OpenRaiser/Intern-Atlas huggingface dataset:
Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftings
Venue: arXiv cs.LG 2024
Year: 2024

We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this, we obtain quadratic dynamics that are Hamiltonian in a transformed coordinate system. To that end, for given generalized position and momentum data, we propose a methodology to learn quadratic dynamical systems, enforcing the Hamiltonian structure in combination with a weakly-enforced symplectic auto-encoder. The obtained Hamiltonian structure exhibits long-term stability of the system, while the cubic Hamiltonian function provides relatively low model complexity. For low-dimensional data, we determine a higher-dimensional transformed coordinate system, whereas for high-dimensional data, we find a lower-dimensional coordinate system with the desired properties. We demonstrate the proposed methodology by means of both low-dimensional and high-dimensional nonlinear Hamiltonian systems.
Skolem Meets Bateman-Horn
Venue: arXiv cs.DM 2024
Year: 2024

The Skolem Problem asks to determine whether a given integer linear recurrence sequence has a zero term. This problem arises across a wide range of topics in computer science, including loop termination, formal languages, automata theory, and control theory, amongst many others. Decidability of the Skolem Problem is notoriously open. The state of the art is a decision procedure for recurrences of order at most 4: an advance achieved some 40 years ago, based on Baker's theorem on linear forms in logarithms of algebraic numbers. A new approach to the Skolem Problem was recently initiated via the notion of a Universal Skolem Set: a set $S$ of positive integers such that it is decidable whether a given non-degenerate linear recurrence sequence has a zero in $S$. Clearly, proving decidability of the Skolem Problem is equivalent to showing that $\mathbb{N}$ itself is a Universal Skolem Set. The main contribution of the present paper is to construct a Universal Skolem Set that has lower density at least $0.29$. We show moreover that this set has density one subject to the Bateman-Horn conjecture. The latter is a central unifying hypothesis concerning the frequency of prime numbers among the values of systems of polynomials.
Arithmetic with Language Models: from Memorization to Computation
Venue: arXiv cs.AI 2024
Year: 2024

A better understanding of the emergent computation and problem-solving capabilities of recent large language models is of paramount importance to further improve them and broaden their applicability. This work investigates how a language model, trained to predict the next token, can perform arithmetic computations generalizing beyond training data. Binary addition and multiplication constitute a good testbed for this purpose, since they require a very small vocabulary and exhibit relevant input/output discontinuities making smooth input interpolation ineffective for novel data. We successfully trained a light language model to learn these tasks and ran a number of experiments to investigate the extrapolation capabilities and internal information processing. Our findings support the hypothesis that the language model works as an Encoding-Regression-Decoding machine where the computation takes place in the value space once the input token representation is mapped to an appropriate internal representation.
Reverse Stable Diffusion: What prompt was used to generate this image?
Venue: arXiv cs.CV 2024
Year: 2024

Text-to-image diffusion models have recently attracted the interest of many researchers, and inverting the diffusion process can play an important role in better understanding the generative process and how to engineer prompts in order to obtain the desired images. To this end, we study the task of predicting the prompt embedding given an image generated by a generative diffusion model. We consider a series of white-box and black-box models (with and without access to the weights of the diffusion network) to deal with the proposed task. We propose a novel learning framework comprising a joint prompt regression and multi-label vocabulary classification objective that generates improved prompts. To further improve our method, we employ a curriculum learning procedure that promotes the learning of image-prompt pairs with lower labeling noise (i.e. that are better aligned). We conduct experiments on the DiffusionDB data set, predicting text prompts from images generated by Stable Diffusion. In addition, we make an interesting discovery: training a diffusion model on the prompt generation task can make the model generate images that are much better aligned with the input prompts, when the model is directly reused for text-to-image generation. Our code is publicly available for download at https://github.com/CroitoruAlin/Reverse-Stable-Diffusion.
Simultaneously Approximating All $\ell_p$-norms in Correlation Clustering
Venue: arXiv cs.DS 2024
Year: 2024

This paper considers correlation clustering on unweighted complete graphs. We give a combinatorial algorithm that returns a single clustering solution that is simultaneously $O(1)$-approximate for all $\ell_p$-norms of the disagreement vector; in other words, a combinatorial $O(1)$-approximation of the all-norms objective for correlation clustering. This is the first proof that minimal sacrifice is needed in order to optimize different norms of the disagreement vector. In addition, our algorithm is the first combinatorial approximation algorithm for the $\ell_2$-norm objective, and more generally the first combinatorial algorithm for the $\ell_p$-norm objective when $1 < p < \infty$. It is also faster than all previous algorithms that minimize the $\ell_p$-norm of the disagreement vector, with run-time $O(n^ω)$, where $O(n^ω)$ is the time for matrix multiplication on $n \times n$ matrices. When the maximum positive degree in the graph is at most $Δ$, this can be improved to a run-time of $O(nΔ^2 \log n)$.
Memory capacity of two layer neural networks with smooth activations
Venue: arXiv cs.LG 2024
Year: 2024

Determining the memory capacity of two layer neural networks with $m$ hidden neurons and input dimension $d$ (i.e., $md+2m$ total trainable parameters), which refers to the largest size of general data the network can memorize, is a fundamental machine learning question. For activations that are real analytic at a point and, if restricting to a polynomial there, have sufficiently high degree, we establish a lower bound of $\lfloor md/2\rfloor$ and optimality up to a factor of approximately $2$. All practical activations, such as sigmoids, Heaviside, and the rectified linear unit (ReLU), are real analytic at a point. Furthermore, the degree condition is mild, requiring, for example, that $\binom{k+d-1}{d-1}\ge n$ if the activation is $x^k$. Analogous prior results were limited to Heaviside and ReLU activations -- our result covers almost everything else. In order to analyze general activations, we derive the precise generic rank of the network's Jacobian, which can be written in terms of Hadamard powers and the Khatri-Rao product. Our analysis extends classical linear algebraic facts about the rank of Hadamard powers. Overall, our approach differs from prior works on memory capacity and holds promise for extending to deeper models and other architectures.
Learning Regionalization using Accurate Spatial Cost Gradients within a Differentiable High-Resolution Hydrological Model: Application to the French Mediterranean Region
Venue: arXiv cs.LG 2024
Year: 2024

Estimating spatially distributed hydrological parameters in ungauged catchments poses a challenging regionalization problem and requires imposing spatial constraints given the sparsity of discharge data. A possible approach is to search for a transfer function that quantitatively relates physical descriptors to conceptual model parameters. This paper introduces a Hybrid Data Assimilation and Parameter Regionalization (HDA-PR) approach incorporating learnable regionalization mappings, based on either multi-linear regressions or artificial neural networks (ANNs), into a differentiable hydrological model. This approach demonstrates how two differentiable codes can be linked and their gradients chained, enabling the exploitation of heterogeneous datasets across extensive spatio-temporal computational domains within a high-dimensional regionalization context, using accurate adjoint-based gradients. The inverse problem is tackled with a multi-gauge calibration cost function accounting for information from multiple observation sites. HDA-PR was tested on high-resolution, hourly and kilometric regional modeling of 126 flash-flood-prone catchments in the French Mediterranean region. The results highlight a strong regionalization performance of HDA-PR especially in the most challenging upstream-to-downstream extrapolation scenario with ANN, achieving median Nash-Sutcliffe efficiency (NSE) scores from 0.6 to 0.71 for spatial, temporal, spatio-temporal validations, and improving NSE by up to 30% on average compared to the baseline model calibrated with lumped parameters. ANN enables to learn a non-linear descriptors-to-parameters mapping which provides better model controllability than a linear mapping for complex calibration cases.
Incorporating Recklessness to Collaborative Filtering based Recommender Systems
Venue: arXiv cs.IR 2024
Year: 2024

Recommender systems are intrinsically tied to a reliability/coverage dilemma: The more reliable we desire the forecasts, the more conservative the decision will be and thus, the fewer items will be recommended. This causes a detriment to the predictive capability of the system, as it is only able to estimate potential interest in items for which there is a consensus in their evaluation, rather than being able to estimate potential interest in any item. In this paper, we propose the inclusion of a new term in the learning process of matrix factorization-based recommender systems, called recklessness, that takes into account the variance of the output probability distribution of the predicted ratings. In this way, gauging this recklessness measure we can force more spiky output distribution, enabling the control of the risk level desired when making decisions about the reliability of a prediction. Experimental results demonstrate that recklessness not only allows for risk regulation but also improves the quantity and quality of predictions provided by the recommender system.
Cognitive TransFuser: Semantics-guided Transformer-based Sensor Fusion for Improved Waypoint Prediction
Venue: arXiv cs.RO 2024
Year: 2024

Sensor fusion approaches for intelligent self-driving agents remain key to driving scene understanding given visual global contexts acquired from input sensors. Specifically, for the local waypoint prediction task, single-modality networks are still limited by strong dependency on the sensitivity of the input sensor, and thus recent works therefore promote the use of multiple sensors in fusion in feature level in practice. While it is well known that multiple data modalities encourage mutual contextual exchange, it requires global 3D scene understanding in real-time with minimal computation upon deployment to practical driving scenarios, thereby placing greater significance on the training strategy given a limited number of practically usable sensors. In this light, we exploit carefully selected auxiliary tasks that are highly correlated with the target task of interest (e.g., traffic light recognition and semantic segmentation) by fusing auxiliary task features and also using auxiliary heads for waypoint prediction based on imitation learning. Our RGB-LIDAR-based multi-task feature fusion network, coined Cognitive TransFuser, augments and exceeds the baseline network by a significant margin for safer and more complete road navigation in the CARLA simulator. We validate the proposed network on the Town05 Short and Town05 Long Benchmark through extensive experiments, achieving up to 44.2 FPS real-time inference time.
A Survey of Beam Management for mmWave and THz Communications Towards 6G
Venue: arXiv cs.IT 2024
Year: 2024

Communication in millimeter wave (mmWave) and even terahertz (THz) frequency bands is ushering in a new era of wireless communications. Beam management, namely initial access and beam tracking, has been recognized as an essential technique to ensure robust mmWave/THz communications, especially for mobile scenarios. However, narrow beams at higher carrier frequency lead to huge beam measurement overhead, which has a negative impact on beam acquisition and tracking. In addition, the beam management process is further complicated by the fluctuation of mmWave/THz channels, the random movement patterns of users, and the dynamic changes in the environment. For mmWave and THz communications toward 6G, we have witnessed a substantial increase in research and industrial attention on artificial intelligence (AI), reconfigurable intelligent surface (RIS), and integrated sensing and communications (ISAC). The introduction of these enabling technologies presents both open opportunities and unique challenges for beam management. In this paper, we present a comprehensive survey on mmWave and THz beam management. Further, we give some insights on technical challenges and future research directions in this promising area.
A Bi-variant Variational Model for Diffeomorphic Image Registration with Relaxed Jacobian Determinant Constraints
Venue: arXiv cs.CV 2024
Year: 2024

Diffeomorphic registration is a widely used technique for finding a smooth and invertible transformation between two coordinate systems, which are measured using template and reference images. The point-wise volume-preserving constraint $\det(\nabla\bmφ(\bm{x})) =1$ is effective in some cases, but may be too restrictive in others, especially when local deformations are relatively large. This can result in poor matching when enforcing large local deformations. In this paper, we propose a new bi-variant diffeomorphic image registration model that introduces a soft constraint on the Jacobian equation $\det(\nabla\bmφ(\bm{x})) = f(\bm{x}) > 0$. This allows local deformations to shrink and grow within a flexible range $0<κ_{m}<\det(\nabla\bmφ(\bm{x}))<κ_{M}$. The Jacobian determinant of transformation is explicitly controlled by optimizing the relaxation function $f(\bm{x})$. To prevent deformation folding and improve the smoothness of the transformation, a positive constraint is imposed on the optimization of the relaxation function $f(\bm{x})$, and a regularizer is used to ensure the smoothness of $f(\bm{x})$. Furthermore, the positivity constraint ensures that $f(\bm{x})$ is as close to one as possible, which helps to achieve a volume-preserving transformation on average. We also analyze the existence of the minimizer for the variational model and propose a penalty-splitting algorithm with a multilevel strategy to solve this model. Numerical experiments demonstrate the convergence of the proposed algorithm and show that the positivity constraint can effectively control the range of relative volume without compromising the accuracy of the registration. Moreover, the proposed model generates diffeomorphic maps for large local deformations and outperforms several existing registration models in terms of performance.
Learning to Generate Training Datasets for Robust Semantic Segmentation
Venue: arXiv cs.CV 2024
Year: 2024

Semantic segmentation methods have advanced significantly. Still, their robustness to real-world perturbations and object types not seen during training remains a challenge, particularly in safety-critical applications. We propose a novel approach to improve the robustness of semantic segmentation techniques by leveraging the synergy between label-to-image generators and image-to-label segmentation models. Specifically, we design Robusta, a novel robust conditional generative adversarial network to generate realistic and plausible perturbed images that can be used to train reliable segmentation models. We conduct in-depth studies of the proposed generative model, assess the performance and robustness of the downstream segmentation network, and demonstrate that our approach can significantly enhance the robustness in the face of real-world perturbations, distribution shifts, and out-of-distribution samples. Our results suggest that this approach could be valuable in safety-critical applications, where the reliability of perception modules such as semantic segmentation is of utmost importance and comes with a limited computational budget in inference. We release our code at https://github.com/ENSTA-U2IS-AI/robusta.
Feature Noise Resilient for QoS Prediction with Probabilistic Deep Supervision
Venue: arXiv cs.SE 2024
Year: 2024

Accurate Quality of Service (QoS) prediction is essential for enhancing user satisfaction in web recommendation systems, yet existing prediction models often overlook feature noise, focusing predominantly on label noise. In this paper, we present the Probabilistic Deep Supervision Network (PDS-Net), a robust framework designed to effectively identify and mitigate feature noise, thereby improving QoS prediction accuracy. PDS-Net operates with a dual-branch architecture: the main branch utilizes a decoder network to learn a Gaussian-based prior distribution from known features, while the second branch derives a posterior distribution based on true labels. A key innovation of PDS-Net is its condition-based noise recognition loss function, which enables precise identification of noisy features in objects (users or services). Once noisy features are identified, PDS-Net refines the feature's prior distribution, aligning it with the posterior distribution, and propagates this adjusted distribution to intermediate layers, effectively reducing noise interference. Extensive experiments conducted on two real-world QoS datasets demonstrate that PDS-Net consistently outperforms existing models, achieving an average improvement of 8.91% in MAE on Dataset D1 and 8.32% on Dataset D2 compared to the ate-of-the-art. These results highlight PDS-Net's ability to accurately capture complex user-service relationships and handle feature noise, underscoring its robustness and versatility across diverse QoS prediction environments.
SureFED: Robust Federated Learning via Uncertainty-Aware Inward and Outward Inspection
Venue: arXiv cs.LG 2024
Year: 2024

In this work, we introduce SureFED, a novel framework for byzantine robust federated learning. Unlike many existing defense methods that rely on statistically robust quantities, making them vulnerable to stealthy and colluding attacks, SureFED establishes trust using the local information of benign clients. SureFED utilizes an uncertainty aware model evaluation and introspection to safeguard against poisoning attacks. In particular, each client independently trains a clean local model exclusively using its local dataset, acting as the reference point for evaluating model updates. SureFED leverages Bayesian models that provide model uncertainties and play a crucial role in the model evaluation process. Our framework exhibits robustness even when the majority of clients are compromised, remains agnostic to the number of malicious clients, and is well-suited for non-IID settings. We theoretically prove the robustness of our algorithm against data and model poisoning attacks in a decentralized linear regression setting. Proof-of Concept evaluations on benchmark image classification data demonstrate the superiority of SureFED over the state of the art defense methods under various colluding and non-colluding data and model poisoning attacks.
An Empirical Study of the Non-determinism of ChatGPT in Code Generation
Venue: arXiv cs.SE 2024
Year: 2024

There has been a recent explosion of research on Large Language Models (LLMs) for software engineering tasks, in particular code generation. However, results from LLMs can be highly unstable; nondeterministically returning very different codes for the same prompt. Non-determinism is a potential menace to scientific conclusion validity. When non-determinism is high, scientific conclusions simply cannot be relied upon unless researchers change their behaviour to control for it in their empirical analyses. This paper conducts an empirical study to demonstrate that non-determinism is, indeed, high, thereby underlining the need for this behavioural change. We choose to study ChatGPT because it is already highly prevalent in the code generation research literature. We report results from a study of 829 code generation problems from three code generation benchmarks (i.e., CodeContests, APPS, and HumanEval). Our results reveal high degrees of non-determinism: the ratio of coding tasks with zero equal test output across different requests is 75.76%, 51.00%, and 47.56% for CodeContests, APPS, and HumanEval, respectively. In addition, we find that setting the temperature to 0 does not guarantee determinism in code generation, although it indeed brings less non-determinism than the default configuration (temperature=1). These results confirm that there is, currently, a significant threat to scientific conclusion validity. In order to put LLM-based research on firmer scientific foundations, researchers need to take into account non-determinism in drawing their conclusions.
Beyond First Impressions: Integrating Joint Multi-modal Cues for Comprehensive 3D Representation
Venue: arXiv cs.CV 2024
Year: 2024

In recent years, 3D understanding has turned to 2D vision-language pre-trained models to overcome data scarcity challenges. However, existing methods simply transfer 2D alignment strategies, aligning 3D representations with single-view 2D images and coarse-grained parent category text. These approaches introduce information degradation and insufficient synergy issues, leading to performance loss. Information degradation arises from overlooking the fact that a 3D representation should be equivalent to a series of multi-view images and more fine-grained subcategory text. Insufficient synergy neglects the idea that a robust 3D representation should align with the joint vision-language space, rather than independently aligning with each modality. In this paper, we propose a multi-view joint modality modeling approach, termed JM3D, to obtain a unified representation for point cloud, text, and image. Specifically, a novel Structured Multimodal Organizer (SMO) is proposed to address the information degradation issue, which introduces contiguous multi-view images and hierarchical text to enrich the representation of vision and language modalities. A Joint Multi-modal Alignment (JMA) is designed to tackle the insufficient synergy problem, which models the joint modality by incorporating language knowledge into the visual modality. Extensive experiments on ModelNet40 and ScanObjectNN demonstrate the effectiveness of our proposed method, JM3D, which achieves state-of-the-art performance in zero-shot 3D classification. JM3D outperforms ULIP by approximately 4.3% on PointMLP and achieves an improvement of up to 6.5% accuracy on PointNet++ in top-1 accuracy for zero-shot 3D classification on ModelNet40. The source code and trained models for all our experiments are publicly available at https://github.com/Mr-Neko/JM3D.