Miracle-dz/UniFAR-FTUs huggingface dataset:
Non-Uniform Smoothness for Gradient Descent

The analysis of gradient descent-type methods typically relies on the Lipschitz continuity of the objective gradient. This generally requires an expensive hyperparameter tuning process to appropriately calibrate a stepsize for a given problem. In this work we introduce a local first-order smoothness oracle (LFSO) which generalizes the Lipschitz continuous gradients smoothness condition and is applicable to any twice-differentiable function. We show that this oracle can encode all relevant problem information for tuning stepsizes for a suitably modified gradient descent method and give global and local convergence results. We also show that LFSOs in this modified first-order method can yield global linear convergence rates for non-strongly convex problems with extremely flat minima, and thus improve over the lower bound on rates achievable by general (accelerated) first-order methods.
A Low-Rank Approach to Minimize Sensor-to-Actuator Communication in Finite-Horizon Output Feedback

Many modern controllers are composed of different components that communicate in real-time over some network with limited resources. In this letter, we are interested in designing a controller that can be implemented with a minimum number of sensor-to-actuator messages, while satisfying safety constraints over a finite horizon. For finite horizon problems, a linear time-varying controller with memory can be represented as a block-lower-triangular matrix. We show that the rank of this matrix exactly captures the minimum number of messages needed to be sent from the sensors to actuators to implement such a controller. Moreover, we introduce a novel matrix factorization called causal factorization that gives the required implementation. Finally, we show that the rank of the controller is the same as the rank of the Youla parameter, enabling the Youla parametrization (or analogous parametrizations) to be used to design the controller, which reduces the overall design problem into a rank minimization one over a convex set. Finally, convex relaxations for rank are used to demonstrate that our approach leads to 20-50% less messages on a simulation than a benchmark method.
Neurophysiological Response Based on Auditory Sense for Brain Modulation Using Monaural Beat

Brain modulation is a modification process of brain activity through external stimulations. However, which condition can induce the activation is still unclear. Therefore, we aimed to identify brain activation conditions using 40 Hz monaural beat (MB). Under this stimulation, auditory sense status which is determined by frequency and power range is the condition to consider. Hence, we designed five sessions to compare; no stimulation, audible (AB), inaudible in frequency, inaudible in power, and inaudible in frequency and power. Ten healthy participants underwent each stimulation session for ten minutes with electroencephalogram (EEG) recording. For analysis, we calculated the power spectral density (PSD) of EEG for each session and compared them in frequency, time, and five brain regions. As a result, we observed the prominent power peak at 40 Hz in only AB. The induced EEG amplitude increase started at one minute and increased until the end of the session. These results of AB had significant differences in frontal, central, temporal, parietal, and occipital regions compared to other stimulations. From the statistical analysis, the PSD of the right temporal region was significantly higher than the left. We figure out the role that the auditory sense is important to lead brain activation. These findings help to understand the neurophysiological principle and effects of auditory stimulation.
A Spectral Diffusion Prior for Hyperspectral Image Super-Resolution

Fusion-based hyperspectral image (HSI) super-resolution aims to produce a high-spatial-resolution HSI by fusing a low-spatial-resolution HSI and a high-spatial-resolution multispectral image. Such a HSI super-resolution process can be modeled as an inverse problem, where the prior knowledge is essential for obtaining the desired solution. Motivated by the success of diffusion models, we propose a novel spectral diffusion prior for fusion-based HSI super-resolution. Specifically, we first investigate the spectrum generation problem and design a spectral diffusion model to model the spectral data distribution. Then, in the framework of maximum a posteriori, we keep the transition information between every two neighboring states during the reverse generative process, and thereby embed the knowledge of trained spectral diffusion model into the fusion problem in the form of a regularization term. At last, we treat each generation step of the final optimization problem as its subproblem, and employ the Adam to solve these subproblems in a reverse sequence. Experimental results conducted on both synthetic and real datasets demonstrate the effectiveness of the proposed approach. The code of the proposed approach will be available on https://github.com/liuofficial/SDP.
Domain Aligned CLIP for Few-shot Classification

Large vision-language representation learning models like CLIP have demonstrated impressive performance for zero-shot transfer to downstream tasks while largely benefiting from inter-modal (image-text) alignment via contrastive objectives. This downstream performance can further be enhanced by full-scale fine-tuning which is often compute intensive, requires large labelled data, and can reduce out-of-distribution (OOD) robustness. Furthermore, sole reliance on inter-modal alignment might overlook the rich information embedded within each individual modality. In this work, we introduce a sample-efficient domain adaptation strategy for CLIP, termed Domain Aligned CLIP (DAC), which improves both intra-modal (image-image) and inter-modal alignment on target distributions without fine-tuning the main model. For intra-modal alignment, we introduce a lightweight adapter that is specifically trained with an intra-modal contrastive objective. To improve inter-modal alignment, we introduce a simple framework to modulate the precomputed class text embeddings. The proposed few-shot fine-tuning framework is computationally efficient, robust to distribution shifts, and does not alter CLIP's parameters. We study the effectiveness of DAC by benchmarking on 11 widely used image classification tasks with consistent improvements in 16-shot classification upon strong baselines by about 2.3% and demonstrate competitive performance on 4 OOD robustness benchmarks.
On the Foundation of Distributionally Robust Reinforcement Learning

Motivated by the need for a robust policy in the face of environment shifts between training and the deployment, we contribute to the theoretical foundation of distributionally robust reinforcement learning (DRRL). This is accomplished through a comprehensive modeling framework centered around distributionally robust Markov decision processes (DRMDPs). This framework obliges the decision maker to choose an optimal policy under the worst-case distributional shift orchestrated by an adversary. By unifying and extending existing formulations, we rigorously construct DRMDPs that embraces various modeling attributes for both the decision maker and the adversary. These attributes include adaptability granularity, exploring history-dependent, Markov, and Markov time-homogeneous decision maker and adversary dynamics. Additionally, we delve into the flexibility of shifts induced by the adversary, examining SA and S-rectangularity. Within this DRMDP framework, we investigate conditions for the existence or absence of the dynamic programming principle (DPP). From an algorithmic standpoint, the existence of DPP holds significant implications, as the vast majority of existing data and computationally efficiency RL algorithms are reliant on the DPP. To study its existence, we comprehensively examine combinations of controller and adversary attributes, providing streamlined proofs grounded in a unified methodology. We also offer counterexamples for settings in which a DPP with full generality is absent.
Single-Image 3D Human Digitization with Shape-guided Diffusion

We present an approach to generate a 360-degree view of a person with a consistent, high-resolution appearance from a single input image. NeRF and its variants typically require videos or images from different viewpoints. Most existing approaches taking monocular input either rely on ground-truth 3D scans for supervision or lack 3D consistency. While recent 3D generative models show promise of 3D consistent human digitization, these approaches do not generalize well to diverse clothing appearances, and the results lack photorealism. Unlike existing work, we utilize high-capacity 2D diffusion models pretrained for general image synthesis tasks as an appearance prior of clothed humans. To achieve better 3D consistency while retaining the input identity, we progressively synthesize multiple views of the human in the input image by inpainting missing regions with shape-guided diffusion conditioned on silhouette and surface normal. We then fuse these synthesized multi-view images via inverse rendering to obtain a fully textured high-resolution 3D mesh of the given person. Experiments show that our approach outperforms prior methods and achieves photorealistic 360-degree synthesis of a wide range of clothed humans with complex textures from a single image.
An explicit substructuring method for overlapping domain decomposition based on stochastic calculus

In a recent paper [{\em F. Bernal, J. Mor\'on-Vidal and J.A. Acebr\'on, Comp.$\&$ Math. App. 146:294-308 (2023)}] an hybrid supercomputing algorithm for elliptic equations has been put forward. The idea is that the interfacial nodal solutions solve a linear system, whose coefficients are expectations of functionals of stochastic differential equations confined within patches of about subdomain size. Compared to standard substructuring techniques such as the Schur complement method for the skeleton, the hybrid approach renders an explicit and sparse shrunken matrix -- hence suitable for being substructured again. The ultimate goal is to push strong scalability beyond the state of the art, by leveraging the scope for parallelisation of stochastic calculus. Here, we present a major revamping of that framework, based on the insight of embedding the domain in a cover of overlapping circles (in two dimensions). This allows for efficient Fourier interpolation along the interfaces (now circumferences) and -- crucially -- for the evaluation of most of the interfacial system entries as the solution of small boundary value problems on a circle. This is both extremely efficient (as they can be solved in parallel and by the pseudospectral method) and free of Monte Carlo error. Stochastic numerics are only needed on the relatively few circles intersecting the domain boundary. In sum, the new formulation is significantly faster, simpler and more accurate, while retaining all of the advantageous properties of PDDSparse. Numerical experiments are included for the purpose of illustration.
Multistage Collaborative Knowledge Distillation from Large Language Models

We study semi-supervised sequence generation tasks where labeled data are too scarce to effectively finetune a model and at the same time few-shot prompting of a large language model (LLM) has suboptimal performance. This happens when a task, such as parsing, is expensive to annotate and also unfamiliar to a pretrained LLM. In this paper, we present a discovery that student models distilled from an in-context learned LLM can often generalize better than their teacher on such tasks. Leveraging this finding, we present a new method – multistage collaborative knowledge distillation from an LLM ( MCKD ) – for such tasks. MCKD first few-shot prompts an LLM to produce pseudola-bels for unlabeled data. At each intermediate knowledge distillation (KD) stage, a new pair of students is trained on disjoint partitions of the pseudolabeled data. Each student then produces new and improved pseudolabels for its unseen partition to be used in the next stage of distillation. We demonstrate the advantage of multistage cross-partition labeling on several syntactic and semantic parsing tasks. On CRAFT biomedical parsing, for example, 3-stage MCKD with 50 labeled examples outperforms the prompted LLM and vanilla KD by 7.5% and 3.7% parsing F1, respectively, and matches the performance of supervised finetuning with 500 examples.
Ratios conjecture of cubic $L$-functions of prime moduli

We develop $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of cubic Hecke $L$-functions of prime moduli over the Eisenstein field using multiple Dirichlet series under the generalized Riemann hypothesis. As applications, we evaluate asymptotically the first moment of central values as well as the one-level density of the same family of $L$-functions.
Algorithmic Cheap Talk

The literature on strategic communication originated with the influential cheap talk model, which precedes the Bayesian persuasion model by three decades. This model describes an interaction between two agents: sender and receiver. The sender knows some state of the world which the receiver does not know, and tries to influence the receiver's action by communicating a cheap talk message to the receiver. This paper initiates the algorithmic study of cheap talk in a finite environment (i.e., a finite number of states and receiver's possible actions). We first prove that approximating the sender-optimal or the welfare-maximizing cheap talk equilibrium up to a certain additive constant or multiplicative factor is NP-hard. Fortunately, we identify three naturally-restricted cases that admit efficient algorithms for finding a sender-optimal equilibrium. These include a state-independent sender's utility structure, a constant number of states or a receiver having only two actions.
Deconfinement Dynamics of Fractons in Tilted Bose-Hubbard Chains

Fractonic constraints can lead to exotic properties of quantum many-body systems. Here, we investigate the dynamics of fracton excitations on top of the ground states of a one-dimemnsional, dipole-conserving Bose-Hubbard model. We show that nearby fractons undergo a collective motion mediated by exchanging virtual dipole excitations, which provides a powerful dynamical tool to characterize the underlying ground state phases. We find that in the gapped Mott insulating phase, fractons are confined to each other as motion requires the exchange of massive dipoles. When crossing the phase transition into a gapless Luttinger liquid of dipoles, fractons deconfine. Their transient deconfinement dynamics scales diffusively and exhibits strong but subleading contributions described by a quantum Lifshitz model. We examine prospects for the experimental realization in tilted Bose-Hubbard chains by numerically simulating the adiabatic state preparation and subsequent time evolution, and find clear signatures of the low-energy fracton dynamics.
Context Adaptive Cooperation

Reliable broadcast and consensus are the two pillars that support a lot of non-trivial fault-tolerant distributed middleware and fault-tolerant distributed systems. While they have close definitions, they strongly differ in the underlying assumptions needed to implement each of them. Reliable broadcast can be implemented in asynchronous systems in the presence of crash or Byzantine failures while Consensus cannot. This key difference stems from the fact that consensus involves synchronization between multiple processes that concurrently propose values, while reliable broadcast simply involves delivering a message from a predefined sender. This paper strikes a balance between these two agreement abstractions in the presence of Byzantine failures. It proposes CAC, a novel agreement abstraction that enables multiple processes to broadcast messages simultaneously, while guaranteeing that (despite potential conflicts, asynchrony, and Byzantine behaviors) the non-faulty processes will agree on messages deliveries. We show that this novel abstraction can enable more efficient algorithms for a variety of applications (such as money transfer where several people can share a same account). This is obtained by focusing the need for synchronization only on the processes that actually need to synchronize.
Data Augmentations in Deep Weight Spaces

Learning in weight spaces, where neural networks process the weights of other deep neural networks, has emerged as a promising research direction with applications in various fields, from analyzing and editing neural fields and implicit neural representations, to network pruning and quantization. Recent works designed architectures for effective learning in that space, which takes into account its unique, permutation-equivariant, structure. Unfortunately, so far these architectures suffer from severe overfitting and were shown to benefit from large datasets. This poses a significant challenge because generating data for this learning setup is laborious and time-consuming since each data sample is a full set of network weights that has to be trained. In this paper, we address this difficulty by investigating data augmentations for weight spaces, a set of techniques that enable generating new data examples on the fly without having to train additional input weight space elements. We first review several recently proposed data augmentation schemes %that were proposed recently and divide them into categories. We then introduce a novel augmentation scheme based on the Mixup method. We evaluate the performance of these techniques on existing benchmarks as well as new benchmarks we generate, which can be valuable for future studies.
Colouring versus density in integers and Hales-Jewett cubes

We construct for every integer $k\geq 3$ and every real $\mu\in(0, \frac{k-1}{k})$ a set of integers $X=X(k, \mu)$ which, when coloured with finitely many colours, contains a monochromatic $k$-term arithmetic progression, whilst every finite $Y\subseteq X$ has a subset $Z\subseteq Y$ of size $|Z|\geq \mu |Y|$ that is free of arithmetic progressions of length $k$. This answers a question of Erd\H{o}s, Ne\v{s}et\v{r}il, and the second author. Moreover, we obtain an analogous multidimensional statement and a Hales-Jewett version of this result.
Can MusicGen Create Training Data for MIR Tasks?

We are investigating the broader concept of using AI-based generative music systems to generate training data for Music Information Retrieval (MIR) tasks. To kick off this line of work, we ran an initial experiment in which we trained a genre classifier on a fully artificial music dataset created with MusicGen. We constructed over 50 000 genre- conditioned textual descriptions and generated a collection of music excerpts that covers five musical genres. Our preliminary results show that the proposed model can learn genre-specific characteristics from artificial music tracks that generalise well to real-world music recordings.
Learning Fair Division from Bandit Feedback

This work addresses learning online fair division under uncertainty, where a central planner sequentially allocates items without precise knowledge of agents' values or utilities. Departing from conventional online algorithm, the planner here relies on noisy, estimated values obtained after allocating items. We introduce wrapper algorithms utilizing \textit{dual averaging}, enabling gradual learning of both the type distribution of arriving items and agents' values through bandit feedback. This approach enables the algorithms to asymptotically achieve optimal Nash social welfare in linear Fisher markets with agents having additive utilities. We establish regret bounds in Nash social welfare and empirically validate the superior performance of our proposed algorithms across synthetic and empirical datasets.
Few-shot Transfer Learning for Knowledge Base Question Answering: Fusing Supervised Models with In-Context Learning

Existing Knowledge Base Question Answering (KBQA) architectures are hungry for annotated data, which make them costly and time-consuming to deploy. We introduce the problem of few-shot transfer learning for KBQA, where the target domain offers only a few labeled examples, but a large labeled training dataset is available in a source domain. We propose a novel KBQA architecture called FuSIC-KBQA that performs KB-retrieval using multiple source-trained retrievers, re-ranks using an LLM and uses this as input for LLM few-shot in-context learning to generate logical forms, which are further refined using execution-guided feedback. Experiments over four source-target KBQA pairs of varying complexity show that FuSIC-KBQA significantly outperforms adaptations of SoTA KBQA models for this setting. Additional experiments in the in-domain setting show that FuSIC-KBQA also outperforms SoTA KBQA models when training data is limited.
A short note on super-hedging an arbitrary number of European options with integer-valued strategies

The usual theory of asset pricing in finance assumes that the financial strategies, i.e. the quantity of risky assets to invest, are real-valued so that they are not integer-valued in general, see the Black and Scholes model for instance. This is clearly contrary to what it is possible to do in the real world. Surprisingly, it seems that there is no many contributions in that direction in the literature, except for a finite number of states. In this paper, for arbitrary {\Omega}, we show that, in discrete-time, it is possible to evaluate the minimal super-hedging price when we restrict ourselves to integer-valued strategies. To do so, we only consider terminal claims that are continuous piecewise affine functions of the underlying asset. We formulate a dynamic programming principle that can be directly implemented on an historical data and which also provides the optimal integer-valued strategy. The problem with general payoffs remains open but should be solved with the same approach.
On the Computation of the Gaussian Rate-Distortion-Perception Function

In this paper, we study the computation of the rate-distortion-perception function (RDPF) for a multivariate Gaussian source under mean squared error (MSE) distortion and, respectively, Kullback-Leibler divergence, geometric Jensen-Shannon divergence, squared Hellinger distance, and squared Wasserstein-2 distance perception metrics. To this end, we first characterize the analytical bounds of the scalar Gaussian RDPF for the aforementioned divergence functions, also providing the RDPF-achieving forward"test-channel"realization. Focusing on the multivariate case, we establish that, for tensorizable distortion and perception metrics, the optimal solution resides on the vector space spanned by the eigenvector of the source covariance matrix. Consequently, the multivariate optimization problem can be expressed as a function of the scalar Gaussian RDPFs of the source marginals, constrained by global distortion and perception levels. Leveraging this characterization, we design an alternating minimization scheme based on the block nonlinear Gauss-Seidel method, which optimally solves the problem while identifying the Gaussian RDPF-achieving realization. Furthermore, the associated algorithmic embodiment is provided, as well as the convergence and the rate of convergence characterization. Lastly, for the"perfect realism"regime, the analytical solution for the multivariate Gaussian RDPF is obtained. We corroborate our results with numerical simulations and draw connections to existing results.