In deep learning, auxiliary objectives are often used to facilitate learning in situations where data is scarce, or the principal task is extremely complex. This idea is primarily inspired by the improved generalization capability induced by solving multiple tasks simultaneously, which leads to a more robust shared representation. Nevertheless, finding optimal auxiliary tasks that give rise to the desired improvement is a crucial problem that often requires hand-crafted solutions or expensive meta-learning approaches. In this paper, we propose a novel framework, dubbed Detaux, whereby a weakly supervised disentanglement procedure is used to discover new unrelated classification tasks and the associated labels that can be exploited with the principal task in any Multi-Task Learning (MTL) model. The disentanglement procedure works at a representation level, isolating a subspace related to the principal task, plus an arbitrary number of orthogonal subspaces. In the most disentangled subspaces, through a clustering procedure, we generate the additional classification tasks, and the associated labels become their representatives. Subsequently, the original data, the labels associated with the principal task, and the newly discovered ones can be fed into any MTL framework. Extensive validation on both synthetic and real data, along with various ablation studies, demonstrate promising results, revealing the potential in what has been, so far, an unexplored connection between learning disentangled representations and MTL. The code will be made publicly available upon acceptance.

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 450 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting.

In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and modified graphs. Classically, these maps are represented as binary node-to-node correspondence matrices and used as-is to transfer node-wise features between the graphs. In this paper, we argue that simply changing this map representation can bring notable benefits to graph learning tasks. Drawing inspiration from recent progress in geometry processing, we introduce a spectral representation for maps that is easy to integrate into existing graph learning models. This spectral representation is a compact and straightforward plug-in replacement and is robust to topological changes of the graphs. Remarkably, the representation exhibits structural properties that make it interpretable, drawing an analogy with recent results on smooth manifolds. We demonstrate the benefits of incorporating spectral maps in graph learning pipelines, addressing scenarios where a node-to-node map is not well defined, or in the absence of exact isomorphism. Our approach bears practical benefits in knowledge distillation and hierarchical learning, where we show comparable or improved performance at a fraction of the computational cost.

Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape. Some recent works show how the intrinsic geometry of a full shape can be recovered from its spectrum, but there are approaches that consider the more challenging problem of recovering the geometry from the spectral information of partial shapes. In this paper, we propose a possible way to fill this gap. We introduce a learning-based method to estimate the Laplacian spectrum of the union of partial non-rigid 3D shapes, without actually computing the 3D geometry of the union or any correspondence between those partial shapes. We do so by operating purely in the spectral domain and by defining the union operation between short sequences of eigenvalues. We show that the approximated union spectrum can be used as-is to reconstruct the complete geometry [MRC*19], perform region localization on a template [RTO*19] and retrieve shapes from a database, generalizing ShapeDNA [RWP06] to work with partialities. Working with eigenvalues allows us to deal with unknown correspondence, different sampling, and different discretizations (point clouds and meshes alike), making this operation especially robust and general. Our approach is data-driven and can generalize to isometric and non-isometric deformations of the surface, as long as these stay within the same semantic class (e.g., human bodies or horses), as well as to partiality artifacts not seen at training time.

We introduce Explanatory Learning (EL), a framework to let machines use existing knowledge buried in symbolic sequences -- e.g. explanations written in hieroglyphic -- by autonomously learning to interpret them. In EL, the burden of interpreting symbols is not left to humans or rigid human-coded compilers, as done in Program Synthesis. Rather, EL calls for a learned interpreter, built upon a limited collection of symbolic sequences paired with observations of several phenomena. This interpreter can be used to make predictions on a novel phenomenon given its explanation, and even to find that explanation using only a handful of observations, like human scientists do. We formulate the EL problem as a simple binary classification task, so that common end-to-end approaches aligned with the dominant empiricist view of machine learning could, in principle, solve it. To these models, we oppose Critical Rationalist Networks (CRNs), which instead embrace a rationalist view on the acquisition of knowledge. CRNs express several desired properties by construction, they are truly explainable, can adjust their processing at test-time for harder inferences, and can offer strong confidence guarantees on their predictions. As a final contribution, we introduce Odeen, a basic EL environment that simulates a small flatland-style universe full of phenomena to explain. Using Odeen as a testbed, we show how CRNs outperform empiricist end-to-end approaches of similar size and architecture (Transformers) in discovering explanations for novel phenomena.

We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and redundancy principles. By two different interpretations (exploiting properties of power series of matrices and relying on Markov chains fundamentals) we can evaluate the values of paths (i.e., feature subsets) of arbitrary lengths, eventually go to infinite, from which we dub our framework Infinite Feature Selection (Inf-FS). Going to infinite allows to constrain the computational complexity of the selection process, and to rank the features in an elegant way, that is, considering the value of any path (subset) containing a particular feature. We also propose a simple unsupervised strategy to cut the ranking, so providing the subset of features to keep. In the experiments, we analyze diverse settings with heterogeneous features, for a total of 11 benchmarks, comparing against 18 widely-known comparative approaches. The results show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori, or when the decision of the subset cardinality is part of the process.

In an era where accumulating data is easy and storing it inexpensive, feature selection plays a central role in helping to reduce the high-dimensionality of huge amounts of otherwise meaningless data. In this paper, we propose a graph-based method for feature selection that ranks features by identifying the most important ones into arbitrary set of cues. Mapping the problem on an affinity graph-where features are the nodes-the solution is given by assessing the importance of nodes through some indicators of centrality, in particular, the Eigen-vector Centrality (EC). The gist of EC is to estimate the importance of a feature as a function of the importance of its neighbors. Ranking central nodes individuates candidate features, which turn out to be effective from a classification point of view, as proved by a thoroughly experimental section. Our approach has been tested on 7 diverse datasets from recent literature (e.g., biological data and object recognition, among others), and compared against filter, embedded and wrappers methods. The results are remarkable in terms of accuracy, stability and low execution time.