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The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization

Neural Information Processing Systems

Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive study. It has been recognized that they may cycle, and there is no good understanding of their limit points when they do not. When they converge, do they converge to local min-max solutions? We characterize the limit points of two basic first order methods, namely Gradient Descent/Ascent (GDA) and Optimistic Gradient Descent Ascent (OGDA). We show that both dynamics avoid unstable critical points for almost all initializations. Moreover, for small step sizes and under mild assumptions, the set of OGDA-stable critical points is a superset of GDA-stable critical points, which is a superset of local min-max solutions (strict in some cases). The connecting thread is that the behavior of these dynamics can be studied from a dynamical systems perspective.



The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization

Neural Information Processing Systems

Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive study. It has been recognized that they may cycle, and there is no good understanding of their limit points when they do not. When they converge, do they converge to local min-max solutions? We characterize the limit points of two basic first order methods, namely Gradient Descent/Ascent (GDA) and Optimistic Gradient Descent Ascent (OGDA). We show that both dynamics avoid unstable critical points for almost all initializations. Moreover, for small step sizes and under mild assumptions, the set of OGDA-stable critical points is a superset of GDA-stable critical points, which is a superset of local min-max solutions (strict in some cases). The connecting thread is that the behavior of these dynamics can be studied from a dynamical systems perspective.


ImpMIA: Leveraging Implicit Bias for Membership Inference Attack under Realistic Scenarios

Golbari, Yuval, Wasserman, Navve, Vardi, Gal, Irani, Michal

arXiv.org Artificial Intelligence

Determining which data samples were used to train a model--known as Membership Inference Attack (MIA)--is a well-studied and important problem with implications for data privacy. Black-box methods presume access only to the model's outputs and often rely on training auxiliary reference models. While they have shown strong empirical performance, they rely on assumptions that rarely hold in real-world settings: (i) the attacker knows the training hyperparameters; (ii) all available non-training samples come from the same distribution as the training data; and (iii) the fraction of training data in the evaluation set is known. In this paper, we demonstrate that removing these assumptions leads to a significant drop in the performance of black-box attacks. We introduce ImpMIA, a Membership Inference Attack that exploits the Implicit Bias of neural networks, hence removes the need to rely on any reference models and their assumptions. ImpMIA is a white-box attack - a setting which assumes access to model weights and is becoming increasingly realistic given that many models are publicly available (e.g., via Hugging Face). Building on maximum-margin implicit bias theory, ImpMIA uses the Karush-Kuhn-Tucker (KKT) optimality conditions to identify training samples. This is done by finding the samples whose gradients most strongly reconstruct the trained model's parameters. As a result, ImpMIA achieves state-of-the-art performance compared to both black and white box attacks in realistic settings where only the model weights and a superset of the training data are available. Ensuring that trained models do not leak information about their training sets is a critical challenge. Membership inference attacks (MIAs) evaluate this risk by determining whether a given example was part of a model's training data. MIAs can be broadly divided into two categories: black-box, which assume only query access to model outputs (Shokri et al., 2017; Y eom et al., 2018; Li & Zhang, 2021; Carlini et al., 2022), and white-box, which exploit access to internal parameters such as weights or gradients (Nasr et al., 2019; Leino & Fredrikson, 2020; Cohen & Giryes, 2024). The most effective black-box MIAs are reference-model-based attacks. These methods estimate the distribution of losses for members (training samples) versus non-members by training auxiliary reference models that mimic the target model, thereby learning its loss behavior. However, training large sets of reference models is computationally expensive, and--more importantly--their effectiveness depends on the reference models being accurate surrogates of the target.


Superset Technique for Approximate Recovery in One-Bit Compressed Sensing

Larkin Flodin, Venkata Gandikota, Arya Mazumdar

Neural Information Processing Systems

One-bit compressed sensing (1bCS) is a method of signal acquisition under extreme measurement quantization that gives important insights on the limits of signal compression and analog-to-digital conversion. The setting is also equivalent to the problem of learning a sparse hyperplane-classifier. In this paper, we propose a generic approach for signal recovery in nonadaptive 1bCS that leads to improved sample complexity for approximate recovery for a variety of signal models, including nonnegative signals and binary signals. We construct 1bCS matrices that are universal - i.e. work for all signals under a model - and at the same time recover very general random sparse signals with high probability. In our approach, we divide the set of samples (measurements) into two parts, and use the first part to recover the superset of the support of a sparse vector. The second set of measurements is then used to approximate the signal within the superset.


Hyperband-based Bayesian Optimization for Black-box Prompt Selection

Schneider, Lennart, Wistuba, Martin, Klein, Aaron, Golebiowski, Jacek, Zappella, Giovanni, Merra, Felice Antonio

arXiv.org Artificial Intelligence

Optimal prompt selection is crucial for maximizing large language model (LLM) performance on downstream tasks. As the most powerful models are proprietary and can only be invoked via an API, users often manually refine prompts in a black-box setting by adjusting instructions and few-shot examples until they achieve good performance as measured on a validation set. Recent methods addressing static black-box prompt selection face significant limitations: They often fail to leverage the inherent structure of prompts, treating instructions and few-shot exemplars as a single block of text. Moreover, they often lack query-efficiency by evaluating prompts on all validation instances, or risk sub-optimal selection of a prompt by using random subsets of validation instances. We introduce HbBoPs, a novel Hyperband-based Bayesian optimization method for black-box prompt selection addressing these key limitations. Our approach combines a structural-aware deep kernel Gaussian Process to model prompt performance with Hyperband as a multi-fidelity scheduler to select the number of validation instances for prompt evaluations. The structural-aware modeling approach utilizes separate embeddings for instructions and few-shot exemplars, enhancing the surrogate model's ability to capture prompt performance and predict which prompt to evaluate next in a sample-efficient manner. Together with Hyperband as a multi-fidelity scheduler we further enable query-efficiency by adaptively allocating resources across different fidelity levels, keeping the total number of validation instances prompts are evaluated on low. Extensive evaluation across ten benchmarks and three LLMs demonstrate that HbBoPs outperforms state-of-the-art methods.


Fixture calibration with guaranteed bounds from a few correspondence-free surface points

Haugaard, Rasmus Laurvig, Kim, Yitaek, Iversen, Thorbjørn Mosekjær

arXiv.org Artificial Intelligence

Calibration of fixtures in robotic work cells is essential but also time consuming and error-prone, and poor calibration can easily lead to wasted debugging time in downstream tasks. Contact-based calibration methods let the user measure points on the fixture's surface with a tool tip attached to the robot's end effector. Most such methods require the user to manually annotate correspondences on the CAD model, however, this is error-prone and a cumbersome user experience. We propose a correspondence-free alternative: The user simply measures a few points from the fixture's surface, and our method provides a tight superset of the poses which could explain the measured points. This naturally detects ambiguities related to symmetry and uninformative points and conveys this uncertainty to the user. Perhaps more importantly, it provides guaranteed bounds on the pose. The computation of such bounds is made tractable by the use of a hierarchical grid on SE(3). Our method is evaluated both in simulation and on a real collaborative robot, showing great potential for easier and less error-prone fixture calibration. Project page at https://sites.google.com/view/ttpose


The Case for Dataset-Centric Visualization

#artificialintelligence

Different BI tools offer different approaches to building dashboards. On one end of the spectrum, you have tools that prescribe having one query per chart and on the other end you have tools that espouse implementing a complex semantic layer. I believe there's a middle path that lies between both extremes, and I call it the dataset-centric approach. In the dataset-centric approach, the tool is connected to individual datasets that are expected to contain all of the metrics and dimensions for a given subject area. In this post, I'll describe the strengths and tradeoffs for each of the approaches and make the case for the dataset-centric approach as the ideal one for fast-moving data teams.


70-Page Paper From Yoshua Bengio Team: GFlowNet Foundations

#artificialintelligence

There's no slowing down the godfathers of deep learning, who continue to innovate. Several years ago Geoffrey Hinton introduced Capsule Networks (CapsNets) for dynamic image modelling, and this past summer a Yoshua Bengio team proposed Generative Flow Networks (GFlowNets), a low-network-based generative method that can turn a given positive reward into a generative policy that samples with a probability proportional to the return. GFlowNets achieve competitive results on molecule synthesis domain tasks and perform well on a simple domain where there are many modes to the reward function. In the new paper GFlowNet Foundations, a research team from Mila, University of Montreal, McGill University, Stanford University, CIFAR and Microsoft Azure AI builds upon GFlowNets, providing an in-depth formal foundation and expansion of the set of theoretical results for a broad range of scenarios, especially active learning. GFlowNets are inspired by the way information propagates in temporal-difference reinforcement learning.


NIST SRE CTS Superset: A large-scale dataset for telephony speaker recognition

Sadjadi, Seyed Omid

arXiv.org Artificial Intelligence

This document provides a brief description of the National Institute of Standards and Technology (NIST) speaker recognition evaluation (SRE) conversational telephone speech (CTS) Superset. The CTS Superset has been created in an attempt to provide the research community with a large-scale dataset along with uniform metadata that can be used to effectively train and develop telephony (narrowband) speaker recognition systems. It contains a large number of telephony speech segments from more than 6800 speakers with speech durations distributed uniformly in the [10s, 60s] range. The segments have been extracted from the source corpora used to compile prior SRE datasets (SRE1996-2012), including the Greybeard corpus as well as the Switchboard and Mixer series collected by the Linguistic Data Consortium (LDC). In addition to the brief description, we also report speaker recognition results on the NIST 2020 CTS Speaker Recognition Challenge, obtained using a system trained with the CTS Superset. The results will serve as a reference baseline for the challenge.