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Single-Index Models are high-dimensional regression problems with planted structure, whereby labels depend on an unknown one-dimensional projection of the input via a generic, non-linear, and potentially non-deterministic transformation. As such, they encompass a broad class of statistical inference tasks, and provide a rich template to study statistical and computational trade-offs in the high-dimensional regime. While the information-theoretic sample complexity to recover the hidden direction is linear in the dimension $d$, we show that computationally efficient algorithms, both within the Statistical Query (SQ) and the Low-Degree Polynomial (LDP) framework, necessarily require $\Omega(d^{k^\star/2})$ samples, where $k^\star$ is a "generative" exponent associated with the model that we explicitly characterize. Moreover, we show that this sample complexity is also sufficient, by establishing matching upper bounds using a partial-trace algorithm. Therefore, our results provide evidence of a sharp computational-to-statistical gap (under both the SQ and LDP class) whenever $k^\star>2$. To complete the study, we provide examples of smooth and Lipschitz deterministic target functions with arbitrarily large generative exponents $k^\star$.

In this paper, we investigate the conditions under which link analysis algorithms prevent minority groups from reaching high ranking slots. We find that the most common link-based algorithms using centrality metrics, such as PageRank and HITS, can reproduce and even amplify bias against minority groups in networks. Yet, their behavior differs: one one hand, we empirically show that PageRank mirrors the degree distribution for most of the ranking positions and it can equalize representation of minorities among the top ranked nodes; on the other hand, we find that HITS amplifies pre-existing bias in homophilic networks through a novel theoretical analysis, supported by empirical results. We find the root cause of bias amplification in HITS to be the level of homophily present in the network, modeled through an evolving network model with two communities. We illustrate our theoretical analysis on both synthetic and real datasets and we present directions for future work.

In this work, we introduce DeepIPC, a novel end-to-end model tailored for autonomous driving, which seamlessly integrates perception and control tasks. Unlike traditional models that handle these tasks separately, DeepIPC innovatively combines a perception module, which processes RGBD images for semantic segmentation and generates bird's eye view (BEV) mappings, with a controller module that utilizes these insights along with GNSS and angular speed measurements to accurately predict navigational waypoints. This integration allows DeepIPC to efficiently translate complex environmental data into actionable driving commands. Our comprehensive evaluation demonstrates DeepIPC's superior performance in terms of drivability and multi-task efficiency across diverse real-world scenarios, setting a new benchmark for end-to-end autonomous driving systems with a leaner model architecture. The experimental results underscore DeepIPC's potential to significantly enhance autonomous vehicular navigation, promising a step forward in the development of autonomous driving technologies. For further insights and replication, we will make our code and datasets available at //github.com/oskarnatan/DeepIPC.

We study a setting in which a community wishes to identify a strongly supported proposal from a space of alternatives, in order to change the status quo. We describe a deliberation process in which agents dynamically form coalitions around proposals that they prefer over the status quo. We formulate conditions on the space of proposals and on the ways in which coalitions are formed that guarantee deliberation to succeed, that is, to terminate by identifying a proposal with the largest possible support. Our results provide theoretical foundations for the analysis of deliberative processes such as the ones that take place in online systems for democratic deliberation support.

In this paper, we propose new techniques for solving geometric optimization problems involving interpoint distances of a point set in the plane. Given a set $P$ of $n$ points in the plane and an integer $1 \leq k \leq \binom{n}{2}$, the distance selection problem is to find the $k$-th smallest interpoint distance among all pairs of points of $P$. The previously best deterministic algorithm solves the problem in $O(n^{4/3} \log^2 n)$ time [Katz and Sharir, SIAM J. Comput. 1997 and SoCG 1993]. In this paper, we improve their algorithm to $O(n^{4/3} \log n)$ time. Using similar techniques, we also give improved algorithms on both the two-sided and the one-sided discrete Fr\'{e}chet distance with shortcuts problem for two point sets in the plane. For the two-sided problem (resp., one-sided problem), we improve the previous work [Avraham, Filtser, Kaplan, Katz, and Sharir, ACM Trans. Algorithms 2015 and SoCG 2014] by a factor of roughly $\log^2(m+n)$ (resp., $(m+n)^{\epsilon}$), where $m$ and $n$ are the sizes of the two input point sets, respectively. Other problems whose solutions can be improved by our techniques include the reverse shortest path problems for unit-disk graphs. Our techniques are quite general and we believe they will find many other applications in future.

In this article, we study the relationship between notions of depth for sequences, namely, Bennett's notions of strong and weak depth, and deep $\Pi^0_1$ classes, introduced by the authors and motivated by previous work of Levin. For the first main result of the study, we show that every member of a $\Pi^0_1$ class is order-deep, a property that implies strong depth. From this result, we obtain new examples of strongly deep sequences based on properties studied in computability theory and algorithmic randomness. We further show that not every strongly deep sequence is a member of a deep $\Pi^0_1$ class. For the second main result, we show that the collection of strongly deep sequences is negligible, which is equivalent to the statement that the probability of computing a strongly deep sequence with some random oracle is 0, a property also shared by every deep $\Pi^0_1$ class. Finally, we show that variants of strong depth, given in terms of a priori complexity and monotone complexity, are equivalent to weak depth.

For robots to perform assistive tasks in unstructured home environments, they must learn and reason on the semantic knowledge of the environments. Despite a resurgence in the development of semantic reasoning architectures, these methods assume that all the training data is available a priori. However, each user's environment is unique and can continue to change over time, which makes these methods unsuitable for personalized home service robots. Although research in continual learning develops methods that can learn and adapt over time, most of these methods are tested in the narrow context of object classification on static image datasets. In this paper, we combine ideas from continual learning, semantic reasoning, and interactive machine learning literature and develop a novel interactive continual learning architecture for continual learning of semantic knowledge in a home environment through human-robot interaction. The architecture builds on core cognitive principles of learning and memory for efficient and real-time learning of new knowledge from humans. We integrate our architecture with a physical mobile manipulator robot and perform extensive system evaluations in a laboratory environment over two months. Our results demonstrate the effectiveness of our architecture to allow a physical robot to continually adapt to the changes in the environment from limited data provided by the users (experimenters), and use the learned knowledge to perform object fetching tasks.

In this paper, we develop an LLM-powered framework for the curation and evaluation of emerging opinion mining in online health communities. We formulate emerging opinion mining as a pairwise stance detection problem between (title, comment) pairs sourced from Reddit, where post titles contain emerging health-related claims on a topic that is not predefined. The claims are either explicitly or implicitly expressed by the user. We detail (i) a method of claim identification -- the task of identifying if a post title contains a claim and (ii) an opinion mining-driven evaluation framework for stance detection using LLMs. We facilitate our exploration by releasing a novel test dataset, Long COVID-Stance, or LC-stance, which can be used to evaluate LLMs on the tasks of claim identification and stance detection in online health communities. Long Covid is an emerging post-COVID disorder with uncertain and complex treatment guidelines, thus making it a suitable use case for our task. LC-Stance contains long COVID treatment related discourse sourced from a Reddit community. Our evaluation shows that GPT-4 significantly outperforms prior works on zero-shot stance detection. We then perform thorough LLM model diagnostics, identifying the role of claim type (i.e. implicit vs explicit claims) and comment length as sources of model error.

Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.