Miracle-dz/UniFAR-FTUs huggingface dataset:
Security of differential phase shift QKD from relativistic principles

The design of quantum protocols for secure key generation poses many challenges: On the one hand, they need to be practical concerning experimental realisations. On the other hand, their theoretical description must be simple enough to allow for a security proof against all possible attacks. Often, these two requirements are in conflict with each other, and the differential phase shift (DPS) QKD protocol exemplifies these difficulties: It is designed to be implementable with current optical telecommunication technology, which, for this protocol, comes at the cost that many standard security proof techniques do not apply to it. After about 20 years since its invention, this work presents the first full security proof of DPS QKD against general attacks, including finite-size effects. The proof combines techniques from quantum information theory, quantum optics, and relativity. We first give a security proof of a QKD protocol whose security stems from relativistic constraints. We then show that security of DPS QKD can be reduced to security of the relativistic protocol. In addition, we show that coherent attacks on the DPS protocol are, in fact, stronger than collective attacks. Our results have broad implications for the development of secure and reliable quantum communication technologies, as they shed light on the range of applicability of state-of-the-art security proof techniques.
Online Learning in Stackelberg Games with an Omniscient Follower

We study the problem of online learning in a two-player decentralized cooperative Stackelberg game. In each round, the leader first takes an action, followed by the follower who takes their action after observing the leader's move. The goal of the leader is to learn to minimize the cumulative regret based on the history of interactions. Differing from the traditional formulation of repeated Stackelberg games, we assume the follower is omniscient, with full knowledge of the true reward, and that they always best-respond to the leader's actions. We analyze the sample complexity of regret minimization in this repeated Stackelberg game. We show that depending on the reward structure, the existence of the omniscient follower may change the sample complexity drastically, from constant to exponential, even for linear cooperative Stackelberg games. This poses unique challenges for the learning process of the leader and the subsequent regret analysis.
Pre-training for Speech Translation: CTC Meets Optimal Transport

The gap between speech and text modalities is a major challenge in speech-to-text translation (ST). Different methods have been proposed to reduce this gap, but most of them require architectural changes in ST training. In this work, we propose to mitigate this issue at the pre-training stage, requiring no change in the ST model. First, we show that the connectionist temporal classification (CTC) loss can reduce the modality gap by design. We provide a quantitative comparison with the more common cross-entropy loss, showing that pre-training with CTC consistently achieves better final ST accuracy. Nevertheless, CTC is only a partial solution and thus, in our second contribution, we propose a novel pre-training method combining CTC and optimal transport to further reduce this gap. Our method pre-trains a Siamese-like model composed of two encoders, one for acoustic inputs and the other for textual inputs, such that they produce representations that are close to each other in the Wasserstein space. Extensive experiments on the standard CoVoST-2 and MuST-C datasets show that our pre-training method applied to the vanilla encoder-decoder Transformer achieves state-of-the-art performance under the no-external-data setting, and performs on par with recent strong multi-task learning systems trained with external data. Finally, our method can also be applied on top of these multi-task systems, leading to further improvements for these models. Code and pre-trained models are available at https://github.com/formiel/fairseq.
Understanding Incremental Learning of Gradient Descent: A Fine-grained Analysis of Matrix Sensing

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019): GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.
Stability of a channel flow subject to wall blowing and suction in the form of a traveling wave

Inspired by the recent finding by Min et al. [J. Fluid Mech. 558, 309 (2006)], the stability of a channel flow subject to wall blowing and suction in the form of a traveling wave is investigated by combined use of the Floquet analysis, direct numerical simulation, and singular value decomposition analysis. Results show that stability highly depends on the phase speed of the traveling wave; most disturbances become highly unstable when the phase speed is around 40% of the centerline velocity, while streamwise streak-type three-dimensional disturbances become stabilized with transient growth suppressed when the phase speed exceeds the centerline velocity for both subcritical and supercritical Reynolds numbers. This destabilization is interpreted by investigation of wave interactions. An upstream-traveling wave, which reduces mean drag, does not stabilize the flow.
Theoretical Analysis of Offline Imitation With Supplementary Dataset

Behavioral cloning (BC) can recover a good policy from abundant expert data, but may fail when expert data is insufficient. This paper considers a situation where, besides the small amount of expert data, a supplementary dataset is available, which can be collected cheaply from sub-optimal policies. Imitation learning with a supplementary dataset is an emergent practical framework, but its theoretical foundation remains under-developed. To advance understanding, we first investigate a direct extension of BC, called NBCU, that learns from the union of all available data. Our analysis shows that, although NBCU suffers an imitation gap that is larger than BC in the worst case, there exist special cases where NBCU performs better than or equally well as BC. This discovery implies that noisy data can also be helpful if utilized elaborately. Therefore, we further introduce a discriminator-based importance sampling technique to re-weight the supplementary data, proposing the WBCU method. With our newly developed landscape-based analysis, we prove that WBCU can outperform BC in mild conditions. Empirical studies show that WBCU simultaneously achieves the best performance on two challenging tasks where prior state-of-the-art methods fail.
Traveling waves in reaction-diffusion equations with delay in both diffusion and reaction terms

We study the existence of traveling waves of reaction-diffusion systems with delays in both diffusion and reaction terms of the form $\partial u(x,t)/\partial t = \Delta u(x,t-\tau_1)+f(u(x,t),u(x,t-\tau_2))$, where $\tau_1,\tau_2$ are positive constants. We extend the monotone iteration method to systems that satisfy typical monotone conditions by thoroughly studying the sign of the Green function associated with a linear functional differential equation. Namely, we show that for small positive $r$ the functional equation $x''(t)-ax'(t+r)-bx(t+r)=f(t)$, where $a\not=0, b>0$ has a unique bounded solution for each given bounded and continuous $f(t)$. Moreover, if $r>0$ is sufficiently small, $f(t)\ge 0$ for $t\in {\mathbb R}$, then the unique bounded solution $x_f(t)\le 0$ for all $t\in {\mathbb R}$. In the framework of the monotone iteration method that is developed based on this result, upper and lower solutions are found for Fisher-KPP and Belousov-Zhabotinski equations to show that traveling waves exist for these equations when delays are small in both diffusion and reaction terms. The obtained results appear to be new.
Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees

The completeness axiom renders the explanation of a post-hoc XAI method only locally faithful to the model, i.e. for a single decision. For the trustworthy application of XAI, in particular for high-stake decisions, a more global model understanding is required. Recently, concept-based methods have been proposed, which are however not guaranteed to be bound to the actual model reasoning. To circumvent this problem, we propose Multi-dimensional Concept Discovery (MCD) as an extension of previous approaches that fulfills a completeness relation on the level of concepts. Our method starts from general linear subspaces as concepts and does neither require reinforcing concept interpretability nor re-training of model parts. We propose sparse subspace clustering to discover improved concepts and fully leverage the potential of multi-dimensional subspaces. MCD offers two complementary analysis tools for concepts in input space: (1) concept activation maps, that show where a concept is expressed within a sample, allowing for concept characterization through prototypical samples, and (2) concept relevance heatmaps, that decompose the model decision into concept contributions. Both tools together enable a detailed understanding of the model reasoning, which is guaranteed to relate to the model via a completeness relation. This paves the way towards more trustworthy concept-based XAI. We empirically demonstrate the superiority of MCD against more constrained concept definitions.
Homotopy skein modules of orientable 3-manifolds

Abstract We define the homotopy skein module of an arbitrary orientable 3-manifold M. This module is similar to the ordinary skein module defined by the second author but is more appropriate when considering oriented links in M up to link homotopy rather than isotopy. We compute the homotopy skein module of M = F × I for any orientable surface F and show that it is free. In the case where M = F × I the homotopy skein module may be given an algebra structure and we show that as an algebra it is isomorphic to the universal enveloping algebra of the Goldman–Wolpert Lie algebra of F. We show, also in this case, that the homotopy skein module is a quantization of the symmetric tensor algebra associated to the Goldman–Wolpert Lie algebra.
Dual Diffusion Architecture for Fisheye Image Rectification: Synthetic-to-Real Generalization

Fisheye image rectification has a long-term unresolved issue with synthetic-to-real generalization. In most previous works, the model trained on the synthetic images obtains unsatisfactory performance on the real-world fisheye image. To this end, we propose a Dual Diffusion Architecture (DDA) for the fisheye rectification with a better generalization ability. The proposed DDA is simultaneously trained with paired synthetic fisheye images and unlabeled real fisheye images. By gradually introducing noises, the synthetic and real fisheye images can eventually develop into a consistent noise distribution, improving the generalization and achieving unlabeled real fisheye correction. The original image serves as the prior guidance in existing DDPMs (Denoising Diffusion Probabilistic Models). However, the non-negligible indeterminate relationship between the prior condition and the target affects the generation performance. Especially in the rectification task, the radial distortion can cause significant artifacts. Therefore, we provide an unsupervised one-pass network that produces a plausible new condition to strengthen guidance. This network can be regarded as an alternate scheme for fast producing reliable results without iterative inference. Compared with the state-of-the-art methods, our approach can reach superior performance in both synthetic and real fisheye image corrections.
Complexity of equilibria in binary public goods games on undirected graphs

We study the complexity of computing equilibria in binary public goods games on undirected graphs. In such a game, players correspond to vertices in a graph and face a binary choice of performing an action, or not. Each player's decision depends only on the number of neighbors in the graph who perform the action and is encoded by a per-player binary pattern. We show that games with decreasing patterns (where players only want to act up to a threshold number of adjacent players doing so) always have a pure Nash equilibrium and that one is reached from any starting profile by following a polynomially bounded sequence of best responses. For non-monotonic patterns of the form 10k10* (where players want to act alone or alongside k + 1 neighbors), we show that it is NP-hard to decide whether a pure Nash equilibrium exists. We further investigate a generalization of the model that permits ties of varying strength: an edge with integral weight w behaves as w parallel edges. While, in this model, a pure Nash equilibrium still exists for decreasing patters, we show that the task of computing one is PLS-complete.
Primordial black holes in loop quantum gravity: The eﬀect on the threshold

Primordial black holes form in the early Universe and constitute one of the most viable candidates for dark matter. The study of their formation process requires the determination of a critical energy density perturbation threshold δ c , which in general depends on the underlying gravity theory. Up to now, the majority of analytic and numerical techniques calculate δ c within the framework of general relativity. In this work, using simple physical arguments we estimate semi-analytically the PBH formation threshold within the framework of quantum gravity, working for concreteness within loop quantum gravity (LQG), which constitutes a non-perturbative and background-independent quantization of general relativity. In particular, for low mass PBHs formed close to the quantum bounce, we ﬁnd a reduction in the value of δ c up to 50% compared to the general relativistic regime quantifying for the ﬁrst time to the best of our knowledge how quantum eﬀects can inﬂuence PBH formation within a quantum gravity framework. Finally, by varying the Barbero-Immirzi parameter γ of LQG we show its eﬀect on the value of δ c while using the observational/phenomenological signatures associated to ultra-light PBHs, namely the ones aﬀected by LQG eﬀects, we propose the PBH portal as a novel probe to constrain the potential quantum nature of gravity.
A Robust Optimisation Perspective on Counterexample-Guided Repair of Neural Networks

Counterexample-guided repair aims at creating neural networks with mathematical safety guarantees, facilitating the application of neural networks in safety-critical domains. However, whether counterexample-guided repair is guaranteed to terminate remains an open question. We approach this question by showing that counterexample-guided repair can be viewed as a robust optimisation algorithm. While termination guarantees for neural network repair itself remain beyond our reach, we prove termination for more restrained machine learning models and disprove termination in a general setting. We empirically study the practical implications of our theoretical results, demonstrating the suitability of common verifiers and falsifiers for repair despite a disadvantageous theoretical result. Additionally, we use our theoretical insights to devise a novel algorithm for repairing linear regression models based on quadratic programming, surpassing existing approaches.
Connectivity based Real-Time fMRI Neurofeedback Training in Youth with a History of Major Depressive Disorder.

BACKGROUND Real-time functional magnetic resonance imaging neurofeedback (rtfMRI-nf) has proven to be a powerful technique to help subjects to gauge and enhance emotional control. Traditionally, rtfMRI-nf has focused on emotional regulation through self-regulation of amygdala. Recently, rtfMRI studies have observed that regulation of a target brain region is accompanied by connectivity changes beyond the target region. Therefore, the aim of present study is to investigate the use of connectivity between amygdala and prefrontal regions as the target of neurofeedback training in healthy individuals and subjects with a life-time history of major depressive disorder (MDD) performing an emotion regulation task. METHOD Ten remitted MDD subjects and twelve healthy controls (HC) performed an emotion regulation task in 4 runs of rtfMRI-nf training followed by one transfer run without neurofeedback conducted in a single session. The functional connectivity between amygdala and prefrontal cortex was presented as a feedback bar concurrent with the emotion regulation task. Participants' emotional state was measured by the Positive and Negative Affect Schedule (PANAS) prior to and following the rtfMRI-nf. Psychological assessments were used to determine subjects' history of depression. RESULTS Participants with a history of MDD showed a trend of decreasing functional connectivity across the four rtfMRI-nf runs, and there was a marginally significant interaction between the MDD history and number of training runs. The HC group showed a significant increase of frontal cortex activation between the second and third neurofeedback runs. Comparing PANAS scores before and after connectivity-based rtfMRI-nf, we observed a significant decrease in negative PANAS score in the whole group overall, and a significant decrease in positive PANAS score in the MDD group alone.
Diffusion Models as Artists: Are we Closing the Gap between Humans and Machines?

An important milestone for AI is the development of algorithms that can produce drawings that are indistinguishable from those of humans. Here, we adapt the 'diversity vs. recognizability' scoring framework from Boutin et al, 2022 and find that one-shot diffusion models have indeed started to close the gap between humans and machines. However, using a finer-grained measure of the originality of individual samples, we show that strengthening the guidance of diffusion models helps improve the humanness of their drawings, but they still fall short of approximating the originality and recognizability of human drawings. Comparing human category diagnostic features, collected through an online psychophysics experiment, against those derived from diffusion models reveals that humans rely on fewer and more localized features. Overall, our study suggests that diffusion models have significantly helped improve the quality of machine-generated drawings; however, a gap between humans and machines remains -- in part explainable by discrepancies in visual strategies.
Higgs Inflation: constraining the top quark mass and breaking the $H_0$-$\sigma_8$ correlation

Extending previous results [JHEP 11 (2021) 091], we explore aspects of the reheating mechanism for non-minimal Higgs inflation in the strong coupling regime. We constrain the radiative corrections for the inflaton's potential by considering the Coleman-Weinberg approximation and use the Renormalization Group Equations for the Higgs field to derive an upper limit on the quark top mass, $m_t$. Using the current Cosmic Microwave Background, Baryon Acoustic Oscillation, and Supernova data, we obtain $m_t \leq 170.44$ GeV, confirming the observational compatibility of the model with recent $m_t$ estimates reported by the CMS collaboration. We also analyze the breakdown of the well-known correlation involving the Hubble constant $H_0$ and the clustering parameter $\sigma_8$, which makes the model interesting in light of the cosmological tensions discussed over the last decade.
Neural networks learn to magnify areas near decision boundaries

In machine learning, there is a long history of trying to build neural networks that can learn from fewer example data by baking in strong geometric priors. However, it is not always clear a priori what geometric constraints are appropriate for a given task. Here, we consider the possibility that one can uncover useful geometric inductive biases by studying how training molds the Riemannian geometry induced by unconstrained neural network feature maps. We first show that at infinite width, neural networks with random parameters induce highly symmetric metrics on input space. This symmetry is broken by feature learning: networks trained to perform classification tasks learn to magnify local areas along decision boundaries. This holds in deep networks trained on high-dimensional image classification tasks, and even in self-supervised representation learning. These results begins to elucidate how training shapes the geometry induced by unconstrained neural network feature maps, laying the groundwork for an understanding of this richly nonlinear form of feature learning.
Particle interferometry in a moat regime

Dense strongly interacting matter can exhibit regimes with spatial modulations, akin to crystalline phases. In this case particles can have a moat spectrum with minimal energy at nonzero momentum. We show that particle interferometry is a sensitive probe of such a regime in heavy-ion collisions. To this end, we develop a field-theoretical formalism that relates particle spectra to in-medium real-time correlation functions of quantum fields on curved hypersurfaces of spacetime. This is then applied to the study of Bose-Einstein correlations in a moat regime in heavy-ion collisions. The resulting two-particle spectra exhibit peaks at nonzero average pair momentum, in contrast to the two-particle spectra in a normal phase, which peak at zero momentum. These peaks lead to non-trivial structures in the ratio of two-particle correlation functions, which should be experimentally measurable if the resolution in the direction of average pair momentum is sufficiently large. We propose these structures in the correlation-function ratios as clear signature of a moat regime and spatially modulated phases in quantum chromodynamics (QCD).
Task-Agnostic Graph Neural Network Evaluation via Adversarial Collaboration

It has been increasingly demanding to develop reliable methods to evaluate the progress of Graph Neural Network (GNN) research for molecular representation learning. Existing GNN benchmarking methods for molecular representation learning focus on comparing the GNNs' performances on some node/graph classification/regression tasks on certain datasets. However, there lacks a principled, task-agnostic method to directly compare two GNNs. Additionally, most of the existing self-supervised learning works incorporate handcrafted augmentations to the data, which has several severe difficulties to be applied on graphs due to their unique characteristics. To address the aforementioned issues, we propose GraphAC (Graph Adversarial Collaboration) -- a conceptually novel, principled, task-agnostic, and stable framework for evaluating GNNs through contrastive self-supervision. We introduce a novel objective function: the Competitive Barlow Twins, that allow two GNNs to jointly update themselves from direct competitions against each other. GraphAC succeeds in distinguishing GNNs of different expressiveness across various aspects, and has demonstrated to be a principled and reliable GNN evaluation method, without necessitating any augmentations.