We develop and investigate a general theory of representations of second-order functionals, based on a notion of a right comodule for a monad on the category of containers. We show how the notion of comodule representability naturally subsumes classic representations of continuous functionals with well-founded trees. We find other kinds of representations by varying the monad, the comodule, and in some cases the underlying category of containers. Examples include uniformly continuous or finitely supported functionals, functionals querying their arguments precisely once, or at most once, functionals interacting with an ambient environment through computational effects, as well as functionals trivially representing themselves. Many of these rely on our construction of a monad on containers from a monad on shapes and a weak Mendler-style monad algebra on the universe for positions. We show that comodule representability on the category of propositional containers, which have positions valued in a universe of propositions, is closely related to instance reducibility in constructive mathematics, and through it to Weihrauch reducibility in computability theory.
相關內容
Unlabeled sensing is the problem of solving a linear system of equations, where the right-hand-side vector is known only up to a permutation. In this work, we study fields of rational functions related to symmetric polynomials and their images under a linear projection of the variables; as a consequence, we establish that the solution to an n-dimensional unlabeled sensing problem with generic data can be obtained as the unique solution to a system of n + 1 polynomial equations of degrees 1, 2, . . . , n + 1 in n unknowns. Besides the new theoretical insights, this development offers the potential for scaling up algebraic unlabeled sensing algorithms.
Compromise estimation entails using a weighted average of outputs from several candidate models, and is a viable alternative to model selection when the choice of model is not obvious. As such, it is a tool used by both frequentists and Bayesians, and in both cases, the literature is vast and includes studies of performance in simulations and applied examples. However, frequentist researchers often prove oracle properties, showing that a proposed average asymptotically performs at least as well as any other average comprising the same candidates. On the Bayesian side, such oracle properties are yet to be established. This paper considers Bayesian stacking estimators, and evaluates their performance using frequentist asymptotics. Oracle properties are derived for estimators stacking Bayesian linear and logistic regression models, and combined with Monte Carlo experiments that show Bayesian stacking may outperform the best candidate model included in the stack. Thus, the result is not only a frequentist motivation of a fundamentally Bayesian procedure, but also an extended range of methods available to frequentist practitioners.
Inferring causal relationships in the decision-making processes of machine learning algorithms is a crucial step toward achieving explainable Artificial Intelligence (AI). In this research, we introduce a novel causality measure and a distance metric derived from Lempel-Ziv (LZ) complexity. We explore how the proposed causality measure can be used in decision trees by enabling splits based on features that most strongly \textit{cause} the outcome. We further evaluate the effectiveness of the causality-based decision tree and the distance-based decision tree in comparison to a traditional decision tree using Gini impurity. While the proposed methods demonstrate comparable classification performance overall, the causality-based decision tree significantly outperforms both the distance-based decision tree and the Gini-based decision tree on datasets generated from causal models. This result indicates that the proposed approach can capture insights beyond those of classical decision trees, especially in causally structured data. Based on the features used in the LZ causal measure based decision tree, we introduce a causal strength for each features in the dataset so as to infer the predominant causal variables for the occurrence of the outcome.
We provide a convergence analysis of gradient descent for the problem of agnostically learning a single ReLU function with moderate bias under Gaussian distributions. Unlike prior work that studies the setting of zero bias, we consider the more challenging scenario when the bias of the ReLU function is non-zero. Our main result establishes that starting from random initialization, in a polynomial number of iterations gradient descent outputs, with high probability, a ReLU function that achieves an error that is within a constant factor of the optimal error of the best ReLU function with moderate bias. We also provide finite sample guarantees, and these techniques generalize to a broader class of marginal distributions beyond Gaussians.
It is becoming increasingly difficult to improve the performance of a a single process (thread) on a computer due to physical limitations. Modern systems use multi-core processors in which multiple processes (threads) may run concurrently. A lock-free data structure can allow these processes to communicate with each other without requiring mutual exclusion, and may increase the amount of work they may perform in parallel rather than sequentially, thus improving the performance of the system as a whole. This paper contains an implementation of Ko's Lock-Free Binary Trie, which stores a dynamic set of keys from an ordered universe. It supports insert, remove, search and predecessor operations. One novel component of this implementation is a lock-free linked list which allows multiple processes to attempt to insert the same node, but which prevents a node from being reinserted once it has been removed from the list. The final section of this paper contains an experimental comparison of this implementation against other data structures which implement the same abstract data type (ADT) as the lock-free trie. Analysis of these experiments reveal that the implementation of Ko's Trie performs better than existing theoretical implementations of this ADT when the universe of keys is large, when removes are rare and when the number of processes performing operations concurrently is low.
Amplification by subsampling is one of the main primitives in machine learning with differential privacy (DP): Training a model on random batches instead of complete datasets results in stronger privacy. This is traditionally formalized via mechanism-agnostic subsampling guarantees that express the privacy parameters of a subsampled mechanism as a function of the original mechanism's privacy parameters. We propose the first general framework for deriving mechanism-specific guarantees, which leverage additional information beyond these parameters to more tightly characterize the subsampled mechanism's privacy. Such guarantees are of particular importance for privacy accounting, i.e., tracking privacy over multiple iterations. Overall, our framework based on conditional optimal transport lets us derive existing and novel guarantees for approximate DP, accounting with R\'enyi DP, and accounting with dominating pairs in a unified, principled manner. As an application, we analyze how subsampling affects the privacy of groups of multiple users. Our tight mechanism-specific bounds outperform tight mechanism-agnostic bounds and classic group privacy results.
This work uniquely identifies and characterizes four prevalent multimodal model architectural patterns in the contemporary multimodal landscape. Systematically categorizing models by architecture type facilitates monitoring of developments in the multimodal domain. Distinct from recent survey papers that present general information on multimodal architectures, this research conducts a comprehensive exploration of architectural details and identifies four specific architectural types. The types are distinguished by their respective methodologies for integrating multimodal inputs into the deep neural network model. The first two types (Type A and B) deeply fuses multimodal inputs within the internal layers of the model, whereas the following two types (Type C and D) facilitate early fusion at the input stage. Type-A employs standard cross-attention, whereas Type-B utilizes custom-designed layers for modality fusion within the internal layers. On the other hand, Type-C utilizes modality-specific encoders, while Type-D leverages tokenizers to process the modalities at the model's input stage. The identified architecture types aid the monitoring of any-to-any multimodal model development. Notably, Type-C and Type-D are currently favored in the construction of any-to-any multimodal models. Type-C, distinguished by its non-tokenizing multimodal model architecture, is emerging as a viable alternative to Type-D, which utilizes input-tokenizing techniques. To assist in model selection, this work highlights the advantages and disadvantages of each architecture type based on data and compute requirements, architecture complexity, scalability, simplification of adding modalities, training objectives, and any-to-any multimodal generation capability.
Self-supervised learning, dubbed the dark matter of intelligence, is a promising path to advance machine learning. Yet, much like cooking, training SSL methods is a delicate art with a high barrier to entry. While many components are familiar, successfully training a SSL method involves a dizzying set of choices from the pretext tasks to training hyper-parameters. Our goal is to lower the barrier to entry into SSL research by laying the foundations and latest SSL recipes in the style of a cookbook. We hope to empower the curious researcher to navigate the terrain of methods, understand the role of the various knobs, and gain the know-how required to explore how delicious SSL can be.
Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191