Mathematical verfier achieves success in mathematical reasoning tasks by validating the correctness of solutions. However, existing verifiers are trained with binary classification labels, which are not informative enough for the model to accurately assess the solutions. To mitigate the aforementioned insufficiency of binary labels, we introduce step-wise natural language feedbacks as rationale labels (i.e., the correctness of the current step and the explanations). In this paper, we propose \textbf{Math-Minos}, a natural language feedback enhanced verifier by constructing automatically-generated training data and a two-stage training paradigm for effective training and efficient inference. Our experiments reveal that a small set (30k) of natural language feedbacks can significantly boost the performance of the verifier by the accuracy of 1.6\% (86.6\% $\rightarrow$ 88.2\%) on GSM8K and 0.8\% (37.8\% $\rightarrow$ 38.6\%) on MATH. We have released our code and data for further exploration.
Gait asymmetry, a consequence of various neurological or physical conditions such as aging and stroke, detrimentally impacts bipedal locomotion, causing biomechanical alterations, increasing the risk of falls and reducing quality of life. Addressing this critical issue, this paper introduces a novel diagnostic method for gait symmetry analysis through the use of an assistive robotic Smart Walker equipped with an innovative asymmetry detection scheme. This method analyzes sensor measurements capturing the interaction torque between user and walker. By applying a seasonal-trend decomposition tool, we isolate gait-specific patterns within these data, allowing for the estimation of stride durations and calculation of a symmetry index. Through experiments involving 5 experimenters, we demonstrate the Smart Walker's capability in detecting and quantifying gait asymmetry by achieving an accuracy of 84.9% in identifying asymmetric cases in a controlled testing environment. Further analysis explores the classification of these asymmetries based on their underlying causes, providing valuable insights for gait assessment. The results underscore the potential of the device as a precise, ready-to-use monitoring tool for personalized rehabilitation, facilitating targeted interventions for enhanced patient outcomes.
Kolmogorov Arnold Networks (KAN) are highly efficient in inference and can handle complex patterns once trained, making them desirable for production environments and ensuring a fast service experience in the finance and electronic shopping industries. However, we found that KAN, in general, is not suitable for fraud detection problems. We also discovered a quick method to determine whether a problem is solvable by KAN: if the data can be effectively separated using spline interpolation with varying intervals after applying Principal Component Analysis (PCA) to reduce the data dimensions to two, KAN can outperform most machine learning algorithms. Otherwise, it indicates KAN may not solve the problem effectively compared to other machine learning algorithms. We also propose a heuristic approach for selecting the appropriate hyperparameters for KAN to significantly accelerate training time compared to grid search hyperparameter tuning, which usually takes a month for a comprehensive grid search. Specifically, the width parameter should generally follow a pyramid structure, allowing efficient spline mixing, and k should be fixed at 15, with the grid number fixed at 5. This streamlined approach minimizes the number of evaluations required, significantly speeding up the hyperparameter tuning process while still achieving robust performance metrics.
In the realm of autonomous driving,accurately detecting occluded or distant objects,referred to as weak positive sample ,presents significant challenges. These challenges predominantly arise during query initialization, where an over-reliance on heatmap confidence often results in a high rate of false positives, consequently masking weaker detections and impairing system performance. To alleviate this issue, we propose a novel approach, Co-Fix3D, which employs a collaborative hybrid multi-stage parallel query generation mechanism for BEV representations. Our method incorporates the Local-Global Feature Enhancement (LGE) module, which refines BEV features to more effectively highlight weak positive samples. It uniquely leverages the Discrete Wavelet Transform (DWT) for accurate noise reduction and features refinement in localized areas, and incorporates an attention mechanism to more comprehensively optimize global BEV features. Moreover, our method increases the volume of BEV queries through a multi-stage parallel processing of the LGE, significantly enhancing the probability of selecting weak positive samples. This enhancement not only improves training efficiency within the decoder framework but also boosts overall system performance. Notably, Co-Fix3D achieves superior results on the stringent nuScenes benchmark, outperforming all previous models with a 69.1% mAP and 72.9% NDS on the LiDAR-based benchmark, and 72.3% mAP and 74.1% NDS on the multi-modality benchmark, without relying on test-time augmentation or additional datasets. The source code will be made publicly available upon acceptance.
We consider the problem of learning stable matchings with unknown preferences in a decentralized and uncoordinated manner, where "decentralized" means that players make decisions individually without the influence of a central platform, and "uncoordinated" means that players do not need to synchronize their decisions using pre-specified rules. First, we provide a game formulation for this problem with known preferences, where the set of pure Nash equilibria (NE) coincides with the set of stable matchings, and mixed NE can be rounded to a stable matching. Then, we show that for hierarchical markets, applying the exponential weight (EXP) learning algorithm to the stable matching game achieves logarithmic regret in a fully decentralized and uncoordinated fashion. Moreover, we show that EXP converges locally and exponentially fast to a stable matching in general markets. We also introduce another decentralized and uncoordinated learning algorithm that globally converges to a stable matching with arbitrarily high probability. Finally, we provide stronger feedback conditions under which it is possible to drive the market faster toward an approximate stable matching. Our proposed game-theoretic framework bridges the discrete problem of learning stable matchings with the problem of learning NE in continuous-action games.
Restoring limb motor function in individuals with spinal cord injury (SCI), stroke, or amputation remains a critical challenge, one which affects millions worldwide. Recent studies show through surface electromyography (EMG) that spared motor neurons can still be voluntarily controlled, even without visible limb movement . These signals can be decoded and used for motor intent estimation; however, current wearable solutions lack the necessary hardware and software for intuitive interfacing of the spared degrees of freedom after neural injuries. To address these limitations, we developed a wireless, high-density EMG bracelet, coupled with a novel software framework, MyoGestic. Our system allows rapid and tailored adaptability of machine learning models to the needs of the users, facilitating real-time decoding of multiple spared distinctive degrees of freedom. In our study, we successfully decoded the motor intent from two participants with SCI, two with spinal stroke , and three amputees in real-time, achieving several controllable degrees of freedom within minutes after wearing the EMG bracelet. We provide a proof-of-concept that these decoded signals can be used to control a digitally rendered hand, a wearable orthosis, a prosthesis, or a 2D cursor. Our framework promotes a participant-centered approach, allowing immediate feedback integration, thus enhancing the iterative development of myocontrol algorithms. The proposed open-source software framework, MyoGestic, allows researchers and patients to focus on the augmentation and training of the spared degrees of freedom after neural lesions, thus potentially bridging the gap between research and clinical application and advancing the development of intuitive EMG interfaces for diverse neural lesions.
In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions, say $P_0$ and $P_1$. In the scenario where the knowledge of distributions is replaced by empirically observed statistics from the respective distributions, the gain of sequentiality is less understood when subject to universality constraints over all possible $P_0,P_1$. In this work, the gap is mended by a unified study on sequentiality in the universal binary classification problem, where the universality constraints are set on the expected stopping time as well as the type-I error exponent. The type-I error exponent is required to achieve a pre-set distribution-dependent constraint $\lambda(P_0,P_1)$ for all $P_0,P_1$. Under the proposed framework, different sequential setups are investigated so that fair comparisons can be made with the fixed-length counterpart. By viewing these sequential classification problems as special cases of a general sequential composite hypothesis testing problem, the optimal type-II error exponents are characterized. Specifically, in the general sequential composite hypothesis testing problem subject to universality constraints, upper and lower bounds on the type-II error exponent are proved, and a sufficient condition for which the bounds coincide is given. The results for sequential classification problems are then obtained accordingly. With the characterization of the optimal error exponents, the benefit of sequentiality is shown both analytically and numerically by comparing the sequential and the fixed-length cases in representative examples of type-I exponent constraint $\lambda$.
We prove that quantum-hard one-way functions imply simulation-secure quantum oblivious transfer (QOT), which is known to suffice for secure computation of arbitrary quantum functionalities. Furthermore, our construction only makes black-box use of the quantum-hard one-way function. Our primary technical contribution is a construction of extractable and equivocal quantum bit commitments based on the black-box use of quantum-hard one-way functions in the standard model. Instantiating the Cr\'epeau-Kilian (FOCS 1988) framework with these commitments yields simulation-secure QOT.
Perturbation robustness evaluates the vulnerabilities of models, arising from a variety of perturbations, such as data corruptions and adversarial attacks. Understanding the mechanisms of perturbation robustness is critical for global interpretability. We present a model-agnostic, global mechanistic interpretability method to interpret the perturbation robustness of image models. This research is motivated by two key aspects. First, previous global interpretability works, in tandem with robustness benchmarks, e.g. mean corruption error (mCE), are not designed to directly interpret the mechanisms of perturbation robustness within image models. Second, we notice that the spectral signal-to-noise ratios (SNR) of perturbed natural images exponentially decay over the frequency. This power-law-like decay implies that: Low-frequency signals are generally more robust than high-frequency signals -- yet high classification accuracy can not be achieved by low-frequency signals alone. By applying Shapley value theory, our method axiomatically quantifies the predictive powers of robust features and non-robust features within an information theory framework. Our method, dubbed as \textbf{I-ASIDE} (\textbf{I}mage \textbf{A}xiomatic \textbf{S}pectral \textbf{I}mportance \textbf{D}ecomposition \textbf{E}xplanation), provides a unique insight into model robustness mechanisms. We conduct extensive experiments over a variety of vision models pre-trained on ImageNet to show that \textbf{I-ASIDE} can not only \textbf{measure} the perturbation robustness but also \textbf{provide interpretations} of its mechanisms.
A fundamental goal of scientific research is to learn about causal relationships. However, despite its critical role in the life and social sciences, causality has not had the same importance in Natural Language Processing (NLP), which has traditionally placed more emphasis on predictive tasks. This distinction is beginning to fade, with an emerging area of interdisciplinary research at the convergence of causal inference and language processing. Still, research on causality in NLP remains scattered across domains without unified definitions, benchmark datasets and clear articulations of the remaining challenges. In this survey, we consolidate research across academic areas and situate it in the broader NLP landscape. We introduce the statistical challenge of estimating causal effects, encompassing settings where text is used as an outcome, treatment, or as a means to address confounding. In addition, we explore potential uses of causal inference to improve the performance, robustness, fairness, and interpretability of NLP models. We thus provide a unified overview of causal inference for the computational linguistics community.
The problem of Multiple Object Tracking (MOT) consists in following the trajectory of different objects in a sequence, usually a video. In recent years, with the rise of Deep Learning, the algorithms that provide a solution to this problem have benefited from the representational power of deep models. This paper provides a comprehensive survey on works that employ Deep Learning models to solve the task of MOT on single-camera videos. Four main steps in MOT algorithms are identified, and an in-depth review of how Deep Learning was employed in each one of these stages is presented. A complete experimental comparison of the presented works on the three MOTChallenge datasets is also provided, identifying a number of similarities among the top-performing methods and presenting some possible future research directions.