IFW-BLS: Dual-Robust Broad Learning System with Intuitionistic Fuzzy Wave Loss

Broad Learning System is an efficient randomized learning model that expands network width through feature and enhancement nodes and estimates the output weights without deep backpropagation. Its standard least-squares training, however, is vulnerable in two different ways: (i) large residuals caused by noise, outliers, or corrupted labels can dominate the objective, and (ii) all samples are treated as equally reliable even when some lie in ambiguous or locally conflicting regions. This paper proposes IFW-BLS, an Intuitionistic Fuzzy Wave Broad Learning System that addresses these two sources of fragility within one optimization model. The first robustness mechanism is residual-level protection, obtained by replacing the squared loss with the bounded, smooth, and asymmetric wave loss. Boundedness prevents extreme residuals from receiving unbounded influence, while asymmetry allows positive and negative deviations to be penalized differently when the dominant error direction varies. The second mechanism is sample-level credibility control, obtained through intuitionistic fuzzy scores that combine global class-center consistency with local neighborhood conflict. The resulting model evaluates the wave loss on credibility-weighted residuals, so unreliable samples are down-weighted before the bounded loss further limits the effect of extreme errors. A Nesterov accelerated gradient based optimizer is used to solve the proposed objective, avoiding the explicit matrix inversion used in conventional BLS. Experiments on UCI benchmark datasets validate the superiority of the proposed IFW-BLS model over the baseline models; additional corruption experiments also show more stable performance than BLS under noise and outlier contamination.

Information Density Imbalance in Visual Object Detection

In object detection, the number of instances is typically used to determine whether a dataset exhibits a long-tailed distribution, implicitly assuming that the model will perform poorly on categories with fewer instances. This assumption has led to extensive research on category bias in datasets with imbalanced instance numbers. However, even in datasets where instance numbers are relatively balanced, models still exhibit category bias, indicating that instance count alone cannot explain this phenomenon. In this work, we first introduce the concept and measurement of information density. We then observe a significant negative correlation between a category's information density and its accuracy, and we investigate how the training process impacts this relationship. Empirical studies suggest that information density imbalance may be a potential source of category bias. To preliminarily validate the potential of information density, we made simple improvements to three advanced object detection loss functions using this concept. Experiments on the Pascal VOC, COCO-LT, and LVIS datasets demonstrate that information density can significantly reduce model bias while effectively enhancing the overall performance of existing loss functions. This study provides a new perspective for understanding the generalized bias phenomenon in object detection models and offers new tools for designing fairer loss functions and training strategies.

Evaluating Loss Functions in Differentiable Out-of-Domain Sound-Matching with Partial Parameter Distance

In out-of-domain (OOD) sound-matching, a synthesizer is optimized to mimic a sound it did not generate. OOD evaluation of loss functions is underexplored in part because the standard "parameter loss" metric requires a shared parameter space between target and imitator, which OOD settings lack. We introduce Partial Parameter Distance (PPD), which applies parameter loss only to the critical parameters that mismatched synthesizers share (e.g., filter cutoffs), enabling automatically evaluated OOD experiments; we verify its results with blinded listening tests. Across seven scenarios involving band-pass filtering, amplitude modulation, and pitch-bending, we evaluate four differentiable loss functions (SIMSE_Spec, L1_Spec, JTFS, DTW_Envelope). Loss-function effectiveness remains tightly coupled to the method of synthesis: SIMSE_Spec excels at filter-cutoff recovery, DTW_Envelope at amplitude-modulation recovery, and JTFS at smooth pitch trajectories. Parameter-based evaluation agrees with listening tests on the top-ranked loss function in five of seven scenarios, demonstrating its utility as a diagnostic tool.

Robust Losses from Univariate Base Functions for Noisy-Label Learning

Learning with noisy labels is a fundamental problem in training reliable deep neural networks. Robust loss functions provide a direct and effective way to mitigate the adverse effects of label noise. However, most existing robust losses are designed directly at the level of the final multiclass objective, which makes it difficult to systematically characterize and extend their robustness properties. In this paper, we propose a general framework that constructs robust multiclass losses from univariate base functions. By defining mapping operators from base functions to multiclass losses, the robustness of the induced losses can be characterized through simple properties of the base functions. We develop two complementary construction schemes, Target Separation and Binary Reduction, corresponding to inter-class independent and inter-class dependent formulations, respectively. For both schemes, we analyze their symmetry and asymmetry properties and derive corresponding sufficient conditions, which provide theoretical criteria for noise-robust loss design. The proposed framework also provides a new route to constructing symmetric losses, serving as a complement to normalization-based symmetric loss designs. Extensive experiments on synthetic and real-world noisy-label benchmarks demonstrate that the proposed losses achieve competitive or superior performance under various noise settings.

Robust XGBoosting for Regression

XGBoost is a very popular and powerful method for prediction. It iteratively fits simple decision trees to the residuals of the previous step. An efficient and scalable implementation is available. The standard loss function for XGBoost is the quadratic loss, but a Huber loss can also be used. In this paper, we study the robustness of XGBoost and show that its performance can be affected by vertical outliers and leverage points. To address this, we explore alternative loss functions, based on M-, S-, and τ -estimators from robust regression. Our results indicate that a two-step procedure, referred to as MM-XGBoost, provides the best trade-off between robustness and prediction accuracy.

Comparison of Loss Functions for Robust Deep Learning-based Echocardiography Segmentation when Learning with Partially Labelled Data from Multiple Domains

Echocardiography is the first imaging modality used for assessing cardiac function, and accurate segmentation of cardiac structures is essential for deriving biomarkers. However, the development of effective automated segmentation models for multiple cardiac structures is challenged by the difficulty of training on datasets from different sources that are often partially-labelled. This study aims to address this challenge by evaluating the performance of three loss functions - adaptive categorical cross entropy (aCCE) loss, marginal loss, and the adaptive binary cross entropy (aBCE) loss - in handling partially-labelled data. We conduct a comprehensive comparison of these loss functions across multiple scenarios and network architectures: intra-domain and inter-domain tasks, with both single and multiple partial-labels, and varying proportions of fully-labelled to partially-labelled data. Our experiments reveal that all three loss functions exhibit strong performance in intra-domain segmentation tasks, effectively handling label variations within the same domain. For inter-domain tasks, where models are trained on datasets with a domain shift, the aBCE and marginal losses show superior performance when dealing with the case of one label being missing from some training examples. In scenarios involving more than one label being missing, marginal loss outperforms the other methods, demonstrating its robustness in such complex conditions. These results highlight the strengths of each loss function depending on the labelling scenario, emphasizing the importance of selecting the appropriate loss function to optimize model performance. This study represents the first investigation of techniques for handling partially-labelled data from multiple different domains in echocardiography segmentation and provides a comprehensive comparison of loss-based solutions.

Weighted Score-Oriented Losses for Temporally Localized Event Prediction

Operational event-detection systems are rarely assessed by pointwise accuracy alone. In anomaly detection, changepoint detection, and warning systems, the utility of an alarm depends on its temporal position relative to an event. This produces a score-loss mismatch. Neural networks are commonly trained with classical loss functions, such as cross-entropy, whereas deployment decisions are obtained by thresholding network predictions, merging alarms through post-processing rules, and evaluating them with event-based metrics defined by detection windows and false-alarm costs. This paper studies a temporally localized specialization of weighted score-oriented loss (wSOL) for event prediction. Starting from score-oriented losses based on expected confusion matrices and from the weighted SOL framework of Marchetti et al., we consider temporal weights that discount near-event false positives and reduce false-negative penalties when an event is preceded by an admissible alarm. The resulting objective is differentiable with respect to the network predictions, and therefore can be optimized by back-propagation. It can be instantiated with balanced accuracy, true skill statistic, F1, critical success index, and related confusion-matrix scores. We evaluate the proposed approach by comparing cross-entropy, unweighted score-oriented loss, and wSOL on three benchmark datasets for time-series event prediction and detection. The results show that wSOL can improve performance when the evaluation utility is localized in time and is not already encoded by the pointwise labels.

Alternate loss functions and regression models that achieve robustness to outliers by modulating the learning rate

Most real-world datasets used for training supervised learning models are contaminated with noisy data and outliers leading to large prediction errors. This paper proposes a new approach for achieving robustness where the learning rate is modulated by a factor that is sensitive to outliers. In this approach a reduction of the learning rate is shown to be achieved by using alternate loss functions that are infinitely differentiable, strictly convex or quasiconvex and more closely approximate the absolute error than Huber and log-cosh losses. A comparison of the performance of regression models trained with different loss functions on a wide variety of benchmarks and datasets is presented to demonstrate the superior performance of the Square Root Loss (SRL) and Smooth Mean Absolute Error (SMAE) losses proposed in this paper. Two new robust linear regression models are presented. Highly vectorized robust parameter update formulae that take advantage of modern GPUs for both stochastic and batch gradient descent are presented.

Towards Robust Training in NNGPT AutoML Pipeline: A Loss-Optimizer Pairing Selection Study

The choice of loss function and optimizer is an important decision, that shapes further model training. Yet automated architecture search pipelines (AutoML) benefits significantly more from the optimal pairing selection and vice versa. This paper investigates whether a single recipe is sufficient for heterogeneous architecture pools, or whether the optimal pairing varies across structurally diverse models. We conduct a systematic empirical study of all $3 \times 6 = 18$ combinations of six optimizers (SGD+Momentum, Adam, AdamW, RMSprop, Adagrad, Adadelta), paired with three loss functions: Cross-Entropy (CEL), Negative Log-Likelihood (NLL), and the recently introduced genetically evolved NGL loss across the base models presented in LEMUR heterogeneous architecture pool on six image classification datasets (CelebA-Gender, CIFAR-10, CIFAR-100, ImageNette, MNIST, SVHN). The 18 loss-optimizer configurations are applied to each of the 33 compatible base architectures taken from the LEMUR pool, resulting in 594 variants that were generated fully automatically by a source-level injection pipeline and evaluated under fixed hyperparameters, ensuring that observed accuracy differences are attributable solely to the loss-optimizer pairing. Our results confirm that no single pairing is universally optimal. Cross-Entropy with Adam or AdamW is the most robust choice across architecture families and datasets. NGL is a competitive alternative to CEL on standard convolutional classifiers, but only when paired with adaptive optimizers; it degrades substantially with SGD or accumulation-based methods. Adagrad and Adadelta consistently underperform under fixed hyperparameters regardless of loss function, highlighting their sensitivity to learning rate tuning. These findings provide actionable guidance for loss-optimizer selection within NNGPT Framework.

Tailoring Strictly Proper Scoring Rules for Downstream Tasks: An Application to Causal Inference

Probabilistic models are typically trained using task-agnostic objectives like log-loss, which can lead to significant errors in downstream estimation. This disconnect is especially critical in Inverse Probability Weighting (IPW) for causal inference, where propensity score errors near $0$ and $1$ often lead to high bias and variance. We propose a principled framework for deriving task-specific strictly proper scoring rules by matching the local curvature of the downstream error metric. We apply this to the Average Treatment Effect (ATE) estimation, deriving a closed-form loss and its corresponding canonical probability mapping that can be readily integrated with any model like a neural network or a gradient boosting algorithm. Extensive evaluations on causal inference benchmarks demonstrate that our tailored objective consistently outperforms standard likelihood-based and covariate-balancing approaches.

Linear-Core Surrogates: Smooth Loss Functions with Linear Rates for Classification and Structured Prediction

The choice of loss function in classification involves a fundamental trade-off: smooth losses (like Cross-Entropy) enable fast optimization rates but yield slow square-root consistency bounds, while piecewise-linear losses (like Hinge) offer fast linear consistency rates but suffer from non-differentiability. We propose Linear-Core (LC) Surrogates, a new family of convex loss functions that resolve this tension by stitching a linear core to a smooth tail. We prove that these surrogates are differentiable everywhere while retaining strict linear $H$-consistency bounds, effectively combining the optimization benefits of smoothness with the statistical efficiency of margin-based losses. In the structured prediction setting, we show that this smoothness unlocks a massive computational and energy advantage: it allows for an unbiased stochastic gradient estimator that bypasses the quadratic complexity $O(|\mathscr{Y}|^2)$ of exact inference (e.g., Viterbi). Empirically, our method achieves a 23$\times$ speedup over Structured SVMs on large-vocabulary sequence tagging tasks and demonstrates superior robustness to instance-dependent label noise, outperforming Cross-Entropy by 2.6% on corrupted CIFAR-10.

Instance Awareness of Multi-class Semantic Segmentation Loss Functions

Instance-sensitive losses for semantic segmentation such as blob loss and CC loss were designed to address instance imbalance, ensuring small lesions generate the same gradient as large ones, but operate only on single-class segmentation. In multi-class settings, class imbalance poses an additional problem: rare classes with few instances receive a disproportionately small share of the training signal. We show that extending instance-sensitive losses to multi-class segmentation via a one-vs-rest class decomposition repurposes them to also address class imbalance, as uniform averaging over classes ensures each class contributes equally regardless of frequency. We further show that inverse-size weighting, which destabilizes training when applied globally due to weight imbalances across rare and common classes, becomes effective when integrated within the per-component loss, confining the reweighting to each component's spatial context. On the BraTS-METS 2025 dataset (260 test cases), multi-class CC loss improves foreground Dice (0.64 +/- 0.26 vs. 0.59 +/- 0.27 baseline) and rare-class Dice, while maintaining Panoptic Quality at DSC threshold 0.5. Multi-class blob loss achieves the best Panoptic Quality at threshold 0.5 (0.40 +/- 0.24 vs. 0.38 +/- 0.25 baseline) and recognition quality (0.53 +/- 0.29 vs. 0.49 +/- 0.30). Integrating inverse-size weighting within the per-component loss increases rare-class Dice to 0.44 +/- 0.36 at the cost of reduced detection quality.