This work solves an open problem regarding the rate of time-bounded Kolmogorov complexity and polynomial-time dimension, conditioned on a hardness assumption. Hitchcock and Vinodchandran (CCC 2004) show that the polynomial-time dimension of infinite sequences (denoted ${\mathrm{cdim}}_\mathrm{P}$) defined using betting algorithms called gales, is lower bounded by the asymptotic lower rate of polynomial-time Kolmogorov complexity (denoted $\mathcal{K}_\text{poly}$). Hitchcock and Vindochandran and Stull asked whether the converse relationship also holds. This question has thus far resisted resolution. The corresponding unbounded notions, namely, the constructive dimension and the asymptotic lower rate of unbounded Kolmogorov complexity are equal for every sequence. Analogous notions are equal even at finite-state level. In view of these results, it is reasonable to conjecture that the polynomial-time quantities are identical for every sequence and set of sequences. However, under a plausible assumption which underlies modern cryptography - namely the existence of one-way functions, we refute the conjecture thereby giving a negative answer to the open question posed by Hitchcock and Vinodchandran and Stull . We show the following, conditioned on the existence of one-way functions: There are sets $\mathcal{F}$ of infinite sequences whose polytime dimension strictly exceeds $\mathcal{K}_\text{poly}(\mathcal{F})$, that is ${\mathrm{cdim}}_\mathrm{P}(\mathcal{F}) > \mathcal{K}_\text{poly}(\mathcal{F})$. We establish a stronger version of this result, that there are individual sequences $X$ whose poly-time dimension strictly exceeds $\mathcal{K}_\text{poly}(X)$, that is ${\mathrm{cdim}}_\mathrm{P}(X) > \mathcal{K}_\text{poly}(X)$. Further, we show that the gap between these quantities can be made arbitrarily close to 1. We also establish similar bounds for strong poly-time dimension
The number of categories of instances in the real world is normally huge, and each instance may contain multiple labels. To distinguish these massive labels utilizing machine learning, eXtreme Label Classification (XLC) has been established. However, as the number of categories increases, the number of parameters and nonlinear operations in the classifier also rises. This results in a Classifier Computational Overload Problem (CCOP). To address this, we propose a Multi-Head Encoding (MHE) mechanism, which replaces the vanilla classifier with a multi-head classifier. During the training process, MHE decomposes extreme labels into the product of multiple short local labels, with each head trained on these local labels. During testing, the predicted labels can be directly calculated from the local predictions of each head. This reduces the computational load geometrically. Then, according to the characteristics of different XLC tasks, e.g., single-label, multi-label, and model pretraining tasks, three MHE-based implementations, i.e., Multi-Head Product, Multi-Head Cascade, and Multi-Head Sampling, are proposed to more effectively cope with CCOP. Moreover, we theoretically demonstrate that MHE can achieve performance approximately equivalent to that of the vanilla classifier by generalizing the low-rank approximation problem from Frobenius-norm to Cross-Entropy. Experimental results show that the proposed methods achieve state-of-the-art performance while significantly streamlining the training and inference processes of XLC tasks. The source code has been made public at //github.com/Anoise/MHE.
We propose a novel formalism for describing Structural Causal Models (SCMs) as fixed-point problems on causally ordered variables, eliminating the need for Directed Acyclic Graphs (DAGs), and establish the weakest known conditions for their unique recovery given the topological ordering (TO). Based on this, we design a two-stage causal generative model that first infers in a zero-shot manner a valid TO from observations, and then learns the generative SCM on the ordered variables. To infer TOs, we propose to amortize the learning of TOs on synthetically generated datasets by sequentially predicting the leaves of graphs seen during training. To learn SCMs, we design a transformer-based architecture that exploits a new attention mechanism enabling the modeling of causal structures, and show that this parameterization is consistent with our formalism. Finally, we conduct an extensive evaluation of each method individually, and show that when combined, our model outperforms various baselines on generated out-of-distribution problems. The code is available on \href{//github.com/microsoft/causica/tree/main/research_experiments/fip}{Github}.
Recent work has empirically shown that Vision-Language Models (VLMs) struggle to fully understand the compositional properties of the human language, usually modeling an image caption as a "bag of words". As a result, they perform poorly on compositional tasks, which require a deeper understanding of the different entities of a sentence (subject, verb, etc.) jointly with their mutual relationships in order to be solved. In this paper, we model the dependency relations among textual and visual tokens using a Causal Graphical Model (CGM), built using a dependency parser, and we train a decoder conditioned by the VLM visual encoder. Differently from standard autoregressive or parallel predictions, our decoder's generative process is partially-ordered following the CGM structure. This structure encourages the decoder to learn only the main causal dependencies in a sentence discarding spurious correlations. Using extensive experiments on five compositional benchmarks, we show that our method significantly outperforms all the state-of-the-art compositional approaches by a large margin, and it also improves over methods trained using much larger datasets.
We initiate the focused study of constant-cost randomized communication, with emphasis on its connection to graph representations. We observe that constant-cost randomized communication problems are equivalent to hereditary (i.e. closed under taking induced subgraphs) graph classes which admit constant-size adjacency sketches and probabilistic universal graphs (PUGs), which are randomized versions of the well-studied adjacency labeling schemes and induced-universal graphs. This gives a new perspective on long-standing questions about the existence of these objects, including new methods of constructing adjacency labeling schemes. We ask three main questions about constant-cost communication, or equivalently, constant-size PUGs: (1) Are there any natural, non-trivial problems aside from Equality and k-Hamming Distance which have constant-cost communication? We provide a number of new examples, including deciding whether two vertices have path-distance at most k in a planar graph, and showing that constant-size PUGs are preserved by the Cartesian product operation. (2) What structures of a problem explain the existence or non-existence of a constant-cost protocol? We show that in many cases a Greater-Than subproblem is such a structure. (3) Is the Equality problem complete for constant-cost randomized communication? We show that it is not: there are constant-cost problems which do not reduce to Equality.
The development of autonomous agents which can interact with other agents to accomplish a given task is a core area of research in artificial intelligence and machine learning. Towards this goal, the Autonomous Agents Research Group develops novel machine learning algorithms for autonomous systems control, with a specific focus on deep reinforcement learning and multi-agent reinforcement learning. Research problems include scalable learning of coordinated agent policies and inter-agent communication; reasoning about the behaviours, goals, and composition of other agents from limited observations; and sample-efficient learning based on intrinsic motivation, curriculum learning, causal inference, and representation learning. This article provides a broad overview of the ongoing research portfolio of the group and discusses open problems for future directions.
Despite the recent progress in deep learning, most approaches still go for a silo-like solution, focusing on learning each task in isolation: training a separate neural network for each individual task. Many real-world problems, however, call for a multi-modal approach and, therefore, for multi-tasking models. Multi-task learning (MTL) aims to leverage useful information across tasks to improve the generalization capability of a model. This thesis is concerned with multi-task learning in the context of computer vision. First, we review existing approaches for MTL. Next, we propose several methods that tackle important aspects of multi-task learning. The proposed methods are evaluated on various benchmarks. The results show several advances in the state-of-the-art of multi-task learning. Finally, we discuss several possibilities for future work.
Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.
The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.
Graphical causal inference as pioneered by Judea Pearl arose from research on artificial intelligence (AI), and for a long time had little connection to the field of machine learning. This article discusses where links have been and should be established, introducing key concepts along the way. It argues that the hard open problems of machine learning and AI are intrinsically related to causality, and explains how the field is beginning to understand them.
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.