Daily Papers

While researchers are finding concepts represented as linear directions in language models, a bag of linear directions fails to capture relational structure. To better understand this dichotomy, we study a model with known linear representations, but trained in a highly structured domain -- the board game Othello. While the model's internal board-state representation is linearly decodable, we find additional structure in the form of tensor product representations (TPRs). We train TPR probes to recover shared structure amongst the linear probes, yielding a factorization into square-embeddings, color-embeddings, and a binding matrix that composes them to construct the model's board-state representation. We find geometric signatures within the weights of our TPR probe that align with the structure of the board, but perhaps more importantly, that the linear probes can be recovered directly from the parameters of our TPR probe. Our findings suggest that directional representations may be projections of more structured underlying representations.

Vector Symbolic Architectures (VSAs) give a way to represent a complex object as a single fixed-length vector, so that similar objects have similar vector representations. These vector representations then become easy to use for machine learning or nearest-neighbor search. We review a previously proposed VSA method, MBAT (Matrix Binding of Additive Terms), which uses multiplication by random matrices for binding related terms. However, multiplying by such matrices introduces instabilities which can harm performance. Making the random matrices be orthogonal matrices provably fixes this problem. With respect to larger scale applications, we see how to apply MBAT vector representations for any data expressed in JSON. JSON is used in numerous programming languages to express complex data, but its native format appears highly unsuited for machine learning. Expressing JSON as a fixed-length vector makes it readily usable for machine learning and nearest-neighbor search. Creating such JSON vectors also shows that a VSA needs to employ binding operations that are non-commutative. VSAs are now ready to try with full-scale practical applications, including healthcare, pharmaceuticals, and genomics. Keywords: MBAT (Matrix Binding of Additive Terms), VSA (Vector Symbolic Architecture), HDC (Hyperdimensional Computing), Distributed Representations, Binding, Orthogonal Matrices, Recurrent Connections, Machine Learning, Search, JSON, VSA Applications

Food polysaccharides have emerged as suitable carriers of active substances and as additives to food and nutraceutical formulations, showing potential to stabilize bioactive compounds during the storage of microencapsulate preparations, even in the gastrointestinal tract following the intake of bioactive compounds, thereby improving their bioaccessibility and bioavailability. This review provides a comprehensive overview of the main polysaccharides employed as wall materials, including starch, maltodextrin, alginate, pectin, inulin, chitosan, and gum arabic, and discusses how structural interactions and physicochemical properties can benefit the microencapsulation of polyphenols and pigments. The main findings and principles of the major encapsulation techniques, including spray drying, freeze drying, extrusion, emulsification, and coacervation, related to the production of microparticles, were briefly described. Polysaccharides can entrap hydrophilic and hydrophobic compounds by physical interactions, forming a barrier around the nucleus or binding to the bioactive compound. Intermolecular binding between polysaccharides in the wall matrix, polyphenols, and pigments in the nucleus can confer up to 90% of encapsulation efficiency, governed mainly by hydrogen bonds and electrostatic interactions. The mixture of wall polysaccharides in the microparticles synthesis favors the encapsulation solubility, storage stability, bioaccessibility, and bioactivity of the microencapsulate compounds. Clinical trials on the bioefficacy of polyphenols and pigments loaded in polysaccharide microparticles are scarce and require further evidence to reinforce the use of this technology.

Modeling the interaction between proteins and ligands and accurately predicting their binding structures is a critical yet challenging task in drug discovery. Recent advancements in deep learning have shown promise in addressing this challenge, with sampling-based and regression-based methods emerging as two prominent approaches. However, these methods have notable limitations. Sampling-based methods often suffer from low efficiency due to the need for generating multiple candidate structures for selection. On the other hand, regression-based methods offer fast predictions but may experience decreased accuracy. Additionally, the variation in protein sizes often requires external modules for selecting suitable binding pockets, further impacting efficiency. In this work, we propose FABind, an end-to-end model that combines pocket prediction and docking to achieve accurate and fast protein-ligand binding. FABind incorporates a unique ligand-informed pocket prediction module, which is also leveraged for docking pose estimation. The model further enhances the docking process by incrementally integrating the predicted pocket to optimize protein-ligand binding, reducing discrepancies between training and inference. Through extensive experiments on benchmark datasets, our proposed FABind demonstrates strong advantages in terms of effectiveness and efficiency compared to existing methods. Our code is available at https://github.com/QizhiPei/FABind

The binding between proteins and ligands plays a crucial role in the realm of drug discovery. Previous deep learning approaches have shown promising results over traditional computationally intensive methods, but resulting in poor generalization due to limited supervised data. In this paper, we propose to learn protein-ligand binding representation in a self-supervised learning manner. Different from existing pre-training approaches which treat proteins and ligands individually, we emphasize to discern the intricate binding patterns from fine-grained interactions. Specifically, this self-supervised learning problem is formulated as a prediction of the conclusive binding complex structure given a pocket and ligand with a Transformer based interaction module, which naturally emulates the binding process. To ensure the representation of rich binding information, we introduce two pre-training tasks, i.e.~atomic pairwise distance map prediction and mask ligand reconstruction, which comprehensively model the fine-grained interactions from both structure and feature space. Extensive experiments have demonstrated the superiority of our method across various binding tasks, including protein-ligand affinity prediction, virtual screening and protein-ligand docking.

Foundation models applied to bio-molecular space hold promise to accelerate drug discovery. Molecular representation is key to building such models. Previous works have typically focused on a single representation or view of the molecules. Here, we develop a multi-view foundation model approach, that integrates molecular views of graph, image and text. Single-view foundation models are each pre-trained on a dataset of up to 200M molecules and then aggregated into combined representations. Our multi-view model is validated on a diverse set of 18 tasks, encompassing ligand-protein binding, molecular solubility, metabolism and toxicity. We show that the multi-view models perform robustly and are able to balance the strengths and weaknesses of specific views. We then apply this model to screen compounds against a large (>100 targets) set of G Protein-Coupled receptors (GPCRs). From this library of targets, we identify 33 that are related to Alzheimer's disease. On this subset, we employ our model to identify strong binders, which are validated through structure-based modeling and identification of key binding motifs.

Protein-ligand binding affinity prediction is essential for drug discovery and toxicity assessment. While machine learning (ML) promises fast and accurate predictions, its progress is constrained by the availability of reliable data. In contrast, physics-based methods such as absolute binding free energy perturbation (AB-FEP) deliver high accuracy but are computationally prohibitive for high-throughput applications. To bridge this gap, we introduce ToxBench, the first large-scale AB-FEP dataset designed for ML development and focused on a single pharmaceutically critical target, Human Estrogen Receptor Alpha (ERalpha). ToxBench contains 8,770 ERalpha-ligand complex structures with binding free energies computed via AB-FEP with a subset validated against experimental affinities at 1.75 kcal/mol RMSE, along with non-overlapping ligand splits to assess model generalizability. Using ToxBench, we further benchmark state-of-the-art ML methods, and notably, our proposed DualBind model, which employs a dual-loss framework to effectively learn the binding energy function. The benchmark results demonstrate the superior performance of DualBind and the potential of ML to approximate AB-FEP at a fraction of the computational cost.

The effects of ligand binding on protein structures and their in vivo functions carry numerous implications for modern biomedical research and biotechnology development efforts such as drug discovery. Although several deep learning (DL) methods and benchmarks designed for protein-ligand docking have recently been introduced, to date no prior works have systematically studied the behavior of the latest docking and structure prediction methods within the broadly applicable context of (1) using predicted (apo) protein structures for docking (e.g., for applicability to new proteins); (2) binding multiple (cofactor) ligands concurrently to a given target protein (e.g., for enzyme design); and (3) having no prior knowledge of binding pockets (e.g., for generalization to unknown pockets). To enable a deeper understanding of docking methods' real-world utility, we introduce PoseBench, the first comprehensive benchmark for broadly applicable protein-ligand docking. PoseBench enables researchers to rigorously and systematically evaluate DL methods for apo-to-holo protein-ligand docking and protein-ligand structure prediction using both primary ligand and multi-ligand benchmark datasets, the latter of which we introduce for the first time to the DL community. Empirically, using PoseBench, we find that (1) DL co-folding methods generally outperform comparable conventional and DL docking baselines, yet popular methods such as AlphaFold 3 are still challenged by prediction targets with novel protein sequences; (2) certain DL co-folding methods are highly sensitive to their input multiple sequence alignments, while others are not; and (3) DL methods struggle to strike a balance between structural accuracy and chemical specificity when predicting novel or multi-ligand protein targets. Code, data, tutorials, and benchmark results are available at https://github.com/BioinfoMachineLearning/PoseBench.

Accurate prediction of protein-ligand binding poses is crucial for structure-based drug design, yet existing methods struggle to balance speed, accuracy, and physical plausibility. We introduce Matcha, a novel molecular docking pipeline that combines multi-stage flow matching with learned scoring and physical validity filtering. Our approach consists of three sequential stages applied consecutively to refine docking predictions, each implemented as a flow matching model operating on appropriate geometric spaces (R^3, SO(3), and SO(2)). We enhance the prediction quality through a dedicated scoring model and apply unsupervised physical validity filters to eliminate unrealistic poses. Compared to various approaches, Matcha demonstrates superior performance on Astex and PDBbind test sets in terms of docking success rate and physical plausibility. Moreover, our method works approximately 25 times faster than modern large-scale co-folding models. The model weights and inference code to reproduce our results are available at https://github.com/LigandPro/Matcha.

To correctly use in-context information, language models (LMs) must bind entities to their attributes. For example, given a context describing a "green square" and a "blue circle", LMs must bind the shapes to their respective colors. We analyze LM representations and identify the binding ID mechanism: a general mechanism for solving the binding problem, which we observe in every sufficiently large model from the Pythia and LLaMA families. Using causal interventions, we show that LMs' internal activations represent binding information by attaching binding ID vectors to corresponding entities and attributes. We further show that binding ID vectors form a continuous subspace, in which distances between binding ID vectors reflect their discernability. Overall, our results uncover interpretable strategies in LMs for representing symbolic knowledge in-context, providing a step towards understanding general in-context reasoning in large-scale LMs.

Predicting how a drug-like molecule binds to a specific protein target is a core problem in drug discovery. An extremely fast computational binding method would enable key applications such as fast virtual screening or drug engineering. Existing methods are computationally expensive as they rely on heavy candidate sampling coupled with scoring, ranking, and fine-tuning steps. We challenge this paradigm with EquiBind, an SE(3)-equivariant geometric deep learning model performing direct-shot prediction of both i) the receptor binding location (blind docking) and ii) the ligand's bound pose and orientation. EquiBind achieves significant speed-ups and better quality compared to traditional and recent baselines. Further, we show extra improvements when coupling it with existing fine-tuning techniques at the cost of increased running time. Finally, we propose a novel and fast fine-tuning model that adjusts torsion angles of a ligand's rotatable bonds based on closed-form global minima of the von Mises angular distance to a given input atomic point cloud, avoiding previous expensive differential evolution strategies for energy minimization.

Identifying drug-target interactions is essential for developing effective therapeutics. Binding affinity quantifies these interactions, and traditional approaches rely on computationally intensive 3D structural data. In contrast, language models can efficiently process sequential data, offering an alternative approach to molecular representation. In the current study, we introduce BAPULM, an innovative sequence-based framework that leverages the chemical latent representations of proteins via ProtT5-XL-U50 and ligands through MolFormer, eliminating reliance on complex 3D configurations. Our approach was validated extensively on benchmark datasets, achieving scoring power (R) values of 0.925 pm 0.043, 0.914 pm 0.004, and 0.8132 pm 0.001 on benchmark1k2101, Test2016_290, and CSAR-HiQ_36, respectively. These findings indicate the robustness and accuracy of BAPULM across diverse datasets and underscore the potential of sequence-based models in-silico drug discovery, offering a scalable alternative to 3D-centric methods for screening potential ligands.

Though end-to-end neural approaches have recently been dominating NLP tasks in both performance and ease-of-use, they lack interpretability and robustness. We propose Binder, a training-free neural-symbolic framework that maps the task input to a program, which (1) allows binding a unified API of language model (LM) functionalities to a programming language (e.g., SQL, Python) to extend its grammar coverage and thus tackle more diverse questions, (2) adopts an LM as both the program parser and the underlying model called by the API during execution, and (3) requires only a few in-context exemplar annotations. Specifically, we employ GPT-3 Codex as the LM. In the parsing stage, with only a few in-context exemplars, Codex is able to identify the part of the task input that cannot be answerable by the original programming language, correctly generate API calls to prompt Codex to solve the unanswerable part, and identify where to place the API calls while being compatible with the original grammar. In the execution stage, Codex can perform versatile functionalities (e.g., commonsense QA, information extraction) given proper prompts in the API calls. Binder achieves state-of-the-art results on WikiTableQuestions and TabFact datasets, with explicit output programs that benefit human debugging. Note that previous best systems are all finetuned on tens of thousands of task-specific samples, while Binder only uses dozens of annotations as in-context exemplars without any training. Our code is available at https://github.com/HKUNLP/Binder .

The detection of ligand binding sites for proteins is a fundamental step in Structure-Based Drug Design. Despite notable advances in recent years, existing methods, datasets, and evaluation metrics are confronted with several key challenges: (1) current datasets and methods are centered on individual protein-ligand complexes and neglect that diverse binding sites may exist across multiple complexes of the same protein, introducing significant statistical bias; (2) ligand binding site detection is typically modeled as a discontinuous workflow, employing binary segmentation and subsequent clustering algorithms; (3) traditional evaluation metrics do not adequately reflect the actual performance of different binding site prediction methods. To address these issues, we first introduce UniSite-DS, the first UniProt (Unique Protein)-centric ligand binding site dataset, which contains 4.81 times more multi-site data and 2.08 times more overall data compared to the previously most widely used datasets. We then propose UniSite, the first end-to-end ligand binding site detection framework supervised by set prediction loss with bijective matching. In addition, we introduce Average Precision based on Intersection over Union (IoU) as a more accurate evaluation metric for ligand binding site prediction. Extensive experiments on UniSite-DS and several representative benchmark datasets demonstrate that IoU-based Average Precision provides a more accurate reflection of prediction quality, and that UniSite outperforms current state-of-the-art methods in ligand binding site detection. The dataset and codes will be made publicly available at https://github.com/quanlin-wu/unisite.

Predicting drug-target interaction (DTI) is critical in the drug discovery process. Despite remarkable advances in recent DTI models through the integration of representations from diverse drug and target encoders, such models often struggle to capture the fine-grained interactions between drugs and protein, i.e. the binding of specific drug atoms (or substructures) and key amino acids of proteins, which is crucial for understanding the binding mechanisms and optimising drug design. To address this issue, this paper introduces a novel model, called FusionDTI, which uses a token-level Fusion module to effectively learn fine-grained information for Drug-Target Interaction. In particular, our FusionDTI model uses the SELFIES representation of drugs to mitigate sequence fragment invalidation and incorporates the structure-aware (SA) vocabulary of target proteins to address the limitation of amino acid sequences in structural information, additionally leveraging pre-trained language models extensively trained on large-scale biomedical datasets as encoders to capture the complex information of drugs and targets. Experiments on three well-known benchmark datasets show that our proposed FusionDTI model achieves the best performance in DTI prediction compared with seven existing state-of-the-art baselines. Furthermore, our case study indicates that FusionDTI could highlight the potential binding sites, enhancing the explainability of the DTI prediction.

Accurate prediction of protein-ligand binding affinities is crucial in drug discovery, particularly during hit-to-lead and lead optimization phases, however, limitations in ligand force fields continue to impact prediction accuracy. In this work, we validate relative binding free energy (RBFE) accuracy using neural network potentials (NNPs) for the ligands. We utilize a novel NNP model, AceForce 1.0, based on the TensorNet architecture for small molecules that broadens the applicability to diverse drug-like compounds, including all important chemical elements and supporting charged molecules. Using established benchmarks, we show overall improved accuracy and correlation in binding affinity predictions compared with GAFF2 for molecular mechanics and ANI2-x for NNPs. Slightly less accuracy but comparable correlations with OPLS4. We also show that we can run the NNP simulations at 2 fs timestep, at least two times larger than previous NNP models, providing significant speed gains. The results show promise for further evolutions of free energy calculations using NNPs while demonstrating its practical use already with the current generation. The code and NNP model are publicly available for research use.

We simplify space binding by focusing on two core components, a single encoder per modality and high-quality data; enabling training state-of-the-art models on a single GPU in a few hours as opposed to multiple days. We present EBind, an Easy, data-centric, and parameter-efficient method to Bind the embedding spaces of multiple contrastive models. We demonstrate that a simple 1.8B-parameter image-text-video-audio-3D model can outperform models 4 to 17x the size. The key to achieving this is a carefully curated dataset of three complementary data sources: i) 6.7M fully-automated multimodal quintuples sourced via SOTA retrieval models, ii) 1M diverse, semi-automated triples annotated by humans as negative, partial, or positive matches, and iii) 3.4M pre-existing captioned data items. We use 13 different evaluations to demonstrate the value of each data source. Due to limitations with existing benchmarks, we further introduce the first high-quality, consensus-annotated zero-shot classification benchmark between audio and PCs. In contrast to related work, we will open-source our code, model weights, and datasets.

Recent research in representation learning utilizes large databases of proteins or molecules to acquire knowledge of drug and protein structures through unsupervised learning techniques. These pre-trained representations have proven to significantly enhance the accuracy of subsequent tasks, such as predicting the affinity between drugs and target proteins. In this study, we demonstrate that by incorporating knowledge graphs from diverse sources and modalities into the sequences or SMILES representation, we can further enrich the representation and achieve state-of-the-art results on established benchmark datasets. We provide preprocessed and integrated data obtained from 7 public sources, which encompass over 30M triples. Additionally, we make available the pre-trained models based on this data, along with the reported outcomes of their performance on three widely-used benchmark datasets for drug-target binding affinity prediction found in the Therapeutic Data Commons (TDC) benchmarks. Additionally, we make the source code for training models on benchmark datasets publicly available. Our objective in releasing these pre-trained models, accompanied by clean data for model pretraining and benchmark results, is to encourage research in knowledge-enhanced representation learning.

Accurate prediction of Drug-Target Affinity (DTA) is of vital importance in early-stage drug discovery, facilitating the identification of drugs that can effectively interact with specific targets and regulate their activities. While wet experiments remain the most reliable method, they are time-consuming and resource-intensive, resulting in limited data availability that poses challenges for deep learning approaches. Existing methods have primarily focused on developing techniques based on the available DTA data, without adequately addressing the data scarcity issue. To overcome this challenge, we present the SSM-DTA framework, which incorporates three simple yet highly effective strategies: (1) A multi-task training approach that combines DTA prediction with masked language modeling (MLM) using paired drug-target data. (2) A semi-supervised training method that leverages large-scale unpaired molecules and proteins to enhance drug and target representations. This approach differs from previous methods that only employed molecules or proteins in pre-training. (3) The integration of a lightweight cross-attention module to improve the interaction between drugs and targets, further enhancing prediction accuracy. Through extensive experiments on benchmark datasets such as BindingDB, DAVIS, and KIBA, we demonstrate the superior performance of our framework. Additionally, we conduct case studies on specific drug-target binding activities, virtual screening experiments, drug feature visualizations, and real-world applications, all of which showcase the significant potential of our work. In conclusion, our proposed SSM-DTA framework addresses the data limitation challenge in DTA prediction and yields promising results, paving the way for more efficient and accurate drug discovery processes. Our code is available at https://github.com/QizhiPei/SSM-DTA{Github}.

Generative models for structure-based drug design (SBDD) have shown promising results in recent years. Existing works mainly focus on how to generate molecules with higher binding affinity, ignoring the feasibility prerequisites for generated 3D poses and resulting in false positives. We conduct thorough studies on key factors of ill-conformational problems when applying autoregressive methods and diffusion to SBDD, including mode collapse and hybrid continuous-discrete space. In this paper, we introduce MolCRAFT, the first SBDD model that operates in the continuous parameter space, together with a novel noise reduced sampling strategy. Empirical results show that our model consistently achieves superior performance in binding affinity with more stable 3D structure, demonstrating our ability to accurately model interatomic interactions. To our best knowledge, MolCRAFT is the first to achieve reference-level Vina Scores (-6.59 kcal/mol) with comparable molecular size, outperforming other strong baselines by a wide margin (-0.84 kcal/mol). Code is available at https://github.com/AlgoMole/MolCRAFT.

Proteins are fundamental to biology, executing diverse functions through complex physicochemical interactions, and they hold transformative potential across medicine, materials science, and environmental applications. Protein Language Models (pLMs) aim to unlock insights from the vast space of unlabeled protein sequences by learning rich, semantic representations from primary sequences via masked language modeling. However, these models typically exhibit limited generative capacity. In this work, we introduce the Diffusion Sequence Model (DSM), a novel pLM trained with masked diffusion to enable both high-quality representation learning and generative protein design. DSM builds upon the ESM2 architecture by incorporating a masked forward diffusion process inspired by the LLaDA framework. After training, DSM is capable of generating diverse, biomimetic sequences that align with expected amino acid compositions, secondary structures, and predicted functions, even with 90\% token corruption. Furthermore, DSM's learned representations match or exceed those of similarly sized pLMs on downstream tasks. We also introduce DSM(ppi), a variant fine-tuned to generate protein binders by attending to target sequences. We demonstrate DSM(ppi)'s effectiveness on the challenging Bench-tested Binder Benchmark (BenchBB), where both DSM and DSM(ppi) produce candidates with superior predicted binding affinity compared to known binders. Our results establish masked diffusion as a powerful paradigm for unifying protein representation and generation in a single framework.

Recent AI advances have enabled multi-modal systems to model and translate diverse information spaces. Extending beyond text and vision, we introduce OneProt, a multi-modal AI for proteins that integrates structural, sequence, alignment, and binding site data. Using the ImageBind framework, OneProt aligns the latent spaces of modality encoders along protein sequences. It demonstrates strong performance in retrieval tasks and surpasses state-of-the-art methods in various downstream tasks, including metal ion binding classification, gene-ontology annotation, and enzyme function prediction. This work expands multi-modal capabilities in protein models, paving the way for applications in drug discovery, biocatalytic reaction planning, and protein engineering.

Modern AI technologies for drug discovery are distributed across heterogeneous platforms-including web applications, desktop environments, and code libraries-leading to fragmented workflows, inconsistent interfaces, and high integration overhead. We present an agentic end-to-end drug design framework that leverages a Large Language Model (LLM) in conjunction with the Model Context Protocol (MCP) to dynamically coordinate access to biochemical databases, modular toolchains, and task-specific AI models. The system integrates four state-of-the-art components: MaSIF (MaSIF-site and MaSIF-seed-search) for geometric deep learning-based identification of protein-protein interaction (PPI) sites, Rosetta for grafting protein fragments onto protein backbones to form mini proteins, ProteinMPNN for amino acid sequences redesign, and AlphaFold3 for near-experimental accuracy in complex structure prediction. Starting from a target structure, the framework supports de novo binder generation via surface analysis, scaffold grafting and pose construction, sequence optimization, and structure prediction. Additionally, by replacing rigid, script-based workflows with a protocol-driven, LLM-coordinated architecture, the framework improves reproducibility, reduces manual overhead, and ensures extensibility, portability, and auditability across the entire drug design process.

Parameter-efficient fine-tuning optimizes large, pre-trained foundation models by updating a subset of parameters; in this class, Low-Rank Adaptation (LoRA) is particularly effective. Inspired by an effort to investigate the different roles of LoRA matrices during fine-tuning, this paper characterizes and leverages unexpected asymmetry in the importance of low-rank adapter matrices. Specifically, when updating the parameter matrices of a neural network by adding a product BA, we observe that the B and A matrices have distinct functions: A extracts features from the input, while B uses these features to create the desired output. Based on this observation, we demonstrate that fine-tuning B is inherently more effective than fine-tuning A, and that a random untrained A should perform nearly as well as a fine-tuned one. Using an information-theoretic lens, we also bound the generalization of low-rank adapters, showing that the parameter savings of exclusively training B improves the bound. We support our conclusions with experiments on RoBERTa, BART-Large, LLaMA-2, and ViTs.

For learning with noisy labels, the transition matrix, which explicitly models the relation between noisy label distribution and clean label distribution, has been utilized to achieve the statistical consistency of either the classifier or the risk. Previous researches have focused more on how to estimate this transition matrix well, rather than how to utilize it. We propose good utilization of the transition matrix is crucial and suggest a new utilization method based on resampling, coined RENT. Specifically, we first demonstrate current utilizations can have potential limitations for implementation. As an extension to Reweighting, we suggest the Dirichlet distribution-based per-sample Weight Sampling (DWS) framework, and compare reweighting and resampling under DWS framework. With the analyses from DWS, we propose RENT, a REsampling method with Noise Transition matrix. Empirically, RENT consistently outperforms existing transition matrix utilization methods, which includes reweighting, on various benchmark datasets. Our code is available at https://github.com/BaeHeeSun/RENT.

Absolute Binding Free Energy (ABFE) methods are among the most accurate computational techniques for predicting protein-ligand binding affinities, but their utility is limited by the need for many simulations of alchemically modified intermediate states. We propose Direct Binding Free Energy (DBFE), an end-state ABFE method in implicit solvent that requires no alchemical intermediates. DBFE outperforms OBC2 double decoupling on a host-guest benchmark and performs comparably to OBC2 MM/GBSA on a protein-ligand benchmark. Since receptor and ligand simulations can be precomputed and amortized across compounds, DBFE requires only one complex simulation per ligand compared to the many lambda windows needed for double decoupling, making it a promising candidate for virtual screening workflows. We publicly release the code for this method at https://github.com/molecularmodelinglab/dbfe.

In this paper, we propose a new class of metric for table structure recognition (TSR) evaluation, called grid table similarity (GriTS). Unlike prior metrics, GriTS evaluates the correctness of a predicted table directly in its natural form as a matrix. To create a similarity measure between matrices, we generalize the two-dimensional largest common substructure (2D-LCS) problem, which is NP-hard, to the 2D most similar substructures (2D-MSS) problem and propose a polynomial-time heuristic for solving it. This algorithm produces both an upper and a lower bound on the true similarity between matrices. We show using evaluation on a large real-world dataset that in practice there is almost no difference between these bounds. We compare GriTS to other metrics and empirically validate that matrix similarity exhibits more desirable behavior than alternatives for TSR performance evaluation. Finally, GriTS unifies all three subtasks of cell topology recognition, cell location recognition, and cell content recognition within the same framework, which simplifies the evaluation and enables more meaningful comparisons across different types of TSR approaches. Code will be released at https://github.com/microsoft/table-transformer.

Popular parameter-efficient fine-tuning (PEFT) methods, such as LoRA and its variants, freeze pre-trained model weights \(W\) and inject learnable matrices \(\Delta W\). These \(\Delta W\) matrices are structured for efficient parameterization, often using techniques like low-rank approximations or scaling vectors. However, these methods typically show a performance gap compared to full fine-tuning. Although recent PEFT methods have narrowed this gap, they do so at the cost of additional learnable parameters. We propose SVFT, a simple approach that fundamentally differs from existing methods: the structure imposed on \(\Delta W\) depends on the specific weight matrix \(W\). Specifically, SVFT updates \(W\) as a sparse combination of outer products of its singular vectors, training only the coefficients (scales) of these sparse combinations. This approach allows fine-grained control over expressivity through the number of coefficients. Extensive experiments on language and vision benchmarks show that SVFT recovers up to 96% of full fine-tuning performance while training only 0.006 to 0.25% of parameters, outperforming existing methods that only recover up to 85% performance using 0.03 to 0.8% of the trainable parameter budget.

Text-to-image diffusion models particularly Stable Diffusion, have revolutionized the field of computer vision. However, the synthesis quality often deteriorates when asked to generate images that faithfully represent complex prompts involving multiple attributes and objects. While previous studies suggest that blended text embeddings lead to improper attribute binding, few have explored this in depth. In this work, we critically examine the limitations of the CLIP text encoder in understanding attributes and investigate how this affects diffusion models. We discern a phenomenon of attribute bias in the text space and highlight a contextual issue in padding embeddings that entangle different concepts. We propose Magnet, a novel training-free approach to tackle the attribute binding problem. We introduce positive and negative binding vectors to enhance disentanglement, further with a neighbor strategy to increase accuracy. Extensive experiments show that Magnet significantly improves synthesis quality and binding accuracy with negligible computational cost, enabling the generation of unconventional and unnatural concepts.

Computational design of protein-binding proteins is a fundamental capability with broad utility in biomedical research and biotechnology. Recent methods have made strides against some target proteins, but on-demand creation of high-affinity binders without multiple rounds of experimental testing remains an unsolved challenge. This technical report introduces AlphaProteo, a family of machine learning models for protein design, and details its performance on the de novo binder design problem. With AlphaProteo, we achieve 3- to 300-fold better binding affinities and higher experimental success rates than the best existing methods on seven target proteins. Our results suggest that AlphaProteo can generate binders "ready-to-use" for many research applications using only one round of medium-throughput screening and no further optimization.

To adapt a well-trained large model to downstream tasks, we propose constraining learning within its original latent space by leveraging linear combinations of its basis vectors. This approach ensures stable training without compromising the model's capabilities. Traditionally, constructing orthonormal bases from a matrix requires a transfer matrix, which significantly increases storage and computational overhead for parameters and feature maps. In this paper, we introduce Absorb and Decompose for Q, K, V, and O matrices, enabling their orthogonalization without the need for transfer matrices. Furthermore, the Absorb-Decompose operation eliminates redundant vectors, reducing the encoder attention parameters of Whisper-large-v3 by 46.42% without requiring additional training. For parameter-efficient and stable fine-tuning, we orthonormalized Q, K, V, and O and fine-tuned only the singular values, allowing efficient adaptation while constraining changes to the original latent space. When fine-tuning LLaMA-2-7B on eight commonsense reasoning datasets, our method outperforms LoRA by 5.4% and DoRA by 4.4%.

Aligning large language models (LLMs) with human values is imperative to mitigate potential adverse effects resulting from their misuse. Drawing from the sociological insight that acknowledging all parties' concerns is a key factor in shaping human values, this paper proposes a novel direction to align LLMs by themselves: social scene simulation. To achieve this, we present MATRIX, a novel social scene simulator that emulates realistic scenes around a user's input query, enabling the LLM to take social consequences into account before responding. MATRIX serves as a virtual rehearsal space, akin to a Monopolylogue, where the LLM performs diverse roles related to the query and practice by itself. To inject this alignment, we fine-tune the LLM with MATRIX-simulated data, ensuring adherence to human values without compromising inference speed. We theoretically show that the LLM with MATRIX outperforms Constitutional AI under mild assumptions. Finally, extensive experiments validate that our method outperforms over 10 baselines across 4 benchmarks. As evidenced by 875 user ratings, our tuned 13B-size LLM exceeds GPT-4 in aligning with human values. Code is available at https://github.com/pangxianghe/MATRIX.

Molecular docking is an important tool for structure-based drug design, accelerating the efficiency of drug development. Complex and dynamic binding processes between proteins and small molecules require searching and sampling over a wide spatial range. Traditional docking by searching for possible binding sites and conformations is computationally complex and results poorly under blind docking. Quantum-inspired algorithms combining quantum properties and annealing show great advantages in solving combinatorial optimization problems. Inspired by this, we achieve an improved in blind docking by using quantum-inspired combined with gradients learned by deep learning in the encoded molecular space. Numerical simulation shows that our method outperforms traditional docking algorithms and deep learning-based algorithms over 10\%. Compared to the current state-of-the-art deep learning-based docking algorithm DiffDock, the success rate of Top-1 (RMSD<2) achieves an improvement from 33\% to 35\% in our same setup. In particular, a 6\% improvement is realized in the high-precision region(RMSD<1) on molecules data unseen in DiffDock, which demonstrates the well-generalized of our method.

Emerging large-scale text-to-image generative models, e.g., Stable Diffusion (SD), have exhibited overwhelming results with high fidelity. Despite the magnificent progress, current state-of-the-art models still struggle to generate images fully adhering to the input prompt. Prior work, Attend & Excite, has introduced the concept of Generative Semantic Nursing (GSN), aiming to optimize cross-attention during inference time to better incorporate the semantics. It demonstrates promising results in generating simple prompts, e.g., ``a cat and a dog''. However, its efficacy declines when dealing with more complex prompts, and it does not explicitly address the problem of improper attribute binding. To address the challenges posed by complex prompts or scenarios involving multiple entities and to achieve improved attribute binding, we propose Divide & Bind. We introduce two novel loss objectives for GSN: a novel attendance loss and a binding loss. Our approach stands out in its ability to faithfully synthesize desired objects with improved attribute alignment from complex prompts and exhibits superior performance across multiple evaluation benchmarks. More videos and updates can be found on the project page https://sites.google.com/view/divide-and-bind.

Recently, human-computer interaction with various modalities has shown promising applications, like GPT-4o and Gemini. Given the foundational role of multimodal joint representation in understanding and generation pipelines, high-quality omni joint representations would be a step toward co-processing more diverse multimodal information. In this work, we present OmniBind, large-scale multimodal joint representation models ranging in scale from 7 billion to 30 billion parameters, which support 3D, audio, image, and language inputs. Due to the scarcity of data pairs across all modalities, instead of training large models from scratch, we propose remapping and binding the spaces of various pre-trained specialist models together. This approach enables "scaling up" by indirectly increasing the model parameters and the amount of seen data. To effectively integrate various spaces, we dynamically assign weights to different spaces by learning routers with two objectives: cross-modal overall alignment and language representation decoupling. Notably, since binding and routing spaces both only require lightweight networks, OmniBind is extremely training-efficient. Learning the largest 30B model requires merely unpaired unimodal data and approximately 3 days on a single 8-4090 node. Extensive experiments demonstrate the versatility and superiority of OmniBind as an omni representation model, highlighting its great potential for diverse applications, such as any-query and composable multimodal understanding.

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix {sf A} and a positive semi-definite matrix Win R^{ntimes n} with a sparse eigenbasis, we consider the task of maintaining the projection in the form of {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}, where {sf B}={sf A}(Wotimes I) or {sf B}={sf A}(W^{1/2}otimes W^{1/2}). At each iteration, the weight matrix W receives a low rank change and we receive a new vector h. The goal is to maintain the projection matrix and answer the query {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}h with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

Powerful generative AI models of protein-ligand structure have recently been proposed, but few of these methods support both flexible protein-ligand docking and affinity estimation. Of those that do, none can directly model multiple binding ligands concurrently or have been rigorously benchmarked on pharmacologically relevant drug targets, hindering their widespread adoption in drug discovery efforts. In this work, we propose FlowDock, the first deep geometric generative model based on conditional flow matching that learns to directly map unbound (apo) structures to their bound (holo) counterparts for an arbitrary number of binding ligands. Furthermore, FlowDock provides predicted structural confidence scores and binding affinity values with each of its generated protein-ligand complex structures, enabling fast virtual screening of new (multi-ligand) drug targets. For the well-known PoseBusters Benchmark dataset, FlowDock outperforms single-sequence AlphaFold 3 with a 51% blind docking success rate using unbound (apo) protein input structures and without any information derived from multiple sequence alignments, and for the challenging new DockGen-E dataset, FlowDock outperforms single-sequence AlphaFold 3 and matches single-sequence Chai-1 for binding pocket generalization. Additionally, in the ligand category of the 16th community-wide Critical Assessment of Techniques for Structure Prediction (CASP16), FlowDock ranked among the top-5 methods for pharmacological binding affinity estimation across 140 protein-ligand complexes, demonstrating the efficacy of its learned representations in virtual screening. Source code, data, and pre-trained models are available at https://github.com/BioinfoMachineLearning/FlowDock.

Pre-trained models have become the preferred backbone due to the expansion of model parameters, with techniques like Parameter-Efficient Fine-Tuning (PEFTs) typically fixing the parameters of these models. However, pre-trained models may not always be optimal, especially when there are discrepancies between training tasks and target tasks, potentially resulting in negative transfer. To address this, we introduce KIND, which performs Knowledge INtegration and Diversion in diffusion models. KIND first integrates knowledge by decomposing parameter matrices of models using U, Sigma, and V matrices, formally inspired by singular value decomposition (SVD). Then it explicitly partitions the components of these matrices into learngenes and tailors to condense common and class-specific knowledge, respectively, through a class gate. In this way, KIND redefines traditional pre-training methods by adjusting training objectives from maximizing model performance on current tasks to condensing transferable common knowledge, leveraging the Learngene framework. We conduct experiments on ImageNet-1K and compare KIND with PEFT and other learngene methods. Results indicate that KIND achieves state-of-the-art performance compared to other PEFT and learngene methods. Specifically, the images generated by KIND achieves more than 6.54 and 1.07 decrease in FID and sFID on DiT-L/2, utilizing only 45.4M trainable parameters and saving at least 35.4G FLOPs in computational cost.

Large neural networks excel in many domains, but they are expensive to train and fine-tune. A popular approach to reduce their compute or memory requirements is to replace dense weight matrices with structured ones (e.g., sparse, low-rank, Fourier transform). These methods have not seen widespread adoption (1) in end-to-end training due to unfavorable efficiency--quality tradeoffs, and (2) in dense-to-sparse fine-tuning due to lack of tractable algorithms to approximate a given dense weight matrix. To address these issues, we propose a class of matrices (Monarch) that is hardware-efficient (they are parameterized as products of two block-diagonal matrices for better hardware utilization) and expressive (they can represent many commonly used transforms). Surprisingly, the problem of approximating a dense weight matrix with a Monarch matrix, though nonconvex, has an analytical optimal solution. These properties of Monarch matrices unlock new ways to train and fine-tune sparse and dense models. We empirically validate that Monarch can achieve favorable accuracy-efficiency tradeoffs in several end-to-end sparse training applications: speeding up ViT and GPT-2 training on ImageNet classification and Wikitext-103 language modeling by 2x with comparable model quality, and reducing the error on PDE solving and MRI reconstruction tasks by 40%. In sparse-to-dense training, with a simple technique called "reverse sparsification," Monarch matrices serve as a useful intermediate representation to speed up GPT-2 pretraining on OpenWebText by 2x without quality drop. The same technique brings 23% faster BERT pretraining than even the very optimized implementation from Nvidia that set the MLPerf 1.1 record. In dense-to-sparse fine-tuning, as a proof-of-concept, our Monarch approximation algorithm speeds up BERT fine-tuning on GLUE by 1.7x with comparable accuracy.

Prediction of protein-ligand (PL) binding affinity remains the key to drug discovery. Popular approaches in recent years involve graph neural networks (GNNs), which are used to learn the topology and geometry of PL complexes. However, GNNs are computationally heavy and have poor scalability to graph sizes. On the other hand, traditional machine learning (ML) approaches, such as gradient-boosted decision trees (GBDTs), are lightweight yet extremely efficient for tabular data. We propose to use PL interaction features along with PL graph-level features in GBDT. We show that this combination outperforms the existing solutions.

We introduce AbBiBench (Antibody Binding Benchmarking), a benchmarking framework for antibody binding affinity maturation and design. Unlike previous strategies that evaluate antibodies in isolation, typically by comparing them to natural sequences with metrics such as amino acid recovery rate or structural RMSD, AbBiBench instead treats the antibody-antigen (Ab-Ag) complex as the fundamental unit. It evaluates an antibody design's binding potential by measuring how well a protein model scores the full Ab-Ag complex. We first curate, standardize, and share more than 184,500 experimental measurements of antibody mutants across 14 antibodies and 9 antigens-including influenza, lysozyme, HER2, VEGF, integrin, Ang2, and SARS-CoV-2-covering both heavy-chain and light-chain mutations. Using these datasets, we systematically compare 15 protein models including masked language models, autoregressive language models, inverse folding models, diffusion-based generative models, and geometric graph models by comparing the correlation between model likelihood and experimental affinity values. Additionally, to demonstrate AbBiBench's generative utility, we apply it to antibody F045-092 in order to introduce binding to influenza H1N1. We sample new antibody variants with the top-performing models, rank them by the structural integrity and biophysical properties of the Ab-Ag complex, and assess them with in vitro ELISA binding assays. Our findings show that structure-conditioned inverse folding models outperform others in both affinity correlation and generation tasks. Overall, AbBiBench provides a unified, biologically grounded evaluation framework to facilitate the development of more effective, function-aware antibody design models.

Recent advances in vision language models (VLM) have been driven by contrastive models such as CLIP, which learn to associate visual information with their corresponding text descriptions. However, these models have limitations in understanding complex compositional scenes involving multiple objects and their spatial relationships. To address these challenges, we propose a novel approach that diverges from commonly used strategies, which rely on the design of hard-negative augmentations. Instead, our work focuses on integrating inductive biases into pre-trained CLIP-like models to improve their compositional understanding without using any additional hard-negatives. To that end, we introduce a binding module that connects a scene graph, derived from a text description, with a slot-structured image representation, facilitating a structured similarity assessment between the two modalities. We also leverage relationships as text-conditioned visual constraints, thereby capturing the intricate interactions between objects and their contextual relationships more effectively. Our resulting model not only enhances the performance of CLIP-based models in multi-object compositional understanding but also paves the way towards more accurate and sample-efficient image-text matching of complex scenes.

Although text-to-image (T2I) models exhibit remarkable generation capabilities, they frequently fail to accurately bind semantically related objects or attributes in the input prompts; a challenge termed semantic binding. Previous approaches either involve intensive fine-tuning of the entire T2I model or require users or large language models to specify generation layouts, adding complexity. In this paper, we define semantic binding as the task of associating a given object with its attribute, termed attribute binding, or linking it to other related sub-objects, referred to as object binding. We introduce a novel method called Token Merging (ToMe), which enhances semantic binding by aggregating relevant tokens into a single composite token. This ensures that the object, its attributes and sub-objects all share the same cross-attention map. Additionally, to address potential confusion among main objects with complex textual prompts, we propose end token substitution as a complementary strategy. To further refine our approach in the initial stages of T2I generation, where layouts are determined, we incorporate two auxiliary losses, an entropy loss and a semantic binding loss, to iteratively update the composite token to improve the generation integrity. We conducted extensive experiments to validate the effectiveness of ToMe, comparing it against various existing methods on the T2I-CompBench and our proposed GPT-4o object binding benchmark. Our method is particularly effective in complex scenarios that involve multiple objects and attributes, which previous methods often fail to address. The code will be publicly available at https://github.com/hutaihang/ToMe.

Antibodies comprise the most versatile class of binding molecules, with numerous applications in biomedicine. Computational design of antibodies involves generating novel and diverse sequences, while maintaining structural consistency. Unique to antibodies, designing the complementarity-determining region (CDR), which determines the antigen binding affinity and specificity, creates its own unique challenges. Recent deep learning models have shown impressive results, however the limited number of known antibody sequence/structure pairs frequently leads to degraded performance, particularly lacking diversity in the generated sequences. In our work we address this challenge by leveraging Model Reprogramming (MR), which repurposes pretrained models on a source language to adapt to the tasks that are in a different language and have scarce data - where it may be difficult to train a high-performing model from scratch or effectively fine-tune an existing pre-trained model on the specific task. Specifically, we introduce ReprogBert in which a pretrained English language model is repurposed for protein sequence infilling - thus considers cross-language adaptation using less data. Results on antibody design benchmarks show that our model on low-resourced antibody sequence dataset provides highly diverse CDR sequences, up to more than a two-fold increase of diversity over the baselines, without losing structural integrity and naturalness. The generated sequences also demonstrate enhanced antigen binding specificity and virus neutralization ability. Code is available at https://github.com/IBM/ReprogBERT

Deep learning promises to dramatically improve scoring functions for molecular docking, leading to substantial advances in binding pose prediction and virtual screening. To train scoring functions-and to perform molecular docking-one must generate a set of candidate ligand binding poses. Unfortunately, the sampling protocols currently used to generate candidate poses frequently fail to produce any poses close to the correct, experimentally determined pose, unless information about the correct pose is provided. This limits the accuracy of learned scoring functions and molecular docking. Here, we describe two improved protocols for pose sampling: GLOW (auGmented sampLing with sOftened vdW potential) and a novel technique named IVES (IteratiVe Ensemble Sampling). Our benchmarking results demonstrate the effectiveness of our methods in improving the likelihood of sampling accurate poses, especially for binding pockets whose shape changes substantially when different ligands bind. This improvement is observed across both experimentally determined and AlphaFold-generated protein structures. Additionally, we present datasets of candidate ligand poses generated using our methods for each of around 5,000 protein-ligand cross-docking pairs, for training and testing scoring functions. To benefit the research community, we provide these cross-docking datasets and an open-source Python implementation of GLOW and IVES at https://github.com/drorlab/GLOW_IVES .

We provide a concise framework for generalized ensemble theory through a matrix-based approach. By introducing an observation matrix, any discrete probability distribution, including those for non-equilibrium steady states, can be expressed as a generalized Boltzmann distribution, with observables and conjugate variables as the basis and coordinates in a linear space. In this framework, we identify the minimal sufficient statistics required for inferring the Boltzmann distribution. Furthermore, we show that the Hadamard and Vandermonde matrices are suitable observation matrices for spin systems and random walks. In master equation systems, the probability flux observation matrix facilitates the identification of detailed balance violations. Our findings provide a new approach to developing generalized ensemble theory for non-equilibrium steady-state systems.

Generating novel active molecules for a given protein is an extremely challenging task for generative models that requires an understanding of the complex physical interactions between the molecule and its environment. In this paper, we present a novel generative model, BindGPT which uses a conceptually simple but powerful approach to create 3D molecules within the protein's binding site. Our model produces molecular graphs and conformations jointly, eliminating the need for an extra graph reconstruction step. We pretrain BindGPT on a large-scale dataset and fine-tune it with reinforcement learning using scores from external simulation software. We demonstrate how a single pretrained language model can serve at the same time as a 3D molecular generative model, conformer generator conditioned on the molecular graph, and a pocket-conditioned 3D molecule generator. Notably, the model does not make any representational equivariance assumptions about the domain of generation. We show how such simple conceptual approach combined with pretraining and scaling can perform on par or better than the current best specialized diffusion models, language models, and graph neural networks while being two orders of magnitude cheaper to sample.

Model immunization aims to pre-train models that are difficult to fine-tune on harmful tasks while retaining their utility on other non-harmful tasks. Though prior work has shown empirical evidence for immunizing text-to-image models, the key understanding of when immunization is possible and a precise definition of an immunized model remain unclear. In this work, we propose a framework, based on the condition number of a Hessian matrix, to analyze model immunization for linear models. Building on this framework, we design an algorithm with regularization terms to control the resulting condition numbers after pre-training. Empirical results on linear models and non-linear deep-nets demonstrate the effectiveness of the proposed algorithm on model immunization. The code is available at https://github.com/amberyzheng/model-immunization-cond-num.

Supervised machine learning approaches have been increasingly used in accelerating electronic structure prediction as surrogates of first-principle computational methods, such as density functional theory (DFT). While numerous quantum chemistry datasets focus on chemical properties and atomic forces, the ability to achieve accurate and efficient prediction of the Hamiltonian matrix is highly desired, as it is the most important and fundamental physical quantity that determines the quantum states of physical systems and chemical properties. In this work, we generate a new Quantum Hamiltonian dataset, named as QH9, to provide precise Hamiltonian matrices for 999 or 2998 molecular dynamics trajectories and 130,831 stable molecular geometries, based on the QM9 dataset. By designing benchmark tasks with various molecules, we show that current machine learning models have the capacity to predict Hamiltonian matrices for arbitrary molecules. Both the QH9 dataset and the baseline models are provided to the community through an open-source benchmark, which can be highly valuable for developing machine learning methods and accelerating molecular and materials design for scientific and technological applications. Our benchmark is publicly available at https://github.com/divelab/AIRS/tree/main/OpenDFT/QHBench.

Subject-driven image generation is increasingly expected to support fine-grained control over multiple entities within a single image. In multi-reference workflows, users may provide several subject images, a background reference, and long, entity-indexed prompts to control multiple people within one scene. In this setting, a key failure mode is cross-subject attribute misbinding: attributes are preserved, edited, or transferred to the wrong subject. Existing benchmarks and metrics largely emphasize holistic fidelity or per-subject self-similarity, making such failures hard to diagnose. We introduce MultiBind, a benchmark built from real multi-person photographs. Each instance provides slot-ordered subject crops with masks and bounding boxes, canonicalized subject references, an inpainted background reference, and a dense entity-indexed prompt derived from structured annotations. We also propose a dimension-wise confusion evaluation protocol that matches generated subjects to ground-truth slots and measures slot-to-slot similarity using specialists for face identity, appearance, pose, and expression. By subtracting the corresponding ground-truth similarity matrices, our method separates self-degradation from true cross-subject interference and exposes interpretable failure patterns such as drift, swap, dominance, and blending. Experiments on modern multi-reference generators show that MultiBind reveals binding failures that conventional reconstruction metrics miss.

Machine Learning Force Fields (MLFFs) are a promising alternative to expensive ab initio quantum mechanical molecular simulations. Given the diversity of chemical spaces that are of interest and the cost of generating new data, it is important to understand how MLFFs generalize beyond their training distributions. In order to characterize and better understand distribution shifts in MLFFs, we conduct diagnostic experiments on chemical datasets, revealing common shifts that pose significant challenges, even for large foundation models trained on extensive data. Based on these observations, we hypothesize that current supervised training methods inadequately regularize MLFFs, resulting in overfitting and learning poor representations of out-of-distribution systems. We then propose two new methods as initial steps for mitigating distribution shifts for MLFFs. Our methods focus on test-time refinement strategies that incur minimal computational cost and do not use expensive ab initio reference labels. The first strategy, based on spectral graph theory, modifies the edges of test graphs to align with graph structures seen during training. Our second strategy improves representations for out-of-distribution systems at test-time by taking gradient steps using an auxiliary objective, such as a cheap physical prior. Our test-time refinement strategies significantly reduce errors on out-of-distribution systems, suggesting that MLFFs are capable of and can move towards modeling diverse chemical spaces, but are not being effectively trained to do so. Our experiments establish clear benchmarks for evaluating the generalization capabilities of the next generation of MLFFs. Our code is available at https://tkreiman.github.io/projects/mlff_distribution_shifts/.

Drug-protein binding and dissociation dynamics are fundamental to understanding molecular interactions in biological systems. While many tools for drug-protein interaction studies have emerged, especially artificial intelligence (AI)-based generative models, predictive tools on binding/dissociation kinetics and dynamics are still limited. We propose a novel research paradigm that combines molecular dynamics (MD) simulations, enhanced sampling, and AI generative models to address this issue. We propose an enhanced sampling strategy to efficiently implement the drug-protein dissociation process in MD simulations and estimate the free energy surface (FES). We constructed a program pipeline of MD simulations based on this sampling strategy, thus generating a dataset including 26,612 drug-protein dissociation trajectories containing about 13 million frames. We named this dissociation dynamics dataset DD-13M and used it to train a deep equivariant generative model UnbindingFlow, which can generate collision-free dissociation trajectories. The DD-13M database and UnbindingFlow model represent a significant advancement in computational structural biology, and we anticipate its broad applicability in machine learning studies of drug-protein interactions. Our ongoing efforts focus on expanding this methodology to encompass a broader spectrum of drug-protein complexes and exploring novel applications in pathway prediction.

We describe the accurate prediction of ligand-protein interaction (LPI) affinities, also known as drug-target interactions (DTI), with instruction fine-tuned pretrained generative small language models (SLMs). We achieved accurate predictions for a range of affinity values associated with ligand-protein interactions on out-of-sample data in a zero-shot setting. Only the SMILES string of the ligand and the amino acid sequence of the protein were used as the model inputs. Our results demonstrate a clear improvement over machine learning (ML) and free-energy perturbation (FEP+) based methods in accurately predicting a range of ligand-protein interaction affinities, which can be leveraged to further accelerate drug discovery campaigns against challenging therapeutic targets.

We propose a new bound for generalization of neural networks using Koopman operators. Whereas most of existing works focus on low-rank weight matrices, we focus on full-rank weight matrices. Our bound is tighter than existing norm-based bounds when the condition numbers of weight matrices are small. Especially, it is completely independent of the width of the network if the weight matrices are orthogonal. Our bound does not contradict to the existing bounds but is a complement to the existing bounds. As supported by several existing empirical results, low-rankness is not the only reason for generalization. Furthermore, our bound can be combined with the existing bounds to obtain a tighter bound. Our result sheds new light on understanding generalization of neural networks with full-rank weight matrices, and it provides a connection between operator-theoretic analysis and generalization of neural networks.

We present a novel Parameter-Efficient Fine-Tuning (PEFT) method, dubbed as Adaptive Freezing of Low Rank Adaptation (AFLoRA). Specifically, for each pre-trained frozen weight tensor, we add a parallel path of trainable low-rank matrices, namely a down-projection and an up-projection matrix, each of which is followed by a feature transformation vector. Based on a novel freezing score, we the incrementally freeze these projection matrices during fine-tuning to reduce the computation and alleviate over-fitting. Our experimental results demonstrate that we can achieve state-of-the-art performance with an average improvement of up to 0.85% as evaluated on GLUE benchmark while yeilding up to 9.5times fewer average trainable parameters. While compared in terms of runtime, AFLoRA can yield up to 1.86times improvement as opposed to similar PEFT alternatives. Besides the practical utility of our approach, we provide insights on the trainability requirements of LoRA paths at different modules and the freezing schedule for the different projection matrices. Code will be released.

Synthetic data has become increasingly important for training large language models, especially when real data is scarce, expensive, or privacy-sensitive. Many such generation tasks require coordinated multi-agent workflows, where specialized agents collaborate to produce data that is higher quality, more diverse, and structurally richer. However, existing frameworks for multi-agent synthesis often depend on a centralized orchestrator, creating scalability bottlenecks, or are hardcoded for specific domains, limiting flexibility. We present Matrix, a decentralized framework that represents both control and data flow as serialized messages passed through distributed queues. This peer-to-peer design eliminates the central orchestrator. Each task progresses independently through lightweight agents, while compute-intensive operations, such as LLM inference or containerized environments, are handled by distributed services. Built on Ray, Matrix scales to tens of thousands of concurrent agentic workflows and provides a modular, configurable design that enables easy adaptation to a wide range of data generation workflows. We evaluate Matrix across diverse synthesis scenarios, such as multi-agent collaborative dialogue, web-based reasoning data extraction, and tool-use trajectory generation in customer service environments. In all cases, Matrix achieves 2--15times higher data generation throughput under identical hardware resources, without compromising output quality.

This paper makes a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian eigendecomposition and singular value decomposition. The other consists of Gaussian elimination and the Gram-Schmidt procedure with various pivoting rules for computing the Cholesky decomposition and QR decomposition respectively. Both families are cast as special cases of a more general class of factorization algorithms. We provide a randomized pivoting rule that applies to this general class (which differs substantially from the usual pivoting rules for Gaussian elimination / Gram-Schmidt) which results in the same linear rate of convergence for each algorithm, irrespective of which factorization it computes. A second important consequence of this randomized pivoting rule is a provable, effective bound on the numerical stability of the Jacobi eigenvalue algorithm, which addresses a longstanding open problem of Demmel and Veseli\'c `92.

Ligand strain energy, the energy difference between the bound and unbound conformations of a ligand, is an important component of structure-based small molecule drug design. A large majority of observed ligands in protein-small molecule co-crystal structures bind in low-strain conformations, making strain energy a useful filter for structure-based drug design. In this work we present a tool for calculating ligand strain with a high accuracy. StrainRelief uses a MACE Neural Network Potential (NNP), trained on a large database of Density Functional Theory (DFT) calculations to estimate ligand strain of neutral molecules with quantum accuracy. We show that this tool estimates strain energy differences relative to DFT to within 1.4 kcal/mol, more accurately than alternative NNPs. These results highlight the utility of NNPs in drug discovery, and provide a useful tool for drug discovery teams.

Pocket representations play a vital role in various biomedical applications, such as druggability estimation, ligand affinity prediction, and de novo drug design. While existing geometric features and pretrained representations have demonstrated promising results, they usually treat pockets independent of ligands, neglecting the fundamental interactions between them. However, the limited pocket-ligand complex structures available in the PDB database (less than 100 thousand non-redundant pairs) hampers large-scale pretraining endeavors for interaction modeling. To address this constraint, we propose a novel pocket pretraining approach that leverages knowledge from high-resolution atomic protein structures, assisted by highly effective pretrained small molecule representations. By segmenting protein structures into drug-like fragments and their corresponding pockets, we obtain a reasonable simulation of ligand-receptor interactions, resulting in the generation of over 5 million complexes. Subsequently, the pocket encoder is trained in a contrastive manner to align with the representation of pseudo-ligand furnished by some pretrained small molecule encoders. Our method, named ProFSA, achieves state-of-the-art performance across various tasks, including pocket druggability prediction, pocket matching, and ligand binding affinity prediction. Notably, ProFSA surpasses other pretraining methods by a substantial margin. Moreover, our work opens up a new avenue for mitigating the scarcity of protein-ligand complex data through the utilization of high-quality and diverse protein structure databases.

Dense linear layers are the dominant computational bottleneck in foundation models. Identifying more efficient alternatives to dense matrices has enormous potential for building more compute-efficient models, as exemplified by the success of convolutional networks in the image domain. In this work, we systematically explore structured matrices as replacements for dense matrices. We show that different structures often require drastically different initialization scales and learning rates, which are crucial to performance, especially as models scale. Using insights from the Maximal Update Parameterization, we determine the optimal scaling for initialization and learning rates of these unconventional layers. Finally, we measure the scaling laws of different structures to compare how quickly their performance improves with compute. We propose a novel matrix family containing Monarch matrices, the Block Tensor-Train (BTT), which we show performs better than dense matrices for the same compute on multiple tasks. On CIFAR-10/100 with augmentation, BTT achieves exponentially lower training loss than dense when training MLPs and ViTs. BTT matches dense ViT-S/32 performance on ImageNet-1k with 3.8 times less compute and is more efficient than dense for training small GPT-2 language models.

The weight matrix (WM) of a neural network (NN) is its program. The programs of many traditional NNs are learned through gradient descent in some error function, then remain fixed. The WM of a self-referential NN, however, can keep rapidly modifying all of itself during runtime. In principle, such NNs can meta-learn to learn, and meta-meta-learn to meta-learn to learn, and so on, in the sense of recursive self-improvement. While NN architectures potentially capable of implementing such behaviour have been proposed since the '90s, there have been few if any practical studies. Here we revisit such NNs, building upon recent successes of fast weight programmers and closely related linear Transformers. We propose a scalable self-referential WM (SRWM) that learns to use outer products and the delta update rule to modify itself. We evaluate our SRWM in supervised few-shot learning and in multi-task reinforcement learning with procedurally generated game environments. Our experiments demonstrate both practical applicability and competitive performance of the proposed SRWM. Our code is public.

Model merging integrates the weights of multiple task-specific models into a single multi-task model. Despite recent interest in the problem, a significant performance gap between the combined and single-task models remains. In this paper, we investigate the key characteristics of task matrices -- weight update matrices applied to a pre-trained model -- that enable effective merging. We show that alignment between singular components of task-specific and merged matrices strongly correlates with performance improvement over the pre-trained model. Based on this, we propose an isotropic merging framework that flattens the singular value spectrum of task matrices, enhances alignment, and reduces the performance gap. Additionally, we incorporate both common and task-specific subspaces to further improve alignment and performance. Our proposed approach achieves state-of-the-art performance across multiple scenarios, including various sets of tasks and model scales. This work advances the understanding of model merging dynamics, offering an effective methodology to merge models without requiring additional training. Code is available at https://github.com/danielm1405/iso-merging .

We study the complexity of sampling from a distribution over all index subsets of the set {1,...,n} with the probability of a subset S proportional to the determinant of the submatrix L_S of some ntimes n p.s.d. matrix L, where L_S corresponds to the entries of L indexed by S. Known as a determinantal point process, this distribution is used in machine learning to induce diversity in subset selection. In practice, we often wish to sample multiple subsets S with small expected size k = E[|S|] ll n from a very large matrix L, so it is important to minimize the preprocessing cost of the procedure (performed once) as well as the sampling cost (performed repeatedly). For this purpose, we propose a new algorithm which, given access to L, samples exactly from a determinantal point process while satisfying the following two properties: (1) its preprocessing cost is n cdot poly(k), i.e., sublinear in the size of L, and (2) its sampling cost is poly(k), i.e., independent of the size of L. Prior to our results, state-of-the-art exact samplers required O(n^3) preprocessing time and sampling time linear in n or dependent on the spectral properties of L. We also give a reduction which allows using our algorithm for exact sampling from cardinality constrained determinantal point processes with ncdotpoly(k) time preprocessing.

Dynamic neuroimaging data, such as emission tomography measurements of radiotracer transport in blood or cerebrospinal fluid, often exhibit diffusion-like properties. These introduce distance-dependent temporal delays, scale-differences, and stretching effects that limit the effectiveness of conventional linear modeling and decomposition methods. To address this, we present the shift- and stretch-invariant non-negative matrix factorization framework. Our approach estimates both integer and non-integer temporal shifts as well as temporal stretching, all implemented in the frequency domain, where shifts correspond to phase modifications, and where stretching is handled via zero-padding or truncation. The model is implemented in PyTorch (https://github.com/anders-s-olsen/shiftstretchNMF). We demonstrate on synthetic data and brain emission tomography data that the model is able to account for stretching to provide more detailed characterization of brain tissue structure.

Recently, 3D generative models have shown promising performances in structure-based drug design by learning to generate ligands given target binding sites. However, only modeling the target-ligand distribution can hardly fulfill one of the main goals in drug discovery -- designing novel ligands with desired properties, e.g., high binding affinity, easily synthesizable, etc. This challenge becomes particularly pronounced when the target-ligand pairs used for training do not align with these desired properties. Moreover, most existing methods aim at solving de novo design task, while many generative scenarios requiring flexible controllability, such as R-group optimization and scaffold hopping, have received little attention. In this work, we propose DecompOpt, a structure-based molecular optimization method based on a controllable and decomposed diffusion model. DecompOpt presents a new generation paradigm which combines optimization with conditional diffusion models to achieve desired properties while adhering to the molecular grammar. Additionally, DecompOpt offers a unified framework covering both de novo design and controllable generation. To achieve so, ligands are decomposed into substructures which allows fine-grained control and local optimization. Experiments show that DecompOpt can efficiently generate molecules with improved properties than strong de novo baselines, and demonstrate great potential in controllable generation tasks.

Structure-based drug design (SBDD) aims to discover drug candidates by finding molecules (ligands) that bind tightly to a disease-related protein (targets), which is the primary approach to computer-aided drug discovery. Recently, applying deep generative models for three-dimensional (3D) molecular design conditioned on protein pockets to solve SBDD has attracted much attention, but their formulation as probabilistic modeling often leads to unsatisfactory optimization performance. On the other hand, traditional combinatorial optimization methods such as genetic algorithms (GA) have demonstrated state-of-the-art performance in various molecular optimization tasks. However, they do not utilize protein target structure to inform design steps but rely on a random-walk-like exploration, which leads to unstable performance and no knowledge transfer between different tasks despite the similar binding physics. To achieve a more stable and efficient SBDD, we propose Reinforced Genetic Algorithm (RGA) that uses neural models to prioritize the profitable design steps and suppress random-walk behavior. The neural models take the 3D structure of the targets and ligands as inputs and are pre-trained using native complex structures to utilize the knowledge of the shared binding physics from different targets and then fine-tuned during optimization. We conduct thorough empirical studies on optimizing binding affinity to various disease targets and show that RGA outperforms the baselines in terms of docking scores and is more robust to random initializations. The ablation study also indicates that the training on different targets helps improve performance by leveraging the shared underlying physics of the binding processes. The code is available at https://github.com/futianfan/reinforced-genetic-algorithm.

The computational prediction and design of peptide binders targeting specific linear epitopes is crucial in biological and biomedical research, yet it remains challenging due to their highly dynamic nature and the scarcity of experimentally solved binding data. To address this problem, we built an unprecedentedly large-scale library of peptide pairs within stable secondary structures (beta sheets), leveraging newly available AlphaFold predicted structures. We then developed a machine learning method based on the Transformer architecture for the design of specific linear binders, in analogy to a language translation task. Our method, TransformerBeta, accurately predicts specific beta strand interactions and samples sequences with beta sheet-like molecular properties, while capturing interpretable physico-chemical interaction patterns. As such, it can propose specific candidate binders targeting linear epitope for experimental validation to inform protein design.

Graph Neural Networks (GNNs), especially message-passing neural networks (MPNNs), have emerged as powerful architectures for learning on graphs in diverse applications. However, MPNNs face challenges when modeling non-local interactions in graphs such as large conjugated molecules, and social networks due to oversmoothing and oversquashing. Although Spectral GNNs and traditional neural networks such as recurrent neural networks and transformers mitigate these challenges, they often lack generalizability, or fail to capture detailed structural relationships or symmetries in the data. To address these concerns, we introduce Matrix Function Neural Networks (MFNs), a novel architecture that parameterizes non-local interactions through analytic matrix equivariant functions. Employing resolvent expansions offers a straightforward implementation and the potential for linear scaling with system size. The MFN architecture achieves stateof-the-art performance in standard graph benchmarks, such as the ZINC and TU datasets, and is able to capture intricate non-local interactions in quantum systems, paving the way to new state-of-the-art force fields.

The rapid growth of model scale has necessitated substantial computational resources for fine-tuning. Existing approach such as Low-Rank Adaptation (LoRA) has sought to address the problem of handling the large updated parameters in full fine-tuning. However, LoRA utilize random initialization and optimization of low-rank matrices to approximate updated weights, which can result in suboptimal convergence and an accuracy gap compared to full fine-tuning. To address these issues, we propose LoLDU, a Parameter-Efficient Fine-Tuning (PEFT) approach that significantly reduces trainable parameters by 2600 times compared to regular PEFT methods while maintaining comparable performance. LoLDU leverages Lower-Diag-Upper Decomposition (LDU) to initialize low-rank matrices for faster convergence and orthogonality. We focus on optimizing the diagonal matrix for scaling transformations. To the best of our knowledge, LoLDU has the fewest parameters among all PEFT approaches. We conducted extensive experiments across 4 instruction-following datasets, 6 natural language understanding (NLU) datasets, 8 image classification datasets, and image generation datasets with multiple model types (LLaMA2, RoBERTa, ViT, and Stable Diffusion), providing a comprehensive and detailed analysis. Our open-source code can be accessed at https://github.com/SKDDJ/LoLDU{https://github.com/SKDDJ/LoLDU}.

Structure-based drug design (SBDD) aims to efficiently discover high-affinity ligands within vast chemical spaces. However, current generative models struggle with objective misalignment and rigid sampling budgets. We present MolFORM, a fast multi-modal flow matching framework for discrete atom types and continuous coordinates. Crucially, to bridge the gap between generative capability and biochemical objectives, we introduce two distinct post-training strategies: (1) Direct Preference Optimization (DPO), which performs offline alignment using ranked preference pairs; and (2) an online reinforcement learning paradigm that optimizes the generative flow directly on the forward process. Both strategies effectively navigate the chemical space toward high-affinity regions. MolFORM achieves state-of-the-art results on the CrossDocked2020 benchmark (Vina Score -7.60, Diversity 0.75), demonstrating that incorporating preference alignment mechanisms-whether via offline optimization or online reinforcement-is crucial for steering generative models toward high-affinity binding regions. The source code for MolFORM is publicly available at https://github.com/daiheng-zhang/SBDD-MolFORM.

Deep generative models are rapidly advancing structure-based drug design, offering substantial promise for generating small molecule ligands that bind to specific protein targets. However, most current approaches assume a rigid protein binding pocket, neglecting the intrinsic flexibility of proteins and the conformational rearrangements induced by ligand binding, limiting their applicability in practical drug discovery. Here, we propose Apo2Mol, a diffusion-based generative framework for 3D molecule design that explicitly accounts for conformational flexibility in protein binding pockets. To support this, we curate a dataset of over 24,000 experimentally resolved apo-holo structure pairs from the Protein Data Bank, enabling the characterization of protein structure changes associated with ligand binding. Apo2Mol employs a full-atom hierarchical graph-based diffusion model that simultaneously generates 3D ligand molecules and their corresponding holo pocket conformations from input apo states. Empirical studies demonstrate that Apo2Mol can achieve state-of-the-art performance in generating high-affinity ligands and accurately capture realistic protein pocket conformational changes.

Generating molecules with high binding affinities to target proteins (a.k.a. structure-based drug design) is a fundamental and challenging task in drug discovery. Recently, deep generative models have achieved remarkable success in generating 3D molecules conditioned on the protein pocket. However, most existing methods consider molecular generation for protein pockets independently while neglecting the underlying connections such as subpocket-level similarities. Subpockets are the local protein environments of ligand fragments and pockets with similar subpockets may bind the same molecular fragment (motif) even though their overall structures are different. Therefore, the trained models can hardly generalize to unseen protein pockets in real-world applications. In this paper, we propose a novel method DrugGPS for generalizable structure-based drug design. With the biochemical priors, we propose to learn subpocket prototypes and construct a global interaction graph to model the interactions between subpocket prototypes and molecular motifs. Moreover, a hierarchical graph transformer encoder and motif-based 3D molecule generation scheme are used to improve the model's performance. The experimental results show that our model consistently outperforms baselines in generating realistic drug candidates with high affinities in challenging out-of-distribution settings.

Deep ensemble methods often improve predictive performance, yet they suffer from three practical limitations: redundancy among base models that inflates computational cost and degrades conditioning, unstable weighting under multicollinearity, and overfitting in meta-learning pipelines. We propose a regularized meta-learning framework that addresses these challenges through a four-stage pipeline combining redundancy-aware projection, statistical meta-feature augmentation, and cross-validated regularized meta-models (Ridge, Lasso, and ElasticNet). Our multi-metric de-duplication strategy removes near-collinear predictors using correlation and MSE thresholds (τ_{corr}=0.95), reducing the effective condition number of the meta-design matrix while preserving predictive diversity. Engineered ensemble statistics and interaction terms recover higher-order structure unavailable to raw prediction columns. A final inverse-RMSE blending stage mitigates regularizer-selection variance. On the Playground Series S6E1 benchmark (100K samples, 72 base models), the proposed framework achieves an out-of-fold RMSE of 8.582, improving over simple averaging (8.894) and conventional Ridge stacking (8.627), while matching greedy hill climbing (8.603) with substantially lower runtime (4 times faster). Conditioning analysis shows a 53.7\% reduction in effective matrix condition number after redundancy projection. Comprehensive ablations demonstrate consistent contributions from de-duplication, statistical meta-features, and meta-ensemble blending. These results position regularized meta-learning as a stable and deployment-efficient stacking strategy for high-dimensional ensemble systems.

Recently, significant progress has been made in protein-ligand docking, especially in modern deep learning methods, and some benchmarks were proposed, e.g., PoseBench, Plinder. However, these benchmarks suffer from less practical evaluation setups (e.g., blind docking, self docking), or heavy framework that involves training, raising challenges to assess docking methods efficiently. To fill this gap, we proposed PoseX, an open-source benchmark focusing on self-docking and cross-docking, to evaluate the algorithmic advances practically and comprehensively. Specifically, first, we curate a new evaluation dataset with 718 entries for self docking and 1,312 for cross docking; second, we incorporate 22 docking methods across three methodological categories, including (1) traditional physics-based methods (e.g., Schr\"odinger Glide), (2) AI docking methods (e.g., DiffDock), (3) AI co-folding methods (e.g., AlphaFold3); third, we design a relaxation method as post-processing to minimize conformation energy and refine binding pose; fourth, we released a leaderboard to rank submitted models in real time. We draw some key insights via extensive experiments: (1) AI-based approaches have already surpassed traditional physics-based approaches in overall docking accuracy (RMSD). The longstanding generalization issues that have plagued AI molecular docking have been significantly alleviated in the latest models. (2) The stereochemical deficiencies of AI-based approaches can be greatly alleviated with post-processing relaxation. Combining AI docking methods with the enhanced relaxation method achieves the best performance to date. (3) AI co-folding methods commonly face ligand chirality issues, which cannot be resolved by relaxation. The code, curated dataset and leaderboard are released at https://github.com/CataAI/PoseX.

Multimodal recommender systems utilizing multimodal features (e.g., images and textual descriptions) typically show better recommendation accuracy than general recommendation models based solely on user-item interactions. Generally, prior work fuses multimodal features into item ID embeddings to enrich item representations, thus failing to capture the latent semantic item-item structures. In this context, LATTICE proposes to learn the latent structure between items explicitly and achieves state-of-the-art performance for multimodal recommendations. However, we argue the latent graph structure learning of LATTICE is both inefficient and unnecessary. Experimentally, we demonstrate that freezing its item-item structure before training can also achieve competitive performance. Based on this finding, we propose a simple yet effective model, dubbed as FREEDOM, that FREEzes the item-item graph and DenOises the user-item interaction graph simultaneously for Multimodal recommendation. Theoretically, we examine the design of FREEDOM through a graph spectral perspective and demonstrate that it possesses a tighter upper bound on the graph spectrum. In denoising the user-item interaction graph, we devise a degree-sensitive edge pruning method, which rejects possibly noisy edges with a high probability when sampling the graph. We evaluate the proposed model on three real-world datasets and show that FREEDOM can significantly outperform current strongest baselines. Compared with LATTICE, FREEDOM achieves an average improvement of 19.07% in recommendation accuracy while reducing its memory cost up to 6times on large graphs. The source code is available at: https://github.com/enoche/FREEDOM.

A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known scaling matrices proposed in the literature. We define a new scaling matrix that is the convex combination of these matrices. The proposed scaling matrix inherits those interesting properties of the individual matrices and satisfies additional desired requirements. The numerical experiments demonstrate the superiority of the new scaling matrix in solving several important test problems.

We present Matrix3D, a unified model that performs several photogrammetry subtasks, including pose estimation, depth prediction, and novel view synthesis using just the same model. Matrix3D utilizes a multi-modal diffusion transformer (DiT) to integrate transformations across several modalities, such as images, camera parameters, and depth maps. The key to Matrix3D's large-scale multi-modal training lies in the incorporation of a mask learning strategy. This enables full-modality model training even with partially complete data, such as bi-modality data of image-pose and image-depth pairs, thus significantly increases the pool of available training data. Matrix3D demonstrates state-of-the-art performance in pose estimation and novel view synthesis tasks. Additionally, it offers fine-grained control through multi-round interactions, making it an innovative tool for 3D content creation. Project page: https://nju-3dv.github.io/projects/matrix3d.

Various visual foundation models have distinct strengths and weaknesses, both of which can be improved through heterogeneous multi-teacher knowledge distillation without labels, termed "agglomerative models." We build upon this body of work by studying the effect of the teachers' activation statistics, particularly the impact of the loss function on the resulting student model quality. We explore a standard toolkit of statistical normalization techniques to better align the different distributions and assess their effects. Further, we examine the impact on downstream teacher-matching metrics, which motivates the use of Hadamard matrices. With these matrices, we demonstrate useful properties, showing how they can be used for isotropic standardization, where each dimension of a multivariate distribution is standardized using the same scale. We call this technique "PHI Standardization" (PHI-S) and empirically demonstrate that it produces the best student model across the suite of methods studied.

Low-Rank Adaptation (LoRA) has achieved remarkable training results by freezing the original weights and training only low-rank matrices, establishing itself as the predominant fine-tuning method for LLMs. In pursuit of performance closer to full-parameter training, a series of LoRA variants have emerged, such as LoRA+, PISSA, Olora, and LoRA-GA. However, these improvements complicate the initial setup of model training and increase initialization time. More importantly, they overlook the internal interactions of the original weight information. To address these issues, we introduce a novel theory, ``Weight Guide'' aimed at continuously guiding trainable matrices through the original weights during training to enhance the utilization of weight information. Based on this theory, we designed a new PEFT technique called Bone (Block Affine), which not only enhances the utilization of original weight information but also emphasizes the internal connections between weights, leading to faster convergence and better data fitting. Experimental comparisons across two different LLM architectures (LLaMA2, RWKV6) and various parameter scales demonstrate that the Bone structure can achieve rapid convergence and superior data fitting without the need for complex initialization. For example, when fine-tuning LLaMA2-7B on the MetaMathQA dataset and validating on GSM8k and math benchmarks, Bone achieved fine-tuning scores of 49.36 and 8.8, respectively, outperforming PISSA by 5.84\% and 1.96\%.

Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several fine-tuning techniques have been developed to update the pre-trained model weights in a more resource-efficient manner, such as through low-rank adjustments. Yet, almost all of these methods focus on linear weights, neglecting the intricacies of parameter spaces in higher dimensions like 4D. Alternatively, some methods can be adapted for high-dimensional parameter space by compressing changes in the original space into two dimensions and then employing low-rank matrix decomposition. However, these approaches destructs the structural integrity of the involved high-dimensional spaces. To tackle the diversity of dimensional spaces across different foundation models and provide a more precise representation of the changes within these spaces, this paper introduces a generalized parameter-efficient fine-tuning framework, FLoRA, designed for various dimensional parameter space. Specifically, utilizing Tucker decomposition, FLoRA asserts that changes in each dimensional parameter space are based on a low-rank core space which maintains the consistent topological structure with the original space. It then models the changes through this core space alongside corresponding weights to reconstruct alterations in the original space. FLoRA effectively preserves the structural integrity of the change of original N-dimensional parameter space, meanwhile decomposes it via low-rank tensor decomposition. Extensive experiments on computer vision, natural language processing and multi-modal tasks validate FLoRA's effectiveness. Codes are available at https://github.com/SJTU-DeepVisionLab/FLoRA.

We introduce Point-Bind, a 3D multi-modality model aligning point clouds with 2D image, language, audio, and video. Guided by ImageBind, we construct a joint embedding space between 3D and multi-modalities, enabling many promising applications, e.g., any-to-3D generation, 3D embedding arithmetic, and 3D open-world understanding. On top of this, we further present Point-LLM, the first 3D large language model (LLM) following 3D multi-modal instructions. By parameter-efficient fine-tuning techniques, Point-LLM injects the semantics of Point-Bind into pre-trained LLMs, e.g., LLaMA, which requires no 3D instruction data, but exhibits superior 3D and multi-modal question-answering capacity. We hope our work may cast a light on the community for extending 3D point clouds to multi-modality applications. Code is available at https://github.com/ZiyuGuo99/Point-Bind_Point-LLM.

Methods of computational quantum chemistry provide accurate approximations of molecular properties crucial for computer-aided drug discovery and other areas of chemical science. However, high computational complexity limits the scalability of their applications. Neural network potentials (NNPs) are a promising alternative to quantum chemistry methods, but they require large and diverse datasets for training. This work presents a new dataset and benchmark called nabla^2DFT that is based on the nablaDFT. It contains twice as much molecular structures, three times more conformations, new data types and tasks, and state-of-the-art models. The dataset includes energies, forces, 17 molecular properties, Hamiltonian and overlap matrices, and a wavefunction object. All calculations were performed at the DFT level (omegaB97X-D/def2-SVP) for each conformation. Moreover, nabla^2DFT is the first dataset that contains relaxation trajectories for a substantial number of drug-like molecules. We also introduce a novel benchmark for evaluating NNPs in molecular property prediction, Hamiltonian prediction, and conformational optimization tasks. Finally, we propose an extendable framework for training NNPs and implement 10 models within it.

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general solution to a longstanding open problem relevant to a wide variety of applications in robotics, tracking, and control systems. The new inverse complements the Drazin inverse (which is consistent with respect to similarity transformations) and the Moore-Penrose inverse (which is consistent with respect to unitary/orthonormal transformations) to complete a trilogy of generalized matrix inverses that exhausts the standard family of analytically-important linear system transformations. Results are generalized to obtain unit-consistent and unit-invariant matrix decompositions and examples of their use are described.

Video DiTs have advanced video generation, yet they still struggle to model multi-instance or subject-object interactions. This raises a key question: How do these models internally represent interactions? To answer this, we curate MATRIX-11K, a video dataset with interaction-aware captions and multi-instance mask tracks. Using this dataset, we conduct a systematic analysis that formalizes two perspectives of video DiTs: semantic grounding, via video-to-text attention, which evaluates whether noun and verb tokens capture instances and their relations; and semantic propagation, via video-to-video attention, which assesses whether instance bindings persist across frames. We find both effects concentrate in a small subset of interaction-dominant layers. Motivated by this, we introduce MATRIX, a simple and effective regularization that aligns attention in specific layers of video DiTs with multi-instance mask tracks from the MATRIX-11K dataset, enhancing both grounding and propagation. We further propose InterGenEval, an evaluation protocol for interaction-aware video generation. In experiments, MATRIX improves both interaction fidelity and semantic alignment while reducing drift and hallucination. Extensive ablations validate our design choices. Codes and weights will be released.

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model, which is particularly effective on tasks involving long-range dependencies by using a prescribed state matrix called the HiPPO matrix. While this has an interpretable mathematical mechanism for modeling long dependencies, it introduces a custom representation and algorithm that can be difficult to implement. On the other hand, a recent variant of S4 called DSS showed that restricting the state matrix to be fully diagonal can still preserve the performance of the original model when using a specific initialization based on approximating S4's matrix. This work seeks to systematically understand how to parameterize and initialize such diagonal state space models. While it follows from classical results that almost all SSMs have an equivalent diagonal form, we show that the initialization is critical for performance. We explain why DSS works mathematically, by showing that the diagonal restriction of S4's matrix surprisingly recovers the same kernel in the limit of infinite state dimension. We also systematically describe various design choices in parameterizing and computing diagonal SSMs, and perform a controlled empirical study ablating the effects of these choices. Our final model S4D is a simple diagonal version of S4 whose kernel computation requires just 2 lines of code and performs comparably to S4 in almost all settings, with state-of-the-art results for image, audio, and medical time-series domains, and averaging 85\% on the Long Range Arena benchmark.

CLIP (Contrastive Language-Image Pretraining) has become a popular choice for various downstream tasks. However, recent studies have questioned its ability to represent compositional concepts effectively. These works suggest that CLIP often acts like a bag-of-words (BoW) model, interpreting images and text as sets of individual concepts without grasping the structural relationships. In particular, CLIP struggles to correctly bind attributes to their corresponding objects when multiple objects are present in an image or text. In this work, we investigate why CLIP exhibits this BoW-like behavior. We find that the correct attribute-object binding information is already present in individual text and image modalities. Instead, the issue lies in the cross-modal alignment, which relies on cosine similarity. To address this, we propose Linear Attribute Binding CLIP or LABCLIP. It applies a linear transformation to text embeddings before computing cosine similarity. This approach significantly improves CLIP's ability to bind attributes to correct objects, thereby enhancing its compositional understanding.

Post-training is essential for enabling large language models (LLMs) to follow human instructions. However, its effectiveness depends on high-quality instruction data, which is challenging to obtain in the real world due to privacy concerns, data scarcity, and high annotation costs. To fill this gap, inspired by the recent success of using LLMs to simulate human society, we propose MATRIX, a multi-agent simulator that automatically generates diverse text-based scenarios, capturing a wide range of real-world human needs in a realistic and scalable manner. Leveraging these outputs, we introduce a novel scenario-driven instruction generator MATRIX-Gen for controllable and highly realistic data synthesis. Extensive experiments demonstrate that our framework effectively generates both general and domain-specific data. On AlpacaEval 2 and Arena-Hard benchmarks, Llama-3-8B-Base, post-trained on datasets synthesized by MATRIX-Gen with just 20K instruction-response pairs, outperforms Meta's Llama-3-8B-Instruct model, which was trained on over 10M pairs.

We present a novel dual-head deep learning architecture for protein-protein interaction modeling that enables simultaneous prediction of binding affinity (ΔG) and mutation-induced affinity changes (ΔΔG) using only protein sequence information. Our approach offers a significant advancement over existing methods by employing specialized prediction heads that operate on a shared representation network, allowing direct and optimized prediction of both values. To ensure robust generalization, we integrated complementary datasets from SKEMPI v2 and PDBbind with a rigorous protein domain-based splitting strategy that prevents information leakage between training and validation sets. Our architecture combines transformer-based encoders with a novel cross-attention mechanism that processes paired protein sequences directly, without requiring any structural information. The network embeds input sequences using ESM3 representations, then employs a learnable sliced window embedding layer to manage variable-length sequences efficiently. A multi-layer transformer encoder with bidirectional self-attention captures intra-protein patterns, while cross-attention layers enable explicit modeling of interactions between protein pairs. This shared representation network feeds into separate ΔG and ΔΔG prediction heads, allowing task-specific optimization while leveraging common features. The model achieves ΔΔG validation of Pearson correlation at 0.485, while maintaining strong ΔG predictions (Pearson: 0.638). While existing approaches require protein structure data and binding interface information, our model eliminates these constraints. This provides a critical advantage for the numerous proteins with unknown structures or those challenging to crystallize, such as viral and intrinsically disordered proteins.

The Schr\"odinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data space R^{D} and leaves open theoretical and algorithmic questions about applying SB methods to discrete data, e.g, on finite spaces S^{D}. Notable examples of such sets S are codebooks of vector-quantized (VQ) representations of modern autoencoders, tokens in texts, categories of atoms in molecules, etc. In this paper, we provide a theoretical and algorithmic foundation for solving SB in discrete spaces using the recently introduced Iterative Markovian Fitting (IMF) procedure. Specifically, we theoretically justify the convergence of discrete-time IMF (D-IMF) to SB in discrete spaces. This enables us to develop a practical computational algorithm for SB which we call Categorical Schr\"odinger Bridge Matching (CSBM). We show the performance of CSBM via a series of experiments with synthetic data and VQ representations of images.

Effectively leveraging data from multiple quantum-chemical methods is essential for building machine-learned force fields (MLFFs) that are applicable to a wide range of chemical systems. This study systematically investigates two multi-fidelity training strategies, pre-training/fine-tuning and multi-headed training, to elucidate the mechanisms underpinning their success. We identify key factors driving the efficacy of pre-training followed by fine-tuning, but find that internal representations learned during pre-training are inherently method-specific, requiring adaptation of the model backbone during fine-tuning. Multi-headed models offer an extensible alternative, enabling simultaneous training on multiple fidelities. We demonstrate that a multi-headed model learns method-agnostic representations that allow for accurate predictions across multiple label sources. While this approach introduces a slight accuracy compromise compared to sequential fine-tuning, it unlocks new cost-efficient data generation strategies and paves the way towards developing universal MLFFs.

Randomized controlled trials often do not represent the populations where decisions are made, and covariate shift across studies can invalidate standard IPD meta-analysis and transport estimators. We propose a placebo-anchored transport framework that treats source-trial outcomes as abundant proxy signals and target-trial placebo outcomes as scarce, high-fidelity gold labels to calibrate baseline risk. A low-complexity (sparse) correction anchors proxy outcome models to the target population, and the anchored models are embedded in a cross-fitted doubly robust learner, yielding a Neyman-orthogonal, target-site doubly robust estimator for patient-level heterogeneous treatment effects when target treated outcomes are available. We distinguish two regimes: in connected targets (with a treated arm), the method yields target-identified effect estimates; in disconnected targets (placebo-only), it reduces to a principled screen--then--transport procedure under explicit working-model transport assumptions. Experiments on synthetic data and a semi-synthetic IHDP benchmark evaluate pointwise CATE accuracy, ATE error, ranking quality for targeting, decision-theoretic policy regret, and calibration. Across connected settings, the proposed method is best or near-best and improves substantially over proxy-only, target-only, and transport baselines at small target sample sizes; in disconnected settings, it retains strong ranking performance for targeting while pointwise accuracy depends on the strength of the working transport condition.

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically examined the performance of a tensor-based approach, which relies on finding a best rank-one approximation, a problem known to be computationally hard. A tractable alternative approach consists in computing instead the best rank-one (matrix) approximation of an unfolding of the observed tensor data, but its performance was hitherto unknown. We quantify here the performance gap between these two approaches, in particular by deriving the precise algorithmic threshold of the unfolding approach and demonstrating that it exhibits a BBP-type transition behavior. This work is therefore in line with recent contributions which deepen our understanding of why tensor-based methods surpass matrix-based methods in handling structured tensor data.

Protein function is often controlled by ligands that bias the direction of state transitions, such as agonists and antagonists, rather than stabilizing a single conformation. This is especially important for clinically relevant G protein-coupled receptors (GPCRs), where therapeutic efficacy depends on functional directionality. Structure-based design methods optimize binding to static conformations and cannot represent non-reversible, directional effects or systematically distinguish agonist from antagonist behavior. To address this gap, we introduce Transition-Directed Discrete Diffusion for Allosteric Binder Design (TD3B), a sequence-based generative framework that designs binders with specified agonist or antagonist behavior via a directional transition control objective. TD3B combines a target-aware Direction Oracle, a soft binding-affinity gate, and amortized fine-tuning of a pre-trained discrete diffusion model, enabling targeted agonist and antagonist generation decoupled from binding affinity and unattainable by equilibrium-based or inference-only guidance baselines. The code and checkpoints are available at https://huggingface.co/ChatterjeeLab/TD3B.

Foundation models (FMs) are pre-trained on large-scale datasets and then fine-tuned on a downstream task for a specific application. The most successful and most commonly used fine-tuning method is to update the pre-trained weights via a low-rank adaptation (LoRA). LoRA introduces new weight matrices that are usually initialized at random with a uniform rank distribution across model weights. Recent works focus on weight-driven initialization or learning of adaptive ranks during training. Both approaches have only been investigated in isolation, resulting in slow convergence or a uniform rank distribution, in turn leading to sub-optimal performance. We propose to enhance LoRA by initializing the new weights in a data-driven manner by computing singular value decomposition on minibatches of activation vectors. Then, we initialize the LoRA matrices with the obtained right-singular vectors and re-distribute ranks among all weight matrices to explain the maximal amount of variance and continue the standard LoRA fine-tuning procedure. This results in our new method Explained Variance Adaptation (EVA). We apply EVA to a variety of fine-tuning tasks ranging from language generation and understanding to image classification and reinforcement learning. EVA exhibits faster convergence than competitors and attains the highest average score across a multitude of tasks per domain.

Pre-trained language models, trained on large-scale corpora, demonstrate strong generalizability across various NLP tasks. Fine-tuning these models for specific tasks typically involves updating all parameters, which is resource-intensive. Parameter-efficient fine-tuning (PEFT) methods, such as the popular LoRA family, introduce low-rank matrices to learn only a few parameters efficiently. However, during inference, the product of these matrices updates all pre-trained parameters, complicating tasks like knowledge editing that require selective updates. We propose a novel PEFT method, which conducts row and column-wise sparse low-rank adaptation (RoseLoRA), to address this challenge. RoseLoRA identifies and updates only the most important parameters for a specific task, maintaining efficiency while preserving other model knowledge. By adding a sparsity constraint on the product of low-rank matrices and converting it to row and column-wise sparsity, we ensure efficient and precise model updates. Our theoretical analysis guarantees the lower bound of the sparsity with respective to the matrix product. Extensive experiments on five benchmarks across twenty datasets demonstrate that RoseLoRA outperforms baselines in both general fine-tuning and knowledge editing tasks.

Tables are a popular and efficient means of presenting structured information. They are used extensively in various kinds of documents including web pages. Tables display information as a two-dimensional matrix, the semantics of which is conveyed by a mixture of structure (rows, columns), headers, caption, and content. Recent research has started to consider tables as first class objects, not just as an addendum to texts, yielding interesting results for problems like table matching, table completion, or value imputation. All of these problems inherently rely on an accurate measure for the semantic similarity of two tables. We present TabSim, a novel method to compute table similarity scores using deep neural networks. Conceptually, TabSim represents a table as a learned concatenation of embeddings of its caption, its content, and its structure. Given two tables in this representation, a Siamese neural network is trained to compute a score correlating with the tables' semantic similarity. To train and evaluate our method, we created a gold standard corpus consisting of 1500 table pairs extracted from biomedical articles and manually scored regarding their degree of similarity, and adopted two other corpora originally developed for a different yet similar task. Our evaluation shows that TabSim outperforms other table similarity measures on average by app. 7% pp F1-score in a binary similarity classification setting and by app. 1.5% pp in a ranking scenario.

We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are correlated with the target classes, called the class-attribute matrix. We develop the first non-trivial lower bound on the worst-case error of the best map from attributes to classes for this setting, even with perfect attribute detectors. The lower bound characterizes the theoretical intrinsic difficulty of the zero-shot problem based on the available information -- the class-attribute matrix -- and the bound is practically computable from it. Our lower bound is tight, as we show that we can always find a randomized map from attributes to classes whose expected error is upper bounded by the value of the lower bound. We show that our analysis can be predictive of how standard zero-shot methods behave in practice, including which classes will likely be confused with others.

We introduce IntFold, a controllable foundation model for both general and specialized biomolecular structure prediction. IntFold demonstrates predictive accuracy comparable to the state-of-the-art AlphaFold3, while utilizing a superior customized attention kernel. Beyond standard structure prediction, IntFold can be adapted to predict allosteric states, constrained structures, and binding affinity through the use of individual adapters. Furthermore, we introduce a novel confidence head to estimate docking quality, offering a more nuanced assessment for challenging targets such as antibody-antigen complexes. Finally, we share insights gained during the training process of this computationally intensive model.

We introduce ReALLM, a novel approach for compression and memory-efficient adaptation of pre-trained language models that encompasses most of the post-training quantization and fine-tuning methods for a budget of <4 bits. Pre-trained matrices are decomposed into a high-precision low-rank component and a vector-quantized latent representation (using an autoencoder). During the fine-tuning step, only the low-rank components are updated. Our results show that pre-trained matrices exhibit different patterns. ReALLM adapts the shape of the encoder (small/large embedding, high/low bit VQ, etc.) to each matrix. ReALLM proposes to represent each matrix with a small embedding on b bits and a neural decoder model D_phi with its weights on b_phi bits. The decompression of a matrix requires only one embedding and a single forward pass with the decoder. Our weight-only quantization algorithm yields the best results on language generation tasks (C4 and WikiText-2) for a budget of 3 bits without any training. With a budget of 2 bits, ReALLM achieves state-of-the art performance after fine-tuning on a small calibration dataset.

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.

Large-scale foundation models have demonstrated exceptional performance in language and vision tasks. However, the numerous dense matrix-vector operations involved in these large networks pose significant computational challenges during inference. To address these challenges, we introduce the Block-Level Adaptive STructured (BLAST) matrix, designed to learn and leverage efficient structures prevalent in the weight matrices of linear layers within deep learning models. Compared to existing structured matrices, the BLAST matrix offers substantial flexibility, as it can represent various types of structures that are either learned from data or computed from pre-existing weight matrices. We demonstrate the efficiency of using the BLAST matrix for compressing both language and vision tasks, showing that (i) for medium-sized models such as ViT and GPT-2, training with BLAST weights boosts performance while reducing complexity by 70% and 40%, respectively; and (ii) for large foundation models such as Llama-7B and DiT-XL, the BLAST matrix achieves a 2x compression while exhibiting the lowest performance degradation among all tested structured matrices. Our code is available at https://github.com/changwoolee/BLAST.

We require decomposition methods for the ABCD-matrix formulation in rotationally symmetric paraxial geometric optics when designing a multi-component optical system from a given single paraxial specification (represented by an ABCD matrix) to optimize non-paraxial specifications (e.g., optical aberrations). In this study, we propose two kinds of three-matrix decomposition of ABCD matrices by focusing on the fact that the ABCD matrices have three real-number degrees of freedom. In addition, we formulate a transformation between the two kinds of decomposition for a single matrix, which can increase or decrease the number of refraction surfaces in the optical configuration while keeping the paraxial specifications fixed. This nature is useful for the optical design of multi-component systems with optimized non-paraxial characteristics.

We consider a family of linear systems A_mu alpha=C with system matrix A_mu depending on a parameter mu and for simplicity parameter-independent right-hand side C. These linear systems typically result from the finite-dimensional approximation of a parameter-dependent boundary-value problem. We derive a procedure based on the Empirical Interpolation Method to obtain a separated representation of the system matrix in the form A_muapproxsum_{m}beta_m(mu)A_{mu_m} for some selected values of the parameter. Such a separated representation is in particular useful in the Reduced Basis Method. The procedure is called nonintrusive since it only requires to access the matrices A_{mu_m}. As such, it offers a crucial advantage over existing approaches that instead derive separated representations requiring to enter the code at the level of assembly. Numerical examples illustrate the performance of our new procedure on a simple one-dimensional boundary-value problem and on three-dimensional acoustic scattering problems solved by a boundary element method.

Determining the binding pose of a ligand to a protein, known as molecular docking, is a fundamental task in drug discovery. Generative approaches promise faster, improved, and more diverse pose sampling than physics-based methods, but are often hindered by chemically implausible outputs, poor generalisability, and high computational cost. To address these challenges, we introduce a novel fragmentation scheme, leveraging inductive biases from structural chemistry, to decompose ligands into rigid-body fragments. Building on this decomposition, we present SigmaDock, an SE(3) Riemannian diffusion model that generates poses by learning to reassemble these rigid bodies within the binding pocket. By operating at the level of fragments in SE(3), SigmaDock exploits well-established geometric priors while avoiding overly complex diffusion processes and unstable training dynamics. Experimentally, we show SigmaDock achieves state-of-the-art performance, reaching Top-1 success rates (RMSD<2 & PB-valid) above 79.9% on the PoseBusters set, compared to 12.7-30.8% reported by recent deep learning approaches, whilst demonstrating consistent generalisation to unseen proteins. SigmaDock is the first deep learning approach to surpass classical physics-based docking under the PB train-test split, marking a significant leap forward in the reliability and feasibility of deep learning for molecular modelling.

Designing enzyme backbones with substrate-specific functionality is a critical challenge in computational protein engineering. Current generative models excel in protein design but face limitations in binding data, substrate-specific control, and flexibility for de novo enzyme backbone generation. To address this, we introduce EnzyBind, a dataset with 11,100 experimentally validated enzyme-substrate pairs specifically curated from PDBbind. Building on this, we propose EnzyControl, a method that enables functional and substrate-specific control in enzyme backbone generation. Our approach generates enzyme backbones conditioned on MSA-annotated catalytic sites and their corresponding substrates, which are automatically extracted from curated enzyme-substrate data. At the core of EnzyControl is EnzyAdapter, a lightweight, modular component integrated into a pretrained motif-scaffolding model, allowing it to become substrate-aware. A two-stage training paradigm further refines the model's ability to generate accurate and functional enzyme structures. Experiments show that our EnzyControl achieves the best performance across structural and functional metrics on EnzyBind and EnzyBench benchmarks, with particularly notable improvements of 13\% in designability and 13\% in catalytic efficiency compared to the baseline models. The code is released at https://github.com/Vecteur-libre/EnzyControl.

Protein representation learning is critical for numerous biological tasks. Recently, large transformer-based protein language models (pLMs) pretrained on large scale protein sequences have demonstrated significant success in sequence-based tasks. However, pLMs lack structural context. Conversely, graph neural networks (GNNs) designed to leverage 3D structural information have shown promising generalization in protein-related prediction tasks, but their effectiveness is often constrained by the scarcity of labeled structural data. Recognizing that sequence and structural representations are complementary perspectives of the same protein entity, we propose a multimodal bidirectional hierarchical fusion framework to effectively merge these modalities. Our framework employs attention and gating mechanisms to enable effective interaction between pLMs-generated sequential representations and GNN-extracted structural features, improving information exchange and enhancement across layers of the neural network. This bidirectional and hierarchical (Bi-Hierarchical) fusion approach leverages the strengths of both modalities to capture richer and more comprehensive protein representations. Based on the framework, we further introduce local Bi-Hierarchical Fusion with gating and global Bi-Hierarchical Fusion with multihead self-attention approaches. Our method demonstrates consistent improvements over strong baselines and existing fusion techniques in a variety of protein representation learning benchmarks, including enzyme EC classification, model quality assessment, protein-ligand binding affinity prediction, protein-protein binding site prediction, and B cell epitopes prediction. Our method establishes a new state-of-the-art for multimodal protein representation learning, emphasizing the efficacy of Bi-Hierarchical Fusion in bridging sequence and structural modalities.

Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In this work, we propose a novel algorithm to find efficient low-rank subnetworks. Remarkably, these subnetworks are determined and adapted already during the training phase and the overall time and memory resources required by both training and evaluating them are significantly reduced. The main idea is to restrict the weight matrices to a low-rank manifold and to update the low-rank factors rather than the full matrix during training. To derive training updates that are restricted to the prescribed manifold, we employ techniques from dynamic model order reduction for matrix differential equations. This allows us to provide approximation, stability, and descent guarantees. Moreover, our method automatically and dynamically adapts the ranks during training to achieve the desired approximation accuracy. The efficiency of the proposed method is demonstrated through a variety of numerical experiments on fully-connected and convolutional networks.

Preconditioned gradient methods are among the most general and powerful tools in optimization. However, preconditioning requires storing and manipulating prohibitively large matrices. We describe and analyze a new structure-aware preconditioning algorithm, called Shampoo, for stochastic optimization over tensor spaces. Shampoo maintains a set of preconditioning matrices, each of which operates on a single dimension, contracting over the remaining dimensions. We establish convergence guarantees in the stochastic convex setting, the proof of which builds upon matrix trace inequalities. Our experiments with state-of-the-art deep learning models show that Shampoo is capable of converging considerably faster than commonly used optimizers. Although it involves a more complex update rule, Shampoo's runtime per step is comparable to that of simple gradient methods such as SGD, AdaGrad, and Adam.

The motif-scaffolding problem is a central task in computational protein design: Given the coordinates of atoms in a geometry chosen to confer a desired biochemical function (a motif), the task is to identify diverse protein structures (scaffolds) that include the motif and maintain its geometry. Significant recent progress on motif-scaffolding has been made due to computational evaluation with reliable protein structure prediction and fixed-backbone sequence design methods. However, significant variability in evaluation strategies across publications has hindered comparability of results, challenged reproducibility, and impeded robust progress. In response we introduce MotifBench, comprising (1) a precisely specified pipeline and evaluation metrics, (2) a collection of 30 benchmark problems, and (3) an implementation of this benchmark and leaderboard at github.com/blt2114/MotifBench. The MotifBench test cases are more difficult compared to earlier benchmarks, and include protein design problems for which solutions are known but on which, to the best of our knowledge, state-of-the-art methods fail to identify any solution.

Fine-tuning is a crucial paradigm for adapting pre-trained large language models to downstream tasks. Recently, methods like Low-Rank Adaptation (LoRA) have been shown to match the performance of fully fine-tuned models on various tasks with an extreme reduction in the number of trainable parameters. Even in settings where both methods learn similarly accurate models, are their learned solutions really equivalent? We study how different fine-tuning methods change pre-trained models by analyzing the model's weight matrices through the lens of their spectral properties. We find that full fine-tuning and LoRA yield weight matrices whose singular value decompositions exhibit very different structure; moreover, the fine-tuned models themselves show distinct generalization behaviors when tested outside the adaptation task's distribution. More specifically, we first show that the weight matrices trained with LoRA have new, high-ranking singular vectors, which we call intruder dimensions. Intruder dimensions do not appear during full fine-tuning. Second, we show that LoRA models with intruder dimensions, despite achieving similar performance to full fine-tuning on the target task, become worse models of the pre-training distribution and adapt less robustly to multiple tasks sequentially. Higher-rank, rank-stabilized LoRA models closely mirror full fine-tuning, even when performing on par with lower-rank LoRA models on the same tasks. These results suggest that models updated with LoRA and full fine-tuning access different parts of parameter space, even when they perform equally on the fine-tuned distribution. We conclude by examining why intruder dimensions appear in LoRA fine-tuned models, why they are undesirable, and how their effects can be minimized.

In this article, we introduce a novel normalization technique for neural network weight matrices, which we term weight conditioning. This approach aims to narrow the gap between the smallest and largest singular values of the weight matrices, resulting in better-conditioned matrices. The inspiration for this technique partially derives from numerical linear algebra, where well-conditioned matrices are known to facilitate stronger convergence results for iterative solvers. We provide a theoretical foundation demonstrating that our normalization technique smoothens the loss landscape, thereby enhancing convergence of stochastic gradient descent algorithms. Empirically, we validate our normalization across various neural network architectures, including Convolutional Neural Networks (CNNs), Vision Transformers (ViT), Neural Radiance Fields (NeRF), and 3D shape modeling. Our findings indicate that our normalization method is not only competitive but also outperforms existing weight normalization techniques from the literature.

Planning effective interventions in biological systems requires treatment-effect models that adapt to unseen biological contexts by identifying their specific underlying mechanisms. Yet single-cell perturbation datasets span only a handful of biological contexts, and existing methods cannot leverage new interventional evidence at inference time to adapt beyond their training data. To meta-learn a perturbation effect estimator, we present MapPFN, a prior-data fitted network (PFN) pretrained on synthetic data generated from a prior over causal perturbations. Given a set of experiments, MapPFN uses in-context learning to predict post-perturbation distributions, without gradient-based optimization. Despite being pretrained on in silico gene knockouts alone, MapPFN identifies differentially expressed genes, matching the performance of models trained on real single-cell data. Our code and data are available at https://github.com/marvinsxtr/MapPFN.

Distribution shift presents a significant challenge in machine learning, where models often underperform during the test stage when faced with a different distribution than the one they were trained on. This paper focuses on domain shifts, which occur when the model is applied to new domains that are different from the ones it was trained on, and propose a new approach called D^3G. Unlike previous methods that aim to learn a single model that is domain invariant, D^3G leverages domain similarities based on domain metadata to learn domain-specific models. Concretely, D^3G learns a set of training-domain-specific functions during the training stage and reweights them based on domain relations during the test stage. These domain relations can be directly obtained and learned from domain metadata. Under mild assumptions, we theoretically prove that using domain relations to reweight training-domain-specific functions achieves stronger out-of-domain generalization compared to the conventional averaging approach. Empirically, we evaluate the effectiveness of D^3G using real-world datasets for tasks such as temperature regression, land use classification, and molecule-protein binding affinity prediction. Our results show that D^3G consistently outperforms state-of-the-art methods.

We study sampling algorithms for β-ensembles with time complexity less than cubic in the cardinality of the ensemble. Following Dumitriu & Edelman (2002), we see the ensemble as the eigenvalues of a random tridiagonal matrix, namely a random Jacobi matrix. First, we provide a unifying and elementary treatment of the tridiagonal models associated to the three classical Hermite, Laguerre and Jacobi ensembles. For this purpose, we use simple changes of variables between successive reparametrizations of the coefficients defining the tridiagonal matrix. Second, we derive an approximate sampler for the simulation of β-ensembles, and illustrate how fast it can be for polynomial potentials. This method combines a Gibbs sampler on Jacobi matrices and the diagonalization of these matrices. In practice, even for large ensembles, only a few Gibbs passes suffice for the marginal distribution of the eigenvalues to fit the expected theoretical distribution. When the conditionals in the Gibbs sampler can be simulated exactly, the same fast empirical convergence is observed for the fluctuations of the largest eigenvalue. Our experimental results support a conjecture by Krishnapur et al. (2016), that the Gibbs chain on Jacobi matrices of size N mixes in O(log(N)).

Recent years have witnessed a surge in the development of protein foundation models, significantly improving performance in protein prediction and generative tasks ranging from 3D structure prediction and protein design to conformational dynamics. However, the capabilities and limitations associated with these models remain poorly understood due to the absence of a unified evaluation framework. To fill this gap, we introduce ProteinBench, a holistic evaluation framework designed to enhance the transparency of protein foundation models. Our approach consists of three key components: (i) A taxonomic classification of tasks that broadly encompass the main challenges in the protein domain, based on the relationships between different protein modalities; (ii) A multi-metric evaluation approach that assesses performance across four key dimensions: quality, novelty, diversity, and robustness; and (iii) In-depth analyses from various user objectives, providing a holistic view of model performance. Our comprehensive evaluation of protein foundation models reveals several key findings that shed light on their current capabilities and limitations. To promote transparency and facilitate further research, we release the evaluation dataset, code, and a public leaderboard publicly for further analysis and a general modular toolkit. We intend for ProteinBench to be a living benchmark for establishing a standardized, in-depth evaluation framework for protein foundation models, driving their development and application while fostering collaboration within the field.

Vision-language models (VLMs) like CLIP have shown impressive zero-shot and few-shot learning capabilities across diverse applications. However, adapting these models to new fine-grained domains remains difficult due to reliance on prompt engineering and the high cost of full model fine-tuning. Existing adaptation approaches rely on augmented components, such as prompt tokens and adapter modules, which could limit adaptation quality, destabilize the model, and compromise the rich knowledge learned during pretraining. In this work, we present CLIP-SVD, a novel multi-modal and parameter-efficient adaptation technique that leverages Singular Value Decomposition (SVD) to modify the internal parameter space of CLIP without injecting additional modules. Specifically, we fine-tune only the singular values of the CLIP parameter matrices to rescale the basis vectors for domain adaptation while retaining the pretrained model. This design enables enhanced adaptation performance using only 0.04\% of the model's total parameters and better preservation of its generalization ability. CLIP-SVD achieves state-of-the-art classification results on 11 natural and 10 biomedical datasets, outperforming previous methods in both accuracy and generalization under few-shot settings. Additionally, we leverage a natural language-based approach to analyze the effectiveness and dynamics of the CLIP adaptation to allow interpretability of CLIP-SVD. The code is publicly available at https://github.com/HealthX-Lab/CLIP-SVD.

The molecular characterization of tumor samples by multiple omics data sets of different types or modalities (e.g. gene expression, mutation, CpG methylation) has become an invaluable source of information for assessing the expected performance of individual drugs and their combinations. Merging the relevant information from the omics data modalities provides the statistical basis for determining suitable therapies for specific cancer patients. Different data modalities may each have their specific structures that need to be taken into account during inference. In this paper, we assume that each omics data modality has a low-rank structure with only few relevant features that affect the prediction and we propose to use a composite local nuclear norm penalization for learning drug sensitivity. Numerical results show that the composite low-rank structure can improve the prediction performance compared to using a global low-rank approach or elastic net regression.

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), have significantly reduced the number of trainable parameters needed in fine-tuning large language models (LLMs). Subsequent developments of LoRA-style adapters have diverged into two main directions: (1) enhancing model expressivity with high-rank adapters, and (2) pushing for further parameter reduction, as exemplified by vector-based methods. However, these approaches present a trade-off, as achieving the expressivity of high-rank weight updates typically comes at the cost of sacrificing the extreme parameter efficiency offered by vector-based techniques. To address this issue, we propose a vector-based random \textbf{Te}nsor network for high-\textbf{R}ank \textbf{A}daptation (TeRA), a novel PEFT method that achieves high-rank weight updates while retaining the parameter efficiency of vector-based PEFT adapters. This is achieved by parameterizing the tensorized weight update matrix as a Tucker-like tensor network (TN), in which large randomly initialized factors are frozen and shared across layers, while only small layer-specific scaling vectors, formed by entries in diagonal factor matrices, are trained. This design effectively decouples the rank of the weight update matrix from the number of trainable parameters. Comprehensive experiments demonstrate that TeRA matches or even outperforms high-rank adapters, while requiring a trainable parameter count similar to vector-based methods. Theoretical analysis and ablation studies further validate the effectiveness of our approach.