Discretisation invariance, a recent innovation in scientific machine learning, is a requirement that ensures an architecture can process inputs of different resolutions. In this post, we formally define this property, provide examples, generate datasets, train architectures, and discuss whether discretisation invariance is living up to its promise.

Modern Video Large Language Models (VLLMs) often rely on uniform frame sampling for video understanding, but this approach frequently fails to capture critical information due to frame redundancy and variations in video content. We propose MaxInfo, the first training-free method based on the maximum volume principle, which is available in Fast and Slow versions and a Chunk-based version that selects and retains the most representative frames from a video. By maximizing the geometric volume formed by selected embeddings, MaxInfo ensures that the chosen frames cover the most informative regions of the embedding space, effectively reducing redundancy while preserving diversity. This method enhances the quality of input representations and improves long video comprehension performance across benchmarks. For instance, MaxInfo achieves a 3.28

For low-dimensional problems (d≤3), spectral methods can achieve exceptionally high accuracy. For middle-dimensional problems (4 ≤ d ≲ 10), spectral methods remain feasible through specific techniques such as sparse grids or hyperbolic cross. However, for high-dimensional problems (d≫ 10), spectral methods suffer frome the curse of dimensionality. Physics-informed neural networks (PINNs) have emerged as a promising approach to overcome this challenge, offering scalability to high dimensions, but often suffer from limited accuracy and efficiency. Recently proposed spectral-informed neural networks (SINNs) combine spectral methods with PINNs, operating directly in the spectral domain to avoid spatial derivative computations and to reduce memory consumption. In this work, we introduce Modified SINNs, which integrate coefficient decay scaling and basis embeddings motivated by harmonic analysis to enhance accuracy in high-dimensional problems and enable accurate approximation of unknown spectral coefficients. Numerical experiments on steady and time-dependent partial differential equations demonstrate that Modified SINNs outperform sparse grid spectral methods on middle-dimensional problems with incomplete spectral information and achieve superior accuracy compared to PINNs on high-dimensional problems.

Adapting large language models (LLMs) to clinical workflows often requires costly fine-tuning or manual prompt and pipeline engineering. We study LLM-guided MAP-Elites evolution as an inference-time alternative for discovering medical decision strategies and provide an implementation repository at https://github.com/univanxx/llm_guided_evo_medical. We formulate urgency triage, interactive consultation, and medical image classification as evolutionary searches over executable artifacts optimized by task-specific fitness functions. Across all three settings, evolution improves over manually designed baselines under practical constraints. In triage, evolved programs increase Semigran accuracy from 77.3% to 87.1% and emergency recall from 0.60 to 0.97, while improving safety-weighted held-out MIMIC-ESI performance. In interactive consultation, evolved policies improve the accuracy–cost frontier across Llama-3, Qwen-3.5, and Gemma-4 and transfer to held-out iCRAFTMD. In PneumoniaMNIST, prompt-only evolution improves frozen MedGemma VLMs while preserving strict JSON outputs. Qualitative analysis shows that the gains come from interpretable program-level mechanisms, calibrated triage boundaries, targeted evidence acquisition, selective commitment, and finding-oriented visual decision rules, rather than superficial prompt rewording alone.

Physics-informed neural networks have emerged as a powerful tool for solving partial differential equations (PDEs) by integrating physical constraints into neural network training, but their performance is sensitive to the sampling of points. Motivated by the impressive performance of quasi-Monte Carlo methods in high dimensional problems, this paper proposes Quasi-Random Physics-Informed Neural Networks (QRPINNs), which sample train ing points from low-discrepancy sequences instead of the domain of PDEs. Theoretically, QRPINNs are shown to exhibit a faster convergence rate than PINNs. Empirically, experiments demonstrate that QRPINNs outperform PINNs and some representative adaptive sampling methods in high-dimensional PDEs. Furthermore, combining QRPINNs with adaptive sampling further enhances both accuracy and efficiency.

Neural image compression (NIC) has become the state-of-the-art for rate-distortion performance, yet its security vulnerabilities remain significantly less understood than those of classifiers. Existing adversarial attacks on NICs are often naive adaptations of pixel-space methods, overlooking the unique, structured nature of the compression pipeline. In this work, we propose a more advanced class of vulnerabilities by introducing T-MLA, the first targeted multiscale log-exponential attack framework. We introduce adversarial perturbations in the wavelet domain that concentrate on less perceptually salient coefficients, improving the stealth of the attack. Extensive evaluation across multiple state-of-the-art NIC architectures on standard image compression benchmarks reveals a large drop in reconstruction quality while the perturbations remain visually imperceptible. On standard NIC benchmarks, T-MLA achieves targeted degradation of reconstruction quality while improving perturbation imperceptibility (higher PSNR/VIF of the perturbed inputs) compared to PGD-style baselines at comparable attack success, as summarized in our main results. Our findings reveal a critical security flaw at the core of generative and content delivery pipelines.

Accurate detection of all pathological findings in 3D medical images remains a significant challenge, as supervised models are limited to detecting only the few pathology classes annotated in existing datasets. To address this, we frame pathology detection as an unsupervised visual anomaly segmentation (UVAS) problem, leveraging the inherent rarity of pathological patterns compared to healthy ones. We enhance the existing density-based UVAS framework with two key innovations: (1) dense self-supervised learning for feature extraction, eliminating the need for supervised pretraining, and (2) learned, masking-invariant dense features as conditioning variables, replacing hand-crafted positional encodings. Trained on over 30,000 unlabeled 3D CT volumes, our fully self-supervised model, Screener, outperforms existing UVAS methods on four large-scale test datasets comprising 1,820 scans with diverse pathologies. Furthermore, in a low-shot supervised fine-tuning setting, Screener surpasses existing self-supervised pretraining methods, establishing it as a state-of-the-art foundation for pathology segmentation. The code and pretrained models will be made publicly available.

Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a substantial number of potential tensor permutations can lead to a tensor network with the same structure but varying expressive capabilities. In this paper, we take tensor ring decomposition for density estimator, which significantly reduces the number of permutation candidates while enhancing expressive capability compared with existing used decompositions. Additionally, a mixture model that incorporates multiple permutation candidates with adaptive weights is further designed, resulting in increased expressive flexibility and comprehensiveness. Different from the prevailing directions of tensor network structure/permutation search, our approach provides a new viewpoint inspired by ensemble learning. This approach acknowledges that suboptimal permutations can offer distinctive information besides that of optimal permutations. Experiments show the superiority of the proposed approach in estimating probability density for moderately dimensional datasets and sampling to capture intricate details.

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of the problem. A practical way to apply such a scheme is to compute subspaces for a selected set of parameters in the computationally demanding offline stage and in the online stage approximate subspace for unknown parameters by interpolation. For realistic problems the space of parameters is high dimensional, which renders classical interpolation strategies infeasible or unreliable. We propose to relax the interpolation problem to regression, introduce several loss functions suitable for subspace data, and use a neural network as an approximation to high-dimensional target function. To further simplify a learning problem we introduce redundancy: in place of predicting subspace of a given dimension we predict larger subspace. We show theoretically that this strategy decreases the complexity of the mapping for elliptic eigenproblems with constant coefficients and makes the mapping smoother for general smooth function on the Grassmann manifold. Empirical results also show that accuracy significantly improves when larger-than-needed subspaces are predicted. With the set of numerical illustrations we demonstrate that subspace regression can be useful for a range of tasks including parametric eigenproblems, deflation techniques, relaxation methods, optimal control and solution of parametric partial differential equations.

Large linear systems are ubiquitous in modern computational science and engineering. Their efficient solution is frequently challenging, especially in conjunction with problems described by parametric PDEs, where many such systems have to be solved. The primary approach for solving large linear systems is the use of Krylov subspace iterative methods with well-designed preconditioners. Recently, graph neural networks (GNNs) have been used in conjunction with solving parametric PDEs, and have been shown to be promising tool for designing preconditioners. Nevertheless, the GNN-based preconditioners reported in the literature have worse effect on system's spectrum than analogous preconditioners from classical linear algebra. Here we employ well-established preconditioners from linear algebra as starting point for training GNN to obtain preconditioners that yield a more substantial reduction in the condition number of the systems when compared to classical preconditioners. Numerical experiments demonstrate the efficiency of our approach in comparison to classical and known neural network-based methods for parametric PDEs. In addition, a heuristic justification for the loss function employed in this study is provided, and we demonstrate that preconditioners obtained by learning with this loss function reduce the condition number in a way that is more desirable for the conjugate gradient iterative method.

Sliced Mutual Information (SMI) is widely used as a scalable alternative to mutual information for measuring non-linear statistical dependence. Despite its advantages, such as faster convergence, robustness to high dimensionality, and nullification only under statistical independence, we demonstrate that SMI is highly susceptible to data manipulation and exhibits counterintuitive behavior. Through extensive benchmarking and theoretical analysis, we show that SMI saturates easily, fails to detect increases in statistical dependence (even under linear transformations designed to enhance the extraction of information), prioritizes redundancy over informative content, and in some cases, performs worse than simpler dependence measures like the correlation coefficient.

LLM-guided evolutionary computation, most notably AlphaEvolve, has been remarkably successful in discovering novel mathematical constructions by solving challenging optimization problems. The standard approach is to evolve a monolithic program that directly outputs a candidate solution. We present ImprovEvolve, an algorithmic alternative that drastically reduces cognitive load on the LLM. Instead of prompting the model for an end-to-end optimizer, we evolve a program with three specialized operators of initialization, local improvement, and perturbation. We then approach the optimum by iteratively applying local improvements and intensity-scheduled perturbations, effectively driving a basin-hopping search with LLM-evolved subroutines. For hexagon in hexagon packing, ImprovEvolve discovers new state-of-the-art packings of 11, 12, 15, and 16 hexagons, and additionally for 14, 17, and 23 hexagons after minimal expert tuning of the generated code. For the second autocorrelation inequality, the evolved and human-scaled program pushes the lower bound from 0.96102 to 0.96258. For spherical codes, the ImprovEvolve program lowers the best-known maximum cosine for the majority of 90 randomly chosen diverse state-of-the-art spherical codes, achieving relative improvements of up to 2.4

The growing demand for energy-efficient, high-performance AI systems has led to increased attention on alternative computing platforms (e.g., photonic, neuromorphic) due to their potential to accelerate learning and inference. However, integrating such physical components into deep learning pipelines remains challenging, as physical devices often offer limited expressiveness, and their non-differentiable nature renders on-device backpropagation difficult or infeasible. This motivates the development of hybrid architectures that combine digital neural networks with reconfigurable physical layers, which effectively behave as black boxes. In this work, we present a framework for the end-to-end training of such hybrid networks. This framework integrates stochastic zeroth-order optimization for updating the physical layer’s internal parameters with a dynamic low-rank surrogate model that enables gradient propagation through the physical layer. A key component of our approach is the implicit projector-splitting integrator algorithm, which updates the lightweight surrogate model after each forward pass with minimal hardware queries, thereby avoiding costly full matrix reconstruction. We demonstrate our method across diverse deep learning tasks, including: computer vision (deep convolutional network on the CIFAR-10 dataset), audio classification (ECAPA-TDNN model on the UrbanSound8K dataset), and language modeling (a decoder-only transformer model on the FineWeb corpus). Notably, across all modalities, the proposed approach achieves near-digital baseline accuracy and consistently enables effective end-to-end training of hybrid models incorporating various non-differentiable physical components (spatial light modulators, microring resonators, and Mach-Zehnder interferometers). This work bridges hardware-aware deep learning and gradient-free optimization, thereby offering a practical pathway for integrating non-differentiable physical components into scalable, end-to-end trainable AI systems.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an indispensable paradigm for enhancing reasoning in Large Language Models (LLMs). However, standard policy optimization methods, such as Group Relative Policy Optimization (GRPO), often converge to low-entropy policies, leading to severe mode collapse and limited output diversity. We analyze this issue from the perspective of sampling probability dynamics, identifying that the standard objective disproportionately reinforces the highest-likelihood paths, thereby suppressing valid alternative reasoning chains. To address this, we propose a novel Advantage Re-weighting Mechanism (ARM) designed to equilibrate the confidence levels across all correct responses. By incorporating Prompt Perplexity and Answer Confidence into the advantage estimation, our method dynamically reshapes the reward signal to attenuate the gradient updates of over-confident reasoning paths, while redistributing probability mass toward under-explored correct solutions. Empirical results demonstrate that our approach significantly enhances generative diversity and response entropy while maintaining competitive accuracy, effectively achieving a superior trade-off between exploration and exploitation in reasoning tasks. Empirical results on Qwen2.5 and DeepSeek models across mathematical and coding benchmarks show that ProGRPO significantly mitigates entropy collapse. Specifically, on Qwen2.5-7B, our method outperforms GRPO by 5.7

The conceptual design phase in architecture and urban planning, particularly building massing, is complex and heavily reliant on designer intuition and manual effort. To address this, we propose an automated framework for generating building massing based on functional requirements and site context. A primary obstacle to such data-driven methods has been the lack of suitable datasets. Consequently, we introduce the CoMa-20K dataset, a comprehensive collection that includes detailed massing geometries, associated economical and programmatic data, and visual representations of the development site within its existing urban context. We benchmark this dataset by formulating massing generation as a conditional task for Vision-Language Models (VLMs), evaluating both fine-tuned and large zero-shot models. Our experiments reveal the inherent complexity of the task while demonstrating the potential of VLMs to produce context-sensitive massing options. The dataset and analysis establish a foundational benchmark and highlight significant opportunities for future research in data-driven architectural design.

In a rapidly growing field of model training there is a constant practical interest in parameter-efficient fine-tuning and various techniques that use a small amount of training data to adapt the model to a narrow task. However, there is an open question: how to combine several adapters tuned for different tasks into one which is able to yield adequate results on both tasks? Specifically, merging subject and style adapters for generative models remains unresolved. In this paper we seek to show that in the case of orthogonal fine-tuning (OFT), we can use structured orthogonal parametrization and its geometric properties to get the formulas for training-free adapter merging. In particular, we derive the structure of the manifold formed by the recently proposed Group-and-Shuffle ($\mathcal{GS}$) orthogonal matrices, and obtain efficient formulas for the geodesics approximation between two points. Additionally, we propose a $\text{spectra restoration}$ transform that restores spectral properties of the merged adapter for higher-quality fusion. We conduct experiments in subject-driven generation tasks showing that our technique to merge two $\mathcal{GS}$ orthogonal matrices is capable of uniting concept and style features of different adapters. To the best of our knowledge, this is the first training-free method for merging multiplicative orthogonal adapters. Code is available via the $\href{https://github.com/ControlGenAI/OrthoFuse}{link}$.

Successful mutation strategies in evolutionary code search may contain reusable knowledge that is useful beyond a single run, and in some cases may transfer across related tasks and domains. However, existing LLM-driven evolutionary frameworks largely discard such knowledge, repeatedly rediscovering similar ideas and limiting opportunities for cross-run and cross-task learning. We introduce EvoMem, a persistent memory architecture for LLM-based evolutionary program search that captures and reuses candidate mutation knowledge. EvoMem converts successful mutation events into structured, task-aware advice for future runs. It operates in two phases: after each run, it extracts and stores promising ideas with provenance, and during subsequent evolution, it retrieves a small set of relevant instructions based on the current task and program context to guide mutation. Across geometric optimization, multi-hop question answering, GPU kernel optimization, and related benchmarks, our experiments show positive average improvements in target metrics or search speed for most evaluated settings, while also revealing variability across tasks. Overall, EvoMem provides evidence that persistent memory can reduce some redundant exploration and improve the reuse and adaptation of successful strategies in LLM-driven evolutionary search.

In scientific computing, the burgeoning usage of physics-informed neural networks (PINNs) for solving partial differential equations(PDEs) has spurred the need for, and ongoing research into, more accurate and efficient PINNs. One bottleneck of current PINNs is the computation of the high-order derivatives via automatic differentiation which often necessitates substantial computing resources especially when dealing with complex PDEs and high dimensional problems. To tackle this, we propose a spectral-based neural network that substitutes the differential operator with a multiplication. Compared to PINNs, our framework requires less GPU memory and a shorter training time. Furthermore, the exponential convergence of the spectral basis makes our approach more accurate. Moreover, to handle the different situations between the physics domain and the spectral domain, we provide a strategy to efficiently train networks in spectral domain. Through a series of comprehensive experiments, we validate the aforementioned merits of our proposed network.

Conversion of spoken mathematical expressions is a challenging task that involves transcribing speech into a strictly structured symbolic representation while addressing the ambiguity inherent in the pronunciation of equations. Although significant progress has been achieved in automatic speech recognition (ASR) and language models (LM), the problem of converting spoken mathematics into LaTeX remains underexplored. This task directly applies to educational and research domains, such as lecture transcription or note creation. Based on ASR post-correction, prior work requires 2 transcriptions, focuses only on isolated equations, has a limited test set, and provides neither training data nor multilingual coverage. To address these issues, we present the first fully open-source large-scale dataset, comprising over 66,000 human-annotated audio samples of mathematical equations and sentences in English and Russian, drawn from diverse scientific domains. In addition to the ASR post-correction models and few-shot prompting, we apply audio language models, demonstrating comparable character error rate (CER) results on the MathSpeech benchmark (28\% vs. 30\%) for the equations conversion. In contrast, on the proposed S2L-equations benchmark, our models outperform the MathSpeech model by a substantial margin of more than 36 percentage points, even after accounting for LaTeX formatting artifacts (27\% vs. 64\%). We establish the first benchmark for mathematical sentence recognition (S2L-sentences) and achieve an equation CER of 40\%. This work lays the groundwork for future advances in multimodal AI, with a particular focus on mathematical content recognition.

The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce a framework that overcomes this limitation by exploiting the low-rank structure of potential energy surfaces through tensor train (TT) decomposition. Our approach combines two complementary TT-based strategies: the algebraic TTOpt method, which utilizes maximum volume sampling, and the probabilistic PROTES method, which employs generative sampling. A key innovation is the development of physically constrained encoding schemes that incorporate molecular constraints directly into the discretization process. We demonstrate the efficacy of our method by identifying global minima of Lennard-Jones clusters containing up to 45 atoms. Furthermore, we establish its practical applicability to real-world systems by optimizing 20-atom carbon clusters using a machine-learned moment tensor potential, achieving geometries consistent with quantum-accurate simulations. This work establishes TT decomposition as a powerful tool for molecular structure prediction and provides a general framework adaptable to a wide range of high-dimensional optimization problems in computational material science.