The loss landscapes of neural networks contain minima and saddle points that may be connected in flat regions or appear in isolation. We identify and characterize a special structure in the loss landscape: channels along which the loss decreases extremely slowly, while the output weights of at least two neurons, ai and aj, diverge to infinity, and their input weight vectors, wi and wj, become equal to each other. At convergence, the two neurons implement a gated linear unit: aiσ(wi x) + ajσ(wj x) cσ(w x) + (v x)σ (w x). Geometrically, these channels to infinity are asymptotically parallel to symmetry-induced lines of critical points. Gradient flow solvers, and related optimization methods like SGD or ADAM, reach the channels with high probability in diverse regression settings, but without careful inspection they look like flat local minima with finite parameter values. Our characterization provides a comprehensive picture of these quasi-flat regions in terms of gradient dynamics, geometry, and functional interpretation. The emergence of gated linear units at the end of the channels highlights a surprising aspect of the computational capabilities of fully connected layers.

Vision-language models (VLMs) like CLIP exhibit strong zero-shot capabilities but often fail to generalize under distribution shifts. Test-time adaptation (TTA) allows models to update at inference time without labeled data, typically via entropy minimization. However, this objective is fundamentally misaligned with the contrastive image-text training of VLMs, limiting adaptation performance and introducing failure modes such as pseudo-label drift and class collapse. We propose CLIPTTA, a new gradient-based TTA method for vision-language models that leverages a soft contrastive loss aligned with CLIP's pre-training objective. We provide a theoretical analysis of CLIPTTA's gradients, showing how its batchaware design mitigates the risk of collapse. We further extend CLIPTTA to the open-set setting, where both in-distribution (ID) and out-of-distribution (OOD) samples are encountered, using an Outlier Contrastive Exposure (OCE) loss to improve OOD detection. Evaluated on 75 datasets spanning diverse distribution shifts, CLIPTTA consistently outperforms entropy-based objectives and is highly competitive with state-of-the-art TTA methods, outperforming them on a large number of datasets and exhibiting more stable performance across diverse shifts. Source code is available at: CLIPTTARepository.

Trump turns on the charm after extended'alpha' handshake with Macron and kisses for Brigitte at Palace of Versailles Sensational REAL reason Jelly Roll is divorcing Bunnie XO: Insiders reveal'preacher's wife' bombshell that's the talk of Nashville... truth about legendary rocker cuckolding rumor... and G-string mishap LIZ JONES: The cracks in Harry and Meghan's perfect facade have started to show. It's so obvious he's tiring of her tone-deaf approach... and I predict there's serious trouble in store Taylor Swift's bottomless thirst for attention, her greed and sheer tackiness are now truly unbearable... this latest stunt has shown her true colors: MAUREEN CALLAHAN NBA star's fiancee breaks her silence after friend, 26, mysteriously dropped dead at her luxury bachelorette party in St Barts Luxury fashion tycoon beloved by the stars hangs her head in shame as she's indicted for allegedly exploiting her workers and stealing $50k from their wages Jeff Bezos mercilessly mocked for taking'fake phone calls' when out with wife Lauren Sanchez Anguished family members flee court over sick details of Gilgo Beach murderer's kill room: Live updates'She has not been transparent... the damage has been done': How influencer Elle Darby'betrayed' thousands of young female fans...as insiders tell MOLLY CLAYTON how she cashed in As a divorced mother-of-three, cocaine was my little treat while my fellow middle-class friends had a few wines. What happened next was every family's worst nightmare... this is my warning to mums who'dabble' Desperate search for mom-of-three who hasn't been seen in three days as husband pleads for her return The shocking betrayal behind Jelly Roll's divorce from Bunnie XO is so utterly cruel... but have you yet spotted her revenge: JACQUELYNN POWERS Devastating supply crunch forces Apple to raise prices on iPhones and other devices, calling the move'unavoidable' Jeff's Dream Team: Bezos recruits world's top architects to build most expensive mega mansion on Billionaire Bunker island The Ring star Daveigh Chase's friends searched for her on LA's Skid Row in months before her shock death at 35 Watch horrifying drone video that follows woman's plunge to death after bungee team threw her from bridge without rope Renowned scientist Neil deGrasse Tyson tells US government to'Show the alien!' after latest UFO disclosure Astrophysicist Neil deGrasse Tyson wants the US government to'Show the alien!' after the latest UFO disclosure from the Trump administration . Tyson, 67, joined The Fox News Rundown on Monday, explaining how the overwhelming amount of irrefutable evidence should finally be topped off with a picture of an extraterrestrial being. 'Is it too much to ask at this point for them to just show the alien?

Counterfactual explanations play a pivotal role in explainable artificial intelligence (XAI) by offering intuitive, human-understandable alternatives that elucidate machine learning model decisions. Despite their significance, existing methods for generating counterfactuals often require constant access to the predictive model, involve computationally intensive optimization for each instance and lack the flexibility to adapt to new user-defined constraints without retraining. In this paper, we propose DiCoFlex, a novel model-agnostic, conditional generative framework that produces multiple diverse counterfactuals in a single forward pass. Leveraging conditional normalizing flows trained solely on labeled data, DiCoFlex addresses key limitations by enabling real-time user-driven customization of constraints such as sparsity and actionability at inference time. Extensive experiments on standard benchmark datasets show that DiCoFlex outperforms existing methods in terms of validity, diversity, proximity, and constraint adherence, making it a practical and scalable solution for counterfactual generation in sensitive decision-making domains.

The role of reinforcement learning (RL) in enhancing the reasoning of large language models (LLMs) is becoming increasingly significant. Despite the success of RL in many scenarios, there are still many challenges in improving the reasoning of LLMs. One key challenge is the sparse reward, which introduces more training variance in policy optimization and makes it difficult to obtain a good estimation for value function in Actor-Critic (AC) methods. To address these issues, we introduce Direct Advantage-Based Policy Optimization (DAPO), a novel step-level offline RL algorithm with theoretical guarantees for enhancing the reasoning abilities of LLMs. Unlike response-level methods (such as DPO and GRPO) that the update directions of all reasoning steps are governed by the outcome reward uniformly, DAPO employs a critic function to provide step-level dense signals for policy optimization. Additionally, the actor and critic in DAPO are trained independently, ensuring that critic is a good estimation of true state value function and avoiding the co-training instability observed in standard AC methods. We train DAPO on mathematical and code problems and then evaluate its performance on multiple benchmarks. Our results show that DAPO can effectively enhance the mathematical and code capabilities on both SFT models and RL models, demonstrating the effectiveness of DAPO.

Offline reinforcement learning in high-dimensional, discrete action spaces is challenging due to the exponential scaling of the joint action space with the number of sub-actions and the complexity of modeling sub-action dependencies. Existing methods either exhaustively evaluate the action space, making them computationally infeasible, or factorize Q-values, failing to represent joint sub-action effects. We propose Branch Value Estimation (BraVE), a value-based method that uses tree-structured action traversal to evaluate a linear number of joint actions while preserving dependency structure. BraVE outperforms prior offline RL methods by up to 20 in environments with over four million actions. 2

Measuring the alignment between representations lets us understand similarities between the feature spaces of different models, such as Vision Transformers trained under diverse paradigms. However, traditional measures for representational alignment yield only scalar values that obscure how these spaces agree in terms of learned features. To address this, we combine alignment analysis with concept discovery, allowing a fine-grained breakdown of alignment into individual concepts. This approach reveals both universal concepts across models and each representation's internal concept structure. We introduce a new definition of concepts as non-linear manifolds, hypothesizing they better capture the geometry of the featurespace. A sanity check demonstrates the advantage of this manifold-based definition over linear baselines for concept-based alignment. Finally, our alignment analysis of four different ViTs shows that increased supervision tends to reduce semantic organization in learned representations.

Trump turns on the charm after extended'alpha' handshake with Macron and kisses for Brigitte at Palace of Versailles Sensational REAL reason Jelly Roll is divorcing Bunnie XO: Insiders reveal'preacher's wife' bombshell that's the talk of Nashville... truth about legendary rocker cuckolding rumor... and G-string mishap LIZ JONES: The cracks in Harry and Meghan's perfect facade have started to show. It's so obvious he's tiring of her tone-deaf approach... and I predict there's serious trouble in store Taylor Swift's bottomless thirst for attention, her greed and sheer tackiness are now truly unbearable... this latest stunt has shown her true colors: MAUREEN CALLAHAN NBA star's fiancee breaks her silence after friend, 26, mysteriously dropped dead at her luxury bachelorette party in St Barts Luxury fashion tycoon beloved by the stars hangs her head in shame as she's indicted for allegedly exploiting her workers and stealing $50k from their wages Jeff Bezos mercilessly mocked for taking'fake phone calls' when out with wife Lauren Sanchez Anguished family members flee court over sick details of Gilgo Beach murderer's kill room: Live updates'She has not been transparent... the damage has been done': How influencer Elle Darby'betrayed' thousands of young female fans...as insiders tell MOLLY CLAYTON how she cashed in As a divorced mother-of-three, cocaine was my little treat while my fellow middle-class friends had a few wines. What happened next was every family's worst nightmare... this is my warning to mums who'dabble' Desperate search for mom-of-three who hasn't been seen in three days as husband pleads for her return The shocking betrayal behind Jelly Roll's divorce from Bunnie XO is so utterly cruel... but have you yet spotted her revenge: JACQUELYNN POWERS Devastating supply crunch forces Apple to raise prices on iPhones and other devices, calling the move'unavoidable' Jeff's Dream Team: Bezos recruits world's top architects to build most expensive mega mansion on Billionaire Bunker island The Ring star Daveigh Chase's friends searched for her on LA's Skid Row in months before her shock death at 35 Watch horrifying drone video that follows woman's plunge to death after bungee team threw her from bridge without rope Stonehenge's secret SISTER: Archaeologists discover an ancient monument just three miles away that may have served as a'prototype' for the famous stones Archaeologists have discovered a secret sister monument to Stonehenge that might have served as a'prototype' for the famous stones. This ancient site is just three miles away from Stonehenge itself, located in the village of Bulford, Wiltshire. Consisting of two wooden poles placed 400 feet (120 metres) apart, this long-lost monument might appear rather basic at first glance.

On biomedical tabular data, flexible models such as deep networks, gradient-boosted trees, and kernel methods are repeatedly matched or beaten by linear and logistic regression given the same features. The usual reaction is to treat this as a model-side shortfall, to be fixed with more data, a better architecture, or tuning, on the assumption that the nonlinear structure is there and the model has failed to capture it. We argue that these fixes cannot help when the binding limit is the measurement rather than the model, as it frequently is in biomedicine. Additive noise blurs the population-optimal predictor, and because blurring removes a function's fine, rapidly varying detail before its broad shape, it erases nonlinear structure faster than linear structure. A degree-$k$ interaction is attenuated by the $k$-th power of feature reliability, while the linear part is attenuated only once. At the reliabilities typical of biomedical measurement, the nonlinear advantage can vanish even when the underlying biology is strongly nonlinear, and what the noise removes cannot be recovered by a larger cohort or a more flexible model, only by better measurement. The nonlinearity is hidden, not absent, and a tie between linear and flexible models is not by itself a verdict on the biology. These pieces are classical, drawn from measurement-error statistics, psychometrics, and Gaussian analysis, and we assemble them into an exact excess-risk identity. Measurement reliability is one of three conditions, alongside sample size and feature representation, that must align for a flexible model to help, and together they leave only a narrow window that most biomedical tasks fall outside. Across 140 UK Biobank tasks, the gap between flexible and linear models, where it exists, carries the predicted noise signature, and the three conditions can be separated by intervention but not by a benchmark alone.

Recent empirical work shows that semantically equivalent paraphrases can fool financial sentiment classifiers: although a paraphrase remains close to the original under a strong reference embedding, it may shift the target model's representation enough to change the predicted class. Existing robustness theory either assumes a single-model threat model or focuses mainly on empirical attack algorithms. We develop a continuous local model of semantic paraphrase perturbations that captures this two-model structure. We show that the worst-case local displacement of the target representation, subject to a proxy-model budget, is governed by the largest generalised eigenvalue of a matrix pencil $(A,B)$ constructed from the Jacobians of the two embedding maps. The resulting attackability index $λ^*(x)$ is intrinsic to the local paraphrase geometry and the chosen embedders, yields a closed-form prediction-flip condition for affine readouts, and supports conservative population and finite-sample attackability certificates. For uniform control over classes of affine readouts, we derive a distribution-free VC bound for binary attackability indicators and a scale-sensitive margin bound based on an attackability-adjusted margin that subtracts a local geometric penalty from the standard classifier margin. We also connect the continuous theory to discrete paraphrase search, identify an asymmetry between successful and unsuccessful finite searches, and give a covering condition under which the discrete and continuous settings agree. Finally, we propose an empirical verification framework using soft-token relaxations and generated paraphrase sets to assess the local eigenvalue geometry, prediction-flip condition, and finite-search approximation on a deployed financial-text classifier.