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As complex machine learning models continue to find applications in high-stakes decision-making scenarios, it is crucial that we can explain and understand their predictions. Post-hoc explanation methods provide useful insights by identifying important features in an input $\mathbf{x}$ with respect to the model output $f(\mathbf{x})$. In this work, we formalize and study two precise notions of feature importance for general machine learning models: sufficiency and necessity. We demonstrate how these two types of explanations, albeit intuitive and simple, can fall short in providing a complete picture of which features a model finds important. To this end, we propose a unified notion of importance that circumvents these limitations by exploring a continuum along a necessity-sufficiency axis. Our unified notion, we show, has strong ties to other popular definitions of feature importance, like those based on conditional independence and game-theoretic quantities like Shapley values. Crucially, we demonstrate how a unified perspective allows us to detect important features that could be missed by either of the previous approaches alone.

We study 2d $SU(N)$ QCD with an adjoint Dirac fermion. Assuming that the IR limit of the massless theory is captured by a WZW coset CFT, we show that this CFT can be decomposed into a sum of distinct CFTs, each representing a superselection sector (universe) of the gauge theory corresponding to different flux tube sectors. The CFTs describing each universe are related by non-invertible topological lines that exhibit a mixed anomaly with the $\mathbb{Z}^{(1)}_N$ 1-form symmetry. These symmetries exist along the entire RG flow thereby implying deconfinement of the massless theory. We begin by outlining the general features of the model for arbitrary $N$ and then provide a detailed analysis for $N=2$ and $N=3$. In these specific cases, we explicitly determine the IR partition function, identify the symmetries, and explore relevant deformations. Based on these findings and in alignment with various previous studies, we propose a phase diagram for the massive $SU(2)$ gauge theory and calculate its confining string tension., Comment: 36 pages + appendices

We analyse the impact of using tempered likelihoods in the production of posterior predictions. Our findings reveal that once the sample size is at least moderately large and the temperature is not too small, then likelihood tempering has virtually no impact on the resulting posterior predictions., Comment: 7 (+14 supplementary) pages (excluding references); 3 (+4 supplementary) figures

Emerging artificial intelligence (AI) and machine learning (ML) workloads present new challenges of managing the collective communication used in distributed training across hundreds or even thousands of GPUs. This paper presents STrack, a novel hardware-offloaded reliable transport protocol aimed at improving the performance of AI /ML workloads by rethinking key aspects of the transport layer. STrack optimizes congestion control and load balancing in tandem: it incorporates an adaptive load balancing algorithm leveraging ECN, while adopts RTT as multi-bit congestion indicators for precise congestion window adjustment. Additionally, STrack facilitates out-of-order delivery, selective retransmission, and swift loss recovery in hardware for multipath environment. The extensive simulation comparing STrack and RoCEv2 demonstrates that STrack outperforms RoCEv2 by up to 6X with synthetic workloads and by 27.4% with collective workloads, even with the optimized RoCEv2 system setup.

Selective Classification, wherein models can reject low-confidence predictions, promises reliable translation of machine-learning based classification systems to real-world scenarios such as clinical diagnostics. While current evaluation of these systems typically assumes fixed working points based on pre-defined rejection thresholds, methodological progress requires benchmarking the general performance of systems akin to the $\mathrm{AUROC}$ in standard classification. In this work, we define 5 requirements for multi-threshold metrics in selective classification regarding task alignment, interpretability, and flexibility, and show how current approaches fail to meet them. We propose the Area under the Generalized Risk Coverage curve ($\mathrm{AUGRC}$), which meets all requirements and can be directly interpreted as the average risk of undetected failures. We empirically demonstrate the relevance of $\mathrm{AUGRC}$ on a comprehensive benchmark spanning 6 data sets and 13 confidence scoring functions. We find that the proposed metric substantially changes metric rankings on 5 out of the 6 data sets.

Voting mechanisms are widely accepted and used methods for decentralized decision-making. Ensuring the acceptance of the voting mechanism's outcome is a crucial characteristic of robust voting systems. Consider this scenario: A group of individuals wants to choose an option from a set of alternatives without requiring an identification or proof-of-personhood system. Moreover, they want to implement utilitarianism as their selection criteria. In such a case, players could submit votes multiple times using dummy accounts, commonly known as a Sybil attack (SA), which presents a challenge for decentralized organizations. Is there a voting mechanism that always prevents players from benefiting by casting votes multiple times (SA-proof) while also selecting the alternative that maximizes the added valuations of all players (efficient)? One-person-one-vote is neither SA-proof nor efficient. Coin voting is SA-proof but not efficient. Quadratic voting is efficient but not SA-proof. This study uses Bayesian mechanism design to propose a solution. The mechanism's structure is as follows: Players make wealth deposits to indicate the strength of their preference for each alternative. Each player then receives an amount based on their deposit and the voting outcome. The proposed mechanism relies on two main concepts: 1) Transfers are influenced by the outcome in a way that each player's optimal action depends only on individual preferences and the number of alternatives; 2) A player who votes through multiple accounts slightly reduces the expected utility of all players more than the individual benefit gained. This study demonstrates that if players are risk-neutral and each player has private information about their preferences and beliefs, then the mechanism is SA-proof and efficient. This research provides new insights into the design of more robust decentralized decision-making mechanisms.

Sparse auto-encoders are useful for extracting low-dimensional representations from high-dimensional data. However, their performance degrades sharply when the input noise at test time differs from the noise employed during training. This limitation hinders the applicability of auto-encoders in real-world scenarios where the level of noise in the input is unpredictable. In this paper, we formalize single hidden layer sparse auto-encoders as a transform learning problem. Leveraging the transform modeling interpretation, we propose an optimization problem that leads to a predictive model invariant to the noise level at test time. In other words, the same pre-trained model is able to generalize to different noise levels. The proposed optimization algorithm, derived from the square root lasso, is translated into a new, computationally efficient auto-encoding architecture. After proving that our new method is invariant to the noise level, we evaluate our approach by training networks using the proposed architecture for denoising tasks. Our experimental results demonstrate that the trained models yield a significant improvement in stability against varying types of noise compared to commonly used architectures.

Semantic segmentation is an essential component of medical image analysis research, with recent deep learning algorithms offering out-of-the-box applicability across diverse datasets. Despite these advancements, segmentation failures remain a significant concern for real-world clinical applications, necessitating reliable detection mechanisms. This paper introduces a comprehensive benchmarking framework aimed at evaluating failure detection methodologies within medical image segmentation. Through our analysis, we identify the strengths and limitations of current failure detection metrics, advocating for the risk-coverage analysis as a holistic evaluation approach. Utilizing a collective dataset comprising five public 3D medical image collections, we assess the efficacy of various failure detection strategies under realistic test-time distribution shifts. Our findings highlight the importance of pixel confidence aggregation and we observe superior performance of the pairwise Dice score (Roy et al., 2019) between ensemble predictions, positioning it as a simple and robust baseline for failure detection in medical image segmentation. To promote ongoing research, we make the benchmarking framework available to the community., Comment: This work has been submitted for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Given a homeomorphism $T \colon X \to X$ of a compact metric space $X$, the stabilized automorphism group $\textrm{Aut}^{\infty}(T)$ of the system $(X,T)$ is the group of self-homeomorphisms of $X$ which commute with some power of $T$. We study the question of spatiality for stabilized automorphism groups of shifts of finite type. We prove that any isomorphism $\Psi \colon \textrm{Aut}^{\infty}(\sigma_{m}) \to \textrm{Aut}^{\infty}(\sigma_{n})$ between stabilized automorphism groups of full shifts is spatially induced by a homeomorphism $\hat{\Psi}$ between respective stabilized spaces of chain recurrent subshifts. This spatialization in particular gives a bijection between the sets of periodic points which intertwines some powers of the shifts, and this bijection recovers the isomorphism at the level of the faithful actions on the sets of periodic points. We also prove that the outer automorphism group of $\textrm{Aut}^{\infty}(\sigma_{n})$ is uncountable, and deduce several other properties of $\textrm{Aut}^{\infty}(\sigma_{n})$ using the spatiality results., Comment: 27 pages

Recent works have extended notions of feature importance to semantic concepts that are inherently interpretable to the users interacting with a black-box predictive model. Yet, precise statistical guarantees, such as false positive rate and false discovery rate control, are needed to communicate findings transparently and to avoid unintended consequences in real-world scenarios. In this paper, we formalize the global (i.e., over a population) and local (i.e., for a sample) statistical importance of semantic concepts for the predictions of opaque models by means of conditional independence, which allows for rigorous testing. We use recent ideas of sequential kernelized independence testing (SKIT) to induce a rank of importance across concepts, and showcase the effectiveness and flexibility of our framework on synthetic datasets as well as on image classification tasks using several and diverse vision-language models.

Recent work in adversarial robustness suggests that natural data distributions are localized, i.e., they place high probability in small volume regions of the input space, and that this property can be utilized for designing classifiers with improved robustness guarantees for $\ell_2$-bounded perturbations. Yet, it is still unclear if this observation holds true for more general metrics. In this work, we extend this theory to $\ell_0$-bounded adversarial perturbations, where the attacker can modify a few pixels of the image but is unrestricted in the magnitude of perturbation, and we show necessary and sufficient conditions for the existence of $\ell_0$-robust classifiers. Theoretical certification approaches in this regime essentially employ voting over a large ensemble of classifiers. Such procedures are combinatorial and expensive or require complicated certification techniques. In contrast, a simple classifier emerges from our theory, dubbed Box-NN, which naturally incorporates the geometry of the problem and improves upon the current state-of-the-art in certified robustness against sparse attacks for the MNIST and Fashion-MNIST datasets.

A full triangulated subcategory $\mathsf{C} \subset \mathsf{T}$ of triangulated category $\mathsf{T}$ is colocalizing if it is stable for products. If, further, $\mathsf{T}$ is monoidal and closed, i.e. $(\mathsf{T}, \otimes)$ is tensor-triangulated with internal homs (denoted $[-,-]$), we say that $\mathsf{C}$ is an $\mathcal{H}$-coideal if $[F, G] \in \mathsf{C}$ for all $G \in \mathsf{C}$ and all $F \in \mathsf{T}$. We prove, for a noetherian scheme $X$, that all $\mathcal{H}$-coideal colocalizing subcategories of $\mathsf{D}_{\mathrm{qc}}(X)$ are classified by subsets of $X$. Every such colocalizing subcategory $\mathsf{C}$ is of the form $\mathsf{C} = \mathsf{L}^\perp$, where $\mathsf{L}$ is a $\otimes$-ideal localizing subcategory., Comment: 16 pages

We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks., Comment: 41st International Conference on Machine Learning (ICML 2024)

Building on the progress in Boolean satisfiability (SAT) solving over the last decades, maximum satisfiability (MaxSAT) has become a viable approach for solving NP-hard optimization problems, but ensuring correctness of MaxSAT solvers has remained an important concern. For SAT, this is largely a solved problem thanks to the use of proof logging, meaning that solvers emit machine-verifiable proofs of (un)satisfiability to certify correctness. However, for MaxSAT, proof logging solvers have started being developed only very recently. Moreover, these nascent efforts have only targeted the core solving process, ignoring the preprocessing phase where input problem instances can be substantially reformulated before being passed on to the solver proper. In this work, we demonstrate how pseudo-Boolean proof logging can be used to certify the correctness of a wide range of modern MaxSAT preprocessing techniques. By combining and extending the VeriPB and CakePB tools, we provide formally verified, end-to-end proof checking that the input and preprocessed output MaxSAT problem instances have the same optimal value. An extensive evaluation on applied MaxSAT benchmarks shows that our approach is feasible in practice.

In recent years, the shortcomings of Bayes posteriors as inferential devices has received increased attention. A popular strategy for fixing them has been to instead target a Gibbs measure based on losses that connect a parameter of interest to observed data. While existing theory for such inference procedures relies on these losses to be analytically available, in many situations these losses must be stochastically estimated using pseudo-observations. The current paper fills this research gap, and derives the first asymptotic theory for Gibbs measures based on estimated losses. Our findings reveal that the number of pseudo-observations required to accurately approximate the exact Gibbs measure depends on the rates at which the bias and variance of the estimated loss converge to zero. These results are particularly consequential for the emerging field of generalised Bayesian inference, for estimated intractable likelihoods, and for biased pseudo-marginal approaches. We apply our results to three Gibbs measures that have been proposed to deal with intractable likelihoods and model misspecification.

Emerging scholarship suggests that the EU legal concept of direct discrimination - where a person is given different treatment on grounds of a protected characteristic - may apply to various algorithmic decision-making contexts. This has important implications: unlike indirect discrimination, there is generally no 'objective justification' stage in the direct discrimination framework, which means that the deployment of directly discriminatory algorithms will usually be unlawful per se. In this paper, we focus on the most likely candidate for direct discrimination in the algorithmic context, termed inherent direct discrimination, where a proxy is inextricably linked to a protected characteristic. We draw on computer science literature to suggest that, in the algorithmic context, 'treatment on the grounds of' needs to be understood in terms of two steps: proxy capacity and proxy use. Only where both elements can be made out can direct discrimination be said to be `on grounds of' a protected characteristic. We analyse the legal conditions of our proposed proxy capacity and proxy use tests. Based on this analysis, we discuss technical approaches and metrics that could be developed or applied to identify inherent direct discrimination in algorithmic decision-making.

Data is growing rapidly in volume and complexity. Proficiency in database query languages is pivotal for crafting effective queries. As coding assistants become more prevalent, there is significant opportunity to enhance database query languages. The Kusto Query Language (KQL) is a widely used query language for large semi-structured data such as logs, telemetries, and time-series for big data analytics platforms. This paper introduces NL2KQL an innovative framework that uses large language models (LLMs) to convert natural language queries (NLQs) to KQL queries. The proposed NL2KQL framework includes several key components: Schema Refiner which narrows down the schema to its most pertinent elements; the Few-shot Selector which dynamically selects relevant examples from a few-shot dataset; and the Query Refiner which repairs syntactic and semantic errors in KQL queries. Additionally, this study outlines a method for generating large datasets of synthetic NLQ-KQL pairs which are valid within a specific database contexts. To validate NL2KQL's performance, we utilize an array of online (based on query execution) and offline (based on query parsing) metrics. Through ablation studies, the significance of each framework component is examined, and the datasets used for benchmarking are made publicly available. This work is the first of its kind and is compared with available baselines to demonstrate its effectiveness.

Floating Car Observers (FCOs) are an innovative method to collect traffic data by deploying sensor-equipped vehicles to detect and locate other vehicles. We demonstrate that even a small penetration rate of FCOs can identify a significant amount of vehicles at a given intersection. This is achieved through the emulation of detection within a microscopic traffic simulation. Additionally, leveraging data from previous moments can enhance the detection of vehicles in the current frame. Our findings indicate that, with a 20-second observation window, it is possible to recover up to 20\% of vehicles that are not visible by FCOs in the current timestep. To exploit this, we developed a data-driven strategy, utilizing sequences of Bird's Eye View (BEV) representations of detected vehicles and deep learning models. This approach aims to bring currently undetected vehicles into view in the present moment, enhancing the currently detected vehicles. Results of different spatiotemporal architectures show that up to 41\% of the vehicles can be recovered into the current timestep at their current position. This enhancement enriches the information initially available by the FCO, allowing an improved estimation of traffic states and metrics (e.g. density and queue length) for improved implementation of traffic management strategies.

Group-IV color centers in diamond are promising candidates for quantum networks due to their dominant zero-phonon line and symmetry-protected optical transitions that connect to coherent spin levels. The negatively charged tin-vacancy (SnV) center possesses long electron spin lifetimes due to its large spin-orbit splitting. However, the magnetic dipole transitions required for microwave spin control are suppressed, and strain is necessary to enable these transitions. Recent work has shown spin control of strained emitters using microwave lines that suffer from Ohmic losses, restricting coherence through heating. We utilize a superconducting coplanar waveguide to measure SnV centers subjected to strain, observing substantial improvement. A detailed analysis of the SnV center electron spin Hamiltonian based on the angle-dependent splitting of the ground and excited states is performed. We demonstrate coherent spin manipulation and obtain a Hahn echo coherence time of up to $T_2 = 430\,\mu$s. With dynamical decoupling, we can prolong coherence to $T_2 = 10\,$ms, about six-fold improved compared to earlier works. We also observe a nearby coupling $^{13}\mathrm{C}$ spin which may serve as a quantum memory. This substantiates the potential of SnV centers in diamond and demonstrates the benefit of superconducting microwave structures., Comment: Main: 9 pages, 5 figures, 1 tables; Supplement: 15 pages, 10 figures, 1 table

Accurate and comprehensive semantic segmentation of Bird's Eye View (BEV) is essential for ensuring safe and proactive navigation in autonomous driving. Although cooperative perception has exceeded the detection capabilities of single-agent systems, prevalent camera-based algorithms in cooperative perception neglect valuable information derived from historical observations. This limitation becomes critical during sensor failures or communication issues as cooperative perception reverts to single-agent perception, leading to degraded performance and incomplete BEV segmentation maps. This paper introduces TempCoBEV, a temporal module designed to incorporate historical cues into current observations, thereby improving the quality and reliability of BEV map segmentations. We propose an importance-guided attention architecture to effectively integrate temporal information that prioritizes relevant properties for BEV map segmentation. TempCoBEV is an independent temporal module that seamlessly integrates into state-of-the-art camera-based cooperative perception models. We demonstrate through extensive experiments on the OPV2V dataset that TempCoBEV performs better than non-temporal models in predicting current and future BEV map segmentations, particularly in scenarios involving communication failures. We show the efficacy of TempCoBEV and its capability to integrate historical cues into the current BEV map, improving predictions under optimal communication conditions by up to 2% and under communication failures by up to 19%. The code will be published on GitHub.

Cognitive agent abstractions can help to engineer intelligent systems across mobile devices. On smartphones, the data obtained from onboard sensors can give valuable insights into the user's current situation. Unfortunately, today's cognitive agent frameworks cannot cope well with the challenging characteristics of sensor data. Sensor data is located on a low abstraction level and the individual data elements are not meaningful when observed in isolation. In contrast, cognitive agents operate on high-level percepts and lack the means to effectively detect complex spatio-temporal patterns in sequences of multiple percepts. In this paper, we present a stream-based perception approach that enables the agents to perceive meaningful situations in low-level sensor data streams. We present a crowdshipping case study where autonomous, self-interested agents collaborate to deliver parcels to their destinations. We show how situations derived from smartphone sensor data can trigger and guide auctions, which the agents use to reach agreements. Experiments with real smartphone data demonstrate the benefits of stream-based agent perception.

Mobile crowdsourcing refers to systems where the completion of tasks necessarily requires physical movement of crowdworkers in an on-demand workforce. Evidence suggests that in such systems, tasks often get assigned to crowdworkers who struggle to complete those tasks successfully, resulting in high failure rates and low service quality. A promising solution to ensure higher quality of service is to continuously adapt the assignment and respond to failure-causing events by transferring tasks to better-suited workers who use different routes or vehicles. However, implementing task transfers in mobile crowdsourcing is difficult because workers are autonomous and may reject transfer requests. Moreover, task outcomes are uncertain and need to be predicted. In this paper, we propose different mechanisms to achieve outcome prediction and task coordination in mobile crowdsourcing. First, we analyze different data stream learning approaches for the prediction of task outcomes. Second, based on the suggested prediction model, we propose and evaluate two different approaches for task coordination with different degrees of autonomy: an opportunistic approach for crowdshipping with collaborative, but non-autonomous workers, and a market-based model with autonomous workers for crowdsensing.

In parcel delivery, the "last mile" from the parcel hub to the customer is costly, especially for time-sensitive delivery tasks that have to be completed within hours after arrival. Recently, crowdshipping has attracted increased attention as a new alternative to traditional delivery modes. In crowdshipping, private citizens ("the crowd") perform short detours in their daily lives to contribute to parcel delivery in exchange for small incentives. However, achieving desirable crowd behavior is challenging as the crowd is highly dynamic and consists of autonomous, self-interested individuals. Leveraging crowdshipping for time-sensitive deliveries remains an open challenge. In this paper, we present an agent-based approach to on-time parcel delivery with crowds. Our system performs data stream processing on the couriers' smartphone sensor data to predict delivery delays. Whenever a delay is predicted, the system attempts to forge an agreement for transferring the parcel from the current deliverer to a more promising courier nearby. Our experiments show that through accurate delay predictions and purposeful task transfers many delays can be prevented that would occur without our approach.

The hfrh-buck (high frequency radiation hardened-buck) is a radiation hardened DC/DC-converter operating at a high switching frequency of 100MHz with a small air core inductor of 22nH. To ensure a high radiation dose, the circuit is designed with core transistors of a 65nm TSMC technology. By stacking the transistors of the power stage, the converter can be supplied with a voltage of up to 4.8V. Stable operation can be achieved at an output voltage of 1.2V with a maximum load current of 1A. The prototype demonstrates the ability to power parallel connected hybrid-pixel modules in the innermost layers., Comment: Proceeding to TWEPP 2023 Topical Workshop on Electronics for Particle Physics, Oct 1-6, 2023, Geremeas, Sardinia, Italy

In this work, we study the realization of non-invertible duality symmetries along the toroidal branch of the $c=2$ conformal manifold. A systematic procedure to construct symmetry defects is implemented to show that all Rational Conformal Field Theories along this branch enjoy duality symmetries. Furthermore, we delve into an in-depth analysis of two representative cases of multicritical theories, were the toroidal branch meets various orbifold branches. For these particular examples, the categorical data and the defect Hilbert spaces associated to the duality symmetries are obtained by resorting to modular covariance. Finally, we study the interplay between these novel symmetries and the various exactly marginal and relevant deformations, including some representative examples of Renormalization Group flows where the infrared is constrained by the non-invertible symmetries and their anomalies., Comment: 45 pages + appendices. Minor improvements, matches journal version

We propose a classifier that can identify ten common home network problems based on the raw textual output of networking tools such as ping, dig, and ip. Our deep learning model uses an encoder-only transformer architecture with a particular pre-tokenizer that we propose for splitting the tool output into token sequences. The use of transformers distinguishes our approach from related work on network problem classification, which still primarily relies on non-deep-learning methods. Our model achieves high accuracy in our experiments, demonstrating the high potential of transformer-based problem classification for the home network., Comment: This work has been partially funded by the German Federal Ministry of Education and Research (BMBF) in the FRONT-RUNNER project (Grant 16KISR005K)

To enable closed form conditioning, a common assumption in Gaussian process (GP) regression is independent and identically distributed Gaussian observation noise. This strong and simplistic assumption is often violated in practice, which leads to unreliable inferences and uncertainty quantification. Unfortunately, existing methods for robustifying GPs break closed-form conditioning, which makes them less attractive to practitioners and significantly more computationally expensive. In this paper, we demonstrate how to perform provably robust and conjugate Gaussian process (RCGP) regression at virtually no additional cost using generalised Bayesian inference. RCGP is particularly versatile as it enables exact conjugate closed form updates in all settings where standard GPs admit them. To demonstrate its strong empirical performance, we deploy RCGP for problems ranging from Bayesian optimisation to sparse variational Gaussian processes.

Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as in the framework of plug-and-play or deep unrolling, where they loosely resemble proximal operators. Yet, something essential is lost in employing these purely data-driven approaches: there is no guarantee that a general deep network represents the proximal operator of any function, nor is there any characterization of the function for which the network might provide some approximate proximal. This not only makes guaranteeing convergence of iterative schemes challenging but, more fundamentally, complicates the analysis of what has been learned by these networks about their training data. Herein we provide a framework to develop learned proximal networks (LPN), prove that they provide exact proximal operators for a data-driven nonconvex regularizer, and show how a new training strategy, dubbed proximal matching, provably promotes the recovery of the log-prior of the true data distribution. Such LPN provide general, unsupervised, expressive proximal operators that can be used for general inverse problems with convergence guarantees. We illustrate our results in a series of cases of increasing complexity, demonstrating that these models not only result in state-of-the-art performance, but provide a window into the resulting priors learned from data.

The susceptibility of modern machine learning classifiers to adversarial examples has motivated theoretical results suggesting that these might be unavoidable. However, these results can be too general to be applicable to natural data distributions. Indeed, humans are quite robust for tasks involving vision. This apparent conflict motivates a deeper dive into the question: Are adversarial examples truly unavoidable? In this work, we theoretically demonstrate that a key property of the data distribution -- concentration on small-volume subsets of the input space -- determines whether a robust classifier exists. We further demonstrate that, for a data distribution concentrated on a union of low-dimensional linear subspaces, utilizing structure in data naturally leads to classifiers that enjoy data-dependent polyhedral robustness guarantees, improving upon methods for provable certification in certain regimes., Comment: Accepted to Neural Information Processing Systems (NeurIPS) 2023

The action of a finite group $G$ on a subshift of finite type $X$ is called free, if every point has trivial stabilizer, and it is called inert, if the induced action on the dimension group of $X$ is trivial. We show that any two free inert actions of a finite group $G$ on an SFT are conjugate by an automorphism of any sufficiently high power of the shift space. This partially answers a question posed by Fiebig. As a consequence we obtain that every two free elements of the stabilized automorphism group of a full shift are conjugate in this group. In addition, we generalize a result of Boyle, Carlsen and Eilers concerning the flow equivalence of $G$-SFTs., Comment: 20 pages

We investigate theories of Nambu-Goldstone bosons where the spontaneously broken continuous symmetry is non-invertible. In such theories, the vacua generically parameterize an orbifold. We study in detail the simplest example of a single free scalar with shift symmetry, modded by reflection symmetry. At singular points of the vacuum manifold, we show that the spectrum of NG excitations is reduced, in particular there are no single-particle states. At the smooth points, on the other hand, single NG modes are present. We show that this is a consequence of the fact that at those points one can construct invertible operators implementing the continuous symmetry on the Hilbert space., Comment: 22 pages; a figure, some comments and a few references have been added; version matches with the one to be published in JHEP

Two dimensional conformal feld theories have been extensively studied in the past. When considered on the torus, they are strongly constrained by modular invariance. However, introducing relevant deformations or chemical potentials pushes these theories away from criticality, where many of their aspects are still poorly understood. In this note we make a step towards filling this gap, by analyzing the theory of a Dirac fermion on the torus, deformed by a mass term and a chemical potential for the particle number symmetry. The theory breaks conformal and Lorentz invariance, and we study its spectrum and partition function. We also focus on two limits that are interesting on their own right: a massless relativistic fermion with nonzero chemical potential (a simple model for CFTs at finite density), and nonrelativistic Schrodinger fermions (of relevance in condensed matter systems). Taking inspiration from recent developments in massive modular forms, we obtain a representation of the torus free energy based on Fourier-transforming over a twisted boundary condition. This dual representation fullfills many properties analogous to modular invariance in CFTs. In particular, we use this result to derive Cardy-like formulas for the high energy density of states of these theories., Comment: 23 pages, v2 reference added

Modern micromanipulation techniques typically involve trapping using electromagnetic, acoustic or flow fields that produce stresses on the trapped particles thereby precluding stress-free manipulations. Here, we show that by employing polyhedral symmetries in a multichannel microfluidic design, we can separate the tasks of displacing and trapping a particle into two distinct sets of flow operations, each characterized and protected by their unique groups of symmetries. By combining only the displacing uniform flow modes to entrain and move targeted particles in arbitrary directions, we were able to realize symmetry-protected, stress-free micromanipulation in 3D. Furthermore, we engineered complex, microscale paths by programming and controlling the flow within each channel in real-time, resulting in multiple particles simultaneously following desired paths in the absence of any supervision or feedback. Our work therefore provides a general symmetry-group-based framework for understanding and engineering microfluidics and a novel platform for 3D stress-free manipulations.