Inductive Learning
beta-risk: a New Surrogate Risk for Learning from Weakly Labeled Data
Valentina Zantedeschi, Rรฉmi Emonet, Marc Sebban
During the past few years, the machine learning community has paid attention to developing new methods for learning from weakly labeled data. This field covers different settings like semi-supervised learning, learning with label proportions, multi-instance learning, noise-tolerant learning, etc. This paper presents a generic framework to deal with these weakly labeled scenarios. We introduce the ฮฒ-risk as a generalized formulation of the standard empirical risk based on surrogate marginbased loss functions. This risk allows us to express the reliability on the labels and to derive different kinds of learning algorithms. We specifically focus on SVMs and propose a soft margin ฮฒ-SVM algorithm which behaves better that the state of the art.
A Non-convex One-Pass Framework for Generalized Factorization Machine and Rank-One Matrix Sensing
We develop an efficient alternating framework for learning a generalized version of Factorization Machine (gFM) on steaming data with provable guarantees. When the instances are sampled from ddimensional random Gaussian vectors and the target second order coefficient matrix in gFM is of rank k, our algorithm converges linearly, achieves O() recovery error after retrieving O(k3dlog(1/)) training instances, consumes O(kd) memory in one-pass of dataset and only requires matrixvector product operations in each iteration. The key ingredient of our framework is a construction of an estimation sequence endowed with a so-called Conditionally Independent RIP condition (CI-RIP). As special cases of gFM, our framework can be applied to symmetric or asymmetric rank-one matrix sensing problems, such as inductive matrix completion and phase retrieval.
On the role of memorization in learned priors for geophysical inverse problems
Siahkoohi, Ali, Sabeddu, Davide
Learned priors based on deep generative models offer data-driven regularization for seismic inversion, but training them requires a dataset of representative subsurface models -- a resource that is inherently scarce in geoscience applications. Since the training objective of most generative models can be cast as maximum likelihood on a finite dataset, any such model risks converging to the empirical distribution -- effectively memorizing the training examples rather than learning the underlying geological distribution. We show that the posterior under such a memorized prior reduces to a reweighted empirical distribution -- i.e., a likelihood-weighted lookup among the stored training examples. For diffusion models specifically, memorization yields a Gaussian mixture prior in closed form, and linearizing the forward operator around each training example gives a Gaussian mixture posterior whose components have widths and shifts governed by the local Jacobian. We validate these predictions on a stylized inverse problem and demonstrate the consequences of memorization through diffusion posterior sampling for full waveform inversion.
Collaboration! Towards Robust Neural Methods for Routing Problems
Despite enjoying desirable efficiency and reduced reliance on domain expertise, existing neural methods for vehicle routing problems (VRPs) suffer from severe robustness issues -- their performance significantly deteriorates on clean instances with crafted perturbations. To enhance robustness, we propose an ensemble-based w.r.t. the defense of neural VRP methods, which is crucial yet underexplored in the literature. Given a neural VRP method, we adversarially train multiple models in a collaborative manner to synergistically promote robustness against attacks, while boosting standard generalization on clean instances. A neural router is designed to adeptly distribute training instances among models, enhancing overall load balancing and collaborative efficacy. Extensive experiments verify the effectiveness and versatility of CNF in defending against various attacks across different neural VRP methods. Notably, our approach also achieves impressive out-of-distribution generalization on benchmark instances.
RankUp: Boosting Semi-Supervised Regression with an Auxiliary Ranking Classifier
State-of-the-art (SOTA) semi-supervised learning techniques, such as FixMatch and it's variants, have demonstrated impressive performance in classification tasks. However, these methods are not directly applicable to regression tasks. In this paper, we present RankUp, a simple yet effective approach that adapts existing semi-supervised classification techniques to enhance the performance of regression tasks. RankUp achieves this by converting the original regression task into a ranking problem and training it concurrently with the original regression objective.
Improving Subgroup Robustness via Data Selection
Machine learning models can often fail on subgroups that are underrepresentedduring training. While dataset balancing can improve performance onunderperforming groups, it requires access to training group annotations and canend up removing large portions of the dataset. In this paper, we introduceData Debiasing with Datamodels (D3M), a debiasing approachwhich isolates and removes specific training examples that drive the model'sfailures on minority groups. Our approach enables us to efficiently traindebiased classifiers while removing only a small number of examples, and doesnot require training group annotations or additional hyperparameter tuning.
Effective Targeted Attacks for Adversarial Self-Supervised Learning
Recently, unsupervised adversarial training (AT) has been highlighted as a means of achieving robustness in models without any label information. Previous studies in unsupervised AT have mostly focused on implementing self-supervised learning (SSL) frameworks, which maximize the instance-wise classification loss to generate adversarial examples. However, we observe that simply maximizing the self-supervised training loss with an untargeted adversarial attack often results in generating ineffective adversaries that may not help improve the robustness of the trained model, especially for non-contrastive SSL frameworks without negative examples. To tackle this problem, we propose a novel positive mining for targeted adversarial attack to generate effective adversaries for adversarial SSL frameworks. Specifically, we introduce an algorithm that selects the most confusing yet similar target example for a given instance based on entropy and similarity, and subsequently perturbs the given instance towards the selected target. Our method demonstrates significant enhancements in robustness when applied to non-contrastive SSL frameworks, and less but consistent robustness improvements with contrastive SSL frameworks, on the benchmark datasets.
Dissecting the Interplay of Attention Paths in a Statistical Mechanics Theory of Transformers
Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable. We develop a statistical mechanics theory of Bayesian learning in this model, deriving exact equations for the network's predictor statistics under the finite-width thermodynamic limit, i.e., $N,P\rightarrow\infty$, $P/N=\mathcal{O}(1)$, where $N$ is the network width and $P$ is the number of training examples. Our theory shows that the predictor statistics are expressed as a sum of independent kernels, each one pairing different attention paths, defined as information pathways through different attention heads across layers. The kernels are weighted according to a task-relevant kernel combination mechanism that aligns the total kernel with the task labels. As a consequence, this interplay between attention paths enhances generalization performance. Experiments confirm our findings on both synthetic and real-world sequence classification tasks. Finally, our theory explicitly relates the kernel combination mechanism to properties of the learned weights, allowing for a qualitative transfer of its insights to models trained via gradient descent. As an illustration, we demonstrate an efficient size reduction of the network, by pruning those attention heads that are deemed less relevant by our theory.
Instruction Tuning With Loss Over Instructions
Instruction tuning plays a crucial role in shaping the outputs of language models (LMs) to desired styles. In this work, we propose a simple yet effective method, Instruction Modelling (IM), which trains LMs by applying a loss function to the instruction and prompt part rather than solely to the output part. Through experiments across 21 diverse benchmarks, we show that, in many scenarios, IM can effectively improve the LM performance on both NLP tasks ( MMLU, TruthfulQA, and HumanEval) and open-ended generation benchmarks ( MT-Bench and AlpacaEval). Remarkably, in the most advantageous case, IM boosts model performance on AlpacaEval 1.0 by over 100%. We identify two key factors influencing the effectiveness of IM: (1) The ratio between instruction length and output length in the training data; and (2) The number of training examples. We observe that IM is especially beneficial when trained on datasets with lengthy instructions paired with brief outputs, or under the Superficial Alignment Hypothesis (SAH) where a small amount of training examples are used for instruction tuning. Further analysis substantiates our hypothesis that our improvement can be attributed to reduced overfitting to instruction tuning datasets.