Transcriptomic foundation models (TFMs) have recently emerged as powerful tools for analyzing gene expression in cells and tissues, supporting key tasks such as cell-type annotation, batch correction, and perturbation prediction. However, the diversity of model implementations and training strategies across recent TFMs, though promising, makes it challenging to isolate the contribution of individual design choices or evaluate their potential synergies. This hinders the field's ability to converge on best practices and limits the reproducibility of insights across studies. We present BMFM-RNA, an open-source, modular software package that unifies diverse TFM pretraining and fine-tuning objectives within a single framework. Leveraging this capability, we introduce a novel training objective, whole cell expression decoder (WCED), which captures global expression patterns using an autoencoder-like CLS bottleneck representation. In this paper, we describe the framework, supported input representations, and training objectives. We evaluated four model checkpoints pretrained on CELLxGENE using combinations of masked language modeling (MLM), WCED and multitask learning. Using the benchmarking capabilities of BMFM-RNA, we show that WCED-based models achieve performance that matches or exceeds state-of-the-art approaches like scGPT across more than a dozen datasets in both zero-shot and fine-tuning tasks. BMFM-RNA, available as part of the biomed-multi-omics project ( https://github.com/BiomedSciAI/biomed-multi-omic ), offers a reproducible foundation for systematic benchmarking and community-driven exploration of optimal TFM training strategies, enabling the development of more effective tools to leverage the latest advances in AI for understanding cell biology.
This study investigates the current landscape and future directions of protein foundation model research. While recent advancements have transformed protein science and engineering, the field lacks a comprehensive benchmark for fair evaluation and in-depth understanding. Since ESM-1B, numerous protein foundation models have emerged, each with unique datasets and methodologies. However, evaluations often focus on limited tasks tailored to specific models, hindering insights into broader generalization and limitations. Specifically, researchers struggle to understand the relationships between tasks, assess how well current models perform across them, and determine the criteria in developing new foundation models. To fill this gap, we present PFMBench, a comprehensive benchmark evaluating protein foundation models across 38 tasks spanning 8 key areas of protein science. Through hundreds of experiments on 17 state-of-the-art models across 38 tasks, PFMBench reveals the inherent correlations between tasks, identifies top-performing models, and provides a streamlined evaluation protocol. Code is available at \href{https://github.com/biomap-research/PFMBench}{\textcolor{blue}{GitHub}}.
Motivation: Spliced alignment refers to the alignment of messenger RNA (mRNA) or protein sequences to eukaryotic genomes. It plays a critical role in gene annotation and the study of gene functions. Accurate spliced alignment demands sophisticated modeling of splice sites, but current aligners use simple models, which may affect their accuracy given dissimilar sequences. Results: We implemented minisplice to learn splice signals with a one-dimensional convolutional neural network (1D-CNN) and trained a model with 7,026 parameters for vertebrate and insect genomes. It captures conserved splice signals across phyla and reveals GC-rich introns specific to mammals and birds. We used this model to estimate the empirical splicing probability for every GT and AG in genomes, and modified minimap2 and miniprot to leverage pre-computed splicing probability during alignment. Evaluation on human long-read RNA-seq data and cross-species protein datasets showed our method greatly improves the junction accuracy especially for noisy long RNA-seq reads and proteins of distant homology. Availability and implementation: https://github.com/lh3/minisplice
Deep neural networks have set the state-of-the-art in computer vision tasks such as bounding box detection and semantic segmentation. Object detectors and segmentation models assign confidence scores to predictions, reflecting the model's uncertainty in object detection or pixel-wise classification. However, these confidence estimates are often miscalibrated, as their architectures and loss functions are tailored to task performance rather than probabilistic foundation. Even with well calibrated predictions, object detectors fail to quantify uncertainty outside detected bounding boxes, i.e., the model does not make a probability assessment of whether an area without detected objects is truly free of obstacles. This poses a safety risk in applications such as automated driving, where uncertainty in empty areas remains unexplored. In this work, we propose an object detection model grounded in spatial statistics. Bounding box data matches realizations of a marked point process, commonly used to describe the probabilistic occurrence of spatial point events identified as bounding box centers, where marks are used to describe the spatial extension of bounding boxes and classes. Our statistical framework enables a likelihood-based training and provides well-defined confidence estimates for whether a region is drivable, i.e., free of objects. We demonstrate the effectiveness of our method through calibration assessments and evaluation of performance.
This paper introduces a new approach for approximating the learning dynamics of multiple reinforcement learning (RL) agents interacting in a finite-state Markov game. The idea is to rescale the learning process by simultaneously reducing the learning rate and increasing the update frequency, effectively treating the agent's parameters as a slow-evolving variable influenced by the fast-mixing game state. Under mild assumptions-ergodicity of the state process and continuity of the updates-we prove the convergence of this rescaled process to an ordinary differential equation (ODE). This ODE provides a tractable, deterministic approximation of the agent's learning dynamics. An implementation of the framework is available at\,: https://github.com/yannKerzreho/MarkovGameApproximation
Understanding protein function at the molecular level requires connecting residue-level annotations with physical and structural properties. This can be cumbersome and error-prone when functional annotation, computation of physico-chemical properties, and structure visualization are separated. To address this, we introduce ProCaliper, an open-source Python library for computing and visualizing physico-chemical properties of proteins. It can retrieve annotation and structure data from UniProt and AlphaFold databases, compute residue-level properties such as charge, solvent accessibility, and protonation state, and interactively visualize the results of these computations along with user-supplied residue-level data. Additionally, ProCaliper incorporates functional and structural information to construct and optionally sparsify networks that encode the distance between residues and/or annotated functional sites or regions. The package ProCaliper and its source code, along with the code used to generate the figures in this manuscript, are freely available at https://github.com/PNNL-Predictive-Phenomics/ProCaliper.
Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span clustering, anomaly detection, and beyond. In this work, we present a unified framework grounded in mathematical optimization to address matrix seriation from a rigorous, model-based perspective. Our approach leverages combinatorial and mixed-integer optimization to represent seriation objectives and constraints with high fidelity, bridging the gap between traditional heuristic methods and exact solution techniques. We introduce new mathematical programming models for neighborhood-based stress criteria, including nonlinear formulations and their linearized counterparts. For structured settings such as Moore and von Neumann neighborhoods, we develop a novel Hamiltonian path-based reformulation that enables effective control over spatial arrangement and interpretability in the reordered matrix. To assess the practical impact of our models, we carry out an extensive set of experiments on synthetic and real-world datasets, as well as on a newly curated benchmark based on a coauthorship network from the matrix seriation literature. Our results show that these optimization-based formulations not only enhance solution quality and interpretability but also provide a versatile foundation for extending matrix seriation to new domains in data science.
Bias problems in the estimation of $Q$-values are a well-known obstacle that slows down convergence of $Q$-learning and actor-critic methods. One of the reasons of the success of modern RL algorithms is partially a direct or indirect overestimation reduction mechanism. We propose an easy to implement method built on top of distributional reinforcement learning (DRL) algorithms to deal with the overestimation in a locally adaptive way. Our framework is simple to implement, existing distributional algorithms can be improved with a few lines of code. We provide theoretical evidence and use double $Q$-learning to show how to include locally adaptive overestimation control in existing algorithms. Experiments are provided for tabular, Atari, and MuJoCo environments.
Locally adapting parameters within Markov chain Monte Carlo methods while preserving reversibility is notoriously difficult. The success of the No-U-Turn Sampler (NUTS) largely stems from its clever local adaptation of the integration time in Hamiltonian Monte Carlo via a geometric U-turn condition. However, posterior distributions frequently exhibit multi-scale geometries with extreme variations in scale, making it necessary to also adapt the leapfrog integrator's step size locally and dynamically. Despite its practical importance, this problem has remained largely open since the introduction of NUTS by Hoffman and Gelman (2014). To address this issue, we introduce the Within-orbit Adaptive Leapfrog No-U-Turn Sampler (WALNUTS), a generalization of NUTS that adapts the leapfrog step size at fixed intervals of simulated time as the orbit evolves. At each interval, the algorithm selects the largest step size from a dyadic schedule that keeps the energy error below a user-specified threshold. Like NUTS, WALNUTS employs biased progressive state selection to favor states with positions that are further from the initial point along the orbit. Empirical evaluations on multiscale target distributions, including Neal's funnel and the Stock-Watson stochastic volatility time-series model, demonstrate that WALNUTS achieves substantial improvements in sampling efficiency and robustness compared to standard NUTS.
Deep neural networks have demonstrated remarkable performance across numerous learning tasks but often suffer from miscalibration, resulting in unreliable probability outputs. This has inspired many recent works on mitigating miscalibration, particularly through post-hoc recalibration methods that aim to obtain calibrated probabilities without sacrificing the classification performance of pre-trained models. In this study, we summarize and categorize previous works into three general strategies: intuitively designed methods, binning-based methods, and methods based on formulations of ideal calibration. Through theoretical and practical analysis, we highlight ten common limitations in previous approaches. To address these limitations, we propose a probabilistic learning framework for calibration called h-calibration, which theoretically constructs an equivalent learning formulation for canonical calibration with boundedness. On this basis, we design a simple yet effective post-hoc calibration algorithm. Our method not only overcomes the ten identified limitations but also achieves markedly better performance than traditional methods, as validated by extensive experiments. We further analyze, both theoretically and experimentally, the relationship and advantages of our learning objective compared to traditional proper scoring rule. In summary, our probabilistic framework derives an approximately equivalent differentiable objective for learning error-bounded calibrated probabilities, elucidating the correspondence and convergence properties of computational statistics with respect to theoretical bounds in canonical calibration. The theoretical effectiveness is verified on standard post-hoc calibration benchmarks by achieving state-of-the-art performance. This research offers valuable reference for learning reliable likelihood in related fields.
Understanding and modeling enzyme-substrate interactions is crucial for catalytic mechanism research, enzyme engineering, and metabolic engineering. Although a large number of predictive methods have emerged, they do not incorporate prior knowledge of enzyme catalysis to rationally modulate general protein-molecule features that are misaligned with catalytic patterns. To address this issue, we introduce a two-stage progressive framework, OmniESI, for enzyme-substrate interaction prediction through conditional deep learning. By decomposing the modeling of enzyme-substrate interactions into a two-stage progressive process, OmniESI incorporates two conditional networks that respectively emphasize enzymatic reaction specificity and crucial catalysis-related interactions, facilitating a gradual feature modulation in the latent space from general protein-molecule domain to catalysis-aware domain. On top of this unified architecture, OmniESI can adapt to a variety of downstream tasks, including enzyme kinetic parameter prediction, enzyme-substrate pairing prediction, enzyme mutational effect prediction, and enzymatic active site annotation. Under the multi-perspective performance evaluation of in-distribution and out-of-distribution settings, OmniESI consistently delivered superior performance than state-of-the-art specialized methods across seven benchmarks. More importantly, the proposed conditional networks were shown to internalize the fundamental patterns of catalytic efficiency while significantly improving prediction performance, with only negligible parameter increases (0.16%), as demonstrated by ablation studies on key components. Overall, OmniESI represents a unified predictive approach for enzyme-substrate interactions, providing an effective tool for catalytic mechanism cracking and enzyme engineering with strong generalization and broad applicability.
Accurate prediction of antibody-antigen (Ab-Ag) binding affinity is essential for therapeutic design and vaccine development, yet the performance of current models is limited by noisy experimental labels, heterogeneous assay conditions, and poor generalization across the vast antibody and antigen sequence space. We introduce AbRank, a large-scale benchmark and evaluation framework that reframes affinity prediction as a pairwise ranking problem. AbRank aggregates over 380,000 binding assays from nine heterogeneous sources, spanning diverse antibodies, antigens, and experimental conditions, and introduces standardized data splits that systematically increase distribution shift, from local perturbations such as point mutations to broad generalization across novel antigens and antibodies. To ensure robust supervision, AbRank defines an m-confident ranking framework by filtering out comparisons with marginal affinity differences, focusing training on pairs with at least an m-fold difference in measured binding strength. As a baseline for the benchmark, we introduce WALLE-Affinity, a graph-based approach that integrates protein language model embeddings with structural information to predict pairwise binding preferences. Our benchmarks reveal significant limitations in current methods under realistic generalization settings and demonstrate that ranking-based training improves robustness and transferability. In summary, AbRank offers a robust foundation for machine learning models to generalize across the antibody-antigen space, with direct relevance for scalable, structure-aware antibody therapeutic design.
Generating diverse, all-atom conformational ensembles of dynamic proteins such as G-protein-coupled receptors (GPCRs) is critical for understanding their function, yet most generative models simplify atomic detail or ignore conformational diversity altogether. We present latent diffusion for full protein generation (LD-FPG), a framework that constructs complete all-atom protein structures, including every side-chain heavy atom, directly from molecular dynamics (MD) trajectories. LD-FPG employs a Chebyshev graph neural network (ChebNet) to obtain low-dimensional latent embeddings of protein conformations, which are processed using three pooling strategies: blind, sequential and residue-based. A diffusion model trained on these latent representations generates new samples that a decoder, optionally regularized by dihedral-angle losses, maps back to Cartesian coordinates. Using D2R-MD, a 2-microsecond MD trajectory (12 000 frames) of the human dopamine D2 receptor in a membrane environment, the sequential and residue-based pooling strategy reproduces the reference ensemble with high structural fidelity (all-atom lDDT of approximately 0.7; C-alpha-lDDT of approximately 0.8) and recovers backbone and side-chain dihedral-angle distributions with a Jensen-Shannon divergence of less than 0.03 compared to the MD data. LD-FPG thereby offers a practical route to system-specific, all-atom ensemble generation for large proteins, providing a promising tool for structure-based therapeutic design on complex, dynamic targets. The D2R-MD dataset and our implementation are freely available to facilitate further research.
Training large language models (LLMs) typically relies on adaptive optimizers such as Adam, which require significant memory to maintain first- and second-moment matrices, known as optimizer states. While recent works such as GaLore, Fira, and APOLLO have proposed state-compressed variants to reduce memory consumption, a fundamental question remains: What is the minimal amount of optimizer state that is truly necessary to retain state-of-the-art performance in LLM pretraining? In this work, we systematically investigate this question using a bottom-up approach. We find that two memory- and compute-efficient optimization techniques are particularly effective: (1) column-wise gradient normalization significantly boosts the performance of plain SGD without requiring momentum; and (2) adding first-order momentum only to the output layer - where gradient variance is highest - yields performance competitive with fully adaptive methods such as Muon. Based on these insights, we propose SCALE (Stochastic Column-normalized Last-layer Momentum), a new optimizer that combines column-normalized SGD with last-layer momentum, where column normalization refers to normalizing the gradient along the output dimension. Across multiple LLaMA models (60M-1B), SCALE matches or exceeds the performance of Adam while using only 35-45% of the total memory. It also consistently outperforms memory-efficient optimizers such as GaLore, Fira, and APOLLO, making it a strong candidate for large-scale pretraining under memory constraints. For the LLaMA 7B model, SCALE outperforms the state-of-the-art method APOLLO in terms of both perplexity and memory consumption. In addition, our method serves as a minimalist baseline for more sophisticated optimizer design.
Generating high-fidelity and biologically plausible synthetic single-cell RNA sequencing (scRNA-seq) data, especially with conditional control, is challenging due to its high dimensionality, sparsity, and complex biological variations. Existing generative models often struggle to capture these unique characteristics and ensure robustness to structural noise in cellular networks. We introduce LapDDPM, a novel conditional Graph Diffusion Probabilistic Model for robust and high-fidelity scRNA-seq generation. LapDDPM uniquely integrates graph-based representations with a score-based diffusion model, enhanced by a novel spectral adversarial perturbation mechanism on graph edge weights. Our contributions are threefold: we leverage Laplacian Positional Encodings (LPEs) to enrich the latent space with crucial cellular relationship information; we develop a conditional score-based diffusion model for effective learning and generation from complex scRNA-seq distributions; and we employ a unique spectral adversarial training scheme on graph edge weights, boosting robustness against structural variations. Extensive experiments on diverse scRNA-seq datasets demonstrate LapDDPM's superior performance, achieving high fidelity and generating biologically-plausible, cell-type-specific samples. LapDDPM sets a new benchmark for conditional scRNA-seq data generation, offering a robust tool for various downstream biological applications.
Probabilistic models are often used to make predictions in regions of the data space where no observations are available, but it is not always clear whether such predictions are well-informed by previously seen data. In this paper, we propose a knowledge score for predictions from Gaussian process regression (GPR) models that quantifies the extent to which observing data have reduced our uncertainty about a prediction. The knowledge score is interpretable and naturally bounded between 0 and 1. We demonstrate in several experiments that the knowledge score can anticipate when predictions from a GPR model are accurate, and that this anticipation improves performance in tasks such as anomaly detection, extrapolation, and missing data imputation. Source code for this project is available online at https://github.com/KurtButler/GP-knowledge.
This paper focuses on wireless multiple-input multiple-output (MIMO)-orthogonal frequency division multiplex (OFDM) receivers. Traditional wireless receivers have relied on mathematical modeling and Bayesian inference, achieving remarkable success in most areas but falling short in their ability to characterize channel matrices. Neural networks (NNs) have demonstrated significant potential in this aspect. Nevertheless, integrating traditional inference methods with NNs presents challenges, particularly in tracking the error progression. Given the inevitable presence of noise in wireless systems, generative models that are more resilient to noise are garnering increased attention. In this paper, we propose re-evaluating the MIMO-OFDM receiver using diffusion models, which is a common generative approach. With diffusion models, we can effectively leverage prior knowledge of channel matrices and incorporate traditional signal estimation components. Specifically, we explore the diffusion system and introduce an imagination-screening strategy to guide the diffusion process. Furthermore, diffusion models enable adaptation to varying noise levels and pilot schemes using the same NN, significantly reducing training and deployment costs. Simulated results reveal that, for pilot densities ranging from 4-6 pilots per 64-subcarrier block and signal-to-noise ratios (SNRs) from -4 dB to 0 dB, our proposed receiver reduces channel-reconstruction error by up to two times compared to leading deep-learning models, with the most pronounced improvements observed in low-pilot conditions. Additionally, performance enhancements can be achieved with a larger imagination size, despite increased computational complexity.
We study the properties of beamformers in their ability to either maintain or estimate the true signal power of the signal of interest (SOI). Our focus is particularly on the Capon beamformer and the minimum mean squared error (MMSE) beamformer. The Capon beamformer, also known as the minimum power distortionless response (MPDR) or the minimum variance distortionless response (MVDR) beamformer, is a widely used method in array signal processing. A curious feature of both the Capon and the MMSE beamformers is their tendency to either overestimate or underestimate the signal power. That is, they are not asymptotically unbiased (as the sample size approaches infinity). To address this issue, we propose to shrink the Capon beamformer by finding a scaling factor that minimizes the mean squared error (MSE) of the signal power estimate. The new beamformer, referred to as the Capon$^+$ beamformer, is evaluated against the Capon and MMSE beamformers in terms of bias, signal power MSE, and signal waveform MSE. The Capon$^+$ beamformer strikes a better balance between signal power and waveform estimation while also exhibiting minimal bias, which approaches zero as the sample size increases.
We propose a novel directional modulation (DM) design for OFDM transmitters aided by a time-modulated intelligent reflecting surface (TM-IRS). The TM-IRS is configured to preserve the integrity of transmitted signals toward multiple legitimate users while scrambling the signal in all other directions. Existing TM-IRS design methods typically target a single user direction and follow predefined rule-based procedures, making them unsuitable for multi-user scenarios. Here, we propose a generative AI-based approach to design good sets of TM-IRS parameters out of a set of all possible quantized ranges of parameters. The design objective is to maximize the sum rate across the authorized directions. We model the TM-IRS parameter selection as a deterministic Markov decision process (MDP), where each terminal state corresponds to a specific configuration of TM-IRS parameters. GFlowNets are employed to learn a stochastic policy that samples TM-IRS parameter sets with probability proportional to their associated sum rate reward. Experimental results demonstrate that the proposed method effectively enhances the security of the TM-IRS-aided OFDM systems with multi-users. Also, despite the vast size of the TM-IRS configuration space, the GFlowNet is able to converge after training on fewer than 0.000001% of all possible configurations, demonstrating remarkable efficiency compared to exhaustive combinatorial search. Implementation code is available at https://github.com/ZhihaoTao/GFN4TM-RIS to facilitate reproducibility.
Implicit Neural Representations (INRs) have recently shown impressive results, but their fundamental capacity, implicit biases, and scaling behavior remain poorly understood. We investigate the performance of diverse INRs across a suite of 2D and 3D real and synthetic signals with varying effective bandwidth, as well as both overfitting and generalization tasks including tomography, super-resolution, and denoising. By stratifying performance according to model size as well as signal type and bandwidth, our results shed light on how different INR and grid representations allocate their capacity. We find that, for most tasks and signals, a simple regularized grid with interpolation trains faster and to higher quality than any INR with the same number of parameters. We also find limited settings where INRs outperform grids -- namely fitting signals with underlying lower-dimensional structure such as shape contours -- to guide future use of INRs towards the most advantageous applications. Code and synthetic signals used in our analysis are available at https://github.com/voilalab/INR-benchmark.