There is no convincing evidence that backpropagation is a biologically plausible mechanism, and further studies of alternative learning methods are needed. A novel online clustering algorithm is presented that can produce arbitrary shaped clusters from inputs in an unsupervised manner, and requires no prior knowledge of the number of clusters in the input data. This is achieved by finding correlated outputs from functions that capture commonly occurring input patterns. The algorithm can be deemed more biologically plausible than model optimization through backpropagation, although practical applicability may require additional research. However, the method yields satisfactory results on several toy datasets on a noteworthy range of hyperparameters.
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Contrastive learning methods have shown an impressive ability to learn meaningful representations for image or time series classification. However, these methods are less effective for time series forecasting, as optimization of instance discrimination is not directly applicable to predicting the future state from the history context. Moreover, the construction of positive and negative pairs in current technologies strongly relies on specific time series characteristics, restricting their generalization across diverse types of time series data. To address these limitations, we propose SimTS, a simple representation learning approach for improving time series forecasting by learning to predict the future from the past in the latent space. SimTS does not rely on negative pairs or specific assumptions about the characteristics of the particular time series. Our extensive experiments on several benchmark time series forecasting datasets show that SimTS achieves competitive performance compared to existing contrastive learning methods. Furthermore, we show the shortcomings of the current contrastive learning framework used for time series forecasting through a detailed ablation study. Overall, our work suggests that SimTS is a promising alternative to other contrastive learning approaches for time series forecasting.
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled with indicator variables for identifying the support of the continuous variables. In this paper we investigate compact extended formulations for such problems through perspective reformulation techniques. In contrast to the majority of previous work that relies on support function arguments and disjunctive programming techniques to provide convex hull results, we propose a constructive approach that exploits a hidden conic structure induced by perspective functions. To this end, we first establish a convex hull result for a general conic mixed-binary set in which each conic constraint involves a linear function of independent continuous variables and a set of binary variables. We then demonstrate that extended representations of sets associated with epigraphs of rank-one convex functions over constraints modeling indicator relations naturally admit such a conic representation. This enables us to systematically give perspective formulations for the convex hull descriptions of these sets with nonlinear separable or non-separable objective functions, sign constraints on continuous variables, and combinatorial constraints on indicator variables. We illustrate the efficacy of our results on sparse nonnegative logistic regression problems.
Average-K classification is an alternative to top-K classification in which the number of labels returned varies with the ambiguity of the input image but must average to K over all the samples. A simple method to solve this task is to threshold the softmax output of a model trained with the cross-entropy loss. This approach is theoretically proven to be asymptotically consistent, but it is not guaranteed to be optimal for a finite set of samples. In this paper, we propose a new loss function based on a multi-label classification head in addition to the classical softmax. This second head is trained using pseudo-labels generated by thresholding the softmax head while guaranteeing that K classes are returned on average. We show that this approach allows the model to better capture ambiguities between classes and, as a result, to return more consistent sets of possible classes. Experiments on two datasets from the literature demonstrate that our approach outperforms the softmax baseline, as well as several other loss functions more generally designed for weakly supervised multi-label classification. The gains are larger the higher the uncertainty, especially for classes with few samples.
This paper describes a purely functional library for computing level-$p$-complexity of Boolean functions, and applies it to two-level iterated majority. Boolean functions are simply functions from $n$ bits to one bit, and they can describe digital circuits, voting systems, etc. An example of a Boolean function is majority, which returns the value that has majority among the $n$ input bits for odd $n$. The complexity of a Boolean function $f$ measures the cost of evaluating it: how many bits of the input are needed to be certain about the result of $f$. There are many competing complexity measures but we focus on level-$p$-complexity -- a function of the probability $p$ that a bit is 1. The level-$p$-complexity $D_p(f)$ is the minimum expected cost when the input bits are independent and identically distributed with Bernoulli($p$) distribution. We specify the problem as choosing the minimum expected cost of all possible decision trees -- which directly translates to a clearly correct, but very inefficient implementation. The library uses thinning and memoization for efficiency and type classes for separation of concerns. The complexity is represented using polynomials, and the order relation used for thinning is implemented using polynomial factorisation and root-counting. Finally we compute the complexity for two-level iterated majority and improve on an earlier result by J.~Jansson.
Temporal action segmentation is crucial for understanding long-form videos. Previous works on this task commonly adopt an iterative refinement paradigm by using multi-stage models. Our paper proposes an essentially different framework via denoising diffusion models, which nonetheless shares the same inherent spirit of such iterative refinement. In this framework, action predictions are progressively generated from random noise with input video features as conditions. To enhance the modeling of three striking characteristics of human actions, including the position prior, the boundary ambiguity, and the relational dependency, we devise a unified masking strategy for the conditioning inputs in our framework. Extensive experiments on three benchmark datasets, i.e., GTEA, 50Salads, and Breakfast, are performed and the proposed method achieves superior or comparable results to state-of-the-art methods, showing the effectiveness of a generative approach for action segmentation. Our codes will be made available.
This article investigates the challenge of achieving functional tool-use grasping with high-DoF anthropomorphic hands, with the aim of enabling anthropomorphic hands to perform tasks that require human-like manipulation and tool-use. However, accomplishing human-like grasping in real robots present many challenges, including obtaining diverse functional grasps for a wide variety of objects, handling generalization ability for kinematically diverse robot hands and precisely completing object shapes from a single-view perception. To tackle these challenges, we propose a six-step grasp synthesis algorithm based on fine-grained contact modeling that generates physically plausible and human-like functional grasps for category-level objects with minimal human demonstrations. With the contact-based optimization and learned dense shape correspondence, the proposed algorithm is adaptable to various objects in same category and a board range of robot hand models. To further demonstrate the robustness of the framework, over 10K functional grasps are synthesized to train our neural network, named DexFG-Net, which generates diverse sets of human-like functional grasps based on the reconstructed object model produced by a shape completion module. The proposed framework is extensively validated in simulation and on a real robot platform. Simulation experiments demonstrate that our method outperforms baseline methods by a large margin in terms of grasp functionality and success rate. Real robot experiments show that our method achieved an overall success rate of 79\% and 68\% for tool-use grasp on 3-D printed and real test objects, respectively, using a 5-Finger Schunk Hand. The experimental results indicate a step towards human-like grasping with anthropomorphic hands.
The information bottleneck (IB) method offers an attractive framework for understanding representation learning, however its applications are often limited by its computational intractability. Analytical characterization of the IB method is not only of practical interest, but it can also lead to new insights into learning phenomena. Here we consider a generalized IB problem, in which the mutual information in the original IB method is replaced by correlation measures based on Renyi and Jeffreys divergences. We derive an exact analytical IB solution for the case of Gaussian correlated variables. Our analysis reveals a series of structural transitions, similar to those previously observed in the original IB case. We find further that although solving the original, Renyi and Jeffreys IB problems yields different representations in general, the structural transitions occur at the same critical tradeoff parameters, and the Renyi and Jeffreys IB solutions perform well under the original IB objective. Our results suggest that formulating the IB method with alternative correlation measures could offer a strategy for obtaining an approximate solution to the original IB problem.
Most state-of-the-art machine learning techniques revolve around the optimisation of loss functions. Defining appropriate loss functions is therefore critical to successfully solving problems in this field. We present a survey of the most commonly used loss functions for a wide range of different applications, divided into classification, regression, ranking, sample generation and energy based modelling. Overall, we introduce 33 different loss functions and we organise them into an intuitive taxonomy. Each loss function is given a theoretical backing and we describe where it is best used. This survey aims to provide a reference of the most essential loss functions for both beginner and advanced machine learning practitioners.
This paper presents SimCLR: a simple framework for contrastive learning of visual representations. We simplify recently proposed contrastive self-supervised learning algorithms without requiring specialized architectures or a memory bank. In order to understand what enables the contrastive prediction tasks to learn useful representations, we systematically study the major components of our framework. We show that (1) composition of data augmentations plays a critical role in defining effective predictive tasks, (2) introducing a learnable nonlinear transformation between the representation and the contrastive loss substantially improves the quality of the learned representations, and (3) contrastive learning benefits from larger batch sizes and more training steps compared to supervised learning. By combining these findings, we are able to considerably outperform previous methods for self-supervised and semi-supervised learning on ImageNet. A linear classifier trained on self-supervised representations learned by SimCLR achieves 76.5% top-1 accuracy, which is a 7% relative improvement over previous state-of-the-art, matching the performance of a supervised ResNet-50. When fine-tuned on only 1% of the labels, we achieve 85.8% top-5 accuracy, outperforming AlexNet with 100X fewer labels.
Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit the given data to reveal the underlying cluster structure. Some types of losses---such as k-means, or its non-linear version: kernelized k-means (centroid based), and DBSCAN (density based)---are popular choices due to their good empirical performance on a range of applications. Although every so often the clustering output using these standard losses fails to reveal the underlying structure, and the practitioner has to custom-design their own variation. In this work we take an intrinsically different approach to clustering: rather than fitting a dataset to a specific clustering loss, we train a recurrent model that learns how to cluster. The model uses as training pairs examples of datasets (as input) and its corresponding cluster identities (as output). By providing multiple types of training datasets as inputs, our model has the ability to generalize well on unseen datasets (new clustering tasks). Our experiments reveal that by training on simple synthetically generated datasets or on existing real datasets, we can achieve better clustering performance on unseen real-world datasets when compared with standard benchmark clustering techniques. Our meta clustering model works well even for small datasets where the usual deep learning models tend to perform worse.
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