NLP exhibit grouping loss, notably in distribution shifts settings, which highlights the importance of pre-production validation.
MEDFAIR: Benchmarking Fairness for Medical Imaging
Authors: Yongshuo Zong; Yongxin Yang; Timothy Hospedales
Venue: ICLR 2023 (ICLR 2023 notable top 25%)

Abstract: A multitude of work has shown that machine learning-based medical diagnosis systems can be biased against certain subgroups of people. This has motivated a growing number of bias mitigation algorithms that aim to address fairness issues in machine learning. However, it is difficult to compare their effectiveness in medical imaging for two reasons. First, there is little consensus on the criteria to assess fairness. Second, existing bias mitigation algorithms are developed under different settings, e.g., datasets, model selection strategies, backbones, and fairness metrics, making a direct comparison and evaluation based on existing results impossible. In this work, we introduce MEDFAIR, a framework to benchmark the fairness of machine learning models for medical imaging. MEDFAIR covers eleven algorithms from various categories, ten datasets from different imaging modalities, and three model selection criteria. Through extensive experiments, we find that the under-studied issue of model selection criterion can have a significant impact on fairness outcomes; while in contrast, state-of-the-art bias mitigation algorithms do not significantly improve fairness outcomes over empirical risk minimization (ERM) in both in-distribution and out-of-distribution settings. We evaluate fairness from various perspectives and make recommendations for different medical application scenarios that require different ethical principles. Our framework provides a reproducible and easy-to-use entry point for the development and evaluation of future bias mitigation algorithms in deep learning. Code is available at https://github.com/ys-zong/MEDFAIR.
Linearised Implicit Variational Inference
Authors: Anshuk Uppal; Wouter Boomsma; Jes Frellsen
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: Bayesian neural networks (BNNs) are touted for robustness under data drift, resilience to overfitting and catastrophic forgetting whilst also producing actionable uncertainty estimates. In variational inference, these elegant properties are contingent on the expressivity of the variational approximation. Posteriors over parameters of large models are usually multimodal and highly correlated and hence cannot be well-approximated by simple, prescribed densities. We posit implicit variational distributions specified using differentiable generators are more flexible and propose a novel bound for training BNNs using such approximations (amortized neural samplers). The proposed bound uses an approximation of the variational distribution's entropy by locally linearising the generator. Unlike existing works, our method does not require a discriminator network and moves away from an unfavourable adversarial objective. Our formulation resembles normalizing flows but does not necessitate invertibility of the generator. Moreover, we use a differentiable numerical lower bound on the Jacobians of the generator, mitigating computational concerns. We report log-likelihoods on UCI datasets competitive with deep ensembles and test our method on out-of-distribution benchmarks.
Interpretable Geometric Deep Learning via Learnable Randomness Injection
Authors: Siqi Miao; Yunan Luo; Mia Liu; Pan Li
Venue: ICLR 2023 (ICLR 2023 poster)

Abstract: Point cloud data is ubiquitous in scientific fields. Recently, geometric deep learning (GDL) has been widely applied to solve prediction tasks with such data. However, GDL models are often complicated and hardly interpretable, which poses concerns to scientists who are to deploy these models in scientific analysis and experiments. This work proposes a general mechanism, learnable randomness injection (LRI), which allows building inherently interpretable models based on general GDL backbones. LRI-induced models, once trained, can detect the points in the point cloud data that carry information indicative of the prediction label. We also propose four datasets from real scientific applications that cover the domains of high-energy physics and biochemistry to evaluate the LRI mechanism. Compared with previous post-hoc interpretation methods, the points detected by LRI align much better and stabler with the ground-truth patterns that have actual scientific meanings. LRI is grounded by the information bottleneck principle, and thus LRI-induced models are also more robust to distribution shifts between training and test scenarios. Our code and datasets are available at https://github.com/Graph-COM/LRI.
Neural Networks Efficiently Learn Low-Dimensional Representations with SGD
Authors: Alireza Mousavi-Hosseini; Sejun Park; Manuela Girotti; Ioannis Mitliagkas; Murat A Erdogdu
Venue: ICLR 2023 (ICLR 2023 notable top 25%)

Abstract: We study the problem of training a two-layer neural network (NN) of arbitrary width using stochastic gradient descent (SGD) where the input $\boldsymbol{x}\in \mathbb{R}^d$ is Gaussian and the target $y \in \mathbb{R}$ follows a multiple-index model, i.e., $y=g(\langle\boldsymbol{u_1},\boldsymbol{x}\rangle,...,\langle\boldsymbol{u_k},\boldsymbol{x}\rangle)$ with a noisy link function $g$. We prove that the first-layer weights in the NN converge to the $k$-dimensional principal subspace spanned by the vectors $\boldsymbol{u_1},...,\boldsymbol{u_k}$ of the true model, when online SGD with weight decay is used for training. This phenomenon has several important consequences when $k \ll d$. First, by employing uniform convergence on this smaller subspace, we establish a generalization error bound of $\mathcal{O}(\sqrt{{kd}/{T}})$ after $T$ iterations of SGD, which is independent of the width of the NN. We further demonstrate that, by recovering the principal direction, SGD-trained ReLU NNs can learn a single-index target of the form $y=f(\langle\boldsymbol{u},\boldsymbol{x}\rangle) + \epsilon$ with a sample complexity linear in $d$ (up to log factors), where $f$ is a monotonic function with at most polynomial growth, and $\epsilon$ is the noise. This is in contrast to the known $d^{\Omega(p)}$ samples required to learn any degree $p$ polynomial in the kernel regime, and shows that SGD-trained NNs can outperform the Neural Tangent Kernel at initialization. Finally, we establish compressibility guarantees for NNs using that SGD produces an approximately rank-$k$ first-layer weight matrix.
Editing models with task arithmetic
Authors: Gabriel Ilharco; Marco Tulio Ribeiro; Mitchell Wortsman; Ludwig Schmidt; Hannaneh Hajishirzi; Ali Farhadi
Venue: ICLR 2023 (ICLR 2023 poster)

Abstract: Changing how pre-trained models behave---e.g., improving their performance on a downstream task or mitigating biases learned during pre-training---is a common practice when developing machine learning systems. In this work, we propose a new paradigm for steering the behavior of neural networks, centered around task vectors. A task vector specifies a direction in the weight space of a pre-trained model, such that movement in that direction improves performance on the task. We build task vectors by subtracting the weights of a pre-trained model from the weights of the same model after fine-tuning on a task. We show that these task vectors can be modified and combined together through arithmetic operations such as negation and addition, and the behavior of the resulting model is steered accordingly. Moreover, task vectors can be added together to improve performance on multiple tasks at once. Finally, when tasks are linked by an analogy relationship of the form ``A is to B as C is to D", combining task vectors from three of the tasks can improve performance on the fourth, even when no data from the fourth task is used for training.
Learning Top-k Classification with Label Ranking
Authors: Bin Cao; Kai Wang; JING FAN; Jianwei Yin
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: Class confusability and multi-label nature of examples inevitably arise in classification tasks with the increasing number of classes, which poses a huge challenge to classification. To mitigate this problem, top-$k$ classification is proposed, where the classifier is allowed to predict $k$ label candidates and the prediction result is considered correct as long as the ground truth label is included in the $k$ labels. However, existing top-k classification methods neglect the ranking of the ground truth label among the predicted $k$ labels, which has high application value. In this paper, we propose a novel three-stage approach to learn top-$k$ classification with label ranking. We first propose an ensemble based relabeling method and relabel the training data with $k$ labels, which is used to train the top-$k$ classifier. We then propose a novel top-$k$ classification loss function that aims to improve the ranking of the ground truth label. Finally, we have conducted extensive experiments on four text datasets and four image datasets, and the experimental results show that our method could significantly improve the performance of existing methods.
Fine-grain Inference on Out-of-Distribution Data with Hierarchical Classification
Authors: Randolph Linderman; Jingyang Zhang; Nathan Inkawhich; Hai Li; Yiran Chen
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: Machine learning methods must be trusted to make appropriate decisions in real-world environments, even when faced with out-of-distribution (OOD) samples. Many current approaches simply aim to detect OOD examples and alert the user when an unrecognized input is given. However, when the OOD sample significantly overlaps with the training data, a binary anomaly detection is not interpretable or explainable, and provides little information to the user. We propose a new model for OOD detection that makes predictions at varying levels of granularity—as the inputs become more ambiguous, the model predictions become coarser and more conservative. Consider an animal classifier that encounters an unknown bird species and a car. Both cases are OOD, but the user gains more information if the classifier recognizes that its uncertainty over the particular species is too large and predicts “bird” instead of detecting it as OOD. Furthermore, we diagnose the classifier’s performance at each level of the hierarchy improving the explainability and interpretability of the model’s predictions. We demonstrate the effectiveness of hierarchical classifiers for both fine- and coarse-grained OOD tasks.
Extracting Meaningful Attention on Source Code: An Empirical Study of Developer and Neural Model Code Exploration
Authors: Matteo Paltenghi; Rahul Pandita; Austin Henley; Albert Ziegler
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: The high effectiveness of neural models of code, such as OpenAI Codex and AlphaCode, suggests coding capabilities of models that are at least comparable to those of humans. However, previous work has only used these models for their raw completion, ignoring how the model reasoning, in the form of attention weights, can be used for other downstream tasks. Disregarding the attention weights means discarding a considerable portion of what those models compute when queried. To profit more from the knowledge embedded in these large pre-trained models, this work compares multiple approaches to post-process these valuable attention weights for supporting code exploration. Specifically, we compare to which extent the transformed attention signal of CodeGen, a large and publicly available pre-trained neural model, agrees with how developers look at and explore code when each answering the same sense-making questions about code. At the core of our experimental evaluation, we collect, manually annotate, and open-source a novel eye-tracking dataset comprising 25 developers answering sense-making questions on code over 92 sessions. We empirically evaluate five attention-agnostic heuristics and ten attention-based post processing approaches of the attention signal against our ground truth of developers exploring code, including the novel concept of follow-up attention which exhibits the highest agreement. Beyond the dataset contribution and the empirical study, we also introduce a novel practical application of the attention signal of pre-trained models with completely analytical solutions, going beyond how neural models’ attention mechanisms have traditionally been used.
UL2: Unifying Language Learning Paradigms
Authors: Yi Tay; Mostafa Dehghani; Vinh Q. Tran; Xavier Garcia; Jason Wei; Xuezhi Wang; Hyung Won Chung; Dara Bahri; Tal Schuster; Steven Zheng; Denny Zhou; Neil Houlsby; Donald Metzler
Venue: ICLR 2023 (ICLR 2023 poster)

Abstract: Existing pre-trained models are generally geared towards a particular class of problems. To date, there seems to be still no consensus on what the right architecture and pre-training setup should be. This paper presents a unified framework for pre-training models that are universally effective across datasets and setups. We begin by disentangling architectural archetypes with pre-training objectives -- two concepts that are commonly conflated. Next, we present a generalized and unified perspective for self-supervision in NLP and show how different pre-training objectives can be cast as one another and how interpolating between different objectives can be effective. We then propose Mixture-of-Denoisers (MoD), a pre-training objective that combines diverse pre-training paradigms together. We furthermore introduce a notion of mode switching, wherein downstream fine-tuning is associated with specific pre-training schemes. We conduct extensive ablative experiments to compare multiple pre-training objectives and find that our method pushes the Pareto-frontier by outperforming T5 and/or GPT-like models across multiple diverse setups. Finally, by scaling our model up to 20B parameters, we achieve SOTA performance on 50 well-established supervised NLP tasks ranging from language generation (with automated and human evaluation), language understanding, text classification, question answering, commonsense reasoning, long text reasoning, structured knowledge grounding and information retrieval. Our model also achieve strong results at in-context learning, outperforming 175B GPT-3 on zero-shot SuperGLUE and tripling the performance of T5-XXL on one-shot summarization. Finally, we show that UL2 20B works well with chain-of-thought prompting and reasoning, making it an appealing choice for research into reasoning at a small to medium scale of 20B parameters. We release Flax-based T5X model checkpoints for the 20B model publicly.