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Intraoperative ultrasound imaging is used to facilitate safe brain tumour resection. However, due to challenges with image interpretation and the physical scanning, this tool has yet to achieve widespread adoption in neurosurgery. In this paper, we introduce the components and workflow of a novel, versatile robotic platform for intraoperative ultrasound tissue scanning in neurosurgery. An RGB-D camera attached to the robotic arm allows for automatic object localisation with ArUco markers, and 3D surface reconstruction as a triangular mesh using the ImFusion Suite software solution. Impedance controlled guidance of the US probe along arbitrary surfaces, represented as a mesh, enables collaborative US scanning, i.e., autonomous, teleoperated and hands-on guided data acquisition. A preliminary experiment evaluates the suitability of the conceptual workflow and system components for probe landing on a custom-made soft-tissue phantom. Further assessment in future experiments will be necessary to prove the effectiveness of the presented platform., Comment: 4 pages, 7 figures, accepted (05 December 2023) for publication in IEEE Transaction on Medical Robotics and Bionics

Work on deep learning-based models of grid cells suggests that grid cells generically and robustly arise from optimizing networks to path integrate, i.e., track one's spatial position by integrating self-velocity signals. In previous work, we challenged this path integration hypothesis by showing that deep neural networks trained to path integrate almost always do so, but almost never learn grid-like tuning unless separately inserted by researchers via mechanisms unrelated to path integration. In this work, we restate the key evidence substantiating these insights, then address a response to by authors of one of the path integration hypothesis papers. First, we show that the response misinterprets our work, indirectly confirming our points. Second, we evaluate the response's preferred "unified theory for the origin of grid cells" in trained deep path integrators and show that it is at best "occasionally suggestive," not exact or comprehensive. We finish by considering why assessing model quality through prediction of biological neural activity by regression of activity in deep networks can lead to the wrong conclusions., Comment: arXiv admin note: text overlap with arXiv:2311.16295

Polysemantic neurons -- neurons that activate for a set of unrelated features -- have been seen as a significant obstacle towards interpretability of task-optimized deep networks, with implications for AI safety. The classic origin story of polysemanticity is that the data contains more ``features" than neurons, such that learning to perform a task forces the network to co-allocate multiple unrelated features to the same neuron, endangering our ability to understand networks' internal processing. In this work, we present a second and non-mutually exclusive origin story of polysemanticity. We show that polysemanticity can arise incidentally, even when there are ample neurons to represent all features in the data, a phenomenon we term \textit{incidental polysemanticity}. Using a combination of theory and experiments, we show that incidental polysemanticity can arise due to multiple reasons including regularization and neural noise; this incidental polysemanticity occurs because random initialization can, by chance alone, initially assign multiple features to the same neuron, and the training dynamics then strengthen such overlap. Our paper concludes by calling for further research quantifying the performance-polysemanticity tradeoff in task-optimized deep neural networks to better understand to what extent polysemanticity is avoidable.

To solve the spatial problems of mapping, localization and navigation, the mammalian lineage has developed striking spatial representations. One important spatial representation is the Nobel-prize winning grid cells: neurons that represent self-location, a local and aperiodic quantity, with seemingly bizarre non-local and spatially periodic activity patterns of a few discrete periods. Why has the mammalian lineage learnt this peculiar grid representation? Mathematical analysis suggests that this multi-periodic representation has excellent properties as an algebraic code with high capacity and intrinsic error-correction, but to date, there is no satisfactory synthesis of core principles that lead to multi-modular grid cells in deep recurrent neural networks. In this work, we begin by identifying key insights from four families of approaches to answering the grid cell question: coding theory, dynamical systems, function optimization and supervised deep learning. We then leverage our insights to propose a new approach that combines the strengths of all four approaches. Our approach is a self-supervised learning (SSL) framework - including data, data augmentations, loss functions and a network architecture - motivated from a normative perspective, without access to supervised position information or engineering of particular readout representations as needed in previous approaches. We show that multiple grid cell modules can emerge in networks trained on our SSL framework and that the networks and emergent representations generalize well outside their training distribution. This work contains insights for neuroscientists interested in the origins of grid cells as well as machine learning researchers interested in novel SSL frameworks.

Magnetic fields generated from a laser-foil interaction are measured with high fidelity using a proton radiography scheme with in situ x-ray fiducials. In contrast to prior findings under similar experimental conditions, this technique reveals the self-generated, Biermann-battery fields extend beyond the edge of the expanding plasma plume to a radius of over 3.5 mm by t=+1.4 ns, a result not captured in state-of-the-art magneto-hydrodynamics simulations. An analysis of two mono-energetic proton populations confirms that proton deflection is dominated by magnetic fields far from the interaction (>2 mm) and electric fields are insignificant. Comparisons to prior work suggest a new physics mechanism for the magnetic field generation and transport in laser-solid interactions., Comment: 9 pages, 8 figures

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions that exhibit heterogeneous properties, requiring multiple sensors to handle functions with minimal regularity. To address this issue, discretization-invariant neural operators have been used, allowing the sampling of diverse input functions with different sensor locations. However, existing frameworks still require an equal number of sensors for all functions. In our study, we propose a novel distributed approach to further relax the discretization requirements and solve the heterogeneous dataset challenges. Our method involves partitioning the input function space and processing individual input functions using independent and separate neural networks. A centralized neural network is used to handle shared information across all output functions. This distributed methodology reduces the number of gradient descent back-propagation steps, improving efficiency while maintaining accuracy. We demonstrate that the corresponding neural network is a universal approximator of continuous nonlinear operators and present four numerical examples to validate its performance.

Recently, soft actuator-based exosuits have gained interest, due to their high strength-to-weight ratio, inherent safety, and low cost. We present a novel wrist exosuit actuated by fabric pneumatic artificial muscles that has lightweight wearable components (160 g) and can move the wrist in flexion/extension and ulnar/radial deviation. We derive a model representing the torque exerted by the exosuit and demonstrate the use of the model to choose an optimal design for an example user. We evaluate the accuracy of the model by measuring the exosuit torques throughout the full range of wrist flexion/extension. We show the importance of accounting for the displacement of the mounting points, as this helps to achieve the smallest mean absolute error (0.283 Nm) compared to other models. Furthermore, we present the measurement of the exosuit-actuated range of motion on a passive human wrist. Finally, we demonstrate the device controlling the passive human wrist to move to a desired orientation along a one and a two-degree-of-freedom trajectory. The evaluation results show that, compared to other pneumatically actuated wrist exosuits, the presented exosuit is lightweight and strong (with peak torque of 3.3 Nm) but has a limited range of motion., Comment: Published in: IEEE Transactions on Medical Robotics and Bionics; 15 pages, 14 figures; Supplementary video: https://youtu.be/SH2sNnTaDJk?si=jFtCHOqolv8k4kqQ

In the Fourth Industrial Revolution, wherein artificial intelligence and the automation of machines occupy a central role, the deployment of robots is indispensable. However, the manufacturing process using robots, especially in collaboration with humans, is highly intricate. In particular, modeling the friction torque in robotic joints is a longstanding problem due to the lack of a good mathematical description. This motivates the usage of data-driven methods in recent works. However, model-based and data-driven models often exhibit limitations in their ability to generalize beyond the specific dynamics they were trained on, as we demonstrate in this paper. To address this challenge, we introduce a novel approach based on residual learning, which aims to adapt an existing friction model to new dynamics using as little data as possible. We validate our approach by training a base neural network on a symmetric friction data set to learn an accurate relation between the velocity and the friction torque. Subsequently, to adapt to more complex asymmetric settings, we train a second network on a small dataset, focusing on predicting the residual of the initial network's output. By combining the output of both networks in a suitable manner, our proposed estimator outperforms the conventional model-based approach and the base neural network significantly. Furthermore, we evaluate our method on trajectories involving external loads and still observe a substantial improvement, approximately 60-70\%, over the conventional approach. Our method does not rely on data with external load during training, eliminating the need for external torque sensors. This demonstrates the generalization capability of our approach, even with a small amount of data-only 43 seconds of a robot movement-enabling adaptation to diverse scenarios based on prior knowledge about friction in different settings.

We study a natural complexity measure of Boolean functions known as the (exact) rational degree. For total functions $f$, it is conjectured that $\mathrm{rdeg}(f)$ is polynomially related to $\mathrm{deg}(f)$, where $\mathrm{deg}(f)$ is the Fourier degree. Towards this conjecture, we show that symmetric functions have rational degree at least $\mathrm{deg}(f)/2$ and monotone functions have rational degree at least $\sqrt{\mathrm{deg}(f)}$. We observe that both of these lower bounds are tight. In addition, we show that all read-once depth-$d$ Boolean formulae have rational degree at least $\Omega(\mathrm{deg}(f)^{1/d})$. Furthermore, we show that almost every Boolean function on $n$ variables has rational degree at least $n/2 - O(\sqrt{n})$. In contrast to total functions, we exhibit partial functions that witness unbounded separations between rational and approximate degree, in both directions. As a consequence, we show that for quantum computers, post-selection and bounded-error are incomparable resources in the black-box model., Comment: 17 pages, 3 figures

As labor shortage increases in the health sector, the demand for assistive robotics grows. However, the needed test data to develop those robots is scarce, especially for the application of active 3D object detection, where no real data exists at all. This short paper counters this by introducing such an annotated dataset of real environments. The captured environments represent areas which are already in use in the field of robotic health care research. We further provide ground truth data within one room, for assessing SLAM algorithms running directly on a health care robot.

In search of a simple baseline for Deep Reinforcement Learning in locomotion tasks, we propose a model-free open-loop strategy. By leveraging prior knowledge and the elegance of simple oscillators to generate periodic joint motions, it achieves respectable performance in five different locomotion environments, with a number of tunable parameters that is a tiny fraction of the thousands typically required by DRL algorithms. We conduct two additional experiments using open-loop oscillators to identify current shortcomings of these algorithms. Our results show that, compared to the baseline, DRL is more prone to performance degradation when exposed to sensor noise or failure. Furthermore, we demonstrate a successful transfer from simulation to reality using an elastic quadruped, where RL fails without randomization or reward engineering. Overall, the proposed baseline and associated experiments highlight the existing limitations of DRL for robotic applications, provide insights on how to address them, and encourage reflection on the costs of complexity and generality., Comment: video: https://b2drop.eudat.eu/s/ykDPMM7F9KFyLgi minimal code: https://gist.github.com/araffin/1fb77a8f290ac248b2e76e01164f21e0

We show that the Jordan decomposition of characters of finite reductive groups can be chosen so that if the centralizer of the relevant semisimple element in the dual group is connected, then the map is Galois-equivariant. Further, in this situation, we show that there is a unique Jordan decomposition satisfying conditions analogous to those of Digne--Michel's unique Jordan decomposition in the connected center case., Comment: v2, 19 pages, substantial revision, text reordered and shortened in places. Theorem 2.1 a stronger version of previous results, see (6) of the statement, with shorter proof. New results: Proposition 4.3, Lemma 6.1, Theorem 6.2 and Proposition 6.3

Problem 21 of Brauer's list of problems from 1963 asks whether for any positive integer k there are finitely many isomorphism classes of groups that occur as the defect group of a block with k irreducible characters. We solve this problem for principal blocks. Another long-standing open problem (from 1982) in this area asks whether the defect group of a block with 3 irreducible characters is necessarily the cyclic group of order 3. In most cases we reduce this problem to a question on simple groups that is closely related to the recent solution of Brauer's height zero conjecture.

Proton deflectometry is increasingly used in magnetized high-energy-density plasmas to observe electromagnetic fields. We describe a reconstruction algorithm to recover the electromagnetic fields from proton fluence data in 1-D. The algorithm is verified against analytic solutions and applied to example data. Secondly, we study the role of source fluence uncertainty for 1-D reconstructions. We show that reconstruction boundary conditions can be used to constrain the source fluence profile, and use this to develop a reconstruction using a specified pair of boundary conditions on the magnetic field. From these considerations we experimentally demonstrate a hybrid mesh-fluence reconstruction technique where fields are reconstructed from fluence data in an interior region with boundary conditions supplied by direct mesh measurements at the boundary., Comment: 11 pages, 7 figures. To appear in Phys. Rev. E (2024). For code library, see: https://github.com/wrfox/PRADICAMENT

Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling. Previous works have focused on embedding dynamical systems into networks through two approaches: learning a single solution operator (i.e., the mapping from input parametrized functions to solutions) or learning the governing system of equations (i.e., the constitutive model relative to the state variables). Both of these approaches yield different representations for the same underlying data or function. Additionally, observing that families of differential equations often share key characteristics, we seek one network representation across a wide range of equations. Our method, called Predicting Operators and Symbolic Expressions (PROSE), learns maps from multimodal inputs to multimodal outputs, capable of generating both numerical predictions and mathematical equations. By using a transformer structure and a feature fusion approach, our network can simultaneously embed sets of solution operators for various parametric differential equations using a single trained network. Detailed experiments demonstrate that the network benefits from its multimodal nature, resulting in improved prediction accuracy and better generalization. The network is shown to be able to handle noise in the data and errors in the symbolic representation, including noisy numerical values, model misspecification, and erroneous addition or deletion of terms. PROSE provides a new neural network framework for differential equations which allows for more flexibility and generality in learning operators and governing equations from data.

Inspired by recent work demonstrating the promise of smaller Transformer-based language models pretrained on carefully curated data, we supercharge such approaches by investing heavily in curating a novel, high quality, non-synthetic data mixture based solely on evaluation benchmarks. Using our novel dataset mixture consisting of less than 100 thousand tokens, we pretrain a 1 million parameter transformer-based LLM \textbf{phi-CTNL} (pronounced ``fictional") that achieves perfect results across diverse academic benchmarks, strictly outperforming all known foundation models. \textbf{phi-CTNL} also beats power-law scaling and exhibits a never-before-seen grokking-like ability to accurately predict downstream evaluation benchmarks' canaries., Comment: 3 pages, satire

High-dimensional linear regression is important in many scientific fields. This article considers discrete measured data of underlying smooth latent processes, as is often obtained from chemical or biological systems. Interpretation in high dimensions is challenging because the nullspace and its interplay with regularization shapes regression coefficients. The data's nullspace contains all coefficients that satisfy $\mathbf{Xw}=\mathbf{0}$, thus allowing very different coefficients to yield identical predictions. We developed an optimization formulation to compare regression coefficients and coefficients obtained by physical engineering knowledge to understand which part of the coefficient differences are close to the nullspace. This nullspace method is tested on a synthetic example and lithium-ion battery data. The case studies show that regularization and z-scoring are design choices that, if chosen corresponding to prior physical knowledge, lead to interpretable regression results. Otherwise, the combination of the nullspace and regularization hinders interpretability and can make it impossible to obtain regression coefficients close to the true coefficients when there is a true underlying linear model. Furthermore, we demonstrate that regression methods that do not produce coefficients orthogonal to the nullspace, such as fused lasso, can improve interpretability. In conclusion, the insights gained from the nullspace perspective help to make informed design choices for building regression models on high-dimensional data and reasoning about potential underlying linear models, which are important for system optimization and improving scientific understanding., Comment: Manuscript: 14 pages, 7 figures; Supplementary Information: 4 pages, 2 figures; Code available: https://github.com/JoachimSchaeffer/HDRegAnalytics

We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many inexpensive computational methods for obtaining coarse-scale solutions. Additionally, in many real-world applications, fine-scale solutions can only be observed at a limited number of locations. In order to obtain approximations or predictions of fine-scale solutions over general regions of interest, we propose to learn the operator mapping from coarse-scale solutions to fine-scale solutions using a limited number (and possibly noisy) observations of the fine-scale solutions. The approach is to train multi-fidelity homogenization maps using mathematically motivated neural operators. The operator learning framework can efficiently obtain the solution of multiscale PDEs at any arbitrary point, making our proposed framework a mesh-free solver. We verify our results on multiple numerical examples showing that our approach is an efficient mesh-free solver for multiscale PDEs.

Collective optical Thomson scattering (TS) is a diagnostic commonly used to characterize plasma parameters. These parameters are typically extracted by a fitting algorithm that minimizes the difference between a measured scattered spectrum and an analytic spectrum calculated from the velocity distribution function (VDF) of the plasma. However, most existing TS analysis algorithms assume the VDFs are Maxwellian, and applying an algorithm which makes this assumption does not accurately extract the plasma parameters of a non-Maxwellian plasma due to the effect of non-Maxwellian deviations on the TS spectra. We present new open-source numerical tools for forward modeling analytic spectra from arbitrary VDFs, and show that these tools are able to more accurately extract plasma parameters from synthetic TS spectra generated by non-Maxwellian VDFs compared to standard TS algorithms. Estimated posterior probability distributions of fits to synthetic spectra for a variety of example non-Maxwellian VDFs are used to determine uncertainties in the extracted plasma parameters, and show that correlations between parameters can significantly affect the accuracy of fits in plasmas with non-Maxwellian VDFs.

Language models can be prompted to reason through problems in a manner that significantly improves performance. However, \textit{why} such prompting improves performance is unclear. Recent work showed that using logically \textit{invalid} Chain-of-Thought (CoT) prompting improves performance almost as much as logically \textit{valid} CoT prompting, and that editing CoT prompts to replace problem-specific information with abstract information or out-of-distribution information typically doesn't harm performance. Critics have responded that these findings are based on too few and too easily solved tasks to draw meaningful conclusions. To resolve this dispute, we test whether logically invalid CoT prompts offer the same level of performance gains as logically valid prompts on the hardest tasks in the BIG-Bench benchmark, termed BIG-Bench Hard (BBH). We find that the logically \textit{invalid} reasoning prompts do indeed achieve similar performance gains on BBH tasks as logically valid reasoning prompts. We also discover that some CoT prompts used by previous works contain logical errors. This suggests that covariates beyond logically valid reasoning are responsible for performance improvements., Comment: ICML 2023 Workshop: Knowledge and Logical Reasoning in the Era of Data-driven Learning

As the capabilities of large machine learning models continue to grow, and as the autonomy afforded to such models continues to expand, the spectre of a new adversary looms: the models themselves. The threat that a model might behave in a seemingly reasonable manner, while secretly and subtly modifying its behavior for ulterior reasons is often referred to as deceptive alignment in the AI Safety & Alignment communities. Consequently, we call this new direction Deceptive Alignment Monitoring. In this work, we identify emerging directions in diverse machine learning subfields that we believe will become increasingly important and intertwined in the near future for deceptive alignment monitoring, and we argue that advances in these fields present both long-term challenges and new research opportunities. We conclude by advocating for greater involvement by the adversarial machine learning community in these emerging directions., Comment: Accepted as BlueSky Oral to 2023 ICML AdvML Workshop

We present FACADE, a novel probabilistic and geometric framework designed for unsupervised mechanistic anomaly detection in deep neural networks. Its primary goal is advancing the understanding and mitigation of adversarial attacks. FACADE aims to generate probabilistic distributions over circuits, which provide critical insights to their contribution to changes in the manifold properties of pseudo-classes, or high-dimensional modes in activation space, yielding a powerful tool for uncovering and combating adversarial attacks. Our approach seeks to improve model robustness, enhance scalable model oversight, and demonstrates promising applications in real-world deployment settings., Comment: Accepted as BlueSky Poster at 2023 ICML AdvML Workshop

We present a generalized version of the discretization-invariant neural operator and prove that the network is a universal approximation in the operator sense. Moreover, by incorporating additional terms in the architecture, we establish a connection between this discretization-invariant neural operator network and those discussed before. The discretization-invariance property of the operator network implies that different input functions can be sampled using various sensor locations within the same training and testing phases. Additionally, since the network learns a ``basis'' for the input and output function spaces, our approach enables the evaluation of input functions on different discretizations. To evaluate the performance of the proposed discretization-invariant neural operator, we focus on challenging examples from multiscale partial differential equations. Our experimental results indicate that the method achieves lower prediction errors compared to previous networks and benefits from its discretization-invariant property.

Planetary cores are the seat of rich and complex fluid dynamics, in which the effects of rotation and magnetic field combine. The equilibria governing the strength of the magnetic field produced by the dynamo effect, the organisation and amplitude of the flow, and those of the density field, remain debated despite remarkable progress made in their numerical simulation. This paper proposes a new approach based on the explicit consideration of the variation of time scales {\tau} with spatial scales {\ell} for the different physical phenomena involved. The {\tau}-{\ell} diagrams thus constructed constitute a very complete graphic summary of the dynamics of the object under study. We highlight the role of the available convective power in controlling this dynamics, together with the relevant force balance, for which we derive a very telling {\tau}-{\ell} translation. Several scenarios are constructed and discussed for the Earth's core, shedding new light on the width of convective columns and on the force equilibria to be considered. A QG-MAC scenario adapted from Aubert [2019] gives a good account of the observations. A diversion to Venus reveals the subtlety and relativity of the notion of 'fast rotator'. We discuss scaling laws and their validity domain, and illustrate 'path strategies'. A complete toolbox is provided, allowing everyone to construct a {\tau}-{\ell} diagram of a numerical simulation, a laboratory experiment, a theory, or a natural object. Supplementary material for this article is supplied as a separate archive Nataf_Schaeffer_SupMat.zip, the related data is displayed in document Nataf_Schaeffer_SupMat.pdf., Comment: Supplementary Material available with python programs at: https://gricad-gitlab.univ-grenoble-alpes.fr/natafh/shell_tau-ell_programs