Establishing Universal Approximation Theorems (UATs) for nonlinear operators and their derivatives is a foundational open problem in Operator Learning (OL) and raises delicate questions in Nonlinear Functional Analysis. We prove the first UATs for $k$-times differentiable nonlinear operators and their derivatives via OL architectures, uniformly on compact sets and in weighted Bastiani--Sobolev spaces for general finite input measures. In full Banach-space generality, these are the first complete generalizations of the corresponding influential classical UATs in [Hornik, 1991] to infinite-dimensional spaces and OL, {and launch Derivative-Informed Operator Learning (DIOL) (i.e. learning nonlinear operators and their derivatives)} on general Banach spaces. Based on our UATs, we formulate Bastiani--Sobolev training in DIOL. We present open frontiers where DIOL and our UATs find applications: high-order accuracy in OL; fast constrained optimization in Banach spaces (e.g. optimal control of PDEs, inverse problems) via Learn-Then-Optimize; numerical methods for infinite-dimensional PDEs (e.g. HJB PDEs on Banach spaces from infinite-dimensional optimal control via Optimize-Then-Learn, such as optimal control of PDEs, SPDEs, path-dependent systems, partially observed systems, mean-field control).
We parameterize nonlinear operators via Encoder-Decoder Architectures, classical OL architectures. These include DeepONets, Deep-H-ONets, and PCA-Nets, which our UATs cover.
Our UATs are based on (i) Approximation Properties of Banach spaces; (ii) continuous Bastiani differentiability (weaker than continuous Fr\'echet differentiability); (iii) $C^k_B$ (Bastiani) compact-open topologies; indeed, UA in $C^k$ (Fr\'echet) compact-open topologies (induced by operator norms) fails; (iv) construction of weighted Bastiani--Sobolev spaces, generalizing classical Gaussian Sobolev spaces on Banach spaces.
Transformers encode structure in sequences via an expanding contextual history. However, their purely feedforward architecture fundamentally limits dynamic state tracking. State tracking -- the iterative updating of latent variables reflecting an evolving environment -- involves inherently sequential dependencies that feedforward networks struggle to maintain. Consequently, feedforward models push evolving state representations deeper into their layer stack with each new input step, rendering information inaccessible in shallow layers and ultimately exhausting the model's depth. While this depth limit can be bypassed by dynamic depth models and by explicit or latent thinking that externalizes state representations, these solutions are computationally and memory inefficient. In this article, we argue that temporally extended cognition requires refocusing from explicit thought traces to implicit activation dynamics via recurrent architectures. We introduce a taxonomy of recurrent and continuous-thought transformer architectures, categorizing them by their recurrence axis (depth versus step) and their ratio of input tokens to recurrence steps. Finally, we outline promising research directions, including enhanced state-space models and coarse-grained recurrence, to better integrate state tracking into modern foundation models.
Michael C. Mozer, Shoaib Ahmed Siddiqui, Rosanne Liu· 0 citations
Accurate Earth system prediction requires state inference from incomplete observations, but conventional two-stage data assimilation (DA) is computationally prohibitive because repeated PDE-based ensemble forecasts, observation updates, and intermediate data movement limit ensemble size at high resolution. We introduce STORM, a one-stage generative AI framework that reformulates DA as diffusion-based Bayesian posterior sampling, replacing online PDE ensemble forecasts with scalable AI inference. It further combines a spatiotemporal transformer with a global-attention algorithm that reduces complexity from quadratic to linear through scalable gradient propagation, enabling high-resolution, long-context Earth modeling. STORM scales to 74,400 GPUs on Frontier with 96--99\% strong-scaling efficiency and up to 6 ExaFLOPs sustained BF16 throughput, while enabling 32,768-member ensembles for uncertainty quantification in 34 seconds on 4,096 GPUs. It scales to 20 billion spatiotemporal tokens and 177,000 temporal frames. Hurricane tracking and long-term climate reanalysis demonstrate improved accuracy, including benefits from longer temporal context and recovery of temperature extremes missed by forecast-only predictions.
Xiao Wang, Zezhong Zhang, Isaac Lyngaas et al.· 0 citations
Large language models are prone to hallucinating factually incorrect statements. A key source of these errors is exposure to new factual information through supervised fine-tuning (SFT), which can increase hallucinations w.r.t.~knowledge acquired during pre-training. Since these errors arise as a by-product of knowledge degradation, we explore whether established continual learning tools can mitigate them. We propose a self-distillation-based SFT method that facilitates effective factual learning while minimizing hallucinations w.r.t.~pre-existing knowledge by regularizing output-distribution drift. We also show that when new knowledge acquisition is unnecessary, suppressing factual plasticity by freezing parameter groups preserves task performance while reducing hallucinations. Lastly, we investigate the mechanism, contrasting capacity limitations, behavior cloning, and localized interference. Our experiments show that a main driver is interference among overlapping semantic representations, which self-distillation mitigates and an associative-memory model explains: forgetting grows with the overlap between new and stored facts.
Guy Kaplan, Zorik Gekhman, Zhen Zhu et al.· 0 citations
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Applying steering vectors to large language models (LLMs) is an efficient and effective model alignment technique, but we lack an interpretable explanation for how it works--specifically, what internal mechanisms steering vectors affect and how this results in different model outputs. To investigate the causal mechanisms underlying the effectiveness of steering vectors, we conduct a comprehensive case study on refusal. We propose a multi-token activation patching framework and discover that different steering methodologies leverage functionally interchangeable circuits when applied at the same layer. These circuits reveal that steering vectors primarily interact with the attention mechanism through the OV circuit while largely ignoring the QK circuit. Freezing all attention scores during steering drops performance by only 8.83% across three model families. A mathematical decomposition of the steered OV circuit further reveals semantically interpretable concepts, even in cases where the steering vector itself does not. Leveraging the activation patching results, we show that steering vectors can be sparsified by up to 85-96% while retaining most performance, and that different steering methodologies agree on a subset of important dimensions.
Stephen Cheng, Sarah Wiegreffe, Dinesh Manocha· 0 citations
With the growing demand for long-context LLMs across a wide range of applications, the key-value (KV) cache has become a critical bottleneck for both latency and memory usage. Recently, KV-cache offloading has emerged as a promising approach to reduce memory footprint and inference latency while preserving accuracy. Prior evaluations have largely focused on tasks that do not require extracting large amounts of information from the context. In this work, we study KV-cache offloading on context-intensive tasks: problems where the solution requires looking up a lot of information from the input prompt. We create and release the Text2JSON benchmark, a highly context-intensive task that requires extracting structured knowledge from raw text. We evaluate modern KV offloading on Text2JSON and other context-intensive tasks and find significant performance degradation on both Llama 3 and Qwen 3 models. Our analysis identifies two key reasons for poor accuracy: low-rank projection of keys and unreliable landmarks, and proposes a simpler alternative strategy that significantly improves accuracy across multiple LLM families and benchmarks. These findings highlight the need for a comprehensive and rigorous evaluation of long-context compression techniques.
Andrey Bocharnikov, Ivan Ermakov, Denis Kuznedelev et al.· 0 citations
Speculative decoding (SD) accelerates large language model inference by using a smaller draft model to propose draft tokens that are subsequently verified by a larger target model. However, the performance of standard SD is often limited by the strictly sequential execution of these drafting and verification stages. To address this, this paper proposes MineDraft, a batch parallel speculative decoding (PSD) framework designed to effectively hide drafting latency by overlapping it with verification. Our theoretical analysis shows that PSD is substantially more efficient than standard SD. MineDraft realizes the PSD through a novel batch-parallel design that maintains two batches of requests, overlapping drafting for one batch with verification for the other. Our experimental results show significant improvements of \alg{} in both throughput (up to 75%) and end-to-end latency (up to 39%) over standard SD. Furthermore, we have implemented MineDraft as a plugin for vLLM, demonstrating its practicality for production-ready inference systems.
Zhenwei Tang, Arun Verma, Zijian Zhou et al.· 0 citations
Virtual-cell models aim to predict how cell populations respond to perturbations, but control and treated cells are measured as unpaired populations, complicating the learning of perturbation-specific effects. We present SCALE, a conditional transport model that represents cells as unordered sets and predicts treated populations without cell-level matching. A shared set-aware encoder and conditional DiT backbone learn latent transport, making endpoint supervision directly delta-aligned without an auxiliary delta objective. Across genetic, chemical, developmental and immune perturbations, SCALE recovered gene-expression changes, response directions and population structure. In CRISPR data with dominant cell-line effects, SCALE outperformed competing methods across seven metrics and maintained separation among gene-target representations rather than collapsing them into a shared region. SCALE further prioritized cytokines predicted to produce distinct immune activation and inflammatory responses. Experiments using matched PBMC samples from three donors confirmed these predicted differences. Together, SCALE enables perturbation-specific prediction from unpaired populations and supports experimental prioritization.
Shuizhou Chen, Lang Yu, Xueqin Lin et al.· 0 citations
Retrosynthesis prediction aims to identify reactants that can synthesize a given product molecule. Although molecular large language models (LLMs) have recently shown promising results, most existing methods either generate reactants directly or provide only generic product-level analysis, without explicitly reasoning about bond-disconnection strategies that justify specific reactant choices. This paper proposes RetroReasoner, a retrosynthetic reasoning model that captures chemists' strategic disconnection-based thinking. RetroReasoner is trained with supervised fine-tuning and reinforcement learning. For supervised fine-tuning, SyntheticRetro generates structured disconnection rationales paired with reactant predictions. For reinforcement learning, a round-trip reward evaluates predicted reactants by passing them through a forward synthesis model and rewarding predictions that reconstruct the original product. RetroReasoner can also be applied to multi-step retrosynthetic planning by incorporating it into a parallelized Monte Carlo tree search framework, reducing search time while increasing the number and diversity of valid synthetic pathways. Experimental results show that RetroReasoner outperforms prior baselines, including not only molecular LLMs but also retrosynthesis-specific expert models, and generates a broader range of feasible reactant proposals, especially for challenging reaction instances. The code is available at https://github.com/KU-AGI/RetroReasoner.
Hanbum Ko, Chanhui Lee, Ye Rin Kim et al.· 0 citations
General-purpose large language models (LLMs) that rely on in-context learning do not reliably deliver the scientific understanding and performance required for drug discovery tasks. Simply increasing model size or introducing reasoning tokens does not yield significant performance gains. To address this gap, we introduce the MMAI Gym for Science, a one-stop shop molecular data formats and modalities as well as task-specific reasoning, training, and benchmarking recipes designed to teach foundation models the 'language of molecules' in order to solve practical drug discovery problems. We use MMAI Gym to train an efficient Liquid Foundation Model (LFM) for these applications, demonstrating that smaller, purpose-trained foundation models can outperform substantially larger general-purpose or specialist models on molecular benchmarks. Across essential drug discovery tasks - including molecular optimization, ADMET property prediction, retrosynthesis, drug-target activity prediction, and functional group reasoning - the resulting model achieves near specialist-level performance and, in the majority of settings, surpasses larger models, while remaining more efficient and broadly applicable in the domain.
Maksim Kuznetsov, Zulfat Miftahutdinov, Rim Shayakhmetov et al.· 0 citations
\emph{Integrated communication and computation} (IC$^2$) has emerged as a new paradigm for enabling efficient edge inference in sixth-generation (6G) networks. However, the design of IC$^2$ technologies is hindered by the lack of a tractable theoretical framework for characterizing \emph{end-to-end} (E2E) inference performance. The metric is highly complicated as it needs to account for both channel distortion and artificial intelligence (AI) model architecture and computational complexity. In this work, we address this challenge by developing a tractable analytical model for E2E inference accuracy and leveraging it to design a \emph{channel-adaptive AI} algorithm that maximizes inference throughput, referred to as the edge processing rate (EPR), under latency and accuracy constraints. Specifically, we consider an edge inference system in which a server deploys a backbone model with early exit, which enables flexible computational complexity, to perform inference on data features transmitted by a mobile device. The proposed accuracy model characterizes high-dimensional feature distributions in the angular domain using a Mixture of von Mises (MvM) distribution. This leads to a desired closed-form expression for inference accuracy as a function of quantization bit-width and model traversal depth, which represents channel distortion and computational complexity, respectively. Building upon this accuracy model, we formulate and solve the EPR maximization problem under joint latency and accuracy constraints, leading to a channel-adaptive AI algorithm that achieves full IC$^2$ integration. The proposed algorithm jointly adapts transmit-side feature compression and receive-side model complexity according to channel conditions to maximize overall efficiency and inference throughput. Experimental results demonstrate its superior performance as compared with fixed-complexity counterparts.
Long-context LLMs and Retrieval-Augmented Generation defer state tracking and evidence consolidation to query time, which is brittle when facts evolve and answers depend on latent states. We introduce Unified Memory Agent (UMA) for a one-to-many setting: query-agnostic external memory is constructed once from a stream and reused across multiple future QA sessions. A single policy maintains a structured Memory Bank through CRUD operations and answers using both the Memory Bank and raw context. Task-Stratified GRPO uses the mean reward of QA trajectories branching from each sampled memory state to supervise memory maintenance, while normalizing memory and per-question QA groups separately. We also introduce Ledger-QA, a diagnostic benchmark for long-horizon state tracking over accumulated updates. At the 16k budget, UMA-Generalist achieves the highest average score among compared methods across the test-time-learning and accurate-retrieval benchmarks and transfers to Ledger-QA without task-specific training; UMA-Specialist further improves long-horizon tracking after task adaptation. These results support learned proactive memory management for long-context reasoning.
Kehao Zhang, Shangtong Gui, Sheng Yang et al.· 0 citations
A weeklong summer workshop brought higher education faculty to campus to explore how AI and machine learning materials can be adapted for their classrooms.
Adaptive AI agents can help make BIM data more machine-readable by navigating IFC models, interpreting inconsistent information, and mapping it to defined standards. In this blog, Alok Rawat shares findings from a real-world pilot in construction workflows. The post Adaptive AI Agents in Construction Workflows appeared first on GPT-Lab.
What does it take to trust AI-driven HVAC optimization? Our AI Model Factory combines agents, machine learning, reinforcement learning and deterministic checks in a governed workflow designed for messy, real-world building data. The post We built an AI factory for HVAC control appeared first on GPT-Lab.
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