We reduce the best-known upper bound on the length of a program that enumerates a set in terms of the probability of it being enumerated by a random program. We prove a general result that any linear upper bound for finite sets implies the same linear bound for infinite sets. So far, the best-known upper bound was given by Solovay. He showed that the minimum length of a program enumerating a subset $S$ of natural numbers is bounded by minus three binary logarithms of the probability that a random program will enumerate $S$. Later, Vereshchagin showed that the constant can be improved from three to two for finite sets. In this work, using an improvement of the method proposed by Solovay, we demonstrate that any bound for finite sets implies the same for infinite sets, modulo logarithmic factors. Using Vereshchagin's result, we improve the current best-known upper bound from three to two.
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The extraction of modular object-centric representations for downstream tasks is an emerging area of research. Learning grounded representations of objects that are guaranteed to be stable and invariant promises robust performance across different tasks and environments. Slot Attention (SA) learns object-centric representations by assigning objects to \textit{slots}, but presupposes a \textit{single} distribution from which all slots are randomly initialised. This results in an inability to learn \textit{specialized} slots which bind to specific object types and remain invariant to identity-preserving changes in object appearance. To address this, we present \emph{\textsc{Co}nditional \textsc{S}lot \textsc{A}ttention} (\textsc{CoSA}) using a novel concept of \emph{Grounded Slot Dictionary} (GSD) inspired by vector quantization. Our proposed GSD comprises (i) canonical object-level property vectors and (ii) parametric Gaussian distributions, which define a prior over the slots. We demonstrate the benefits of our method in multiple downstream tasks such as scene generation, composition, and task adaptation, whilst remaining competitive with SA in popular object discovery benchmarks.
Many applications, such as content moderation and recommendation, require reviewing and scoring a large number of alternatives. Doing so robustly is however very challenging. Indeed, voters' inputs are inevitably sparse: most alternatives are only scored by a small fraction of voters. This sparsity amplifies the effects of biased voters introducing unfairness, and of malicious voters seeking to hack the voting process by reporting dishonest scores. We give a precise definition of the problem of robust sparse voting, highlight its underlying technical challenges, and present a novel voting mechanism addressing the problem. We prove that, using this mechanism, no voter can have more than a small parameterizable effect on each alternative's score; a property we call Lipschitz resilience. We also identify conditions of voters comparability under which any unanimous preferences can be recovered, even when each voter provides sparse scores, on a scale that is potentially very different from any other voter's score scale. Proving these properties required us to introduce, analyze and carefully compose novel aggregation primitives which could be of independent interest.
We consider an M/M/1 queueing model where customers can strategically decide whether to join the queue or balk and when to renege. We characterize the class of queueing regimes such that, for any parameters of the model, the socially efficient behavior is an equilibrium outcome.
This book is the result of a seminar in which we reviewed multimodal approaches and attempted to create a solid overview of the field, starting with the current state-of-the-art approaches in the two subfields of Deep Learning individually. Further, modeling frameworks are discussed where one modality is transformed into the other, as well as models in which one modality is utilized to enhance representation learning for the other. To conclude the second part, architectures with a focus on handling both modalities simultaneously are introduced. Finally, we also cover other modalities as well as general-purpose multi-modal models, which are able to handle different tasks on different modalities within one unified architecture. One interesting application (Generative Art) eventually caps off this booklet.
Existing Collaborative Filtering (CF) methods are mostly designed based on the idea of matching, i.e., by learning user and item embeddings from data using shallow or deep models, they try to capture the associative relevance patterns in data, so that a user embedding can be matched with relevant item embeddings using designed or learned similarity functions. However, as a cognition rather than a perception intelligent task, recommendation requires not only the ability of pattern recognition and matching from data, but also the ability of cognitive reasoning in data. In this paper, we propose to advance Collaborative Filtering (CF) to Collaborative Reasoning (CR), which means that each user knows part of the reasoning space, and they collaborate for reasoning in the space to estimate preferences for each other. Technically, we propose a Neural Collaborative Reasoning (NCR) framework to bridge learning and reasoning. Specifically, we integrate the power of representation learning and logical reasoning, where representations capture similarity patterns in data from perceptual perspectives, and logic facilitates cognitive reasoning for informed decision making. An important challenge, however, is to bridge differentiable neural networks and symbolic reasoning in a shared architecture for optimization and inference. To solve the problem, we propose a modularized reasoning architecture, which learns logical operations such as AND ($\wedge$), OR ($\vee$) and NOT ($\neg$) as neural modules for implication reasoning ($\rightarrow$). In this way, logical expressions can be equivalently organized as neural networks, so that logical reasoning and prediction can be conducted in a continuous space. Experiments on real-world datasets verified the advantages of our framework compared with both shallow, deep and reasoning models.
The information bottleneck (IB) method is a technique for extracting information that is relevant for predicting the target random variable from the source random variable, which is typically implemented by optimizing the IB Lagrangian that balances the compression and prediction terms. However, the IB Lagrangian is hard to optimize, and multiple trials for tuning values of Lagrangian multiplier are required. Moreover, we show that the prediction performance strictly decreases as the compression gets stronger during optimizing the IB Lagrangian. In this paper, we implement the IB method from the perspective of supervised disentangling. Specifically, we introduce Disentangled Information Bottleneck (DisenIB) that is consistent on compressing source maximally without target prediction performance loss (maximum compression). Theoretical and experimental results demonstrate that our method is consistent on maximum compression, and performs well in terms of generalization, robustness to adversarial attack, out-of-distribution detection, and supervised disentangling.
Adversarial attack is a technique for deceiving Machine Learning (ML) models, which provides a way to evaluate the adversarial robustness. In practice, attack algorithms are artificially selected and tuned by human experts to break a ML system. However, manual selection of attackers tends to be sub-optimal, leading to a mistakenly assessment of model security. In this paper, a new procedure called Composite Adversarial Attack (CAA) is proposed for automatically searching the best combination of attack algorithms and their hyper-parameters from a candidate pool of \textbf{32 base attackers}. We design a search space where attack policy is represented as an attacking sequence, i.e., the output of the previous attacker is used as the initialization input for successors. Multi-objective NSGA-II genetic algorithm is adopted for finding the strongest attack policy with minimum complexity. The experimental result shows CAA beats 10 top attackers on 11 diverse defenses with less elapsed time (\textbf{6 $\times$ faster than AutoAttack}), and achieves the new state-of-the-art on $l_{\infty}$, $l_{2}$ and unrestricted adversarial attacks.
We introduce an approach for deep reinforcement learning (RL) that improves upon the efficiency, generalization capacity, and interpretability of conventional approaches through structured perception and relational reasoning. It uses self-attention to iteratively reason about the relations between entities in a scene and to guide a model-free policy. Our results show that in a novel navigation and planning task called Box-World, our agent finds interpretable solutions that improve upon baselines in terms of sample complexity, ability to generalize to more complex scenes than experienced during training, and overall performance. In the StarCraft II Learning Environment, our agent achieves state-of-the-art performance on six mini-games -- surpassing human grandmaster performance on four. By considering architectural inductive biases, our work opens new directions for overcoming important, but stubborn, challenges in deep RL.
We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.
This paper proposes a method to modify traditional convolutional neural networks (CNNs) into interpretable CNNs, in order to clarify knowledge representations in high conv-layers of CNNs. In an interpretable CNN, each filter in a high conv-layer represents a certain object part. We do not need any annotations of object parts or textures to supervise the learning process. Instead, the interpretable CNN automatically assigns each filter in a high conv-layer with an object part during the learning process. Our method can be applied to different types of CNNs with different structures. The clear knowledge representation in an interpretable CNN can help people understand the logics inside a CNN, i.e., based on which patterns the CNN makes the decision. Experiments showed that filters in an interpretable CNN were more semantically meaningful than those in traditional CNNs.
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