Deep Neural Collapse Is Provably Optimal for the Deep Unconstrained Features Model

Neural collapse (NC) refers to the surprising structure of the last layer of deep neural networks in the terminal phase of gradient descent training. Recently, an increasing amount of experimental evidence has pointed to the propagation of NC to earlier layers of neural networks. However, while the NC in the last layer is well studied theoretically, much less is known about its multi-layered counterpart - deep neural collapse (DNC). In particular, existing work focuses either on linear layers or only on the last two layers at the price of an extra assumption. Our paper fills this gap by generalizing the established analytical framework for NC - the unconstrained features model - to multiple non-linear layers. Our key technical contribution is to show that, in a deep unconstrained features model, the unique global optimum for binary classification exhibits all the properties typical of DNC. This explains the existing experimental evidence of DNC. We also empirically show that (i) by optimizing deep unconstrained features models via gradient descent, the resulting solution agrees well with our theory, and (ii) trained networks recover the unconstrained features suitable for the occurrence of DNC, thus supporting the validity of this modeling principle.

Robust Learning from Untrusted Sources

Modern machine learning methods often require more data for training than a single expert can provide. Therefore, it has become a standard procedure to collect data from external sources, e.g. via crowdsourcing. Unfortunately, the quality of these sources is not always guaranteed. As additional complications, the data might be stored in a distributed way, or might even have to remain private. In this work, we address the question of how to learn robustly in such scenarios. Studying the problem through the lens of statistical learning theory, we derive a procedure that allows for learning from all available sources, yet automatically suppresses irrelevant or corrupted data. We show by extensive experiments that our method provides significant improvements over alternative approaches from robust statistics and distributed optimization.

MACRO: A Meta-Algorithm for Conditional Risk Minimization

We study conditional risk minimization (CRM), i.e. the problem of learning a hypothesis of minimal risk for prediction at the next step of sequentially arriving dependent data. Despite it being a fundamental problem, successful learning in the CRM sense has so far only been demonstrated using theoretical algorithms that cannot be used for real problems as they would require storing all incoming data. In this work, we introduce MACRO, a meta-algorithm for CRM that does not suffer from this shortcoming, but nevertheless offers learning guarantees. Instead of storing all data it maintains and iteratively updates a set of learning subroutines. With suitable approximations, MACRO applied to real data, yielding improved prediction performance compared to traditional non-conditional learning.

Learning Intelligent Dialogs for Bounding Box Annotation

We introduce Intelligent Annotation Dialogs for bounding box annotation. We train an agent to automatically choose a sequence of actions for a human annotator to produce a bounding box in a minimal amount of time. Specifically, we consider two actions: box verification, where the annotator verifies a box generated by an object detector, and manual box drawing. We explore two kinds of agents, one based on predicting the probability that a box will be positively verified, and the other based on reinforcement learning. We demonstrate that (1) our agents are able to learn efficient annotation strategies in several scenarios, automatically adapting to the image difficulty, the desired quality of the boxes, and the detector strength; (2) in all scenarios the resulting annotation dialogs speed up annotation compared to manual box drawing alone and box verification alone, while also outperforming any fixed combination of verification and drawing in most scenarios; (3) in a realistic scenario where the detector is iteratively re-trained, our agents evolve a series of strategies that reflect the shifting trade-off between verification and drawing as the detector grows stronger.

Proceedings of The 38th Annual Workshop of the Austrian Association for Pattern Recognition (ÖAGM), 2014

The 38th Annual Workshop of the Austrian Association for Pattern Recognition (\"OAGM) will be held at IST Austria, on May 22-23, 2014. The workshop provides a platform for researchers and industry to discuss traditional and new areas of computer vision. This year the main topic is: Pattern Recognition: interdisciplinary challenges and opportunities.

The Most Persistent Soft-Clique in a Set of Sampled Graphs

When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when different graph instances have different edge sets pose a serious challenge. In this work we address this challenge for the problem of finding maximum weighted cliques. We introduce the concept of most persistent soft-clique. This is subset of vertices, that 1) is almost fully or at least densely connected, 2) occurs in all or almost all graph instances, and 3) has the maximum weight. We present a measure of clique-ness, that essentially counts the number of edge missing to make a subset of vertices into a clique. With this measure, we show that the problem of finding the most persistent soft-clique problem can be cast either as: a) a max-min two person game optimization problem, or b) a min-min soft margin optimization problem. Both formulations lead to the same solution when using a partial Lagrangian method to solve the optimization problems. By experiments on synthetic data and on real social network data, we show that the proposed method is able to reliably find soft cliques in graph data, even if that is distorted by random noise or unreliable observations.