Contemporary large models often exhibit behaviors suggesting the presence of low-level primitives that compose into modules with richer functionality, but these fundamental building blocks remain poorly understood. We investigate this compositional structure in linear layers by asking: can we identify/synthesize linear transformations from a minimal set of geometric primitives? Using Clifford algebra, we show that linear layers can be expressed as compositions of bivectors--geometric objects encoding oriented planes--and introduce a differentiable algorithm that decomposes them into products of rotors. This construction uses only O log2 d parameters, versus O(d2) required by dense matrices. Applied to the key, query, and value projections in LLM attention layers, rotor-based layers match the performance of strong baselines such as block-Hadamard and low-rank approximations. Our findings provide an algebraic perspective on how these geometric primitives can compose into higher-level functions within deep models.

Task vectors capture how a model changes during fine-tuning by recording the difference between pre-trained and task-specific weights. The composition of task vectors, a key operator in task arithmetic, enables models to integrate knowledge from multiple tasks without incurring significant additional inference costs. In this paper, we propose variational task vector composition (VTVC), where composition coefficients are taken as latent variables and estimated in a Bayesian inference framework. Unlike previous methods that operate at the task level, our framework focuses on sample-specific composition. Motivated by the observation of structural redundancy in task vectors, we introduce a Spike-and-Slab prior that promotes sparsity and aims to preserve the most informative components. To further address the high variance and sampling inefficiency in sparse, high-dimensional spaces, we develop a gated sampling mechanism that constructs a controllable posterior by filtering the composition coefficients based on both uncertainty and importance. This yields a more stable and interpretable variational framework by deterministically selecting reliable task components, reducing sampling variance while improving transparency and generalization. Experimental results demonstrate that our method achieves state-of-the-art average performance across a diverse range of benchmarks, including image classification and natural language understanding.

We consider the privacy amplification properties of a sampling scheme in which a user's data is used in k steps chosen randomly and uniformly from a sequence (or set) of t steps. This sampling scheme has been recently applied in the context of differentially private optimization [Chua et al., 2024a, Choquette-Choo et al., 2025] and is also motivated by communication-efficient high-dimensional private aggregation [Asi et al., 2025]. Existing analyses of this scheme either rely on privacy amplification by shuffling which leads to overly conservative bounds or require Monte Carlo simulations that are computationally prohibitive in most practical scenarios. We give the first theoretical guarantees and numerical estimation algorithms for this sampling scheme. In particular, we demonstrate that the privacy guarantees of random k-out-of-t allocation can be upper bounded by the privacy guarantees of the well-studied independent (or Poisson) subsampling in which each step uses the user's data with probability (1+o(1))k/t. Further, we provide two additional analysis techniques that lead to numerical improvements in several parameter regimes. Altogether, our bounds give efficiently-computable and nearly tight numerical results for random allocation applied to Gaussian noise addition.

In this work, we introduce RoleBench, a benchmark focused on evaluating compositional generalization in action-based relations (e.g., "mouse chasing cat"). We show that state-of-the-art T2I models and compositional generation methods consistently default to frequent reversed relations (i.e., "cat chasing mouse"), a phenomenon we call role collapse. Related works attribute this to the model's architectural limitation or underrepresentation in the data. Our key insight reveals that while models fail on rare compositions when their inversions are common, they can successfully generate similar intermediate compositions (e.g., "mouse chasing boy"), suggesting that this limitation is also due to the presence of frequent counterparts rather than just the absence of rare compositions. Motivated by this, we hypothesize that directional decomposition can gradually mitigate role collapse. We test this via ReBind, a lightweight framework that teaches role bindings using carefully selected active/passive intermediate compositions. Experiments suggest that intermediate compositions through simple fine-tuning can significantly reduce role collapse, with humans preferring ReBind more than 78% compared to state-of-the-art methods. Our findings highlight the role of distributional asymmetries in compositional failures and offer a simple, effective path for improving generalization.

Model editing has become a de-facto practice to address hallucinations and outdated knowledge of large language models (LLMs). However, existing methods are predominantly evaluated in isolation, i.e., one edit at a time, failing to consider a critical scenario of compositional model editing, where multiple edits must be integrated and jointly utilized to answer real-world multifaceted questions. For instance, in medical domains, if one edit informs LLMs that COVID-19 causes "fever" and another that it causes "loss of taste", a qualified compositional editor should enable LLMs to answer the question "What are the symptoms of COVID-19?" with both "fever" and "loss of taste" (and potentially more). In this work, we define and systematically benchmark this compositional model editing (CME) task, identifying three key undesirable issues that existing methods struggle with: knowledge loss, incorrect preceding and knowledge sinking. To overcome these issues, we propose A3E, a novel compositional editor that (1) adaptively combines and adaptively regularizes pre-trained foundation knowledge in LLMs in the stage of edit training and (2) adaptively merges multiple edits to better meet compositional needs in the stage of edit composing. Extensive experiments demonstrate that A3E improves the composability by at least 22.45% without sacrificing the performance of non-compositional model editing.

Designing effective agentic systems requires the seamless composition and integration of agents, tools, and models within dynamic and uncertain environments. Most existing methods rely on static, semantic retrieval approaches for tool or agent discovery. However, effective reuse and composition of existing components remain challenging due to incomplete capability descriptions and the limitations of retrieval methods. Component selection suffers because the decisions are not based on capability, cost, and real-time utility. To address these challenges, we introduce a structured, automated framework for agentic system composition that is inspired by the knapsack problem. Our framework enables a composer agent to systematically identify, select, and assemble an optimal set of agentic components by jointly considering performance, budget constraints, and compatibility.

Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends critically on robust benchmarks and minimal, information-rich datasets that enable meaningful model evaluation. This paper critically examines common datasets and reported metrics for a crystal structure prediction task--generating the most likely structures given the chemical composition of a material. We focus on three key issues: First, materials datasets should contain unique crystal structures; for example, we show that the widely-utilized carbon-24 dataset only contains 40%unique structures. Second, materials datasets should not be split randomly if polymorphs of many different compositions are numerous, which we find to be the case for the perov-5 and MP-20 datasets.

Diffusion models have become prevalent in generative modeling due to their ability to sample from complex distributions. To improve the quality of generated samples and their compliance with user requirements, two commonly used methods are: (i) Alignment, which involves finetuning a diffusion model to align it with a reward; and (ii) Composition, which combines several pretrained diffusion models together, each emphasizing a desirable attribute in the generated outputs. However, trade-offs often arise when optimizing for multiple rewards or combining multiple models, as they can often represent competing properties. Existing methods cannot guarantee that the resulting model faithfully generates samples with all the desired properties. To address this gap, we propose a constrained optimization framework that unifies alignment and composition of diffusion models by enforcing that the aligned model satisfies reward constraints and/or remains close to each pretrained model. We provide a theoretical characterization of the solutions to the constrained alignment and composition problems and develop a Lagrangian-based primal-dual training algorithm to approximate these solutions. Empirically, we demonstrate our proposed approach in image generation, applying it to alignment and composition, and show that our aligned or composed model satisfies constraints effectively.

Text-to-image (T2I) generation has made remarkable progress, yet existing systems still lack intuitive control over spatial composition, object consistency, and multi-step editing.

Task vectors capture how a model changes during fine-tuning by recording the difference between pre-trained and task-specific weights. The composition of task vectors, a key operator in task arithmetic, enables models to integrate knowledge from multiple tasks without incurring significant additional inference costs. In this paper, we propose variational task vector composition (VTVC), where composition coefficients are taken as latent variables and estimated in a Bayesian inference framework. Unlike previous methods that operate at the task level, our framework focuses on sample-specific composition. Motivated by the observation of structural redundancy in task vectors, we introduce a Spike-and-Slab prior that promotes sparsity and aims to preserve the most informative components. To further address the high variance and sampling inefficiency in sparse, high-dimensional spaces, we develop a gated sampling mechanism that constructs a controllable posterior by filtering the composition coefficients based on both uncertainty and importance. This yields a more stable and interpretable variational framework by deterministically selecting reliable task components, reducing sampling variance while improving transparency and generalization. Experimental results demonstrate that our method achieves state-of-the-art average performance across a diverse range of benchmarks, including image classification and natural language understanding.