Autoencoders (AEs) have emerged as powerful tools for non-linear dimensionality reduction, often surpassing traditional linear methods such as Proper Orthogonal Decomposition (POD) in scenarios characterized by slowly decaying Kolmogorov $n$-widths. In the realm of Reduced-Order Modelling (ROM), these models are increasingly utilized to learn low-dimensional representations of solution manifolds associated with parametric Partial Differential Equations (PDEs). However, the high expressivity of AEs presents a challenge: although trained networks typically minimize reconstruction error, they often struggle to capture the essential properties necessary for building accurate and robust ROMs. Recent works by arXiv:2307.15288v2 and arXiv:2506.11641v1 have tackled this challenge in fully connected AEs by proposing representation-consistent architectures, which preserve some of the properties belonging to POD. This study builds upon that concept by extending representation consistency for convolutional layers. We introduce a novel class of symmetric Convolutional AutoEncoders (CAEs) designed to embody the primary properties of manifold parametrization mappings. When integrated into a ROM framework, this architecture demonstrates significantly improved predictive capabilities. Specifically, we compared the performance of the ROMs based on classical and symmetric CAEs on three one dimensional academic test cases, namely the Linear Advection, the Viscous Burger and the Kuramoto Sivashinsky equation. Numerical results demonstrate that our proposed symmetric approach consistently yields more accurate latent trajectories, lower reconstruction errors, and enhanced model robustness.

Let's start with a game. Open up your chatbot of choice--Claude, ChatGPT, Gemini--and type "Give me a random number between 1 and 10." You're going to get 7. Almost always. Now type "Another" and you'll get 3 or 4. Type "Another" again and you'll get 8 or 9. That won't work every time--but if it did for you, you may wonder if I have superpowers.

The Spark agentic AI assistant is exclusively available to Google AI Ultra subscribers in the US. Google has started rolling out its new agentic AI assistant, Gemini Spark, to Gemini's app for macOS . When the company launched Spark at its I/O developer conference in May, it explained that the assistant turns Gemini into an active partner that can actually do tasks for you. On Mac computers, for instance, you can ask it to (finally) sort the massive number of the PDFs in your Downloads into specific folders. You'll also be able to get it to do tasks on your Workspace apps using files in your computer, such as asking it to create a spreadsheet with invoices saved on your laptop.

The US government has lifted export controls on Anthropic's most advanced artificial intelligence (AI) tools, just weeks after ordering it to restrict access to them over national security concerns, the company has said. Anthropic said in a social media post that it will begin restoring access to Claude Fable 5 and Mythos 5 on Wednesday after being notified that the US Department of Commerce has lifted export controls on the two models. They are the firm's most advanced AI tools, which were abruptly suspended on 12 June over concerns that they could be used by hackers to exploit weaknesses in computer systems. The BBC has contacted the Department of Commerce for comment. Mythos and Fable are two of Anthropic's AI models built on its Claude platform - a rival to the likes of OpenAI's ChatGPT and Google's Gemini. Fable 5 is a version of the AI model for the cosumer market, capable of deep reasoning and can perform complex tasks independently.

Deep neural networks (DNNs) frequently fail to generalize to out-of-distribution (OOD) medical images because of variations in scanners and acquisition protocols. Retraining DNN models to address these distribution shifts is often impractical due to the high cost of acquiring and annotating new medical datasets. To address this, we introduce VarDeepPCA, a novel lightweight variational DNN framework designed to restore/refine degraded segmentation maps by leveraging intrinsic geometric priors. Unlike existing approaches that require target-domain data or extensive pre-training, our VarDeepPCA explicitly learns a distribution of valid anatomical geometries using only small in-distribution (ID) datasets. Theoretically, our novel variational learning framework leverages a reinterpretation of the softmax mapping to implicitly perform exact distribution modeling, thereby enabling computationally efficient, sampling-free learning and inference. This also enables VarDeepPCA to provide uncertainty estimates associated with its restored segmentation maps. We empirically validate our framework across 4 distinct clinical applications, using 14 publicly available datasets, involving segmentation of the myocardium, neuroretinal rim, prostate, and fetal head. Comparisons against 15 existing methods demonstrate that VarDeepPCA consistently restores segmentation maps produced by the existing methods on OOD data to (i) significantly improve anatomical plausibility of geometries and clinical utility of the segmentations, and (ii) significantly reduce errors, without needing any more training data than that used by existing methods.

Many modern Language Model (LM) pipelines return an averaged model, such as an exponential moving average of the training iterates, rather than the final iterate itself. This raises a fundamental question: given that we will return an iterate average, how should we change training to improve the performance of this average? We study this question by formulating optimizer design for the iterate-average estimator as an optimal-control problem. In a continuous-time stochastic quadratic model, we solve for the control strategy that minimizes the error of the returned average subject to a penalty on the size of the intervention. A practical approximation to this controller yields PACE, a lightweight wrapper around AdamW that pulls the live weights toward their exponential moving average with a clipped, per-coordinate control strength. We prove that a stylized version of PACE converges at the standard stochastic convex optimization rate, up to a factor depending on the averaging rule, while in the quadratic setting it can strictly improve the limiting squared error of the iterate-average estimator and can do so by an arbitrarily large factor on some instances. Empirically, our results suggest that PACE improves over AdamW and EMA-evaluated AdamW in supervised fine-tuning of 1-2B parameter LMs and in GPT-2 pretraining on FineWeb for a wide range of learning rates, decay schedules, and other hyperparameters.

Abstractitations, recent work explores online RLHF that iterates between generating on-policy responses and collecting preferences [Lee et al., 2024, Park et al., 2022]. Among online The Self-Improving Alignment (SAIL) algorithmapproaches, SAIL reduces a bilevel alignment formulation addresses distribution shift by reducing a bilevelto a computationally efficient single-level surrogate and formulation of the problem to an efficient, single-reports strong empirical gains [Ding et al., 2024]. Empirically, SAIL has demonstratedisting online pipelines are largely heuristic and do not anastrong performance on this task. However, a for-lytically control the distributional shift induced by iterative mal analysis of its convergence properties has beendata collection [Chakraborty et al., 2024, Shen et al., 2024], lacking. We identify a key theoretical challenge: which has been linked to suboptimal performance in practice the standard SAIL objective function is not guar- [Sharma et al., 2024]. To address this limita-A growing line of work argues that the coupling between tion, we propose a regularized objective, SAILreward learning and policy updates is fundamentally bilevel and should be modeled as such [Chakraborty et al., 2024].RevKL, which incorporates a reverse KullbackAs a follow-up, Ding et al. [2024] reduces the bilevel align-Leibler (KL) divergence penalty to improve the optimization landscape. Our central theoretical con-ment objective to a tractable single-level surrogate and retribution is to prove that this regularized objectiveports strong empirical gains, yet it lacks formal convergence satisfies the Polyak-Lojasiewicz (PL) conditionguarantees. Related theoretical analyses in bilevel/RLHFstyle problems exist [e.g., Yang et al., 2025, Chakrabortywithin a bounded parameter space. We establish et al., 2024, Gaur et al., 2025], yet they either focus onglobal convergence guarantees, achieving a nearlinear sample complexity.

Accurate energy demand forecasting is essential for the reliable operation and planning of modern sustainable energy systems. Spatial-temporal graph neural networks (STGNNs) have recently achieved strong performance in point forecasting by jointly modeling temporal dynamics and relational dependencies across interconnected energy nodes. However, in real-world energy systems, accurate point forecasts alone are insufficient, as operators also require reliable uncertainty estimates to support risk-aware decision-making, grid stability, and operational planning under uncertainty. Conformal prediction provides a principled and model-agnostic framework for uncertainty quantification with statistical coverage guarantees, making it particularly attractive for safety-critical energy applications. However, existing conformal prediction approaches often fail to fully capture the complex spatial-temporal structure of energy systems. To address these limitations, we propose STOIC (Spatial-Temporal Graph Conformal Prediction with In-Context Learning), a novel framework that integrates graph-based forecasting with the zero-shot calibration capabilities of tabular foundation models. STOIC first generates point forecasts using an STGNN and subsequently reformulates spatial-temporal residuals into a tabular representation suitable for in-context learning. Leveraging a tabular foundation model, STOIC calibrates prediction intervals without task-specific retraining, effectively capturing both sequential and relational dependencies. We evaluate STOIC on five diverse benchmarks, including synthetic simulations as well as real-world electricity and district heating networks. Across all datasets, STOIC consistently outperforms existing conformal prediction baselines, delivering more reliable and robust uncertainty estimates for complex graph-structured energy time series.

Modern LLM workflows move coordinate-indexed objects across checkpoints: steering vectors, sparse autoencoders, top-$k$ neuron sets, attribution lists, and merge alignments. This is only well posed after fixing the model's residual-stream gauge, which we show is architecture-dependent: LayerNorm residual charts have permutation gauge $S_d$ (up to a global sign flip), while RMSNorm charts with generic per-channel gain have signed-permutation gauge $B_d = S_d \ltimes \{\pm 1\}^d$. Permutation-only alignment is therefore symmetry-incomplete for RMSNorm models. We introduce sign-marginalized Hungarian matching and prove a sharp failure mode: with decorrelated coordinates, raw signed-correlation matching has a structural permutation-accuracy ceiling at the positive-sign fraction of the true gauge, which sign-marginalization removes. We then make coordinate-preserving transport, not function-level merging, the primary object: composing saved-checkpoint local $B_d$ gauges along same-base fine-tuning trajectories recovers 91.1% of cross-run coordinates at 1500 steps versus 60.3% for endpoint matching, and the gain is not explained by merely routing through the base. The recovered gauge transfers tools that permutation-only alignment breaks: TinyLlama SAE reconstruction has NMSE 0.004 under $B_d$ versus 1.08 under $S_d$; Qwen sentiment steering preserves 95.8% of its effect versus 17.2%; refusal steering reverses sign under $S_d$; coordinate-preserving merges behave the same way. The same covariance governs stateful training: signed transport of AdamW state preserves the resumed trajectory, while permutation-only state follows a different one from a functionally identical checkpoint. Finally, gauge-sweep audits show index-level interpretability claims are reproducible only relative to an explicit gauge.

At an event for pharmaceutical executives, biotech founders, and researchers on Tuesday, Anthropic announced Claude Science, a major new product intended to support scientific research in the same way that Claude Code supports software engineering. Like Claude Code, Claude Science can autonomously carry out meaningful work when given concise, high-level instructions, and it has access to tools that make it particularly useful for research in computational biology and drug development. Along with launching and previewing Claude Science, which is now available to all paid Claude subscribers, Anthropic also announced that it will be using the product to pursue some of its own research into drugs for rare, neglected diseases. This is not Anthropic's first foray into AI for science. In October, the company released plug-ins that help Claude make use of scientific software and databases under the heading "Claude for Life Sciences." But unlike this earlier release, Claude Science is a full-featured, standalone product. Anthropic's decision to elevate Claude Science to the same rank as Claude Code and Claude Cowork indicates that the company is taking AI's scientific applications very seriously--or at least wants to give the impression that it is.