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Miscellaneous Aspects of Machine Learning · Representation Learning

Bei Li, Tong Zheng, Rui Wang, Jiahao Liu, 清妍 郭, Junliang Guo, Xu Tan, Tong Xiao, JingBo Zhu, Jingang Wang 等

Residual networks, as discrete approximations of Ordinary Differential Equations (ODEs), have inspired significant advancements in neural network design, including multistep methods, high-order methods, and multi-particle dynamical systems. The precision of the solution to ODEs significantly affects parameter optimization, thereby impacting model performance. In this work, we present a series of advanced explorations of Transformer architecture design to minimize the error compared to the true ``solution.'' First, we introduce a predictor-corrector learning framework to minimize truncation errors, which consists of a high-order predictor and a multistep corrector. Second, we propose an exponential moving average-based coefficient learning method to strengthen our higher-order predictor. Extensive experiments on large-scale machine translation, abstractive summarization, language modeling, and natural language understanding benchmarks demonstrate the superiority of our approach. On the WMT'14 English-German and English-French tasks, our model achieved BLEU scores of 30.95 and 44.27, respectively. Furthermore, on the OPUS multilingual machine translation task, our model surpasses a robust 3.8B DeepNet by an average of 2.9 SacreBLEU, using only 1/3 parameters. Notably, it also beats LLama models by 5.7 accuracy points on the LM Harness Evaluation.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Samuel Holt, Tennison Liu, Mihaela van der Schaar

Digital Twins (DTs) are computational models that simulate the states and temporal dynamics of real-world systems, playing a crucial role in prediction, understanding, and decision-making across diverse domains. However, existing approaches to DTs often struggle to generalize to unseen conditions in data-scarce settings, a crucial requirement for such models. To address these limitations, our work begins by establishing the essential desiderata for effective DTs. Hybrid Digital Twins (**HDTwins**) represent a promising approach to address these requirements, modeling systems using a composition of both mechanistic and neural components. This hybrid architecture simultaneously leverages (partial) domain knowledge and neural network expressiveness to enhance generalization, with its modular design facilitating improved evolvability. While existing hybrid models rely on expert-specified architectures with only parameters optimized on data, *automatically* specifying and optimizing HDTwins remains intractable due to the complex search space and the need for flexible integration of domain priors. To overcome this complexity, we propose an evolutionary algorithm (**HDTwinGen**) that employs Large Language Models (LLMs) to autonomously propose, evaluate, and optimize HDTwins. Specifically, LLMs iteratively generate novel model specifications, while offline tools are employed to optimize emitted parameters. Correspondingly, proposed models are evaluated and evolved based on targeted feedback, enabling the discovery of increasingly effective hybrid models. Our empirical results reveal that HDTwinGen produces generalizable, sample-efficient, and evolvable models, significantly advancing DTs' efficacy in real-world applications.

Miscellaneous Aspects of Machine Learning · Kernel methods

Anna Korba, Francis Bach, Clémentine CHAZAL

In this paper, we study the statistical and geometrical properties of the Kullback-Leibler divergence with kernel covariance operators (KKL) introduced by [Bach, 2022, Information Theory with Kernel Methods]. Unlike the classical Kullback-Leibler (KL) divergence that involves density ratios, the KKL compares probability distributions through covariance operators (embeddings) in a reproducible kernel Hilbert space (RKHS), and compute the Kullback-Leibler quantum divergence. This novel divergence hence shares parallel but different aspects with both the standard Kullback-Leibler between probability distributions and kernel embeddings metrics such as the maximum mean discrepancy. A limitation faced with the original KKL divergence is its inability to be defined for distributions with disjoint supports. To solve this problem, we propose in this paper a regularised variant that guarantees that divergence is well defined for all distributions. We derive bounds that quantify the deviation of the regularised KKL to the original one, as well as concentration bounds. In addition, we provide a closed-form expression for the regularised KKL, specifically applicable when the distributions consist of finite sets of points, which makes it implementable. Furthermore, we derive a Wasserstein gradient descent scheme of the KKL divergence in the case of discrete distributions, and study empirically its properties to transport a set of points to a target distribution.

Miscellaneous Aspects of Machine Learning · Supervised Learning

BIN HAN, Yi-Xuan Sun, Ya-Lin Zhang, Libang Zhang, Haoran Hu, Longfei Li, Jun Zhou, Guo Ye, HUIMEI HE

This paper considers the problem of learning from multiple sets of inaccurate labels, which can be easily obtained from low-cost annotators, such as rule-based annotators. Previous works typically concentrate on aggregating information from all the annotators, overlooking the significance of data refinement. This paper presents a collaborative refining approach for learning from inaccurate labels. To refine the data, we introduce the annotator agreement as an instrument, which refers to whether multiple annotators agree or disagree on the labels for a given sample. For samples where some annotators disagree, a comparative strategy is proposed to filter noise. Through theoretical analysis, the connections among multiple sets of labels, the respective models trained on them, and the true labels are uncovered to identify relatively reliable labels. For samples where all annotators agree, an aggregating strategy is designed to mitigate potential noise. Guided by theoretical bounds on loss values, a sample selection criterion is introduced and modified to be more robust against potentially problematic values. Through these two methods, all the samples are refined during training, and these refined samples are used to train a lightweight model simultaneously. Extensive experiments are conducted on benchmark and real-world datasets to demonstrate the superiority of our methods.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Nicholas Krämer, Pablo Moreno-Muñoz, Hrittik Roy, Søren Hauberg

Tuning scientific and probabilistic machine learning models - for example, partial differential equations, Gaussian processes, or Bayesian neural networks - often relies on evaluating functions of matrices whose size grows with the data set or the number of parameters.While the state-of-the-art for _evaluating_ these quantities is almost always based on Lanczos and Arnoldi iterations, the present work is the first to explain how to _differentiate_ these workhorses of numerical linear algebra efficiently.To get there, we derive previously unknown adjoint systems for Lanczos and Arnoldi iterations, implement them in JAX, and show that the resulting code can compete with Diffrax when it comes to differentiating PDEs, GPyTorch for selecting Gaussian process models and beats standard factorisation methods for calibrating Bayesian neural networks.All this is achieved without any problem-specific code optimisation.Find the code at [link redacted] and install the library with *pip install [redacted]*.

Miscellaneous Aspects of Machine Learning · Representation Learning

Charles Arnal, David Cohen-Steiner, Vincent Divol

Cech Persistence diagrams (PDs) are topological descriptors routinely used to capture the geometry of complex datasets. They are commonly compared using the Wasserstein distances $\mathrm{OT}_p$; however, the extent to which PDs are stable with respect to these metrics remains poorly understood. We partially close this gap by focusing on the case where datasets are sampled on an $m$-dimensional submanifold of $\mathbb{R}^d$. Under this manifold hypothesis, we show that convergence with respect to the $\mathrm{OT}_p$ metric happens exactly when $p>m$. We also provide improvements upon the bottleneck stability theorem in this case and prove new laws of large numbers for the total $\alpha$-persistence of PDs. Finally, we show how these theoretical findings shed new light on the behavior of the feature maps on the space of PDs that are used in ML-oriented applications of Topological Data Analysis.

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

Zi-Hao Zhou, Siyuan Fang, Zi-Jing Zhou, Tong Wei, Yuanyu Wan, Min-Ling Zhang

Long-tailed semi-supervised learning poses a significant challenge in training models with limited labeled data exhibiting a long-tailed label distribution. Current state-of-the-art LTSSL approaches heavily rely on high-quality pseudo-labels for large-scale unlabeled data. However, these methods often neglect the impact of representations learned by the neural network and struggle with real-world unlabeled data, which typically follows a different distribution than labeled data. This paper introduces a novel probabilistic framework that unifies various recent proposals in long-tail learning. Our framework derives the class-balanced contrastive loss through Gaussian kernel density estimation. We introduce a continuous contrastive learning method, CCL, extending our framework to unlabeled data using *reliable* and *smoothed* pseudo-labels. By progressively estimating the underlying label distribution and optimizing its alignment with model predictions, we tackle the diverse distribution of unlabeled data in real-world scenarios. Extensive experiments across multiple datasets with varying unlabeled data distributions demonstrate that CCL consistently outperforms prior state-of-the-art methods, achieving over 4% improvement on the ImageNet-127 dataset. The supplementary material includes the source code for reproducibility.

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

Marzi Heidari, Hanping Zhang, Yuhong Guo

In recent years, semi-supervised learning (SSL) has gained significant attention due to its ability to leverage both labeled and unlabeled data to improve model performance, especially when labeled data is scarce. However, most current SSL methods rely on heuristics or predefined rules for generating pseudo-labels and leveraging unlabeled data. They are limited to exploiting loss functions and regularization methods within the standard norm. In this paper, we propose a novel Reinforcement Learning (RL) Guided SSL method, RLGSSL, that formulates SSL as a one-armed bandit problem and deploys an innovative RL loss based on weighted reward to adaptively guide the learning process of the prediction model. RLGSSL incorporates a carefully designed reward function that balances the use of labeled and unlabeled data to enhance generalization performance. A semi-supervised teacher-student framework is further deployed to increase the learning stability. We demonstrate the effectiveness of RLGSSL through extensive experiments on several benchmark datasets and show that our approach achieves consistent superior performance compared to state-of-the-art SSL methods.

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

Tyler Ingebrand, Adam Thorpe, Ufuk Topcu

Autonomous systems often encounter environments and scenarios beyond the scope of their training data, which underscores a critical challenge: the need to generalize and adapt to unseen scenarios in real time. This challenge necessitates new mathematical and algorithmic tools that enable adaptation and zero-shot transfer. To this end, we leverage the theory of function encoders, which enables zero-shot transfer by combining the flexibility of neural networks with the mathematical principles of Hilbert spaces. Using this theory, we first present a method for learning a space of dynamics spanned by a set of neural ODE basis functions. After training, the proposed approach can rapidly identify dynamics in the learned space using an efficient inner product calculation. Critically, this calculation requires no gradient calculations or retraining during the online phase. This method enables zero-shot transfer for autonomous systems at runtime and opens the door for a new class of adaptable control algorithms. We demonstrate state-of-the-art system modeling accuracy for two MuJoCo robot environments and show that the learned models can be used for more efficient MPC control of a quadrotor.

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

Ayush Jain, Andrea Montanari, Eren Sasoglu

Collecting large quantities of high-quality data can be prohibitively expensive or impractical, and a bottleneck in machine learning. One may instead augment a small set of $n$ data points from the target distribution with data from more accessible sources, e.g. data collected under different circumstances or synthesized by generative models. We refer to such data as `surrogate data'. We study a weighted empirical risk minimization (ERM) approach for integrating surrogate data into training. We analyze mathematically this method under several classical statistical models, and validate our findings empirically on datasets from different domains. Our main findings are: $(i)$ Integrating surrogate data can significantly reduce the test error on the original distribution. Surprisingly, this can happen even when the surrogate data is unrelated to the original ones. We trace back this behavior to the classical Stein's paradox. $(ii)$ In order to reap the benefit of surrogate data, it is crucial to use optimally weighted ERM. $(iii)$ The test error of models trained on mixtures of real and surrogate data is approximately described by a scaling law. This scaling law can be used to predict the optimal weighting scheme, and to choose the amount of surrogate data to add.

Miscellaneous Aspects of Machine Learning · Supervised Learning

Moses Charikar, Chirag Pabbaraju, Kirankumar Shiragur

Recent advances in large language models have shown capabilities that are extraordinary and near-superhuman. These models operate with such complexity that reliably evaluating and aligning them proves challenging for humans. This leads to the natural question: can guidance from weak models (like humans) adequately direct the capabilities of strong models? In a recent and somewhat surprising work, Burns et al. (2023) empirically demonstrated that when strong models (like GPT-4) are finetuned using labels generated by weak supervisors (like GPT-2), the strong models outperform their weaker counterparts---a phenomenon they term *weak-to-strong generalization*.In this work, we present a theoretical framework for understanding weak-to-strong generalization. Specifically, we show that the improvement in performance achieved by strong models over their weaker counterparts is quantified by the *misfit error* incurred by the strong model on labels generated by the weaker model. Our theory reveals several curious algorithmic insights. For instance, we can predict the amount by which the strong model will improve over the weak model, and also choose among different weak models to train the strong model, based on its misfit error. We validate our theoretical findings through various empirical assessments.

Miscellaneous Aspects of Machine Learning · Kernel methods

Sejun Park, Kihun Hong, Ganguk Hwang

Over the past decade, there is a growing interest in collaborative learning that can enhance AI models of multiple parties.However, it is still challenging to enhance performance them without sharing private data and models from individual parties.One recent promising approach is to develop distillation-based algorithms that exploit unlabeled public data but the results are still unsatisfactory in both theory and practice.To tackle this problem, we rigorously analyze a representative distillation-based algorithm in the view of kernel regression.This work provides the first theoretical results to prove the (nearly) minimax optimality of the nonparametric collaborative learning algorithm that does not directly share local data or models in massively distributed statistically heterogeneous environments.Inspired by our theoretical results, we also propose a practical distillation-based collaborative learning algorithm based on neural network architecture.Our algorithm successfully bridges the gap between our theoretical assumptions and practical settings with neural networks through feature kernel matching.We simulate various regression tasks to verify our theory and demonstrate the practical feasibility of our proposed algorithm.

Miscellaneous Aspects of Machine Learning · Kernel methods

Florian Kalinke, Zoltan Szabo

Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of $M\ge2$ random variables. Probably the most widespread independence measure relying on kernels is the so-called Hilbert-Schmidt independence criterion (HSIC; also referred to as distance covariance in the statistics literature). Despite various existing HSIC estimators designed since its introduction close to two decades ago, the fundamental question of the rate at which HSIC can be estimated is still open. In this work, we prove that the minimax optimal rate of HSIC estimation on $\mathbb{R}^d$ for Borel measures containing the Gaussians with continuous bounded translation-invariant characteristic kernels is $\mathcal{O}\left(n^{-1/2}\right)$. Specifically, our result implies the optimality in the minimax sense of many of the most-frequently used estimators (including the U-statistic, the V-statistic, and the Nyström-based one) on $\mathbb{R}^d$.

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

Maximilien Dreveton, Charbel Chucri, Matthias Grossglauser, Patrick Thiran

The metric backbone of a weighted graph is the union of all-pairs shortest paths. It is obtained by removing all edges $(u,v)$ that are not the shortest path between $u$ and $v$. In networks with well-separated communities, the metric backbone tends to preserve many inter-community edges, because these edges serve as bridges connecting two communities, but tends to delete many intra-community edges because the communities are dense. This suggests that the metric backbone would dilute or destroy the community structure of the network. However, this is not borne out by prior empirical work, which instead showed that the metric backbone of real networks preserves the community structure of the original network well. In this work, we analyze the metric backbone of a broad class of weighted random graphs with communities, and we formally prove the robustness of the community structure with respect to the deletion of all the edges that are not in the metric backbone. An empirical comparison of several graph sparsification techniques confirms our theoretical finding and shows that the metric backbone is an efficient sparsifier in the presence of communities.

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

Baekrok Shin, Junsoo Oh, Hanseul Cho, Chulhee Yun

Warm-starting neural network training by initializing networks with previously learned weights is appealing, as practical neural networks are often deployed under a continuous influx of new data. However, it often leads to *loss of plasticity*, where the network loses its ability to learn new information, resulting in worse generalization than training from scratch. This occurs even under stationary data distributions, and its underlying mechanism is poorly understood. We develop a framework emulating real-world neural network training and identify noise memorization as the primary cause of plasticity loss when warm-starting on stationary data. Motivated by this, we propose **Direction-Aware SHrinking (DASH)**, a method aiming to mitigate plasticity loss by selectively forgetting memorized noise while preserving learned features. We validate our approach on vision tasks, demonstrating improvements in test accuracy and training efficiency.

Miscellaneous Aspects of Machine Learning · Representation Learning

Jie Wang, Tingfa Xu, Lihe Ding, Jianan Li

Achieving robust 3D perception in the face of corrupted data presents an challenging hurdle within 3D vision research. Contemporary transformer-based point cloud recognition models, albeit advanced, tend to overfit to specific patterns, consequently undermining their robustness against corruption. In this work, we introduce the Target-Guided Adversarial Point Cloud Transformer, termed APCT, a novel architecture designed to augment global structure capture through an adversarial feature erasing mechanism predicated on patterns discerned at each step during training. Specifically, APCT integrates an Adversarial Significance Identifier and a Target-guided Promptor. The Adversarial Significance Identifier, is tasked with discerning token significance by integrating global contextual analysis, utilizing a structural salience index algorithm alongside an auxiliary supervisory mechanism. The Target-guided Promptor, is responsible for accentuating the propensity for token discard within the self-attention mechanism, utilizing the value derived above, consequently directing the model attention towards alternative segments in subsequent stages. By iteratively applying this strategy in multiple steps during training, the network progressively identifies and integrates an expanded array of object-associated patterns. Extensive experiments demonstrate that our method achieves state-of-the-art results on multiple corruption benchmarks.

Miscellaneous Aspects of Machine Learning

Xiang Liu, Liangxi Liu, Feiyang Ye, Yunheng Shen, Xia Li, Linshan Jiang, Jialin Li

Efficiently aggregating trained neural networks from local clients into a global model on a server is a widely researched topic in federated learning. Recently, motivated by diminishing privacy concerns, mitigating potential attacks, and reducing communication overhead, one-shot federated learning (i.e., limiting client-server communication into a single round) has gained popularity among researchers. However, the one-shot aggregation performances are sensitively affected by the non-identical training data distribution, which exhibits high statistical heterogeneity in some real-world scenarios. To address this issue, we propose a novel one-shot aggregation method with layer-wise posterior aggregation, named FedLPA. FedLPA aggregates local models to obtain a more accurate global model without requiring extra auxiliary datasets or exposing any private label information, e.g., label distributions. To effectively capture the statistics maintained in the biased local datasets in the practical non-IID scenario, we efficiently infer the posteriors of each layer in each local model using layer-wise Laplace approximation and aggregate them to train the global parameters. Extensive experimental results demonstrate that FedLPA significantly improves learning performance over state-of-the-art methods across several metrics.

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

Xu Yang, Chen Liu, Ying Wei

This paper introduces AMT, an \textbf{A}dversarial \textbf{M}eta-\textbf{T}uning methodology, to boost the robust generalization of pre-trained models in the out-of-domain (OOD) few-shot learning. To address the challenge of transferring knowledge from source domains to unseen target domains, we construct the robust LoRAPool by meta-tuning LoRAs with dual perturbations applied to not only the inputs but also singular values and vectors of the weight matrices at various robustness levels. On top of that, we introduce a simple yet effective test-time merging mechanism to dynamically merge discriminative LoRAs for test-time task customization. Extensive evaluations demonstrate that AMT yields significant improvements, up to 12.92\% in clean generalization and up to 49.72\% in adversarial generalization, over previous state-of-the-art methods across a diverse range of OOD few-shot image classification tasks on three benchmarks, confirming the effectiveness of our approach to boost the robust generalization of pre-trained models. Our code is available at \href{https://github.com/xyang583/AMT}{https://github.com/xyang583/AMT}.

Miscellaneous Aspects of Machine Learning · Representation Learning

Benjamin Rozonoyer, Michael Boratko, Dhruvesh Patel, Wenlong Zhao, Shib Dasgupta, Hung Le, Andrew McCallum

When training node embedding models to represent large directed graphs (digraphs), it is impossible to observe all entries of the adjacency matrix during training. As a consequence most methods employ sampling. For very large digraphs, however, this means many (most) entries may be unobserved during training. In general, observing every entry would be necessary to uniquely identify a graph, however if we know the graph has a certain property some entries can be omitted - for example, only half the entries would be required for a symmetric graph. In this work, we develop a novel framework to identify a subset of entries required to uniquely distinguish a graph among all transitively-closed DAGs. We give an explicit algorithm to compute the provably minimal set of entries, and demonstrate empirically that one can train node embedding models with greater efficiency and performance, provided the energy function has an appropriate inductive bias. We achieve robust performance on synthetic hierarchies and a larger real-world taxonomy, observing improved convergence rates in a resource-constrained setting while reducing the set of training examples by as much as 99%.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Charbel Sakr, Brucek Khailany

We propose ESPACE, an LLM compression technique based on dimensionality reduction of activations. Unlike prior works on weight-centric tensor decomposition, ESPACE projects activations onto a pre-calibrated set of principal components. The activation-centrality of the approach enables retraining LLMs with no loss of expressivity; while at inference, weight decomposition is obtained as a byproduct of matrix multiplication associativity. Theoretical results on the construction of projection matrices with optimal computational accuracy are provided. Experimentally, we find ESPACE enables 50% compression of GPT3, Llama2, and Nemotron4 models with small accuracy degradation, as low as a 0.18 perplexity increase on GPT3-22B. At lower compression rates of 20% to 40%, ESPACE drives GPT3 models to outperforming their baseline, by up to a 0.38 decrease in perplexity for GPT3-8B. ESPACE also reduces GEMM execution time and prefill inference latency on existing hardware. Comparison with related works on compressing Llama2-7B via matrix factorization shows that ESPACE is a first step in advancing the state-of-the-art in tensor decomposition compression of LLMs.