The self-attention mechanism in the transformer architecture is capable of capturing long-range dependencies and it is the main reason behind its effectiveness in processing sequential data. Nevertheless, despite their success, transformers have two significant drawbacks that still limit their broader applicability: (1) In order to remember past information, the self-attention mechanism requires access to the whole history to be provided as context. (2) The inference cost in transformers is expensive. In this paper we introduce recurrent alternatives to the transformer self-attention mechanism that offer a context-independent inference cost, leverage long-range dependencies effectively, and perform well in practice. We evaluate our approaches in reinforcement learning problems where the aforementioned computational limitations make the application of transformers nearly infeasible. We quantify the impact of the different components of our architecture in a diagnostic environment and assess performance gains in 2D and 3D pixel-based partially-observable environments. When compared to a state-of-the-art architecture, GTrXL, inference in our approach is at least 40% cheaper while reducing memory use in more than 50%. Our approach either performs similarly or better than GTrXL, improving more than 37% upon GTrXL performance on harder tasks.
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With the emergence of communication services with stringent requirements such as autonomous driving or on-flight Internet, the sixth-generation (6G) wireless network is envisaged to become an enabling technology for future transportation systems. In this paper, two ways of interactions between 6G networks and transportation are extensively investigated. On one hand, the new usage scenarios and capabilities of 6G over existing cellular networks are firstly highlighted. Then, its potential in seamless and ubiquitous connectivity across the heterogeneous space-air-ground transportation systems is demonstrated, where railways, airplanes, high-altitude platforms and satellites are investigated. On the other hand, we reveal that the introduction of 6G guarantees a more intelligent, efficient and secure transportation system. Specifically, technical analysis on how 6G can empower future transportation is provided, based on the latest research and standardization progresses in localization, integrated sensing and communications, and security. The technical challenges and insights for a road ahead are also summarized for possible inspirations on 6G enabled advanced transportation.
Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments. Assuming that the underlying dynamical process obeys a $d$-dimensional stochastic differential equation of the form $$\mathrm{d}\boldsymbol{x}_t=\boldsymbol{b}(\boldsymbol{x}_t)\mathrm{d} t+\Sigma(\boldsymbol{x}_t)\mathrm{d}\boldsymbol{w}_t,$$ we propose neural network-based estimators of both the drift $\boldsymbol{b}$ and the spatially-inhomogeneous diffusion tensor $D = \Sigma\Sigma^{T}$ and provide statistical convergence guarantees when $\boldsymbol{b}$ and $D$ are $s$-H\"older continuous. Notably, our bound aligns with the minimax optimal rate $N^{-\frac{2s}{2s+d}}$ for nonparametric function estimation even in the presence of correlation within observational data, which necessitates careful handling when establishing fast-rate generalization bounds. Our theoretical results are bolstered by numerical experiments demonstrating accurate inference of spatially-inhomogeneous diffusion tensors.
Most work on the formal verification of neural networks has focused on bounding the set of outputs that correspond to a given set of inputs (for example, bounded perturbations of a nominal input). However, many use cases of neural network verification require solving the inverse problem, or over-approximating the set of inputs that lead to certain outputs. We present the INVPROP algorithm for verifying properties over the preimage of a linearly constrained output set, which can be combined with branch-and-bound to increase precision. Contrary to other approaches, our efficient algorithm is GPU-accelerated and does not require a linear programming solver. We demonstrate our algorithm for identifying safe control regions for a dynamical system via backward reachability analysis, verifying adversarial robustness, and detecting out-of-distribution inputs to a neural network. Our results show that in certain settings, we find over-approximations over 2500x tighter than prior work while being 2.5x faster. By strengthening robustness verification with output constraints, we consistently verify more properties than the previous state-of-the-art on multiple benchmarks, including a large model with 167k neurons in VNN-COMP 2023. Our algorithm has been incorporated into the $\alpha,\!\beta$-CROWN verifier, available at //abcrown.org.
We introduce a reversible theory of exact entanglement manipulation by establishing a necessary and sufficient condition for state transfer under trace-preserving transformations that completely preserve the positivity of partial transpose (PPT). Under these free transformations, we show that logarithmic negativity emerges as the pivotal entanglement measure for determining entangled states' transformations, analogous to the role of entropy in the second law of thermodynamics. Previous results have proven that entanglement is irreversible under quantum operations that completely preserve PPT and leave open the question of reversibility for quantum operations that do not generate entanglement asymptotically. However, we find that going beyond the complete positivity constraint imposed by standard quantum mechanics enables a reversible theory of exact entanglement manipulation, which may suggest a potential incompatibility between the reversibility of entanglement and the fundamental principles of quantum mechanics.
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.
Negative control variables are sometimes used in non-experimental studies to detect the presence of confounding by hidden factors. A negative control outcome (NCO) is an outcome that is influenced by unobserved confounders of the exposure effects on the outcome in view, but is not causally impacted by the exposure. Tchetgen Tchetgen (2013) introduced the Control Outcome Calibration Approach (COCA) as a formal NCO counterfactual method to detect and correct for residual confounding bias. For identification, COCA treats the NCO as an error-prone proxy of the treatment-free counterfactual outcome of interest, and involves regressing the NCO on the treatment-free counterfactual, together with a rank-preserving structural model which assumes a constant individual-level causal effect. In this work, we establish nonparametric COCA identification for the average causal effect for the treated, without requiring rank-preservation, therefore accommodating unrestricted effect heterogeneity across units. This nonparametric identification result has important practical implications, as it provides single proxy confounding control, in contrast to recently proposed proximal causal inference, which relies for identification on a pair of confounding proxies. For COCA estimation we propose three separate strategies: (i) an extended propensity score approach, (ii) an outcome bridge function approach, and (iii) a doubly-robust approach. Finally, we illustrate the proposed methods in an application evaluating the causal impact of a Zika virus outbreak on birth rate in Brazil.
Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.
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.
Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different learning objectives. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results on these tasks, and consistently outperforms baselines on these tasks.
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