Daily Papers

Accurate Point Cloud Registration (PCR) is an important task in 3D data processing, involving the estimation of a rigid transformation between two point clouds. While deep-learning methods have addressed key limitations of traditional non-learning approaches, such as sensitivity to noise, outliers, occlusion, and initialization, they are developed and evaluated on clean, dense, synthetic datasets (limiting their generalizability to real-world industrial scenarios). This paper introduces R3PM-Net, a lightweight, global-aware, object-level point matching network designed to bridge this gap by prioritizing both generalizability and real-time efficiency. To support this transition, two datasets, Sioux-Cranfield and Sioux-Scans, are proposed. They provide an evaluation ground for registering imperfect photogrammetric and event-camera scans to digital CAD models, and have been made publicly available. Extensive experiments demonstrate that R3PM-Net achieves competitive accuracy with unmatched speed. On ModelNet40, it reaches a perfect fitness score of 1 and inlier RMSE of 0.029 cm in only 0.007s, approximately 7 times faster than the state-of-the-art method RegTR. This performance carries over to the Sioux-Cranfield dataset, maintaining a fitness of 1 and inlier RMSE of 0.030 cm with similarly low latency. Furthermore, on the highly challenging Sioux-Scans dataset, R3PM-Net successfully resolves edge cases in under 50 ms. These results confirm that R3PM-Net offers a robust, high-speed solution for critical industrial applications, where precision and real-time performance are indispensable. The code and datasets are available at https://github.com/YasiiKB/R3PM-Net.

Layer normalization (LayerNorm) has been successfully applied to various deep neural networks to help stabilize training and boost model convergence because of its capability in handling re-centering and re-scaling of both inputs and weight matrix. However, the computational overhead introduced by LayerNorm makes these improvements expensive and significantly slows the underlying network, e.g. RNN in particular. In this paper, we hypothesize that re-centering invariance in LayerNorm is dispensable and propose root mean square layer normalization, or RMSNorm. RMSNorm regularizes the summed inputs to a neuron in one layer according to root mean square (RMS), giving the model re-scaling invariance property and implicit learning rate adaptation ability. RMSNorm is computationally simpler and thus more efficient than LayerNorm. We also present partial RMSNorm, or pRMSNorm where the RMS is estimated from p% of the summed inputs without breaking the above properties. Extensive experiments on several tasks using diverse network architectures show that RMSNorm achieves comparable performance against LayerNorm but reduces the running time by 7%~64% on different models. Source code is available at https://github.com/bzhangGo/rmsnorm.

Air pollution constitutes a global problem of paramount importance that affects not only human health, but also the environment. The existence of spatial and temporal data regarding the concentrations of pollutants is crucial for performing air pollution studies and monitor emissions. However, although observation data presents great temporal coverage, the number of stations is very limited and they are usually built in more populated areas. The main objective of this work is to create models capable of inferring pollutant concentrations in locations where no observation data exists. A machine learning model, more specifically the random forest model, was developed for predicting concentrations in the Iberian Peninsula in 2019 for five selected pollutants: NO_2, O_3 SO_2, PM10, and PM2.5. Model features include satellite measurements, meteorological variables, land use classification, temporal variables (month, day of year), and spatial variables (latitude, longitude, altitude). The models were evaluated using various methods, including station 10-fold cross-validation, in which in each fold observations from 10\% of the stations are used as testing data and the rest as training data. The R^2, RMSE and mean bias were determined for each model. The NO_2 and O_3 models presented good values of R^2, 0.5524 and 0.7462, respectively. However, the SO_2, PM10, and PM2.5 models performed very poorly in this regard, with R^2 values of -0.0231, 0.3722, and 0.3303, respectively. All models slightly overestimated the ground concentrations, except the O_3 model. All models presented acceptable cross-validation RMSE, except the O_3 and PM10 models where the mean value was a little higher (12.5934 mu g/m^3 and 10.4737 mu g/m^3, respectively).

This paper presents a differentially private approach to Kaplan-Meier estimation that achieves accurate survival probability estimates while safeguarding individual privacy. The Kaplan-Meier estimator is widely used in survival analysis to estimate survival functions over time, yet applying it to sensitive datasets, such as clinical records, risks revealing private information. To address this, we introduce a novel algorithm that applies time-indexed Laplace noise, dynamic clipping, and smoothing to produce a privacy-preserving survival curve while maintaining the cumulative structure of the Kaplan-Meier estimator. By scaling noise over time, the algorithm accounts for decreasing sensitivity as fewer individuals remain at risk, while dynamic clipping and smoothing prevent extreme values and reduce fluctuations, preserving the natural shape of the survival curve. Our results, evaluated on the NCCTG lung cancer dataset, show that the proposed method effectively lowers root mean squared error (RMSE) and enhances accuracy across privacy budgets (epsilon). At epsilon = 10, the algorithm achieves an RMSE as low as 0.04, closely approximating non-private estimates. Additionally, membership inference attacks reveal that higher epsilon values (e.g., epsilon geq 6) significantly reduce influential points, particularly at higher thresholds, lowering susceptibility to inference attacks. These findings confirm that our approach balances privacy and utility, advancing privacy-preserving survival analysis.

During lung radiotherapy, the position of infrared reflective objects on the chest can be recorded to estimate the tumor location. However, radiotherapy systems have a latency inherent to robot control limitations that impedes the radiation delivery precision. Prediction with online learning of recurrent neural networks (RNN) allows for adaptation to non-stationary respiratory signals, but classical methods such as RTRL and truncated BPTT are respectively slow and biased. This study investigates the capabilities of unbiased online recurrent optimization (UORO) to forecast respiratory motion and enhance safety in lung radiotherapy. We used 9 observation records of the 3D position of 3 external markers on the chest and abdomen of healthy individuals breathing during intervals from 73s to 222s. The sampling frequency was 10Hz, and the amplitudes of the recorded trajectories range from 6mm to 40mm in the superior-inferior direction. We forecast the 3D location of each marker simultaneously with a horizon value between 0.1s and 2.0s, using an RNN trained with UORO. We compare its performance with an RNN trained with RTRL, LMS, and offline linear regression. We provide closed-form expressions for quantities involved in the loss gradient calculation in UORO, thereby making its implementation efficient. Training and cross-validation were performed during the first minute of each sequence. On average over the horizon values considered and the 9 sequences, UORO achieves the lowest root-mean-square (RMS) error and maximum error among the compared algorithms. These errors are respectively equal to 1.3mm and 8.8mm, and the prediction time per time step was lower than 2.8ms (Dell Intel core i9-9900K 3.60 GHz). Linear regression has the lowest RMS error for the horizon values 0.1s and 0.2s, followed by LMS for horizon values between 0.3s and 0.5s, and UORO for horizon values greater than 0.6s.

With the volatile and complex nature of financial data influenced by external factors, forecasting the stock market is challenging. Traditional models such as ARIMA and GARCH perform well with linear data but struggle with non-linear dependencies. Machine learning and deep learning models, particularly Long Short-Term Memory (LSTM) networks, address these challenges by capturing intricate patterns and long-term dependencies. This report compares ARIMA and LSTM models in predicting the S&P 500 index, a major financial benchmark. Using historical price data and technical indicators, we evaluated these models using Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). The ARIMA model showed reasonable performance with an MAE of 462.1, RMSE of 614, and 89.8 percent accuracy, effectively capturing short-term trends but limited by its linear assumptions. The LSTM model, leveraging sequential processing capabilities, outperformed ARIMA with an MAE of 369.32, RMSE of 412.84, and 92.46 percent accuracy, capturing both short- and long-term dependencies. Notably, the LSTM model without additional features performed best, achieving an MAE of 175.9, RMSE of 207.34, and 96.41 percent accuracy, showcasing its ability to handle market data efficiently. Accurately predicting stock movements is crucial for investment strategies, risk assessments, and market stability. Our findings confirm the potential of deep learning models in handling volatile financial data compared to traditional ones. The results highlight the effectiveness of LSTM and suggest avenues for further improvements. This study provides insights into financial forecasting, offering a comparative analysis of ARIMA and LSTM while outlining their strengths and limitations.

We carried out a reproducibility study of InPars recipe for unsupervised training of neural rankers. As a by-product of this study, we developed a simple-yet-effective modification of InPars, which we called InPars-light. Unlike InPars, InPars-light uses only a freely available language model BLOOM and 7x-100x smaller ranking models. On all five English retrieval collections (used in the original InPars study) we obtained substantial (7-30%) and statistically significant improvements over BM25 in nDCG or MRR using only a 30M parameter six-layer MiniLM ranker. In contrast, in the InPars study only a 100x larger MonoT5-3B model consistently outperformed BM25, whereas their smaller MonoT5-220M model (which is still 7x larger than our MiniLM ranker), outperformed BM25 only on MS MARCO and TREC DL 2020. In a purely unsupervised setting, our 435M parameter DeBERTA v3 ranker was roughly at par with the 7x larger MonoT5-3B: In fact, on three out of five datasets, it slightly outperformed MonoT5-3B. Finally, these good results were achieved by re-ranking only 100 candidate documents compared to 1000 used in InPars. We believe that InPars-light is the first truly cost-effective prompt-based unsupervised recipe to train and deploy neural ranking models that outperform BM25.

Prediction of stock prices plays a significant role in aiding the decision-making of investors. Considering its importance, a growing literature has emerged trying to forecast stock prices with improved accuracy. In this study, we introduce an innovative approach for forecasting stock prices with greater accuracy. We incorporate external economic environment-related information along with stock prices. In our novel approach, we improve the performance of stock price prediction by taking into account variations due to future expected macroeconomic policy changes as investors adjust their current behavior ahead of time based on expected future macroeconomic policy changes. Furthermore, we incorporate macroeconomic variables along with historical stock prices to make predictions. Results from this strongly support the inclusion of future economic policy changes along with current macroeconomic information. We confirm the supremacy of our method over the conventional approach using several tree-based machine-learning algorithms. Results are strongly conclusive across various machine learning models. Our preferred model outperforms the conventional approach with an RMSE value of 1.61 compared to an RMSE value of 1.75 from the conventional approach.

Obesity, the leading cause of many non-communicable diseases, occurs mainly for eating more than our body requirements and lack of proper activity. So, being healthy requires heathy diet plans, especially for patients with comorbidities. But it is difficult to figure out the exact quantity of each nutrient because nutrients requirement varies based on physical and disease conditions. In our study we proposed a novel machine learning based system to predict the amount of nutrients one individual requires for being healthy. We applied different machine learning algorithms: linear regression, support vector machine (SVM), decision tree, random forest, XGBoost, LightGBM on fluid and 3 other major micronutrients: carbohydrate, protein, fat consumption prediction. We achieved high accuracy with low root mean square error (RMSE) by using linear regression in fluid prediction, random forest in carbohydrate prediction and LightGBM in protein and fat prediction. We believe our diet recommender system, OBESEYE, is the only of its kind which recommends diet with the consideration of comorbidities and physical conditions and promote encouragement to get rid of obesity.

In the era of mega-constellations, the need for accurate and publicly available information has become fundamental for satellite operators to guarantee the safety of spacecrafts and the Low Earth Orbit (LEO) space environment. This study critically evaluates the accuracy and reliability of publicly available ephemeris data for a LEO mega-constellation - Starlink. The goal of this work is twofold: (i) compare and analyze the quality of the data against high-precision numerical propagation. (ii) Leverage Physics-Informed Machine Learning to extract relevant satellite quantities, such as non-conservative forces, during the decay process. By analyzing two months of real orbital data for approximately 1500 Starlink satellites, we identify discrepancies between high precision numerical algorithms and the published ephemerides, recognizing the use of simplified dynamics at fixed thresholds, planned maneuvers, and limitations in uncertainty propagations. Furthermore, we compare data obtained from multiple sources to track and analyze deorbiting satellites over the same period. Empirically, we extract the acceleration profile of satellites during deorbiting and provide insights relating to the effects of non-conservative forces during reentry. For non-deorbiting satellites, the position Root Mean Square Error (RMSE) was approximately 300 m, while for deorbiting satellites it increased to about 600 m. Through this in-depth analysis, we highlight potential limitations in publicly available data for accurate and robust Space Situational Awareness (SSA), and importantly, we propose a data-driven model of satellite decay in mega-constellations.

We investigate imbalanced regression with tabular data that have an imbalance ratio larger than 1,000 ("highly imbalanced"). Accurately estimating the target values of rare instances is important in applications such as forecasting the intensity of rare harmful Solar Energetic Particle (SEP) events. For regression, the MSE loss does not consider the correlation between predicted and actual values. Typical inverse importance functions allow only convex functions. Uniform sampling might yield mini-batches that do not have rare instances. We propose CISIR that incorporates correlation, Monotonically Decreasing Involution (MDI) importance, and stratified sampling. Based on five datasets, our experimental results indicate that CISIR can achieve lower error and higher correlation than some recent methods. Also, adding our correlation component to other recent methods can improve their performance. Lastly, MDI importance can outperform other importance functions. Our code can be found in https://github.com/Machine-Earning/CISIR.

We present 360Zhinao models with 7B parameter size and context lengths spanning 4K, 32K and 360K, all available at https://github.com/Qihoo360/360zhinao. For rapid development in pretraining, we establish a stable and sensitive ablation environment to evaluate and compare experiment runs with minimal model size. Under such guidance, we perfect our data cleaning and composition strategies to pretrain 360Zhinao-7B-Base on 3.4T tokens. We also mainly emphasize data during alignment, where we strive to balance quantity and quality with filtering and reformatting. With tailored data, 360Zhinao-7B's context window is easily extended to 32K and 360K. RMs and RLHF are trained following SFT and credibly applied to specific tasks. All together these contributions lead to 360Zhinao-7B's competitive performance among models of similar size.

In this empirical article, we introduce INNAprop, an optimization algorithm that combines the INNA method with the RMSprop adaptive gradient scaling. It leverages second-order information and rescaling while keeping the memory requirements of standard DL methods as AdamW or SGD with momentum.After having recalled our geometrical motivations, we provide quite extensive experiments. On image classification (CIFAR-10, ImageNet) and language modeling (GPT-2), INNAprop consistently matches or outperforms AdamW both in training speed and accuracy, with minimal hyperparameter tuning in large-scale settings. Our code is publicly available at https://github.com/innaprop/innaprop.

Classical estimators for ARIMA parameters (MLE, CSS, OLS) assume Gaussian innovations, an assumption frequently violated in financial and economic data exhibiting asymmetric distributions with heavy tails. We develop and validate the second-order polynomial maximization method (PMM2) for estimating ARIMA(p,d,q) models with non-Gaussian innovations. PMM2 is a semiparametric technique that exploits higher-order moments and cumulants without requiring full distributional specification. Monte Carlo experiments (128,000 simulations) across sample sizes N in {100, 200, 500, 1000} and four innovation distributions demonstrate that PMM2 substantially outperforms classical methods for asymmetric innovations. For ARIMA(1,1,0) with N=500, relative efficiency reaches 1.58--1.90 for Gamma, lognormal, and χ^2(3) innovations (37--47\% variance reduction). Under Gaussian innovations PMM2 matches OLS efficiency, avoiding the precision loss typical of robust estimators. The method delivers major gains for moderate asymmetry (|γ_3| geq 0.5) and N geq 200, with computational costs comparable to MLE. PMM2 provides an effective alternative for time series with asymmetric innovations typical of financial markets, macroeconomic indicators, and industrial measurements. Future extensions include seasonal SARIMA models, GARCH integration, and automatic order selection.

Introduction: The paper addresses the challenging problem of predicting the short-term realized volatility of the Bitcoin price using order flow information. The inherent stochastic nature and anti-persistence of price pose difficulties in accurate prediction. Methods: To address this, we propose a method that transforms order flow data over a fixed time interval (snapshots) into images. The order flow includes trade sizes, trade directions, and limit order book, and is mapped into image colour channels. These images are then used to train both a simple 3-layer Convolutional Neural Network (CNN) and more advanced ResNet-18 and ConvMixer, with additionally supplementing them with hand-crafted features. The models are evaluated against classical GARCH, Multilayer Perceptron trained on raw data, and a naive guess method that considers current volatility as a prediction. Results: The experiments are conducted using price data from January 2021 and evaluate model performance in terms of root mean square error (RMSPE). The results show that our order flow representation with a CNN as a predictive model achieves the best performance, with an RMSPE of 0.85+/-1.1 for the model with aggregated features and 1.0+/-1.4 for the model without feature supplementation. ConvMixer with feature supplementation follows closely. In comparison, the RMSPE for the naive guess method was 1.4+/-3.0.

In lung radiotherapy, infrared cameras can track reflective objects on the chest to estimate tumor motion due to breathing, but treatment system latencies hinder radiation beam precision. Real-time recurrent learning (RTRL) is a potential solution that can learn patterns within non-stationary respiratory data but has high complexity. This study assesses the capabilities of resource-efficient online RNN algorithms, namely unbiased online recurrent optimization (UORO), sparse-1 step approximation (SnAp-1), and decoupled neural interfaces (DNI) to forecast respiratory motion during radiotherapy treatment accurately. We use time series containing the 3D positions of external markers on the chest of healthy subjects. We propose efficient implementations for SnAp-1 and DNI that compress the influence and immediate Jacobian matrices and accurately update the linear coefficients used in credit assignment estimation, respectively. Data was originally sampled at 10Hz; we resampled it at 3.33Hz and 30Hz to analyze the effect of the sampling rate on performance. We use UORO, SnAp-1, and DNI to forecast each marker's 3D position with horizons h<=2.1s (the time interval in advance for which the prediction is made) and compare them with RTRL, least mean squares, kernel support vector regression, and linear regression. RNNs trained online achieved similar or better accuracy than most previous works using larger training databases and deep learning, even though we used only the first minute of each sequence to predict motion within that exact sequence. SnAp-1 had the lowest normalized root mean square errors (nRMSEs) averaged over the horizon values considered, equal to 0.335 and 0.157, at 3.33Hz and 10.0Hz, respectively. Similarly, UORO had the lowest nRMSE at 30Hz, equal to 0.086. DNI's inference time (6.8ms per time step at 30Hz, Intel Core i7-13700 CPU) was the lowest among the RNN methods.

Transformers have achieved great success in machine learning applications. Normalization techniques, such as Layer Normalization (LayerNorm, LN) and Root Mean Square Normalization (RMSNorm), play a critical role in accelerating and stabilizing the training of Transformers. While LayerNorm recenters and rescales input vectors, RMSNorm only rescales the vectors by their RMS value. Despite being more computationally efficient, RMSNorm may compromise the representation ability of Transformers. There is currently no consensus regarding the preferred normalization technique, as some models employ LayerNorm while others utilize RMSNorm, especially in recent large language models. It is challenging to convert Transformers with one normalization to the other type. While there is an ongoing disagreement between the two normalization types, we propose a solution to unify two mainstream Transformer architectures, Pre-LN and Pre-RMSNorm Transformers. By removing the inherent redundant mean information in the main branch of Pre-LN Transformers, we can reduce LayerNorm to RMSNorm, achieving higher efficiency. We further propose the Compressed RMSNorm (CRMSNorm) and Pre-CRMSNorm Transformer based on a lossless compression of the zero-mean vectors. We formally establish the equivalence of Pre-LN, Pre-RMSNorm, and Pre-CRMSNorm Transformer variants in both training and inference. It implies that Pre-LN Transformers can be substituted with Pre-(C)RMSNorm counterparts at almost no cost, offering the same arithmetic functionality along with free efficiency improvement. Experiments demonstrate that we can reduce the training and inference time of Pre-LN Transformers by 1% - 10%.

Room impulse responses are a core resource for dereverberation, robust speech recognition, source localization, and room acoustics estimation. We present RIR-Mega, a large collection of simulated RIRs described by a compact, machine friendly metadata schema and distributed with simple tools for validation and reuse. The dataset ships with a Hugging Face Datasets loader, scripts for metadata checks and checksums, and a reference regression baseline that predicts RT60 like targets from waveforms. On a train and validation split of 36,000 and 4,000 examples, a small Random Forest on lightweight time and spectral features reaches a mean absolute error near 0.013 s and a root mean square error near 0.022 s. We host a subset with 1,000 linear array RIRs and 3,000 circular array RIRs on Hugging Face for streaming and quick tests, and preserve the complete 50,000 RIR archive on Zenodo. The dataset and code are public to support reproducible studies.

Evaluating anomaly detection algorithms in time series data is critical as inaccuracies can lead to flawed decision-making in various domains where real-time analytics and data-driven strategies are essential. Traditional performance metrics assume iid data and fail to capture the complex temporal dynamics and specific characteristics of time series anomalies, such as early and delayed detections. We introduce Proximity-Aware Time series anomaly Evaluation (PATE), a novel evaluation metric that incorporates the temporal relationship between prediction and anomaly intervals. PATE uses proximity-based weighting considering buffer zones around anomaly intervals, enabling a more detailed and informed assessment of a detection. Using these weights, PATE computes a weighted version of the area under the Precision and Recall curve. Our experiments with synthetic and real-world datasets show the superiority of PATE in providing more sensible and accurate evaluations than other evaluation metrics. We also tested several state-of-the-art anomaly detectors across various benchmark datasets using the PATE evaluation scheme. The results show that a common metric like Point-Adjusted F1 Score fails to characterize the detection performances well, and that PATE is able to provide a more fair model comparison. By introducing PATE, we redefine the understanding of model efficacy that steers future studies toward developing more effective and accurate detection models.

Motion artefacts in magnetic resonance brain images can have a strong impact on diagnostic confidence. The assessment of MR image quality is fundamental before proceeding with the clinical diagnosis. Motion artefacts can alter the delineation of structures such as the brain, lesions or tumours and may require a repeat scan. Otherwise, an inaccurate (e.g. correct pathology but wrong severity) or incorrect diagnosis (e.g. wrong pathology) may occur. "Image quality assessment" as a fast, automated step right after scanning can assist in deciding if the acquired images are diagnostically sufficient. An automated image quality assessment based on the structural similarity index (SSIM) regression through a residual neural network is proposed in this work. Additionally, a classification into different groups - by subdividing with SSIM ranges - is evaluated. Importantly, this method predicts SSIM values of an input image in the absence of a reference ground truth image. The networks were able to detect motion artefacts, and the best performance for the regression and classification task has always been achieved with ResNet-18 with contrast augmentation. The mean and standard deviation of residuals' distribution were mu=-0.0009 and sigma=0.0139, respectively. Whilst for the classification task in 3, 5 and 10 classes, the best accuracies were 97, 95 and 89\%, respectively. The results show that the proposed method could be a tool for supporting neuro-radiologists and radiographers in evaluating image quality quickly.

With the rapid deployment of SCADA systems, how to effectively analyze industrial signals and detect abnormal states is an urgent need for the industry. Due to the significant heterogeneity of these signals, which we summarize as the M5 problem, previous works only focus on small sub-problems and employ specialized models, failing to utilize the synergies between modalities and the powerful scaling law. However, we argue that the M5 signals can be modeled in a unified manner due to the intrinsic similarity. As a result, we propose FISHER, a Foundation model for multi-modal Industrial Signal compreHEnsive Representation. To support arbitrary sampling rates, FISHER considers the increment of sampling rate as the concatenation of sub-band information. Specifically, FISHER takes the STFT sub-band as the modeling unit and adopts a teacher student SSL framework for pre-training. We also develop the RMIS benchmark, which evaluates the representations of M5 industrial signals on multiple health management tasks. Compared with top SSL models, FISHER showcases versatile and outstanding capabilities with a general performance gain up to 5.03%, along with much more efficient scaling curves. We also investigate the scaling law on downstream tasks and derive potential avenues for future works. FISHER is now open-sourced on https://github.com/jianganbai/FISHER

We propose a simple multiple outlier identification method for parametric location-scale and shape-scale models when the number of possible outliers is not specified. The method is based on a result giving asymptotic properties of extreme z-scores. Robust estimators of model parameters are used defining z-scores. An extensive simulation study was done for comparing of the proposed method with existing methods. For the normal family, the method is compared with the well known Davies-Gather, Rosner's, Hawking's and Bolshev's multiple outlier identification methods. The choice of an upper limit for the number of possible outliers in case of Rosner's test application is discussed. For other families, the proposed method is compared with a method generalizing Gather-Davies method. In most situations, the new method has the highest outlier identification power in terms of masking and swamping values. We also created R package outliersTests for proposed test.

Pretraining methods are typically compared by evaluating the accuracy of linear classifiers, transfer learning performance, or visually inspecting the representation manifold's (RM) lower-dimensional projections. We show that the differences between methods can be understood more clearly by investigating the RM directly, which allows for a more detailed comparison. To this end, we propose a framework and new metric to measure and compare different RMs. We also investigate and report on the RM characteristics for various pretraining methods. These characteristics are measured by applying sequentially larger local alterations to the input data, using white noise injections and Projected Gradient Descent (PGD) adversarial attacks, and then tracking each datapoint. We calculate the total distance moved for each datapoint and the relative change in distance between successive alterations. We show that self-supervised methods learn an RM where alterations lead to large but constant size changes, indicating a smoother RM than fully supervised methods. We then combine these measurements into one metric, the Representation Manifold Quality Metric (RMQM), where larger values indicate larger and less variable step sizes, and show that RMQM correlates positively with performance on downstream tasks.

We propose a new sampler for robust estimators that always selects the sample with the highest probability of consisting only of inliers. After every unsuccessful iteration, the inlier probabilities are updated in a principled way via a Bayesian approach. The probabilities obtained by the deep network are used as prior (so-called neural guidance) inside the sampler. Moreover, we introduce a new loss that exploits, in a geometrically justifiable manner, the orientation and scale that can be estimated for any type of feature, e.g., SIFT or SuperPoint, to estimate two-view geometry. The new loss helps to learn higher-order information about the underlying scene geometry. Benefiting from the new sampler and the proposed loss, we combine the neural guidance with the state-of-the-art MAGSAC++. Adaptive Reordering Sampler with Neurally Guided MAGSAC (ARS-MAGSAC) is superior to the state-of-the-art in terms of accuracy and run-time on the PhotoTourism and KITTI datasets for essential and fundamental matrix estimation. The code and trained models are available at https://github.com/weitong8591/ars_magsac.