Guiding Neural Collapse: Optimising Towards the Nearest Simplex Equiangular Tight Frame

Neural Collapse (NC) is a recently observed phenomenon in neural networks that characterises the solution space of the final classifier layer when trained until zero training loss. Specifically, NC suggests that the final classifier layer converges to a Simplex Equiangular Tight Frame (ETF), which maximally separates the weights corresponding to each class. By duality, the penultimate layer feature means also converge to the same simplex ETF. Since this simple symmetric structure is optimal, our idea is to utilise this property to improve convergence speed. Specifically, we introduce the notion of nearest simplex ETF geometry for the penultimate layer features at any given training iteration, by formulating it as a Riemannian optimisation. Then, at each iteration, the classifier weights are implicitly set to the nearest simplex ETF by solving this inner-optimisation, which is encapsulated within a declarative node to allow backpropagation. Our experiments on synthetic and real-world architectures for classification tasks demonstrate that our approach accelerates convergence and enhances training stability.

Neural Experts: Mixture of Experts for Implicit Neural Representations

Implicit neural representations (INRs) have proven effective in various tasks including image, shape, audio, and video reconstruction. These INRs typically learn the implicit field from sampled input points. This is often done using a single network for the entire domain, imposing many global constraints on a single function. In this paper, we propose a mixture of experts (MoE) implicit neural representation approach that enables learning local piece-wise continuous functions that simultaneously learns to subdivide the domain and fit locally. We show that incorporating a mixture of experts architecture into existing INR formulations provides a boost in speed, accuracy, and memory requirements. Additionally, we introduce novel conditioning and pretraining methods for the gating network that improves convergence to the desired solution. We evaluate the effectiveness of our approach on multiple reconstruction tasks, including surface reconstruction, image reconstruction, and audio signal reconstruction and show improved performance compared to non-MoE methods.

Can We Predict Performance of Large Models across Vision-Language Tasks?

Evaluating large vision-language models (LVLMs) is very expensive, due to the high computational costs and the wide variety of tasks. The good news is that if we already have some observed performance scores, we may be able to infer unknown ones. In this study, we propose a new framework for predicting unknown performance scores based on observed ones from other LVLMs or tasks. We first formulate the performance prediction as a matrix completion task. Specifically, we construct a sparse performance matrix $\boldsymbol{R}$, where each entry $R_{mn}$ represents the performance score of the $m$-th model on the $n$-th dataset. By applying probabilistic matrix factorization (PMF) with Markov chain Monte Carlo (MCMC), we can complete the performance matrix, that is, predict unknown scores. Additionally, we estimate the uncertainty of performance prediction based on MCMC. Practitioners can evaluate their models on untested tasks with higher uncertainty first, quickly reducing errors in performance prediction. We further introduce several improvements to enhance PMF for scenarios with sparse observed performance scores. In experiments, we systematically evaluate 108 LVLMs on 176 datasets from 36 benchmarks, constructing training and testing sets for validating our framework. Our experiments demonstrate the accuracy of PMF in predicting unknown scores, the reliability of uncertainty estimates in ordering evaluations, and the effectiveness of our enhancements for handling sparse data.

Temporally Grounding Instructional Diagrams in Unconstrained Videos

We study the challenging problem of simultaneously localizing a sequence of queries in the form of instructional diagrams in a video. This requires understanding not only the individual queries but also their interrelationships. However, most existing methods focus on grounding one query at a time, ignoring the inherent structures among queries such as the general mutual exclusiveness and the temporal order. Consequently, the predicted timespans of different step diagrams may overlap considerably or violate the temporal order, thus harming the accuracy. In this paper, we tackle this issue by simultaneously grounding a sequence of step diagrams. Specifically, we propose composite queries, constructed by exhaustively pairing up the visual content features of the step diagrams and a fixed number of learnable positional embeddings. Our insight is that self-attention among composite queries carrying different content features suppress each other to reduce timespan overlaps in predictions, while the cross-attention corrects the temporal misalignment via content and position joint guidance. We demonstrate the effectiveness of our approach on the IAW dataset for grounding step diagrams and the YouCook2 benchmark for grounding natural language queries, significantly outperforming existing methods while simultaneously grounding multiple queries.

Temporally Consistent Unbalanced Optimal Transport for Unsupervised Action Segmentation

We propose a novel approach to the action segmentation task for long, untrimmed videos, based on solving an optimal transport problem. By encoding a temporal consistency prior into a Gromov-Wasserstein problem, we are able to decode a temporally consistent segmentation from a noisy affinity/matching cost matrix between video frames and action classes. Unlike previous approaches, our method does not require knowing the action order for a video to attain temporal consistency. Furthermore, our resulting (fused) Gromov-Wasserstein problem can be efficiently solved on GPUs using a few iterations of projected mirror descent. We demonstrate the effectiveness of our method in an unsupervised learning setting, where our method is used to generate pseudo-labels for self-training. We evaluate our segmentation approach and unsupervised learning pipeline on the Breakfast, 50-Salads, YouTube Instructions and Desktop Assembly datasets, yielding state-of-the-art results for the unsupervised video action segmentation task.

The First to Know: How Token Distributions Reveal Hidden Knowledge in Large Vision-Language Models?

Large vision-language models (LVLMs), designed to interpret and respond to human instructions, occasionally generate hallucinated or harmful content due to inappropriate instructions. This study uses linear probing to shed light on the hidden knowledge at the output layer of LVLMs. We demonstrate that the logit distributions of the first tokens contain sufficient information to determine whether to respond to the instructions, including recognizing unanswerable visual questions, defending against multi-modal jailbreaking attack, and identifying deceptive questions. Such hidden knowledge is gradually lost in logits of subsequent tokens during response generation. Then, we illustrate a simple decoding strategy at the generation of the first token, effectively improving the generated content. In experiments, we find a few interesting insights: First, the CLIP model already contains a strong signal for solving these tasks, indicating potential bias in the existing datasets. Second, we observe performance improvement by utilizing the first logit distributions on three additional tasks, including indicting uncertainty in math solving, mitigating hallucination, and image classification. Last, with the same training data, simply finetuning LVLMs improve models' performance but is still inferior to linear probing on these tasks.

An Empirical Study Into What Matters for Calibrating Vision-Language Models

Vision--Language Models (VLMs) have emerged as the dominant approach for zero-shot recognition, adept at handling diverse scenarios and significant distribution changes. However, their deployment in risk-sensitive areas requires a deeper understanding of their uncertainty estimation capabilities, a relatively uncharted area. In this study, we explore the calibration properties of VLMs across different architectures, datasets, and training strategies. In particular, we analyze the uncertainty estimation performance of VLMs when calibrated in one domain, label set or hierarchy level, and tested in a different one. Our findings reveal that while VLMs are not inherently calibrated for uncertainty, temperature scaling significantly and consistently improves calibration, even across shifts in distribution and changes in label set. Moreover, VLMs can be calibrated with a very small set of examples. Through detailed experimentation, we highlight the potential applications and importance of our insights, aiming for more reliable and effective use of VLMs in critical, real-world scenarios.

Towards Optimal Feature-Shaping Methods for Out-of-Distribution Detection

Feature shaping refers to a family of methods that exhibit state-of-the-art performance for out-of-distribution (OOD) detection. These approaches manipulate the feature representation, typically from the penultimate layer of a pre-trained deep learning model, so as to better differentiate between in-distribution (ID) and OOD samples. However, existing feature-shaping methods usually employ rules manually designed for specific model architectures and OOD datasets, which consequently limit their generalization ability. To address this gap, we first formulate an abstract optimization framework for studying feature-shaping methods. We then propose a concrete reduction of the framework with a simple piecewise constant shaping function and show that existing feature-shaping methods approximate the optimal solution to the concrete optimization problem. Further, assuming that OOD data is inaccessible, we propose a formulation that yields a closed-form solution for the piecewise constant shaping function, utilizing solely the ID data. Through extensive experiments, we show that the feature-shaping function optimized by our method improves the generalization ability of OOD detection across a large variety of datasets and model architectures.

Zero-shot Retrieval: Augmenting Pre-trained Models with Search Engines

Large pre-trained models can dramatically reduce the amount of task-specific data required to solve a problem, but they often fail to capture domain-specific nuances out of the box. The Web likely contains the information necessary to excel on any specific application, but identifying the right data a priori is challenging. This paper shows how to leverage recent advances in NLP and multi-modal learning to augment a pre-trained model with search engine retrieval. We propose to retrieve useful data from the Web at test time based on test cases that the model is uncertain about. Different from existing retrieval-augmented approaches, we then update the model to address this underlying uncertainty. We demonstrate substantial improvements in zero-shot performance, e.g. a remarkable increase of 15 percentage points in accuracy on the Stanford Cars and Flowers datasets. We also present extensive experiments that explore the impact of noisy retrieval and different learning strategies.

Revisiting Implicit Differentiation for Learning Problems in Optimal Control

This paper proposes a new method for differentiating through optimal trajectories arising from non-convex, constrained discrete-time optimal control (COC) problems using the implicit function theorem (IFT). Previous works solve a differential Karush-Kuhn-Tucker (KKT) system for the trajectory derivative, and achieve this efficiently by solving an auxiliary Linear Quadratic Regulator (LQR) problem. In contrast, we directly evaluate the matrix equations which arise from applying variable elimination on the Lagrange multiplier terms in the (differential) KKT system. By appropriately accounting for the structure of the terms within the resulting equations, we show that the trajectory derivatives scale linearly with the number of timesteps. Furthermore, our approach allows for easy parallelization, significantly improved scalability with model size, direct computation of vector-Jacobian products and improved numerical stability compared to prior works. As an additional contribution, we unify prior works, addressing claims that computing trajectory derivatives using IFT scales quadratically with the number of timesteps. We evaluate our method on a both synthetic benchmark and four challenging, learning from demonstration benchmarks including a 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.