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The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given architecture. This can lead to high-complexity controls which are impractical in applications. In this paper, we take the opposite, constructive approach: We impose various structural restrictions on system dynamics and consequently characterize the class of functions that can be realized by such a system. The systems are implemented as a cascade interconnection of a neural stochastic differential equation (Neural SDE), a deterministic dynamical system, and a readout map. Both probabilistic and geometric (Lie-theoretic) methods are used to characterize the classes of functions realized by such systems.

Recently, multi-modality models have been introduced because of the complementary information from different sensors such as LiDAR and cameras. It requires paired data along with precise calibrations for all modalities, the complicated calibration among modalities hugely increases the cost of collecting such high-quality datasets, and hinder it from being applied to practical scenarios. Inherit from the previous works, we not only fuse the information from multi-modality without above issues, and also exhaust the information in the RGB modality. We introduced the 2D Detection Annotations Transmittable Aggregation(\textbf{2DDATA}), designing a data-specific branch, called \textbf{Local Object Branch}, which aims to deal with points in a certain bounding box, because of its easiness of acquiring 2D bounding box annotations. We demonstrate that our simple design can transmit bounding box prior information to the 3D encoder model, proving the feasibility of large multi-modality models fused with modality-specific data.

Catastrophic forgetting remains a critical challenge in the field of continual learning, where neural networks struggle to retain prior knowledge while assimilating new information. Most existing studies emphasize mitigating this issue only when encountering new tasks, overlooking the significance of the pre-task phase. Therefore, we shift the attention to the current task learning stage, presenting a novel framework, C&F (Create and Find Flatness), which builds a flat training space for each task in advance. Specifically, during the learning of the current task, our framework adaptively creates a flat region around the minimum in the loss landscape. Subsequently, it finds the parameters' importance to the current task based on their flatness degrees. When adapting the model to a new task, constraints are applied according to the flatness and a flat space is simultaneously prepared for the impending task. We theoretically demonstrate the consistency between the created and found flatness. In this manner, our framework not only accommodates ample parameter space for learning new tasks but also preserves the preceding knowledge of earlier tasks. Experimental results exhibit C&F's state-of-the-art performance as a standalone continual learning approach and its efficacy as a framework incorporating other methods. Our work is available at //github.com/Eric8932/Create-and-Find-Flatness.

Effective representation of data is crucial in various machine learning tasks, as it captures the underlying structure and context of the data. Embeddings have emerged as a powerful technique for data representation, but evaluating their quality and capacity to preserve structural and contextual information remains a challenge. In this paper, we address this need by proposing a method to measure the \textit{representation capacity} of embeddings. The motivation behind this work stems from the importance of understanding the strengths and limitations of embeddings, enabling researchers and practitioners to make informed decisions in selecting appropriate embedding models for their specific applications. By combining extrinsic evaluation methods, such as classification and clustering, with t-SNE-based neighborhood analysis, such as neighborhood agreement and trustworthiness, we provide a comprehensive assessment of the representation capacity. Additionally, the use of optimization techniques (bayesian optimization) for weight optimization (for classification, clustering, neighborhood agreement, and trustworthiness) ensures an objective and data-driven approach in selecting the optimal combination of metrics. The proposed method not only contributes to advancing the field of embedding evaluation but also empowers researchers and practitioners with a quantitative measure to assess the effectiveness of embeddings in capturing structural and contextual information. For the evaluation, we use $3$ real-world biological sequence (proteins and nucleotide) datasets and performed representation capacity analysis of $4$ embedding methods from the literature, namely Spike2Vec, Spaced $k$-mers, PWM2Vec, and AutoEncoder.

Exhibiting an explicit Boolean function with a large high-order nonlinearity is an important problem in cryptography, coding theory, and computational complexity. We prove lower bounds on the second-order, third-order, and higher-order nonlinearities of some trace monomial Boolean functions. We prove lower bounds on the second-order nonlinearities of functions $\mathrm{tr}_n(x^7)$ and $\mathrm{tr}_n(x^{2^r+3})$ where $n=2r$. Among all trace monomials, our bounds match the best second-order nonlinearity lower bounds by \cite{Car08} and \cite{YT20} for odd and even $n$ respectively. We prove a lower bound on the third-order nonlinearity for functions $\mathrm{tr}_n(x^{15})$, which is the best third-order nonlinearity lower bound. For any $r$, we prove that the $r$-th order nonlinearity of $\mathrm{tr}_n(x^{2^{r+1}-1})$ is at least $2^{n-1}-2^{(1-2^{-r})n+\frac{r}{2^{r-1}}-1}- O(2^{\frac{n}{2}})$. For $r \ll \log_2 n$, this is the best lower bound among all explicit functions.

Ordered sequences of data, specified with a join operation to combine sequences, serve as a foundation for the implementation of parallel functional algorithms. This abstract data type can be elegantly and efficiently implemented using balanced binary trees, where a join operation is provided to combine two trees and rebalance as necessary. In this work, we present a verified implementation and cost analysis of joinable red-black trees in $\textbf{calf}$, a dependent type theory for cost analysis. We implement red-black trees and auxiliary intermediate data structures in such a way that all correctness invariants are intrinsically maintained. Then, we describe and verify precise cost bounds on the operations, making use of the red-black tree invariants. Finally, we implement standard algorithms on sequences using the simple join-based signature and bound their cost in the case that red-black trees are used as the underlying implementation. All proofs are formally mechanized using the embedding of $\textbf{calf}$ in the Agda theorem prover.

Given an array A[1: n] of n elements drawn from an ordered set, the sorted range selection problem is to build a data structure that can be used to answer the following type of queries efficiently: Given a pair of indices i, j $ (1\le i\le j \le n)$, and a positive integer k, report the k smallest elements from the sub-array A[i: j] in order. Brodal et al. (Brodal, G.S., Fagerberg, R., Greve, M., and L{\'o}pez-Ortiz, A., Online sorted range reporting. Algorithms and Computation (2009) pp. 173--182) introduced the problem and gave an optimal solution. After O(n log n) time for preprocessing, the query time is O(k). The space used is O(n). In this paper, we propose the only other possible optimal trade-off for the problem. We present a linear space solution to the problem that takes O(k log k) time to answer a range selection query. The preprocessing time is O(n). Moreover, the proposed algorithm reports the output elements one by one in non-decreasing order. Our solution is simple and practical. We also describe an extremely simple method for range minima queries (most of whose parts are known) which takes al most (but not exactly) linear time. We believe that this method may be, in practice, faster and easier to implement in most cases.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

Influenced by the stunning success of deep learning in computer vision and language understanding, research in recommendation has shifted to inventing new recommender models based on neural networks. In recent years, we have witnessed significant progress in developing neural recommender models, which generalize and surpass traditional recommender models owing to the strong representation power of neural networks. In this survey paper, we conduct a systematic review on neural recommender models, aiming to summarize the field to facilitate future progress. Distinct from existing surveys that categorize existing methods based on the taxonomy of deep learning techniques, we instead summarize the field from the perspective of recommendation modeling, which could be more instructive to researchers and practitioners working on recommender systems. Specifically, we divide the work into three types based on the data they used for recommendation modeling: 1) collaborative filtering models, which leverage the key source of user-item interaction data; 2) content enriched models, which additionally utilize the side information associated with users and items, like user profile and item knowledge graph; and 3) context enriched models, which account for the contextual information associated with an interaction, such as time, location, and the past interactions. After reviewing representative works for each type, we finally discuss some promising directions in this field, including benchmarking recommender systems, graph reasoning based recommendation models, and explainable and fair recommendations for social good.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.