This paper summarizes some of the technical background, research ideas, and possible development strategies for achieving machine common sense. Machine common sense has long been a critical-but-missing component of Artificial Intelligence (AI). Recent advances in machine learning have resulted in new AI capabilities, but in all of these applications, machine reasoning is narrow and highly specialized. Developers must carefully train or program systems for every situation. General commonsense reasoning remains elusive. The absence of common sense prevents intelligent systems from understanding their world, behaving reasonably in unforeseen situations, communicating naturally with people, and learning from new experiences. Its absence is perhaps the most significant barrier between the narrowly focused AI applications we have today and the more general, human-like AI systems we would like to build in the future. Machine common sense remains a broad, potentially unbounded problem in AI. There are a wide range of strategies that could be employed to make progress on this difficult challenge. This paper discusses two diverse strategies for focusing development on two different machine commonsense services: (1) a service that learns from experience, like a child, to construct computational models that mimic the core domains of child cognition for objects (intuitive physics), agents (intentional actors), and places (spatial navigation); and (2) service that learns from reading the Web, like a research librarian, to construct a commonsense knowledge repository capable of answering natural language and image-based questions about commonsense phenomena.

A VLT/MUSE population synthesis study of metallicities in the nuclear star-forming rings of four disk galaxies (NGC 613, NGC 1097, NGC 3351, NGC 7552) is presented. Disentangling the spectral contributions of young and old stellar populations, we find a large spread of ages and metallicities of the old stars in the nuclear rings. This indicates a persistent infall of metal-poor gas and ongoing episodic star formation over many gigayears. The young stars have metallicities a factor two to three higher than solar in all galaxies except NGC 3351, where the range is from half to twice solar. Previously reported detections of extremely metal poor regions at young stellar age on the rings of these four galaxies are a methodological artifact of the average over all stars, young and old. In addition, it is important to include contributions of very young stars (<6 Myr) in this environment. For each of the four galaxies, the extinction maps generated through our population synthesis analysis provide support for the infall scenario. They reveal dust lanes along the leading edges of the stellar bars, indicating the flow of interstellar material towards the circumnuclear zone. Prominent stellar clusters show little extinction, most likely because of the onset of stellar winds. Inside and on the nuclear rings, regions that are largely free of extinction are detected.

In a sampling problem, we are given an input x, and asked to sample approximately from a probability distribution D_x. In a search problem, we are given an input x, and asked to find a member of a nonempty set A_x with high probability. (An example is finding a Nash equilibrium.) In this paper, we use tools from Kolmogorov complexity and algorithmic information theory to show that sampling and search problems are essentially equivalent. More precisely, for any sampling problem S, there exists a search problem R_S such that, if C is any "reasonable" complexity class, then R_S is in the search version of C if and only if S is in the sampling version. As one application, we show that SampP=SampBQP if and only if FBPP=FBQP: in other words, classical computers can efficiently sample the output distribution of every quantum circuit, if and only if they can efficiently solve every search problem that quantum computers can solve. A second application is that, assuming a plausible conjecture, there exists a search problem R that can be solved using a simple linear-optics experiment, but that cannot be solved efficiently by a classical computer unless the polynomial hierarchy collapses. That application will be described in a forthcoming paper with Alex Arkhipov on the computational complexity of linear optics.

We present an introduction to the equivariant slice filtration. After reviewing the definitions and basic properties, we determine the slice dimension of various families of naturally arising spectra. This leads to an analysis of pullbacks of slices defined on quotient groups, producing new collections of slices. Building on this, we determine the slice tower for the Eilenberg-Mac Lane spectrum associated to a Mackey functor for a cyclic $p$-group. We then relate the Postnikov tower to the slice tower for various spectra. Finally, we pose a few conjectures about the nature of slices and pullbacks.

We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent information. We explain how one can use the existing algorithm for persistent homology to process any of the four modules, and relate it to a recently introduced persistent cohomology algorithm. We present experimental evidence for the practical efficiency of the latter algorithm.

Ropelength and embedding thickness are related measures of geometric complexity of classical knots and links in Euclidean space. In their recent work, Freedman and Krushkal posed a question regarding lower bounds for embedding thickness of $n$-component links in terms of the Milnor linking numbers. The main goal of the current paper is to provide such estimates and thus generalizing the known linking number bound. In the process, we collect several facts about finite type invariants and ropelength/crossing number of knots. We give examples of families of knots, where such estimates behave better than the well-known knot-genus estimate.

The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed which leads to a mysterious duality between certain categories of sheaves on moduli spaces of (flat) bundles on algebraic curves. Three years ago, in a groundbreaking advance, Kapustin and Witten have linked the geometric Langlands correspondence to the S-duality of 4D supersymmetric gauge theories. This and subsequent works have already led to striking new insights into the geometric Langlands Program, which in particular involve the Homological Mirror Symmetry of the Hitchin moduli spaces of Higgs bundles on algebraic curves associated to two Langlands dual Lie groups.

We make explicit a construction of Serre giving a definition of an algebraic Sato-Tate group associated to an abelian variety over a number field, which is conjecturally linked to the distribution of normalized L-factors as in the usual Sato-Tate conjecture for elliptic curves. The connected part of the algebraic Sato-Tate group is closely related to the Mumford-Tate group, but the group of components carries additional arithmetic information. We then check that in many cases where the Mumford-Tate group is completely determined by the endomorphisms of the abelian variety, the algebraic Sato-Tate group can also be described explicitly in terms of endomorphisms. In particular, we cover all abelian varieties (not necessarily absolutely simple) of dimension at most 3; this result figures prominently in the analysis of Sato-Tate groups for abelian surfaces given recently by Fite, Kedlaya, Rotger, and Sutherland.

Many of the input-parameter-to-output-quantity-of-interest maps that arise in computational science admit a surprising low-dimensional structure, where the outputs vary primarily along a handful of directions in the high-dimensional input space. This type of structure is well modeled by a ridge function, which is a composition of a low-dimensional linear transformation with a nonlinear function. If the goal is to compute statistics of the output (e.g., as in uncertainty quantification or robust design) then one should exploit this low-dimensional structure, when present, to accelerate computations. We develop Gaussian quadrature and the associated polynomial approximation for one-dimensional ridge functions. The key elements of our method are (i) approximating the univariate density of the given linear combination of inputs by repeated convolutions and (ii) a Lanczos-Stieltjes method for constructing orthogonal polynomials and Gaussian quadrature.

We describe a construction of the cyclotomic structure on topological Hochschild homology ($THH$) of a ring spectrum using the Hill-Hopkins-Ravenel multiplicative norm. Our analysis takes place entirely in the category of equivariant orthogonal spectra, avoiding use of the B\"okstedt coherence machinery. We are able to define versions of topological cyclic homology ($TC$) and TR-theory relative to a cyclotomic commutative ring spectrum $A$. We describe spectral sequences computing this relative theory $_ATR$ in terms of $TR$ over the sphere spectrum and vice versa. Furthermore, our construction permits a straightforward definition of the Adams operations on $TR$ and $TC$.

Recent studies have shown that Convolutional Neural Networks (CNN) are relatively easy to attack through the generation of so-called adversarial examples. Such vulnerability also affects CNN-based image forensic tools. Research in deep learning has shown that adversarial examples exhibit a certain degree of transferability, i.e., they maintain part of their effectiveness even against CNN models other than the one targeted by the attack. This is a very strong property undermining the usability of CNN's in security-oriented applications. In this paper, we investigate if attack transferability also holds in image forensics applications. With specific reference to the case of manipulation detection, we analyse the results of several experiments considering different sources of mismatch between the CNN used to build the adversarial examples and the one adopted by the forensic analyst. The analysis ranges from cases in which the mismatch involves only the training dataset, to cases in which the attacker and the forensic analyst adopt different architectures. The results of our experiments show that, in the majority of the cases, the attacks are not transferable, thus easing the design of proper countermeasures at least when the attacker does not have a perfect knowledge of the target detector.

In this paper, we describe the development of symbolic representations annotated on human-robot dialogue data to make dimensions of meaning accessible to autonomous systems participating in collaborative, natural language dialogue, and to enable common ground with human partners. A particular challenge for establishing common ground arises in remote dialogue (occurring in disaster relief or search-and-rescue tasks), where a human and robot are engaged in a joint navigation and exploration task of an unfamiliar environment, but where the robot cannot immediately share high quality visual information due to limited communication constraints. Engaging in a dialogue provides an effective way to communicate, while on-demand or lower-quality visual information can be supplemented for establishing common ground. Within this paradigm, we capture propositional semantics and the illocutionary force of a single utterance within the dialogue through our Dialogue-AMR annotation, an augmentation of Abstract Meaning Representation. We then capture patterns in how different utterances within and across speaker floors relate to one another in our development of a multi-floor Dialogue Structure annotation schema. Finally, we begin to annotate and analyze the ways in which the visual modalities provide contextual information to the dialogue for overcoming disparities in the collaborators' understanding of the environment. We conclude by discussing the use-cases, architectures, and systems we have implemented from our annotations that enable physical robots to autonomously engage with humans in bi-directional dialogue and navigation.

The deployment of pre-trained perception models in novel environments often leads to performance degradation due to distributional shifts. Although recent artificial intelligence approaches for metacognition use logical rules to characterize and filter model errors, improving precision often comes at the cost of reduced recall. This paper addresses the hypothesis that leveraging multiple pre-trained models can mitigate this recall reduction. We formulate the challenge of identifying and managing conflicting predictions from various models as a consistency-based abduction problem, building on the idea of abductive learning (ABL) but applying it to test-time instead of training. The input predictions and the learned error detection rules derived from each model are encoded in a logic program. We then seek an abductive explanation--a subset of model predictions--that maximizes prediction coverage while ensuring the rate of logical inconsistencies (derived from domain constraints) remains below a specified threshold. We propose two algorithms for this knowledge representation task: an exact method based on Integer Programming (IP) and an efficient Heuristic Search (HS). Through extensive experiments on a simulated aerial imagery dataset featuring controlled, complex distributional shifts, we demonstrate that our abduction-based framework outperforms individual models and standard ensemble baselines, achieving, for instance, average relative improvements of approximately 13.6\% in F1-score and 16.6\% in accuracy across 15 diverse test datasets when compared to the best individual model. Our results validate the use of consistency-based abduction as an effective mechanism to robustly integrate knowledge from multiple imperfect models in challenging, novel scenarios.

We construct splitting varieties for triple Massey products. For a,b,c in F^* the triple Massey product < a,b,c> of the corresponding elements of H^1(F, mu_2) contains 0 if and only if there is x in F^* and y in F[\sqrt{a}, \sqrt{c}]^* such that b x^2 = N_{F[\sqrt{a}, \sqrt{c}]/F}(y), where N_{F[\sqrt{a}, \sqrt{c}]/F} denotes the norm, and F is a field of characteristic different from 2. These varieties satisfy the Hasse principle by a result of D.B. Lee and A.R. Wadsworth. This shows that triple Massey products for global fields of characteristic different from 2 always contain 0.

Airborne insects generate a leading edge vortex when they flap their wings. This coherent vortex is a low pressure region that enhances the lift of flapping wings compared to fixed wings. Insect wings are thin membranes strengthened by a system of veins that does not allow large wing deformations. Bat wings are thin compliant skin membranes stretched between their limbs, hand, and body that show larger deformations during flapping wing flight. This study examines the role of the leading edge vortex on highly deformable membrane wings that passively change shape under fluid dynamic loading maintaining a positive camber throughout the hover cycle. Our experiments reveal that unsteady wing deformations suppress the formation of a coherent leading edge vortex as flexibility increases. At lift and energy optimal aeroelastic conditions, there is no more leading edge vortex. Instead, vorticity accumulates in a bound shear layer covering the wing's upper surface from the leading to the trailing edge. Despite the absence of a leading edge vortex, the optimal deformable membrane wings demonstrate enhanced lift and energy efficiency compared to their rigid counterparts. It is possible that small bats rely on this mechanism for efficient hovering. We relate the force production on the wings with their deformation through scaling analyses. Additionally, we identify the geometric angles at the leading and trailing edges as observable indicators of the flow state and use them to map out the transitions of the flow topology and their aerodynamic performance for a wide range of aeroelastic conditions.

Deep Reinforcement Learning (RL) has been explored and verified to be effective in solving decision-making tasks in various domains, such as robotics, transportation, recommender systems, etc. It learns from the interaction with environments and updates the policy using the collected experience. However, due to the limited real-world data and unbearable consequences of taking detrimental actions, the learning of RL policy is mainly restricted within the simulators. This practice guarantees safety in learning but introduces an inevitable sim-to-real gap in terms of deployment, thus causing degraded performance and risks in execution. There are attempts to solve the sim-to-real problems from different domains with various techniques, especially in the era with emerging techniques such as large foundations or language models that have cast light on the sim-to-real. This survey paper, to the best of our knowledge, is the first taxonomy that formally frames the sim-to-real techniques from key elements of the Markov Decision Process (State, Action, Transition, and Reward). Based on the framework, we cover comprehensive literature from the classic to the most advanced methods including the sim-to-real techniques empowered by foundation models, and we also discuss the specialties that are worth attention in different domains of sim-to-real problems. Then we summarize the formal evaluation process of sim-to-real performance with accessible code or benchmarks. The challenges and opportunities are also presented to encourage future exploration of this direction. We are actively maintaining a repository to include the most up-to-date sim-to-real research work to help domain researchers.

The ability to interact with machines using natural human language is becoming not just commonplace, but expected. The next step is not just text interfaces, but speech interfaces and not just with computers, but with all machines including robots. In this paper, we chronicle the recent history of this growing field of spoken dialogue with robots and offer the community three proposals, the first focused on education, the second on benchmarks, and the third on the modeling of language when it comes to spoken interaction with robots. The three proposals should act as white papers for any researcher to take and build upon.

Quantum circuits currently constitute a dominant model for quantum computation. Our work addresses the problem of constructing quantum circuits to implement an arbitrary given quantum computation, in the special case of two qubits. We pursue circuits without ancilla qubits and as small a number of elementary quantum gates as possible. Our lower bound for worst-case optimal two-qubit circuits calls for at least 17 gates: 15 one-qubit rotations and 2 CNOTs. To this end, we constructively prove a worst-case upper bound of 23 elementary gates, of which at most 4 (CNOT) entail multi-qubit interactions. Our analysis shows that synthesis algorithms suggested in previous work, although more general, entail much larger quantum circuits than ours in the special case of two qubits. One such algorithm has a worst case of 61 gates of which 18 may be CNOTs. Our techniques rely on the KAK decomposition from Lie theory as well as the polar and spectral (symmetric Shur) matrix decompositions from numerical analysis and operator theory. They are related to the canonical decomposition of a two-qubit gate with respect to the ``magic basis'' of phase-shifted Bell states, published previously. We further extend this decomposition in terms of elementary gates for quantum computation.