OpenRaiser/Intern-Atlas huggingface dataset:
Symbolic Recovery of Differential Equations: The Identifiability Problem
Venue: arXiv cs.LG 2024
Year: 2024

Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations with the use of machine learning techniques. In contrast to classical methods which assume the structure of the equation to be known and focus on the estimation of specific parameters, these algorithms aim to learn the structure and the parameters simultaneously. While the uniqueness and, therefore, the identifiability of parameters of governing equations are a well-addressed problem in the field of parameter estimation, it has not been investigated for symbolic recovery. However, this problem should be even more present in this field since the algorithms aim to cover larger spaces of governing equations. In this paper, we investigate under which conditions a solution of a differential equation does not uniquely determine the equation itself. For various classes of differential equations, we provide both necessary and sufficient conditions for a function to uniquely determine the corresponding differential equation. We then use our results to devise numerical algorithms aiming to determine whether a function solves a differential equation uniquely. Finally, we provide extensive numerical experiments showing that our algorithms can indeed guarantee the uniqueness of the learned governing differential equation, without assuming any knowledge about the analytic form of function, thereby ensuring the reliability of the learned equation.
Non-Transferability in Communication Channels and Tarski`s Truth Theorem
Venue: arXiv cs.LO 2024
Year: 2024

This article explores the concept of transferability within communication channels, with a particular focus on the inability to transmit certain situations through these channels. The Channel Non-Transferability Theorem establishes that no encoding-decoding mechanism can fully transmit all propositions, along with their truth values, from a transmitter to a receiver. The theorem underscores that when a communication channel attempts to transmit its own error state, it inevitably enters a non-transferable condition. I argue that Tarski`s Truth Undefinability Theorem parallels the concept of non-transferability in communication channels. As demonstrated in this article, the existence of non-transferable codes in communication theory is mathematically equivalent to the undefinability of truth as articulated in Tarski`s theorem. This equivalence is analogous to the relationship between the existence of non-computable functions in computer science and Gödel`s First Incompleteness Theorem in mathematical logic. This new perspective sheds light on additional aspects of Tarski`s theorem, enabling a clearer expression and understanding of its implications. Keywords: Non-Transferability, Channel Theory, Tarski`s Truth Theorem, Semantic.
Limited or Biased: Modeling Sub-Rational Human Investors in Financial Markets
Venue: arXiv cs.AI 2024
Year: 2024

Human decision-making in real-life deviates significantly from the optimal decisions made by fully rational agents, primarily due to computational limitations or psychological biases. While existing studies in behavioral finance have discovered various aspects of human sub-rationality, there lacks a comprehensive framework to transfer these findings into an adaptive human model applicable across diverse financial market scenarios. In this study, we introduce a flexible model that incorporates five different aspects of human sub-rationality using reinforcement learning. Our model is trained using a high-fidelity multi-agent market simulator, which overcomes limitations associated with the scarcity of labeled data of individual investors. We evaluate the behavior of sub-rational human investors using hand-crafted market scenarios and SHAP value analysis, showing that our model accurately reproduces the observations in the previous studies and reveals insights of the driving factors of human behavior. Finally, we explore the impact of sub-rationality on the investor's Profit and Loss (PnL) and market quality. Our experiments reveal that bounded-rational and prospect-biased human behaviors improve liquidity but diminish price efficiency, whereas human behavior influenced by myopia, optimism, and pessimism reduces market liquidity.
Mutual Information Density of Massive MIMO Systems over Rayleigh-Product Channels
Venue: arXiv cs.IT 2024
Year: 2024

The Rayleigh-product channel model is utilized to characterize the rank deficiency caused by keyhole effects. However, the finite blocklength analysis for Rayleigh product channels is not available in the literature. In this paper, we will characterize the mutual information density (MID) and perform the FBL analysis to reveal the impact of rank-deficiency in Rayleigh-product channels. To this end, we first set up a central limit theorem for the MID over Rayleigh-product MIMO channels in the asymptotic regime where the number of scatterers, number of antennas, and blocklength go to infinity at the same pace. Then, we utilize the CLT to obtain the upper and lower bounds for the packet error probability, whose approximations in the high and low signal to noise ratio regimes are then derived to illustrate the impact of rank deficiency. One interesting observation is that rank-deficiency degrades the performance of MIMO systems with FBL and the fundamental limits of Rayleigh-product channels degenerate to those of the Rayleigh case when the number of scatterers approaches infinity.
An Open-source Benchmark of Deep Learning Models for Audio-visual Apparent and Self-reported Personality Recognition
Venue: arXiv cs.CV 2024
Year: 2024

Personality determines a wide variety of human daily and working behaviours, and is crucial for understanding human internal and external states. In recent years, a large number of automatic personality computing approaches have been developed to predict either the apparent personality or self-reported personality of the subject based on non-verbal audio-visual behaviours. However, the majority of them suffer from complex and dataset-specific pre-processing steps and model training tricks. In the absence of a standardized benchmark with consistent experimental settings, it is not only impossible to fairly compare the real performances of these personality computing models but also makes them difficult to be reproduced. In this paper, we present the first reproducible audio-visual benchmarking framework to provide a fair and consistent evaluation of eight existing personality computing models (e.g., audio, visual and audio-visual) and seven standard deep learning models on both self-reported and apparent personality recognition tasks. Building upon a set of benchmarked models, we also investigate the impact of two previously-used long-term modelling strategies for summarising short-term/frame-level predictions on personality computing results. The results conclude: (i) apparent personality traits, inferred from facial behaviours by most benchmarked deep learning models, show more reliability than self-reported ones; (ii) visual models frequently achieved superior performances than audio models on personality recognition; (iii) non-verbal behaviours contribute differently in predicting different personality traits; and (iv) our reproduced personality computing models generally achieved worse performances than their original reported results. Our benchmark is publicly available at \url{https://github.com/liaorongfan/DeepPersonality}.
SSiT: Saliency-guided Self-supervised Image Transformer for Diabetic Retinopathy Grading
Venue: arXiv cs.CV 2024
Year: 2024

Self-supervised Learning (SSL) has been widely applied to learn image representations through exploiting unlabeled images. However, it has not been fully explored in the medical image analysis field. In this work, Saliency-guided Self-Supervised image Transformer (SSiT) is proposed for Diabetic Retinopathy (DR) grading from fundus images. We novelly introduce saliency maps into SSL, with a goal of guiding self-supervised pre-training with domain-specific prior knowledge. Specifically, two saliency-guided learning tasks are employed in SSiT: (1) Saliency-guided contrastive learning is conducted based on the momentum contrast, wherein fundus images' saliency maps are utilized to remove trivial patches from the input sequences of the momentum-updated key encoder. Thus, the key encoder is constrained to provide target representations focusing on salient regions, guiding the query encoder to capture salient features. (2) The query encoder is trained to predict the saliency segmentation, encouraging the preservation of fine-grained information in the learned representations. To assess our proposed method, four publicly-accessible fundus image datasets are adopted. One dataset is employed for pre-training, while the three others are used to evaluate the pre-trained models' performance on downstream DR grading. The proposed SSiT significantly outperforms other representative state-of-the-art SSL methods on all downstream datasets and under various evaluation settings. For example, SSiT achieves a Kappa score of 81.88% on the DDR dataset under fine-tuning evaluation, outperforming all other ViT-based SSL methods by at least 9.48%.
MGTUNet: An new UNet for colon nuclei instance segmentation and quantification
Venue: arXiv cs.CV 2024
Year: 2024

Colorectal cancer (CRC) is among the top three malignant tumor types in terms of morbidity and mortality. Histopathological images are the gold standard for diagnosing colon cancer. Cellular nuclei instance segmentation and classification, and nuclear component regression tasks can aid in the analysis of the tumor microenvironment in colon tissue. Traditional methods are still unable to handle both types of tasks end-to-end at the same time, and have poor prediction accuracy and high application costs. This paper proposes a new UNet model for handling nuclei based on the UNet framework, called MGTUNet, which uses Mish, Group normalization and transposed convolution layer to improve the segmentation model, and a ranger optimizer to adjust the SmoothL1Loss values. Secondly, it uses different channels to segment and classify different types of nucleus, ultimately completing the nuclei instance segmentation and classification task, and the nuclei component regression task simultaneously. Finally, we did extensive comparison experiments using eight segmentation models. By comparing the three evaluation metrics and the parameter sizes of the models, MGTUNet obtained 0.6254 on PQ, 0.6359 on mPQ, and 0.8695 on R2. Thus, the experiments demonstrated that MGTUNet is now a state-of-the-art method for quantifying histopathological images of colon cancer.
How Does a Deep Learning Model Architecture Impact Its Privacy? A Comprehensive Study of Privacy Attacks on CNNs and Transformers
Venue: arXiv cs.CR 2024
Year: 2024

As a booming research area in the past decade, deep learning technologies have been driven by big data collected and processed on an unprecedented scale. However, privacy concerns arise due to the potential leakage of sensitive information from the training data. Recent research has revealed that deep learning models are vulnerable to various privacy attacks, including membership inference attacks, attribute inference attacks, and gradient inversion attacks. Notably, the efficacy of these attacks varies from model to model. In this paper, we answer a fundamental question: Does model architecture affect model privacy? By investigating representative model architectures from convolutional neural networks (CNNs) to Transformers, we demonstrate that Transformers generally exhibit higher vulnerability to privacy attacks than CNNs. Additionally, we identify the micro design of activation layers, stem layers, and LN layers, as major factors contributing to the resilience of CNNs against privacy attacks, while the presence of attention modules is another main factor that exacerbates the privacy vulnerability of Transformers. Our discovery reveals valuable insights for deep learning models to defend against privacy attacks and inspires the research community to develop privacy-friendly model architectures.
Inference from Real-World Sparse Measurements
Venue: arXiv cs.LG 2024
Year: 2024

Real-world problems often involve complex and unstructured sets of measurements, which occur when sensors are sparsely placed in either space or time. Being able to model this irregular spatiotemporal data and extract meaningful forecasts is crucial. Deep learning architectures capable of processing sets of measurements with positions varying from set to set, and extracting readouts anywhere are methodologically difficult. Current state-of-the-art models are graph neural networks and require domain-specific knowledge for proper setup. We propose an attention-based model focused on robustness and practical applicability, with two key design contributions. First, we adopt a ViT-like transformer that takes both context points and read-out positions as inputs, eliminating the need for an encoder-decoder structure. Second, we use a unified method for encoding both context and read-out positions. This approach is intentionally straightforward and integrates well with other systems. Compared to existing approaches, our model is simpler, requires less specialized knowledge, and does not suffer from a problematic bottleneck effect, all of which contribute to superior performance. We conduct in-depth ablation studies that characterize this problematic bottleneck in the latent representations of alternative models that inhibit information utilization and impede training efficiency. We also perform experiments across various problem domains, including high-altitude wind nowcasting, two-day weather forecasting, fluid dynamics, and heat diffusion. Our attention-based model consistently outperforms state-of-the-art models in handling irregularly sampled data. Notably, our model reduces the root mean square error (RMSE) for wind nowcasting from 9.24 to 7.98 and for heat diffusion tasks from 0.126 to 0.084.
On-Demand Sampling: Learning Optimally from Multiple Distributions
Venue: arXiv cs.LG 2024
Year: 2024

Social and real-world considerations such as robustness, fairness, social welfare and multi-agent tradeoffs have given rise to multi-distribution learning paradigms, such as collaborative learning, group distributionally robust optimization, and fair federated learning. In each of these settings, a learner seeks to uniformly minimize its expected loss over $n$ predefined data distributions, while using as few samples as possible. In this paper, we establish the optimal sample complexity of these learning paradigms and give algorithms that meet this sample complexity. Importantly, our sample complexity bounds for multi-distribution learning exceed that of learning a single distribution by only an additive factor of $n \log(n) / ε^2$. This improves upon the best known sample complexity bounds for fair federated learning by Mohri et al. and collaborative learning by Nguyen and Zakynthinou by multiplicative factors of $n$ and $\log(n)/ε^3$, respectively. We also provide the first sample complexity bounds for the group DRO objective of Sagawa et al. To guarantee these optimal sample complexity bounds, our algorithms learn to sample from data distributions on demand. Our algorithm design and analysis are enabled by our extensions of online learning techniques for solving stochastic zero-sum games. In particular, we contribute stochastic variants of no-regret dynamics that can trade off between players' differing sampling costs.
On Tools for Completeness of Kleene Algebra with Hypotheses
Venue: arXiv cs.LO 2024
Year: 2024

In the literature on Kleene algebra, a number of variants have been proposed which impose additional structure specified by a theory, such as Kleene algebra with tests (KAT) and the recent Kleene algebra with observations (KAO), or make specific assumptions about certain constants, as for instance in NetKAT. Many of these variants fit within the unifying perspective offered by Kleene algebra with hypotheses, which comes with a canonical language model constructed from a given set of hypotheses. For the case of KAT, this model corresponds to the familiar interpretation of expressions as languages of guarded strings. A relevant question therefore is whether Kleene algebra together with a given set of hypotheses is complete with respect to its canonical language model. In this paper, we revisit, combine and extend existing results on this question to obtain tools for proving completeness in a modular way. We showcase these tools by giving new and modular proofs of completeness for KAT, KAO and NetKAT, and we prove completeness for new variants of KAT: KAT extended with a constant for the full relation, KAT extended with a converse operation, and a version of KAT where the collection of tests only forms a distributive lattice.
Parallel Order-Based Core Maintenance in Dynamic Graphs
Venue: arXiv cs.DC 2024
Year: 2024

The core numbers of vertices in a graph are one of the most well-studied cohesive subgraph models because of the linear running time. In practice, many data graphs are dynamic graphs that are continuously changing by inserting or removing edges. The core numbers are updated in dynamic graphs with edge insertions and deletions, which is called core maintenance. When a burst of a large number of inserted or removed edges come in, we have to handle these edges on time to keep up with the data stream. There are two main sequential algorithms for core maintenance, \textsc{Traversal} and \textsc{Order}. It is proved that the \textsc{Order} algorithm significantly outperforms the \alg{Traversal} algorithm over all tested graphs with up to 2,083 times speedups. To the best of our knowledge, all existing parallel approaches are based on the \alg{Traversal} algorithm; also, their parallelism exists only for affected vertices with different core numbers, which will reduce to sequential when all vertices have the same core numbers. In this paper, we propose a new parallel core maintenance algorithm based on the \alg{Order} algorithm. Importantly, our new approach always has parallelism, even for the graphs where all vertices have the same core numbers. Extensive experiments are conducted over real-world, temporal, and synthetic graphs on a 64-core machine. The results show that for inserting and removing 100,000 edges using 16-worker, our method achieves up to 289x and 10x times speedups compared with the most efficient existing method, respectively.
Reachability Verification Based Reliability Assessment for Deep Reinforcement Learning Controlled Robotics and Autonomous Systems
Venue: arXiv cs.RO 2024
Year: 2024

Deep Reinforcement Learning (DRL) has achieved impressive performance in robotics and autonomous systems (RAS). A key challenge to its deployment in real-life operations is the presence of spuriously unsafe DRL policies. Unexplored states may lead the agent to make wrong decisions that could result in hazards, especially in applications where DRL-trained end-to-end controllers govern the behaviour of RAS. This paper proposes a novel quantitative reliability assessment framework for DRL-controlled RAS, leveraging verification evidence generated from formal reliability analysis of neural networks. A two-level verification framework is introduced to check the safety property with respect to inaccurate observations that are due to, e.g., environmental noise and state changes. Reachability verification tools are leveraged locally to generate safety evidence of trajectories. In contrast, at the global level, we quantify the overall reliability as an aggregated metric of local safety evidence, corresponding to a set of distinct tasks and their occurrence probabilities. The effectiveness of the proposed verification framework is demonstrated and validated via experiments on real RAS.
Parallel Self-Avoiding Walks for a Low-Autocorrelation Binary Sequences Problem
Venue: arXiv cs.DC 2024
Year: 2024

A low-autocorrelation binary sequences problem with a high figure of merit factor represents a formidable computational challenge. An efficient parallel computing algorithm is required to reach the new best-known solutions for this problem. Therefore, we developed the $\mathit{sokol}_{\mathit{skew}}$ solver for the skew-symmetric search space. The developed solver takes the advantage of parallel computing on graphics processing units. The solver organized the search process as a sequence of parallel and contiguous self-avoiding walks and achieved a speedup factor of 387 compared with $\mathit{lssOrel}$, its predecessor. The $\mathit{sokol}_{\mathit{skew}}$ solver belongs to stochastic solvers and can not guarantee the optimality of solutions. To mitigate this problem, we established the predictive model of stopping conditions according to the small instances for which the optimal skew-symmetric solutions are known. With its help and 99% probability, the $\mathit{sokol}_{\mathit{skew}}$ solver found all the known and seven new best-known skew-symmetric sequences for odd instances from $L=121$ to $L=223$. For larger instances, the solver can not reach 99% probability within our limitations, but it still found several new best-known binary sequences. We also analyzed the trend of the best merit factor values, and it shows that as sequence size increases, the value of the merit factor also increases, and this trend is flatter for larger instances.
Observable Perfect Equilibrium
Venue: arXiv cs.GT 2024
Year: 2024

While Nash equilibrium has emerged as the central game-theoretic solution concept, many important games contain several Nash equilibria and we must determine how to select between them in order to create real strategic agents. Several Nash equilibrium refinement concepts have been proposed and studied for sequential imperfect-information games, the most prominent being trembling-hand perfect equilibrium, quasi-perfect equilibrium, and recently one-sided quasi-perfect equilibrium. These concepts are robust to certain arbitrarily small mistakes, and are guaranteed to always exist; however, we argue that neither of these is the correct concept for developing strong agents in sequential games of imperfect information. We define a new equilibrium refinement concept for extensive-form games called observable perfect equilibrium in which the solution is robust over trembles in publicly-observable action probabilities (not necessarily over all action probabilities that may not be observable by opposing players). Observable perfect equilibrium correctly captures the assumption that the opponent is playing as rationally as possible given mistakes that have been observed (while previous solution concepts do not). We prove that observable perfect equilibrium is always guaranteed to exist, and demonstrate that it leads to a different solution than the prior extensive-form refinements in no-limit poker. We expect observable perfect equilibrium to be a useful equilibrium refinement concept for modeling many important imperfect-information games of interest in artificial intelligence.