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

Deepali Jain, Krzysztof M Choromanski, Kumar Avinava Dubey, Sumeet Singh, Vikas Sindhwani, Tingnan Zhang, Jie Tan

In this work, we propose a new class of learnable optimizers, called Mnemosyne. It is based on the novel spatio-temporal low-rank implicit attention Transformers that can learn to train entire neural network architectures, including other Transformers, without any task-specific optimizer tuning. We show that Mnemosyne: (a) outperforms popular LSTM optimizers (also with new feature engineering to mitigate catastrophic forgetting of LSTMs), (b) can successfully train Transformers while using simple meta-training strategies that require minimal computational resources, (c) matches accuracy-wise SOTA hand-designed optimizers with carefully tuned hyper-parameters (often producing top performing models). Furthermore, Mnemosyne provides space complexity comparable to that of its hand-designed first-order counterparts, which allows it to scale to training larger sets of parameters. We conduct an extensive empirical evaluation of Mnemosyne on: (a) fine-tuning a wide range of Vision Transformers (ViTs) from medium-size architectures to massive ViT-Hs (36 layers, 16 heads), (b) pre-training BERT models and (c) soft prompt-tuning large 11B+ T5XXL models. We complement our results with a comprehensive theoretical analysis of the compact associative memory used by Mnemosyne which we believe was never done before.

Naishan Zheng, man zhou, Chong Zhou, Chen Change Loy

Image restoration techniques, spanning from the convolution to the transformer paradigm, have demonstrated robust spatial representation capabilities to deliver high-quality performance.Yet, many of these methods, such as convolution and the Feed Forward Network (FFN) structure of transformers, primarily leverage the basic first-order channel interactions and have not maximized the potential benefits of higher-order modeling. To address this limitation, our research dives into understanding relationships within the channel dimension and introduces a simple yet efficient, high-order channel-wise operator tailored for image restoration. Instead of merely mimicking high-order spatial interaction, our approach offers several added benefits: Efficiency: It adheres to the zero-FLOP and zero-parameter principle, using a spatial-shifting mechanism across channel-wise groups. Simplicity: It turns the favorable channel interaction and aggregation capabilities into element-wise multiplications and convolution units with $1 \times 1$ kernel. Our new formulation expands the first-order channel-wise interactions seen in previous works to arbitrary high orders, generating a hierarchical receptive field akin to a Rubik's cube through the combined action of shifting and interactions. Furthermore, our proposed Rubik's cube convolution is a flexible operator that can be incorporated into existing image restoration networks, serving as a drop-in replacement for the standard convolution unit with fewer parameters overhead. We conducted experiments across various low-level vision tasks, including image denoising, low-light image enhancement, guided image super-resolution, and image de-blurring. The results consistently demonstrate that our Rubik's cube operator enhances performance across all tasks. Code is publicly available at https://github.com/zheng980629/RubikCube.

Optimization/First-order

Guillaume Wang, Lénaïc Chizat

We study the convergence to local Nash equilibria of gradient methods for two-player zero-sum differentiable games.It is well-known that, in the continuous-time setting, such dynamics converge locally when $S \succ 0$ and may diverge when $S=0$, where $S\succeq 0$ is the symmetric part of the Jacobian at equilibrium that accounts for the "potential" component of the game. We show that these dynamics also converge as soon as $S$ is nonzero (*partial curvature*) and the eigenvectors of the antisymmetric part $A$ are in general position with respect to the kernel of $S$.We then study the convergence rate when $S \ll A$ and prove that it typically depends on the *average* of the eigenvalues of $S$, instead of the minimum as an analogy with minimization problems would suggest.To illustrate our results, we consider the problem of computing mixed Nash equilibria of continuous games. We show that, thanks to partial curvature, conic particle methods -- which optimize over both weights and supports of the mixed strategies -- generically converge faster than fixed-support methods.For min-max games, it is thus beneficial to add degrees of freedom "with curvature": this can be interpreted as yet another benefit of over-parameterization.

Reinforcement Learning

Michele Garibbo, Maxime Robeyns, Laurence Aitchison

Many reinforcement learning approaches rely on temporal-difference (TD) learning to learn a critic.However, TD-learning updates can be high variance.Here, we introduce a model-based RL framework, Taylor TD, which reduces this variance in continuous state-action settings. Taylor TD uses a first-order Taylor series expansion of TD updates.This expansion allows Taylor TD to analytically integrate over stochasticity in the action-choice, and some stochasticity in the state distribution for the initial state and action of each TD update.We include theoretical and empirical evidence that Taylor TD updates are indeed lower variance than standard TD updates. Additionally, we show Taylor TD has the same stable learning guarantees as standard TD-learning with linear function approximation under a reasonable assumption.Next, we combine Taylor TD with the TD3 algorithm, forming TaTD3.We show TaTD3 performs as well, if not better, than several state-of-the art model-free and model-based baseline algorithms on a set of standard benchmark tasks.

Optimization/Convex

Moise Blanchard, Junhui Zhang, Patrick Jaillet

We propose a family of recursive cutting-plane algorithms to solve feasibility problems with constrained memory, which can also be used for first-order convex optimization. Precisely, in order to find a point within a ball of radius $\epsilon$ with a separation oracle in dimension $d$---or to minimize $1$-Lipschitz convex functions to accuracy $\epsilon$ over the unit ball---our algorithms use $\mathcal O(\frac{d^2}{p}\ln \frac{1}{\epsilon})$ bits of memory, and make $\mathcal O((C\frac{d}{p}\ln \frac{1}{\epsilon})^p)$ oracle calls. The family is parametrized by $p\in[d]$ and provides an oracle-complexity/memory trade-off in the sub-polynomial regime $\ln\frac{1}{\epsilon}\gg\ln d$. While several works gave lower-bound trade-offs (impossibility results)---we explicit here their dependence with $\ln\frac{1}{\epsilon}$, showing that these also hold in any sub-polynomial regime---to the best of our knowledge this is the first class of algorithms that provides a positive trade-off between gradient descent and cutting-plane methods in any regime with $\epsilon\leq 1/\sqrt d$. The algorithms divide the $d$ variables into $p$ blocks and optimize over blocks sequentially, with approximate separation vectors constructed using a variant of Vaidya's method. In the regime $\epsilon \leq d^{-\Omega(d)}$, our algorithm with $p=d$ achieves the information-theoretic optimal memory usage and improves the oracle-complexity of gradient descent.

Social Aspects/Accountability, Transparency and Interpretability

Shibal Ibrahim, Gabriel Afriat, Kayhan Behdin, Rahul Mazumder

Generalized Additive Models (GAMs) are a family of flexible and interpretable models with old roots in statistics. GAMs are often used with pairwise interactions to improve model accuracy while still retaining flexibility and interpretability but lead to computational challenges as we are dealing with order of $p^2$ terms. It is desirable to restrict the number of components (i.e., encourage sparsity) for easier interpretability, and better computational and statistical properties. Earlier approaches, considering sparse pairwise interactions, have limited scalability, especially when imposing additional structural interpretability constraints. We propose a flexible GRAND-SLAMIN framework that can learn GAMs with interactions under sparsity and additional structural constraints in a differentiable end-to-end fashion. We customize first-order gradient-based optimization to perform sparse backpropagation to exploit sparsity in additive effects for any differentiable loss function in a GPU-compatible manner. Additionally, we establish novel non-asymptotic prediction bounds for our estimators with tree-based shape functions. Numerical experiments on real-world datasets show that our toolkit performs favorably in terms of performance, variable selection and scalability when compared with popular toolkits to fit GAMs with interactions. Our work expands the landscape of interpretable modeling while maintaining prediction accuracy competitive with non-interpretable black-box models. Our code is available at https://github.com/mazumder-lab/grandslamin.

Theory/Online Learning and Bandits

Julia Olkhovskaya, Jack Mayo, Tim van Erven, Gergely Neu, Chen-Yu Wei

We consider the adversarial linear contextual bandit setting, whichallows for the loss functions associated with each of $K$ arms to changeover time without restriction. Assuming the $d$-dimensional contexts aredrawn from a fixed known distribution, the worst-case expected regretover the course of $T$ rounds is known to scale as $\tilde O(\sqrt{KdT})$. Under the additional assumption that the density of the contextsis log-concave, we obtain a second-order bound of order $\tildeO(K\sqrt{d V_T})$ in terms of the cumulative second moment of thelearner's losses $V_T$, and a closely related first-order bound of order$\tilde O(K\sqrt{d L_T^*})$ in terms of the cumulative loss of the bestpolicy $L_T^*$. Since $V_T$ or $L_T^*$ may be significantly smaller than$T$, these improve over the worst-case regret whenever the environmentis relatively benign. Our results are obtained using a truncated versionof the continuous exponential weights algorithm over the probabilitysimplex, which we analyse by exploiting a novel connection to the linearbandit setting without contexts.

Optimization/Bilevel optimization

Yifan Yang, Peiyao Xiao, Kaiyi Ji

In this paper, we revisit the bilevel optimization problem, in which the upper-level objective function is generally nonconvex and the lower-level objective function is strongly convex. Although this type of problem has been studied extensively, it still remains an open question how to achieve an $\mathcal{O}(\epsilon^{-1.5})$ sample complexity in Hessian/Jacobian-free stochastic bilevel optimization without any second-order derivative computation. To fill this gap, we propose a novel Hessian/Jacobian-free bilevel optimizer named FdeHBO, which features a simple fully single-loop structure, a projection-aided finite-difference Hessian/Jacobian-vector approximation, and momentum-based updates. Theoretically, we show that FdeHBO requires $\mathcal{O}(\epsilon^{-1.5})$ iterations (each using $\mathcal{O}(1)$ samples and only first-order gradient information) to find an $\epsilon$-accurate stationary point. As far as we know, this is the first Hessian/Jacobian-free method with an $\mathcal{O}(\epsilon^{-1.5})$ sample complexity for nonconvex-strongly-convex stochastic bilevel optimization.

Optimization/Bilevel optimization

Sang Choe, Sanket Vaibhav Mehta, Hwijeen Ahn, Willie Neiswanger, Pengtao Xie, Emma Strubell, Eric Xing

Despite its flexibility to learn diverse inductive biases in machine learning programs, meta learning (i.e.,\ learning to learn) has long been recognized to suffer from poor scalability due to its tremendous compute/memory costs, training instability, and a lack of efficient distributed training support. In this work, we focus on making scalable meta learning practical by introducing SAMA, which combines advances in both implicit differentiation algorithms and systems. Specifically, SAMA is designed to flexibly support a broad range of adaptive optimizers in the base level of meta learning programs, while reducing computational burden by avoiding explicit computation of second-order gradient information, and exploiting efficient distributed training techniques implemented for first-order gradients. Evaluated on multiple large-scale meta learning benchmarks, SAMA showcases up to 1.7/4.8x increase in throughput and 2.0/3.8x decrease in memory consumption respectively on single-/multi-GPU setups compared to other baseline meta learning algorithms. Furthermore, we show that SAMA-based data optimization leads to consistent improvements in text classification accuracy with BERT and RoBERTa large language models, and achieves state-of-the-art results in both small- and large-scale data pruning on image classification tasks, demonstrating the practical applicability of scalable meta learning across language and vision domains.

Optimization/Bilevel optimization

Songtao Lu

Functional constrained optimization (FCO) has emerged as a powerful tool for solving various machine learning problems. However, with the rapid increase in applications of neural networks in recent years, it has become apparent that both the objective and constraints often involve nonconvex functions, which poses significant challenges in obtaining high-quality solutions. In this work, we focus on a class of nonconvex FCO problems with nonconvex constraints, where the two optimization variables are nonlinearly coupled in the inequality constraint. Leveraging the primal-dual optimization framework, we propose a smoothed first-order Lagrangian method (SLM) for solving this class of problems. We establish the theoretical convergence guarantees of SLM to the Karush-Kuhn-Tucker (KKT) solutions through quantifying dual error bounds. By establishing connections between this structured FCO and equilibrium-constrained nonconvex problems (also known as bilevel optimization), we apply the proposed SLM to tackle bilevel optimization oriented problems where the lower-level problem is nonconvex. Numerical results obtained from both toy examples and hyper-data cleaning problems demonstrate the superiority of SLM compared to benchmark methods.

Deep Learning/Graph Neural Networks

Dingmin Wang, Yeyuan Chen

As a powerful framework for graph representation learning, Graph Neural Networks (GNNs) have garnered significant attention in recent years. However, to the best of our knowledge, there has been no formal analysis of the logical expressiveness of GNNs as Boolean node classifiers over multi-relational graphs, where each edge carries a specific relation type. In this paper, we investigate $\mathcal{FOC}_2$, a fragment of first-order logic with two variables and counting quantifiers. On the negative side, we demonstrate that the R$^2$-GNN architecture, which extends the local message passing GNN by incorporating global readout, fails to capture $\mathcal{FOC}_2$ classifiers in the general case. Nevertheless, on the positive side, we establish that R$^2$-GNNs models are equivalent to $\mathcal{FOC}_2$ classifiers under certain restricted yet reasonable scenarios. To address the limitations of R$^2$-GNNs regarding expressiveness, we propose a simple graph transformation technique, akin to a preprocessing step, which can be executed in linear time. This transformation enables R$^2$-GNNs to effectively capture any $\mathcal{FOC}_2$ classifiers when applied to the "transformed" input graph. Moreover, we extend our analysis of expressiveness and graph transformation to temporal graphs, exploring several temporal GNN architectures and providing an expressiveness hierarchy for them. To validate our findings, we implement R$^2$-GNNs and the graph transformation technique and conduct empirical tests in node classification tasks against various well-known GNN architectures that support multi-relational or temporal graphs. Our experimental results consistently demonstrate that R$^2$-GNN with the graph transformation outperforms the baseline methods on both synthetic and real-world datasets

Social Aspects/Trustworthy Machine Learning

Zhijin Ge, Hongying Liu, Wang Xiaosen, Fanhua Shang, Yuanyuan Liu

Transfer-based attack adopts the adversarial examples generated on the surrogate model to attack various models, making it applicable in the physical world and attracting increasing interest. Recently, various adversarial attacks have emerged to boost adversarial transferability from different perspectives. In this work, inspired by the observation that flat local minima are correlated with good generalization, we assume and empirically validate that adversarial examples at a flat local region tend to have good transferability by introducing a penalized gradient norm to the original loss function. Since directly optimizing the gradient regularization norm is computationally expensive and intractable for generating adversarial examples, we propose an approximation optimization method to simplify the gradient update of the objective function. Specifically, we randomly sample an example and adopt a first-order procedure to approximate the curvature of the second-order Hessian matrix, which makes computing more efficient by interpolating two Jacobian matrices. Meanwhile, in order to obtain a more stable gradient direction, we randomly sample multiple examples and average the gradients of these examples to reduce the variance due to random sampling during the iterative process. Extensive experimental results on the ImageNet-compatible dataset show that the proposed method can generate adversarial examples at flat local regions, and significantly improve the adversarial transferability on either normally trained models or adversarially trained models than the state-of-the-art attacks. Our codes are available at: https://github.com/Trustworthy-AI-Group/PGN.

Miscellaneous Aspects of Machine Learning/Representation Learning

Xueyuan Lin, Haihong E, Chengjin Xu, Gengxian Zhou, Haoran Luo, Tianyi Hu, Fenglong Su, Ningyuan Li, Mingzhi Sun

Multi-hop logical reasoning over knowledge graph plays a fundamental role in many artificial intelligence tasks. Recent complex query embedding methods for reasoning focus on static KGs, while temporal knowledge graphs have not been fully explored. Reasoning over TKGs has two challenges: 1. The query should answer entities or timestamps; 2. The operators should consider both set logic on entity set and temporal logic on timestamp set.To bridge this gap, we introduce the multi-hop logical reasoning problem on TKGs and then propose the first temporal complex query embedding named Temporal Feature-Logic Embedding framework (TFLEX) to answer the temporal complex queries. Specifically, we utilize fuzzy logic to compute the logic part of the Temporal Feature-Logic embedding, thus naturally modeling all first-order logic operations on the entity set. In addition, we further extend fuzzy logic on timestamp set to cope with three extra temporal operators (**After**, **Before** and **Between**).Experiments on numerous query patterns demonstrate the effectiveness of our method.

Social Aspects/Privacy-preserving Statistics and Machine Learning

Arun Ganesh, Mahdi Haghifam, Thomas Steinke, Abhradeep Guha Thakurta

Differentially private (stochastic) gradient descent is the workhorse of DP private machine learning in both the convex and non-convex settings. Without privacy constraints, second-order methods, like Newton's method, converge faster than first-order methods like gradient descent. In this work, we investigate the prospect of using the second-order information from the loss function to accelerate DP convex optimization. We first develop a private variant of the regularized cubic Newton method of Nesterov and Polyak, and show that for the class of strongly convex loss functions, our algorithm has quadratic convergence and achieves the optimal excess loss. We then design a practical second-order DP algorithm for the unconstrained logistic regression problem. We theoretically and empirically study the performance of our algorithm. Empirical results show our algorithm consistently achieves the best excess loss compared to other baselines and is 10-40x faster than DP-GD/DP-SGD for challenging datasets.

Optimization/Stochastic

Angela Yuan, Chris Junchi Li, Gauthier Gidel, Michael Jordan, Quanquan Gu, Simon Du

We consider the problem of solving stochastic monotone variational inequalities with a separable structure using a stochastic first-order oracle. Building on standard extragradient for variational inequalities we propose a novel algorithm---stochastic \emph{accelerated gradient-extragradient} (AG-EG)---for strongly monotone variational inequalities (VIs). Our approach combines the strengths of extragradient and Nesterov acceleration. By showing that its iterates remain in a bounded domain and applying scheduled restarting, we prove that AG-EG has an optimal convergence rate for strongly monotone VIs. Furthermore, when specializing to the particular case of bilinearly coupled strongly-convex-strongly-concave saddle-point problems, including bilinear games, our algorithm achieves fine-grained convergence rates that match the respective lower bounds, with the stochasticity being characterized by an additive statistical error term that is optimal up to a constant prefactor.

Data-centric AI

Haoru Tan, Sitong Wu, Fei Du, Yukang Chen, Zhibin Wang, Fan Wang, Xiaojuan Qi

In this paper, we propose a novel data-pruning approach called moving-one-sample-out (MoSo), which aims to identify and remove the least informative samples from the training set. The core insight behind MoSo is to determine the importance of each sample by assessing its impact on the optimal empirical risk. This is achieved by measuring the extent to which the empirical risk changes when a particular sample is excluded from the training set. Instead of using the computationally expensive leaving-one-out-retraining procedure, we propose an efficient first-order approximator that only requires gradient information from different training stages. The key idea behind our approximation is that samples with gradients that are consistently aligned with the average gradient of the training set are more informative and should receive higher scores, which could be intuitively understood as follows: if the gradient from a specific sample is consistent with the average gradient vector, it implies that optimizing the network using the sample will yield a similar effect on all remaining samples. Experimental results demonstrate that MoSo effectively mitigates severe performance degradation at high pruning ratios and achieves satisfactory performance across various settings. Experimental results demonstrate that MoSo effectively mitigates severe performance degradation at high pruning ratios and outperforms state-of-the-art methods by a large margin across various settings.

Optimization/Non-Convex

Bohan Wang, Jingwen Fu, Huishuai Zhang, Nanning Zheng, Wei Chen

Recently, Arjevani et al. [1] establish a lower bound of iteration complexity for the first-order optimization under an $L$-smooth condition and a bounded noise variance assumption. However, a thorough review of existing literature on Adam's convergence reveals a noticeable gap: none of them meet the above lower bound. In this paper, we close the gap by deriving a new convergence guarantee of Adam, with only an $L$-smooth condition and a bounded noise variance assumption. Our results remain valid across a broad spectrum of hyperparameters. Especially with properly chosen hyperparameters, we derive an upper bound of the iteration complexity of Adam and show that it meets the lower bound for first-order optimizers. To the best of our knowledge, this is the first to establish such a tight upper bound for Adam's convergence. Our proof utilizes novel techniques to handle the entanglement between momentum and adaptive learning rate and to convert the first-order term in the Descent Lemma to the gradient norm, which may be of independent interest.

Social Aspects/Privacy-preserving Statistics and Machine Learning

Hao Wang, Shivchander Sudalairaj, John Henning, Kristjan Greenewald, Akash Srivastava

Existing private synthetic data generation algorithms are agnostic to downstream tasks. However, end users may have specific requirements that the synthetic data must satisfy. Failure to meet these requirements could significantly reduce the utility of the data for downstream use. We introduce a post-processing technique that improves the utility of the synthetic data with respect to measures selected by the end user, while preserving strong privacy guarantees and dataset quality. Our technique involves resampling from the synthetic data to filter out samples that do not meet the selected utility measures, using an efficient stochastic first-order algorithm to find optimal resampling weights. Through comprehensive numerical experiments, we demonstrate that our approach consistently improves the utility of synthetic data across multiple benchmark datasets and state-of-the-art synthetic data generation algorithms.

Optimization/Convex

Jaeyeon Kim, Asuman Ozdaglar, Chanwoo Park, Ernest Ryu

In convex optimization, first-order optimization methods efficiently minimizing function values have been a central subject study since Nesterov's seminal work of 1983. Recently, however, Kim and Fessler's OGM-G and Lee et al.'s FISTA-G have been presented as alternatives that efficiently minimize the gradient magnitude instead. In this paper, we present H-duality, which represents a surprising one-to-one correspondence between methods efficiently minimizing function values and methods efficiently minimizing gradient magnitude. In continuous-time formulations, H-duality corresponds to reversing the time dependence of the dissipation/friction term. To the best of our knowledge, H-duality is different from Lagrange/Fenchel duality and is distinct from any previously known duality or symmetry relations. Using H-duality, we obtain a clearer understanding of the symmetry between Nesterov's method and OGM-G, derive a new class of methods efficiently reducing gradient magnitudes of smooth convex functions, and find a new composite minimization method that is simpler and faster than FISTA-G.

Miscellaneous Aspects of Machine Learning/General Machine Learning Techniques

Khai Nguyen, Tongzheng Ren, Nhat Ho

Sliced Wasserstein (SW) distance suffers from redundant projections due to independent uniform random projecting directions. To partially overcome the issue, max K sliced Wasserstein (Max-K-SW) distance ($K\geq 1$), seeks the best discriminative orthogonal projecting directions. Despite being able to reduce the number of projections, the metricity of the Max-K-SW cannot be guaranteed in practice due to the non-optimality of the optimization. Moreover, the orthogonality constraint is also computationally expensive and might not be effective. To address the problem, we introduce a new family of SW distances, named Markovian sliced Wasserstein (MSW) distance, which imposes a first-order Markov structure on projecting directions. We discuss various members of the MSW by specifying the Markov structure including the prior distribution, the transition distribution, and the burning and thinning technique. Moreover, we investigate the theoretical properties of MSW including topological properties (metricity, weak convergence, and connection to other distances), statistical properties (sample complexity, and Monte Carlo estimation error), and computational properties (computational complexity and memory complexity). Finally, we compare MSW distances with previous SW variants in various applications such as gradient flows, color transfer, and deep generative modeling to demonstrate the favorable performance of the MSW.