As we climbed the winding road to Bédar, we emerged into a charred and desolate landscape. Molten car parts littered our path and out of the window we saw the whole hillside now coated in a dusty black. At least 13 people, including five believed to be Britons, were killed by Thursday's wildfire in Spain's Almeria province, one of the country's deadliest ever. The toll rose on Sunday after a 93-year-old woman, believed to be British, died of her injuries in hospital. The identities of those killed have not yet been officially confirmed.

Understanding the geometry of neural network loss landscapes is a central question in deep learning, with implications for generalization and optimization. A striking phenomenon is linear mode connectivity (LMC), where independently trained models can be connected by low-or zero-barrier paths, despite appearing to lie in separate loss basins. However, this is often obscured by symmetries in parameter space--such as neuron permutations--which make functionally equivalent models appear dissimilar. Prior work has predominantly focused on neuron reordering through permutations, but such approaches are limited in scope and fail to capture the richer symmetries exhibited by modern architectures such as Transformers. In this work, we introduce a unified framework that captures four symmetry classes--permutations, semi-permutations, orthogonal transformations, and general invertible maps--broadening the set of valid reparameterizations and subsuming many previous approaches as special cases. Crucially, this generalization enables, for the first time, the discovery of low-and zero-barrier linear interpolation paths between independently trained Vision Transformers and GPT-2 models. Furthermore, our framework extends beyond pairwise alignment, to multi-model and width-heterogeneous settings, enabling alignment across architectures of different sizes. These results reveal deeper structure in the loss landscape and underscore the importance of symmetry-aware analysis for understanding model space geometry. Our code is available here.

A.1 Equations for Conformational Energy Landscape Overlap Analysis To quantify the similarity between the protein conformations generated by AI-based models and those in the ProteinConformers dataset, the following three commonly used overlap metrics are employed: Interaction overlap, coverage, and the Jaccard index. These metrics evaluate the extent of agreement in low-energy regions between the protein conformers from different models of the same protein, based on a specified energy threshold. Let A = {Ai,j} and B = {Bi,j} where i,j [0,N], denote the two-dimensional free energy landscapes corresponding of two conformational ensembles. Each element Ai,j and Bi,j represents the free energy value at a specific grid point in the conformational energy landscape. For a given energy threshold τ (e.g., 40 kJ/mol), the number of shared low-energy conformations is defined as: |A B| = Figure 6: Comparison of conformational landscapes for protein T1030, generated by ProteinConformers and protein conformation generative models.

The function of biomolecules such as proteins depends on their ability to interconvert between a wide range of structures or "conformations." Researchers have endeavored for decades to develop computational methods to predict the distribution of conformations, which is far harder to determine experimentally than a static folded structure. We present ConforMix, an inference-time algorithm that enhances sampling of conformational distributions using a combination of classifier guidance, filtering, and free energy estimation. Our approach upgrades diffusion models--whether trained for static structure prediction or conformational generation--to enable more efficient discovery of conformational variability without requiring prior knowledge of major degrees of freedom. ConforMix is orthogonal to improvements in model pretraining and would benefit even a hypothetical model that perfectly reproduced the Boltzmann distribution. Remarkably, when applied to a diffusion model trained for static structure prediction, ConforMix captures structural changes including domain motion, cryptic pocket flexibility, and transporter cycling, while avoiding unphysical states. Case studies of biologically critical proteins demonstrate the scalability, accuracy, and utility of this method.

In-silico prediction of protein mutant stability, measured by the difference in Gibbs free energy change ( G), is fundamental for protein engineering. Current sequence-to-label methods typically employ the two-stage pipeline: (i) encoding mutant sequences using neural networks (e.g., transformers), followed by (ii) the G regression from the latent representations. Although these methods have demonstrated promising performance, their dependence on specialized neural network encoders significantly increases the complexity. Additionally, the requirement to individually compute latent representations for each mutant site negatively impacts computational efficiency and poses the risk of overfitting. This work proposes the Venus-MAXWELL framework, which reformulates mutation G prediction as a sequence-to-landscape task. In Venus-MAXWELL, mutations of a protein and their corresponding Gvalues are organized into a landscape matrix, allowing our framework to learn the G landscape of a protein with a single forward and backward pass during training. Besides, to facilitate future works, we also curated a large-scale G dataset with strict controls on data leakage and redundancy to ensure robust evaluation. Venus-MAXWELL is compatible with multiple protein language models and enables these models for accurate and efficient G prediction. For example, when integrated with the ESM-IF, Venus-MAXWELL achieves higher accuracy than ThermoMPNN with 10 faster in inference speed (despite having 50 more parameters than ThermoMPNN).

Designing protein sequences of both high fitness and novelty is a challenging task in data-efficient protein engineering. Exploration beyond wild-type neighborhoods often leads to biologically implausible sequences or relies on surrogate models that lose fidelity in novel regions. Here, we propose PROSPERO, an active learning framework in which a frozen pre-trained generative model is guided by a surrogate updated from oracle feedback. By integrating fitness-relevant residue selection with biologically-constrained Sequential Monte Carlo sampling, our approach enables exploration beyond wild-type neighborhoods while preserving biological plausibility. We show that our framework remains effective even when the surrogate is misspecified. PROSPERO consistently outperforms or matches existing methods across diverse protein engineering tasks, retrieving sequences of both high fitness and novelty.

Stochastic optimal control methods often struggle in complex non-convex landscapes, frequently becoming trapped in local optima due to their inability to learn from historical trajectory data. This paper introduces Memory-Augmented Potential Field Theory, a unified mathematical framework that integrates historical experience into stochastic optimal control. Our approach dynamically constructs memory-based potential fields that identify and encode key topological features of the state space, enabling controllers to automatically learn from past experiences and adapt their optimization strategy. We provide a theoretical analysis showing that memory-augmented potential fields possess non-convex escape properties, asymptotic convergence characteristics, and computational efficiency. We implement this theoretical framework in a Memory-Augmented Model Predictive Path Integral (MPPI) controller that demonstrates significantly improved performance in challenging non-convex environments. The framework represents a generalizable approach to experience-based learning within control systems (especially robotic dynamics), enhancing their ability to navigate complex state spaces without requiring specialized domain knowledge or extensive offline training.

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.

Remote sensing is critical for disaster monitoring, yet existing datasets lack temporal image pairs and detailed textual annotations. While single-snapshot imagery dominates current resources, it fails to capture dynamic disaster impacts over time. To address this gap, we introduce the Remote Sensing Change Caption (RSCC) dataset, a large-scale benchmark comprising 62,351 pre-/post-disaster image pairs (spanning earthquakes, floods, wildfires, and more) paired with rich, human-like change captions. By bridging the temporal and semantic divide in remote sensing data, RSCC enables robust training and evaluation of vision-language models for disaster-aware bi-temporal understanding. Our results highlight RSCC's ability to facilitate detailed disaster-related analysis, paving the way for more accurate, interpretable, and scalable vision-language applications in remote sensing.

Protein language models (PLMs) learn probability distributions over natural protein sequences. By learning from hundreds of millions of natural protein sequences, protein understanding and design capabilities emerge. Recent works have shown that scaling these models improves structure prediction, but does not seem to improve mutation understanding and representation quality for protein function prediction. We introduce PoET-2, a multimodal, retrieval-augmented protein foundation model that incorporates in-context learning of family-specific evolutionary constraints with optional structure conditioning to learn generative distributions over protein sequences. PoET-2 uses a hierarchical transformer encoder that is equivariant to sequence context ordering and a dual decoder architecture with both causal and masked language modeling objectives, allowing PoET-2 to operate in both fully generative and bidirectional representation learning modes. PoET-2 achieves stateof-the-art performance on zero-shot variant effect prediction, excelling at scoring variants with multiple mutations and challenging indel mutations. In supervised settings, PoET-2 embeddings outperform previous methods for learning sequencefunction relationships, especially with small datasets. This work highlights the benefits of combining retrieval augmentation with multimodal, family-centric modeling for advancing protein foundation models. 1