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Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from $n$ states to $2^n$ states. In this article, we investigate this classical result in a probabilistic setting where we take a deterministic automaton with $n$ states uniformly at random and add just one random transition. These automata are almost deterministic in the sense that only one state has a non-deterministic choice when reading an input letter. In our model, each state has a fixed probability to be final. We prove that for any $d\geq 1$, with non-negligible probability the minimal (deterministic) automaton of the language recognized by such an automaton has more than $n^d$ states; as a byproduct, the expected size of its minimal automaton grows faster than any polynomial. Our result also holds when each state is final with some probability that depends on $n$, as long as it is not too close to $0$ and $1$, at distance at least $\Omega(\frac1{\sqrt{n}})$ to be precise, therefore allowing models with a sublinear number of final states in expectation.

Language models (LMs) have already demonstrated remarkable abilities in understanding and generating both natural and formal language. Despite these advances, their integration with real-world environments such as large-scale knowledge bases (KBs) remains an underdeveloped area, affecting applications such as semantic parsing and indulging in "hallucinated" information. This paper is an experimental investigation aimed at uncovering the robustness challenges that LMs encounter when tasked with knowledge base question answering (KBQA). The investigation covers scenarios with inconsistent data distribution between training and inference, such as generalization to unseen domains, adaptation to various language variations, and transferability across different datasets. Our comprehensive experiments reveal that even when employed with our proposed data augmentation techniques, advanced small and large language models exhibit poor performance in various dimensions. While the LM is a promising technology, the robustness of the current form in dealing with complex environments is fragile and of limited practicality because of the data distribution issue. This calls for future research on data collection and LM learning paradims.

The success of Reinforcement Learning (RL) heavily relies on the ability to learn robust representations from the observations of the environment. In most cases, the representations learned purely by the reinforcement learning loss can differ vastly across states depending on how the value functions change. However, the representations learned need not be very specific to the task at hand. Relying only on the RL objective may yield representations that vary greatly across successive time steps. In addition, since the RL loss has a changing target, the representations learned would depend on how good the current values/policies are. Thus, disentangling the representations from the main task would allow them to focus not only on the task-specific features but also the environment dynamics. To this end, we propose locally constrained representations, where an auxiliary loss forces the state representations to be predictable by the representations of the neighboring states. This encourages the representations to be driven not only by the value/policy learning but also by an additional loss that constrains the representations from over-fitting to the value loss. We evaluate the proposed method on several known benchmarks and observe strong performance. Especially in continuous control tasks, our experiments show a significant performance improvement.

In human cognition, the binding problem describes the open question of how the brain flexibly integrates diverse information into cohesive object representations. Analogously, in machine learning, there is a pursuit for models capable of strong generalization and reasoning by learning object-centric representations in an unsupervised manner. Drawing from neuroscientific theories, Rotating Features learn such representations by introducing vector-valued features that encapsulate object characteristics in their magnitudes and object affiliation in their orientations. The "$\chi$-binding" mechanism, embedded in every layer of the architecture, has been shown to be crucial, but remains poorly understood. In this paper, we propose an alternative "cosine binding" mechanism, which explicitly computes the alignment between features and adjusts weights accordingly, and we show that it achieves equivalent performance. This allows us to draw direct connections to self-attention and biological neural processes, and to shed light on the fundamental dynamics for object-centric representations to emerge in Rotating Features.

Optimal transport aims to learn a mapping of sources to targets by minimizing the cost, which is typically defined as a function of distance. The solution to this problem consists of straight line segments optimally connecting sources to targets, and it does not exhibit branching. These optimal solutions are in stark contrast with both natural, and man-made transportation networks, where branching structures are prevalent. Here we discuss a fast heuristic branching method for optimal transport in networks. We also provide several numerical applications to synthetic examples, a simplified cardiovascular network, and the "Santa Claus" distribution network which includes 141,182 cities around the world, with known location and population.

Neural abstractive summarization models make summaries in an end-to-end manner, and little is known about how the source information is actually converted into summaries. In this paper, we define input sentences that contain essential information in the generated summary as $\textit{source sentences}$ and study how abstractive summaries are made by analyzing the source sentences. To this end, we annotate source sentences for reference summaries and system summaries generated by PEGASUS on document-summary pairs sampled from the CNN/DailyMail and XSum datasets. We also formulate automatic source sentence detection and compare multiple methods to establish a strong baseline for the task. Experimental results show that the perplexity-based method performs well in highly abstractive settings, while similarity-based methods perform robustly in relatively extractive settings. Our code and data are available at //github.com/suhara/sourcesum.

The flexibility of Simultaneous Localization and Mapping (SLAM) algorithms in various environments has consistently been a significant challenge. To address the issue of LiDAR odometry drift in high-noise settings, integrating clustering methods to filter out unstable features has become an effective module of SLAM frameworks. However, reducing the amount of point cloud data can lead to potential loss of information and possible degeneration. As a result, this research proposes a LiDAR odometry that can dynamically assess the point cloud's reliability. The algorithm aims to improve adaptability in diverse settings by selecting important feature points with sensitivity to the level of environmental degeneration. Firstly, a fast adaptive Euclidean clustering algorithm based on range image is proposed, which, combined with depth clustering, extracts the primary structural points of the environment defined as ambient skeleton points. Then, the environmental degeneration level is computed through the dense normal features of the skeleton points, and the point cloud cleaning is dynamically adjusted accordingly. The algorithm is validated on the KITTI benchmark and real environments, demonstrating higher accuracy and robustness in different environments.

High-dimensional problems have long been considered the Achilles' heel of Bayesian optimization algorithms. Spurred by the curse of dimensionality, a large collection of algorithms aim to make it more performant in this setting, commonly by imposing various simplifying assumptions on the objective. In this paper, we identify the degeneracies that make vanilla Bayesian optimization poorly suited to high-dimensional tasks, and further show how existing algorithms address these degeneracies through the lens of lowering the model complexity. Moreover, we propose an enhancement to the prior assumptions that are typical to vanilla Bayesian optimization algorithms, which reduces the complexity to manageable levels without imposing structural restrictions on the objective. Our modification - a simple scaling of the Gaussian process lengthscale prior with the dimensionality - reveals that standard Bayesian optimization works drastically better than previously thought in high dimensions, clearly outperforming existing state-of-the-art algorithms on multiple commonly considered real-world high-dimensional tasks.

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.

Transformer is a type of deep neural network mainly based on self-attention mechanism which is originally applied in natural language processing field. Inspired by the strong representation ability of transformer, researchers propose to extend transformer for computer vision tasks. Transformer-based models show competitive and even better performance on various visual benchmarks compared to other network types such as convolutional networks and recurrent networks. In this paper we provide a literature review of these visual transformer models by categorizing them in different tasks and analyze the advantages and disadvantages of these methods. In particular, the main categories include the basic image classification, high-level vision, low-level vision and video processing. Self-attention in computer vision is also briefly revisited as self-attention is the base component in transformer. Efficient transformer methods are included for pushing transformer into real applications. Finally, we give a discussion about the further research directions for visual transformer.