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Learning from Demonstration (LfD) is a useful paradigm for training policies that solve tasks involving complex motions, such as those encountered in robotic manipulation. In practice, the successful application of LfD requires overcoming error accumulation during policy execution, i.e. the problem of drift due to errors compounding over time and the consequent out-of-distribution behaviours. Existing works seek to address this problem through scaling data collection, correcting policy errors with a human-in-the-loop, temporally ensembling policy predictions or through learning a dynamical system model with convergence guarantees. In this work, we propose and validate an alternative approach to overcoming this issue. Inspired by reservoir computing, we develop a recurrent neural network layer that includes a fixed nonlinear dynamical system with tunable dynamical properties for modelling temporal dynamics. We validate the efficacy of our neural network layer on the task of reproducing human handwriting motions using the LASA Human Handwriting Dataset. Through empirical experiments we demonstrate that incorporating our layer into existing neural network architectures addresses the issue of compounding errors in LfD. Furthermore, we perform a comparative evaluation against existing approaches including a temporal ensemble of policy predictions and an Echo State Network (ESN) implementation. We find that our approach yields greater policy precision and robustness on the handwriting task while also generalising to multiple dynamics regimes and maintaining competitive latency scores., Comment: 21 pages, 9 figures

This paper addresses a challenging interactive task learning scenario we call rearrangement under unawareness: to manipulate a rigid-body environment in a context where the robot is unaware of a concept that's key to solving the instructed task. We propose SECURE, an interactive task learning framework designed to solve such problems by fixing a deficient domain model using embodied conversation. Through dialogue, the robot discovers and then learns to exploit unforeseen possibilities. Using SECURE, the robot not only learns from the user's corrective feedback when it makes a mistake, but it also learns to make strategic dialogue decisions for revealing useful evidence about novel concepts for solving the instructed task. Together, these abilities allow the robot to generalise to subsequent tasks using newly acquired knowledge. We demonstrate that a robot that is semantics-aware -- that is, it exploits the logical consequences of both sentence and discourse semantics in the learning and inference process -- learns to solve rearrangement under unawareness more effectively than a robot that lacks such capabilities., Comment: 10 pages,4 figures, 2 tables

Many natural phenomena are quantified by counts of observable events, from the annihilation of quasiparticles in a lattice to predator-prey encounters on a landscape to spikes in a neural network. These events are triggered at random intervals when an underlying dynamical system occupies a set of reactive states in its phase space. We derive a general expression for the distribution of times between events in such counting processes assuming the underlying triggering dynamics is a stochastic process that converges to a stationary distribution. Our results contribute to resolving a long-standing dichotomy in the study of reaction-diffusion processes, showing the inter-reaction point process interpolates between a reaction- and a diffusion-limited regime. At low reaction rates, the inter-reaction process is Poisson with a rate depending on stationary properties of the event-triggering stochastic process. At high reaction rates, inter-reaction times are dominated by the hitting times to the reactive states. To further illustrate the power of this approach we apply our framework to obtain the counting statistics of two counting processes appearing in several biophysical scenarios. First, we study the common situation of estimating an animal's activity level by how often it crosses a detector, showing that the mean number of crossing events can decrease monotonically with the hitting rate, a seemingly 'paradoxical' result that could possibly lead to misinterpretation of experimental count data. Second, we derive the ensemble statistics for the detection of many particles, recovering and generalizing known results in the biophysics of chemosensation. Overall, we develop a unifying theoretical framework to quantify inter-event time distributions in reaction-diffusion systems that clarifies existing debates in the literature and provide examples of application to real-world scenarios., Comment: 14 pages, 3 figures

Generic polyhedra are interesting mathematical objects to study in their own right. In this paper, we initialize a systematic study of two-dimensional generic polyhedra with an eye towards applications to low-dimensional topology, especially the Andrews-Curtis and Zeeman conjectures. After recalling the basic notions of generic polyhedra and fake surfaces, we derive some interesting properties of fake surfaces. Our main result is a complete classification of acyclic cellular fake surfaces up to complexity 4 and a classification of acyclic cellular fake surfaces without small disks of complexity 5. From this classification, we prove the contractibility conjecture for acyclic cellular fake surfaces of complexity 4, and the embedded disk conjecture up to complexity 5. We provide evidence for the conjectures that the probability of being a spine among fake surfaces is 0 and that every contractible fake surface has an embedded disk., Comment: 21 pages, 9 figures

While most commentators have focused exclusively on how LLMs will transform day-to-day law practice, a substantial structural change could be afoot within the legal sector as a whole. Large increases in productivity and attendant cost savings could encourage law firms and corporate legal departments to develop large language models in-house. A ten percent increase in attorney productivity would encourage an average sized 'Big Law' firm to reduce its associate headcount by 300 to 400 lawyers. This represents cost savings of 60 to 120 million dollars - more than enough to pay for the development of a specialized LLM. Eventually, LLMs will push lawyers into highly specialized and nuanced roles. After fully mature LLMs arrive, the lawyer will continue to play a central role in legal practice, but only in non-routine legal tasks. These tasks will primarily involve value judgments, such as the development of precedent or its reversal, or the allocation of property and other scarce resources. This new mix of lawyer-machine labor, where machines primarily carry out routine legal tasks, and lawyers handle the non-routine, will give rise to a growing demand for lawyers who can exercise good judgment and empathize with the winners and losers of social change. Overall, the Article suggests a possible future where there are fewer lawyers and greater consolidation of the legal sector.

The creation of large, diverse, high-quality robot manipulation datasets is an important stepping stone on the path toward more capable and robust robotic manipulation policies. However, creating such datasets is challenging: collecting robot manipulation data in diverse environments poses logistical and safety challenges and requires substantial investments in hardware and human labour. As a result, even the most general robot manipulation policies today are mostly trained on data collected in a small number of environments with limited scene and task diversity. In this work, we introduce DROID (Distributed Robot Interaction Dataset), a diverse robot manipulation dataset with 76k demonstration trajectories or 350 hours of interaction data, collected across 564 scenes and 84 tasks by 50 data collectors in North America, Asia, and Europe over the course of 12 months. We demonstrate that training with DROID leads to policies with higher performance and improved generalization ability. We open source the full dataset, policy learning code, and a detailed guide for reproducing our robot hardware setup., Comment: Project website: https://droid-dataset.github.io/

Large, high-capacity models trained on diverse datasets have shown remarkable successes on efficiently tackling downstream applications. In domains from NLP to Computer Vision, this has led to a consolidation of pretrained models, with general pretrained backbones serving as a starting point for many applications. Can such a consolidation happen in robotics? Conventionally, robotic learning methods train a separate model for every application, every robot, and even every environment. Can we instead train generalist X-robot policy that can be adapted efficiently to new robots, tasks, and environments? In this paper, we provide datasets in standardized data formats and models to make it possible to explore this possibility in the context of robotic manipulation, alongside experimental results that provide an example of effective X-robot policies. We assemble a dataset from 22 different robots collected through a collaboration between 21 institutions, demonstrating 527 skills (160266 tasks). We show that a high-capacity model trained on this data, which we call RT-X, exhibits positive transfer and improves the capabilities of multiple robots by leveraging experience from other platforms. More details can be found on the project website https://robotics-transformer-x.github.io., Comment: Project website: https://robotics-transformer-x.github.io

Processes of coalescence and fragmentation are used to understand the time-evolution of the mass distribution of various systems and may result in a steady state or in stable deterministic or stochastic cycles. Motivated by applications in insurgency warfare we investigate coalescence-fragmentation systems. We begin with a simple model of size-biased coalescence accompanied by shattering into monomers. Depending on the parameters this model has an approximately power-law-distributed steady state or stochastic cycles of alternating gelation and shattering. We conduct stochastic simulations of this model and its generalizations to include different kernel types, accretion and erosion, and various distributions of non-shattering fragmentation. Our central aim is to explore the robustness of the steady state and gel-shatter cycles to these variations. We show that an approximate power-law steady state persists with the addition of accretion and erosion, and with partial rather than total shattering. However, broader distributions of fragment sizes typically vitiate both the power law steady state and gel-shatter cyclicity. This work clarifies features shown in coalescence/fragmentation model simulations and elucidates the relationship between the microscopic dynamics and observed phenomena in this widely applicable interdisciplinary model type., Comment: 29 pages, 13 Figures

The advent of large language models (LLMs) and their adoption by the legal community has given rise to the question: what types of legal reasoning can LLMs perform? To enable greater study of this question, we present LegalBench: a collaboratively constructed legal reasoning benchmark consisting of 162 tasks covering six different types of legal reasoning. LegalBench was built through an interdisciplinary process, in which we collected tasks designed and hand-crafted by legal professionals. Because these subject matter experts took a leading role in construction, tasks either measure legal reasoning capabilities that are practically useful, or measure reasoning skills that lawyers find interesting. To enable cross-disciplinary conversations about LLMs in the law, we additionally show how popular legal frameworks for describing legal reasoning -- which distinguish between its many forms -- correspond to LegalBench tasks, thus giving lawyers and LLM developers a common vocabulary. This paper describes LegalBench, presents an empirical evaluation of 20 open-source and commercial LLMs, and illustrates the types of research explorations LegalBench enables., Comment: 143 pages, 79 tables, 4 figures

Ecologists have long investigated how demographic and movement parameters determine the spatial distribution and critical habitat size of a population. However, most models oversimplify movement behavior, neglecting how landscape heterogeneity influences individual movement. We relax this assumption and introduce a reaction-advection-diffusion equation that describes population dynamics when individuals exhibit space-dependent movement bias toward preferred regions. Our model incorporates two types of these preferred regions: a high-quality habitat patch, termed `habitat', which is included to model avoidance of degraded habitats like deforested regions; and a preferred location, such as a chemoattractant source or a watering hole, that we allow to be asymmetrically located with respect to habitat edges. In this scenario, the critical habitat size depends on both the relative position of the preferred location and the movement bias intensities. When preferred locations are near habitat edges, the critical habitat size can decrease when diffusion increases, a phenomenon called the drift paradox. Also, ecological traps arise when the habitat overcrowds due to excessive attractiveness or the preferred location is near a low-quality region. Our results highlight the importance of species-specific movement behavior and habitat preference as drivers of population dynamics in fragmented landscapes and, therefore, in the design of protected areas., Comment: 21 pages, 8 figures

We study the effect that the SU(2) symmetry, and the rich Hilbert space structure that it generates in lattice spin systems, has on the average entanglement entropy of highly excited eigenstates of local Hamiltonians and of random pure states. Focusing on the zero total magnetization sector ($J_z=0$) for different fixed total spin $J$, we argue that the average entanglement entropy of highly excited eigenstates of quantum-chaotic Hamiltonians and of random pure states has a leading volume-law term whose coefficient $s_A$ depends on the spin density $j=J/(\mathfrak{j}L)$, with $s_A(j \rightarrow 0)=\ln (2\mathfrak{j}+1)$ and $s_A(j \rightarrow 1)=0$, where $\mathfrak{j}$ is the microscopic spin. We provide numerical evidence that $s_A$ is smaller in highly excited eigenstates of integrable interacting Hamiltonians, which lends support to the expectation that the average eigenstate entanglement entropy can be used as a diagnostic of quantum chaos and integrability for Hamiltonians with non-Abelian symmetries. In the context of Hamiltonian eigenstates we consider spins $\mathfrak{j}=\frac12$ and $1$, while for our calculations based on random pure states we focus on the spin $\mathfrak{j}=\frac12$ case., Comment: 16 pages, 8 figures, as published