We present a Directional Consistency (DC)-driven Adaptive Density Control (ADC) for 3DGaussian Splatting (DC4GS). Whereas the conventional ADC bases its primiti the DC ve of splitting the gradients on the magnitudes into ADC, and of positional realize it gradients, through the we angular further incorporate coherence of the gradients.

Unsupervised anomaly detection is a critical task in many high-social-impact applications such as finance, healthcare, social media, and cybersecurity, where demographics involving age, gender, race, disease, etc. are used frequently. In these scenarios, possible bias from anomaly detection systems can lead to unfair treatment for different groups and even exacerbate social bias. In this work, first, we thoroughly analyze the feasibility and necessary assumptions for ensuring group fairness in unsupervised anomaly detection. Second, we propose a novel fairnessaware anomaly detection method FairAD. From the normal training data, FairAD learns a projection to map data of different demographic groups to a common target distribution that is simple and compact, and hence provides a reliable base to estimate the density of the data. The density can be directly used to identify anomalies while the common target distribution ensures fairness between different groups. Furthermore, we propose a threshold-free fairness metric that provides a global view for model's fairness, eliminating dependence on manual threshold selection. Experiments on real-world benchmarks demonstrate that our method achieves an improved trade-off between detection accuracy and fairness under both balanced and skewed data across different groups.

In this paper, we study the Karush-Kuhn-Tucker (KKT) points of the associated maximum-margin problem in homogeneous neural networks, including fullyconnected and convolutional neural networks. In particular, We investigates the relationship between such KKT points across networks of different widths generated. We introduce and formalize the KKT point embedding principle, establishing that KKT points of a homogeneous network's max-margin problem (PΦ) can be embedded into the KKT points of a larger network's problem (P Φ) via specific linear isometric transformations. We rigorously prove this principle holds for neuron splitting in fully-connected networks and channel splitting in convolutional neural networks. Furthermore, we connect this static embedding to the dynamics of gradient flow training with smooth losses. We demonstrate that trajectories initiated from appropriately mapped points remain mapped throughout training and that the resulting ω-limit sets of directions are correspondingly mapped, thereby preserving the alignment with KKT directions dynamically when directional convergence occurs. We conduct several experiments to justify that trajectories are preserved. Our findings offer insights into the effects of network width, parameter redundancy, and the structural connections between solutions found via optimization in homogeneous networks of varying sizes.

As we increase the number of features in the SAE, hierarchical features tend to split into finer features ("math" may split into "algebra", "geometry", etc.), a phenomenon referred to as feature splitting. However, we show that sparse decomposition and splitting of hierarchical features is not robust. Specifically, we show that seemingly monosemantic features fail to fire where they should, and instead get "absorbed" into their children features. We coin this phenomenon feature absorption, and show that it is caused by optimizing for sparsity in SAEs whenever the underlying features form a hierarchy. We introduce a metric to detect absorption in SAEs, and validate our findings empirically on hundreds of LLM SAEs. Our investigation suggests that varying SAE sizes or sparsity is insufficient to solve this issue. We discuss the implications of feature absorption in SAEs and some potential approaches to solve the fundamental theoretical issues before SAEs can be used for interpreting LLMs robustly and at scale.

We present a Directional Consistency (DC)-driven Adaptive Density Control (ADC) for 3D Gaussian Splatting (DC4GS). Whereas the conventional ADC bases its primitive splitting on the magnitudes of positional gradients, we further incorporate the DC of the gradients into ADC, and realize it through the angular coherence of the gradients.

In this paper, we study the Karush-Kuhn-Tucker (KKT) points of the associated maximum-margin problem in homogeneous neural networks, including fully-connected and convolutional neural networks. In particular, We investigates the relationship between such KKT points across networks of different widths generated. We introduce and formalize the \textbf{KKT point embedding principle}, establishing that KKT points of a homogeneous network's max-margin problem ($P_{\Phi}$) can be embedded into the KKT points of a larger network's problem ($P_{\tilde{\Phi}}$) via specific linear isometric transformations. We rigorously prove this principle holds for neuron splitting in fully-connected networks and channel splitting in convolutional neural networks. Furthermore, we connect this static embedding to the dynamics of gradient flow training with smooth losses. We demonstrate that trajectories initiated from appropriately mapped points remain mapped throughout training and that the resulting $\omega$-limit sets of directions are correspondingly mapped, thereby preserving the alignment with KKT directions dynamically when directional convergence occurs. We conduct several experiments to justify that trajectories are preserved. Our findings offer insights into the effects of network width, parameter redundancy, and the structural connections between solutions found via optimization in homogeneous networks of varying sizes.

Contents1 1 PrinCut 22 1.1 How to use PrinCut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Do not distribute. 1 PrinCut22 1.1 How to use PrinCut23 The PrinCut GUI is shown in Figure 1. PrinCut is a MATLAB app, and its package is also provided24 in the supplementary. The left shows raw data without annotation. The right shows both raw data and annotation overlay.

Formal model evaluation methods typically certify that a model satisfies a prescribed target key performance indicator (KPI) level. However, in many applications, the relevant target KPI level may not be known a priori, and the user may instead wish to compare candidate models by analyzing the full trade-offs between performance and reliability achievable at test time by the models. This task, requiring the reliable estimate of the test-time KPI distributions, is made more complicated by the fact that the same data must often be used both to pre-select a subset of candidate models and to estimate their KPI distributions, causing a potential post-selection bias. In this work, we introduce post-selection distributional model evaluation (PS-DME), a general framework for statistically valid distributional model assessment after arbitrary data-dependent model pre-selection. Building on e-values, PS-DME controls post-selection false coverage rate (FCR) for the distributional KPI estimates and is proved to be more sample efficient than a baseline method based on sample splitting. Experiments on synthetic data, text-to-SQL decoding with large language models, and telecom network performance evaluation demonstrate that PS-DME enables reliable comparison of candidate configurations across a range of reliability levels, supporting the statistically reliable exploration of performance--reliability trade-offs.

First, wepresent a unified framework that encompasses previous methods.