UPS: Towards Foundation Models for PDE Solving via Cross-Modal Adaptation

We introduce UPS (Unified PDE Solver), an effective and data-efficient approach to solve diverse spatiotemporal PDEs defined over various domains, dimensions, and resolutions. UPS unifies different PDEs into a consistent representation space and processes diverse collections of PDE data using a unified network architecture that combines LLMs with domain-specific neural operators. We train the network via a two-stage cross-modal adaptation process, leveraging ideas of modality alignment and multi-task learning. By adapting from pretrained LLMs and exploiting text-form meta information, we are able to use considerably fewer training samples than previous methods while obtaining strong empirical results. UPS outperforms existing baselines, often by a large margin, on a wide range of 1D and 2D datasets in PDEBench, achieving state-of-the-art results on 8 of 10 tasks considered. Meanwhile, it is capable of few-shot transfer to different PDE families, coefficients, and resolutions.

Tag-LLM: Repurposing General-Purpose LLMs for Specialized Domains

Large Language Models (LLMs) have demonstrated remarkable proficiency in understanding and generating natural language. However, their capabilities wane in highly specialized domains underrepresented in the pretraining corpus, such as physical and biomedical sciences. This work explores how to repurpose general LLMs into effective task solvers for specialized domains. We introduce a novel, model-agnostic framework for learning custom input tags, which are parameterized as continuous vectors appended to the LLM's embedding layer, to condition the LLM. We design two types of input tags: domain tags are used to delimit specialized representations (e.g., chemical formulas) and provide domain-relevant context; function tags are used to represent specific functions (e.g., predicting molecular properties) and compress function-solving instructions. We develop a three-stage protocol to learn these tags using auxiliary data and domain knowledge. By explicitly disentangling task domains from task functions, our method enables zero-shot generalization to unseen problems through diverse combinations of the input tags. It also boosts LLM's performance in various specialized domains, such as predicting protein or chemical properties and modeling drug-target interactions, outperforming expert models tailored to these tasks.

Cross-Modal Fine-Tuning: Align then Refine

Fine-tuning large-scale pretrained models has led to tremendous progress in well-studied modalities such as vision and NLP. However, similar gains have not been observed in many other modalities due to a lack of relevant pretrained models. In this work, we propose ORCA, a general cross-modal fine-tuning framework that extends the applicability of a single large-scale pretrained model to diverse modalities. ORCA adapts to a target task via an align-then-refine workflow: given the target input, ORCA first learns an embedding network that aligns the embedded feature distribution with the pretraining modality. The pretrained model is then fine-tuned on the embedded data to exploit the knowledge shared across modalities. Through extensive experiments, we show that ORCA obtains state-of-the-art results on 3 benchmarks containing over 60 datasets from 12 modalities, outperforming a wide range of hand-designed, AutoML, general-purpose, and task-specific methods. We highlight the importance of data alignment via a series of ablation studies and demonstrate ORCA's utility in data-limited regimes.

Efficient Architecture Search for Diverse Tasks

While neural architecture search (NAS) has enabled automated machine learning (AutoML) for well-researched areas, its application to tasks beyond computer vision is still under-explored. As less-studied domains are precisely those where we expect AutoML to have the greatest impact, in this work we study NAS for efficiently solving diverse problems. Seeking an approach that is fast, simple, and broadly applicable, we fix a standard convolutional network (CNN) topology and propose to search for the right kernel sizes and dilations its operations should take on. This dramatically expands the model's capacity to extract features at multiple resolutions for different types of data while only requiring search over the operation space. To overcome the efficiency challenges of naive weight-sharing in this search space, we introduce DASH, a differentiable NAS algorithm that computes the mixture-of-operations using the Fourier diagonalization of convolution, achieving both a better asymptotic complexity and an up-to-10x search time speedup in practice. We evaluate DASH on NAS-Bench-360, a suite of ten tasks designed for benchmarking NAS in diverse domains. DASH outperforms state-of-the-art methods in aggregate, attaining the best-known automated performance on seven tasks. Meanwhile, on six of the ten tasks, the combined search and retraining time is less than 2x slower than simply training a CNN backbone that is far less accurate.

Iterative Teacher-Aware Learning

In human pedagogy, teachers and students can interact adaptively to maximize communication efficiency. The teacher adjusts her teaching method for different students, and the student, after getting familiar with the teacher's instruction mechanism, can infer the teacher's intention to learn faster. Recently, the benefits of integrating this cooperative pedagogy into machine concept learning in discrete spaces have been proved by multiple works. However, how cooperative pedagogy can facilitate machine parameter learning hasn't been thoroughly studied. In this paper, we propose a gradient optimization based teacher-aware learner who can incorporate teacher's cooperative intention into the likelihood function and learn provably faster compared with the naive learning algorithms used in previous machine teaching works. We give theoretical proof that the iterative teacher-aware learning (ITAL) process leads to local and global improvements. We then validate our algorithms with extensive experiments on various tasks including regression, classification, and inverse reinforcement learning using synthetic and real data. We also show the advantage of modeling teacher-awareness when agents are learning from human teachers.

Theoretically Principled Deep RL Acceleration via Nearest Neighbor Function Approximation

Recently, deep reinforcement learning (RL) has achieved remarkable empirical success by integrating deep neural networks into RL frameworks. However, these algorithms often require a large number of training samples and admit little theoretical understanding. To mitigate these issues, we propose a theoretically principled nearest neighbor (NN) function approximator that can improve the value networks in deep RL methods. Inspired by human similarity judgments, the NN approximator estimates the action values using rollouts on past observations and can provably obtain a small regret bound that depends only on the intrinsic complexity of the environment. We present (1) Nearest Neighbor Actor-Critic (NNAC), an online policy gradient algorithm that demonstrates the practicality of combining function approximation with deep RL, and (2) a plug-and-play NN update module that aids the training of existing deep RL methods. Experiments on classical control and MuJoCo locomotion tasks show that the NN-accelerated agents achieve higher sample efficiency and stability than the baseline agents. Based on its theoretical benefits, we believe that the NN approximator can be further applied to other complex domains to speed-up learning.

Emergence of Pragmatics from Referential Game between Theory of Mind Agents

Pragmatics studies how context can contribute to language meanings [1]. In human communication, language is never interpreted out of context, and sentences can usually convey more information than their literal meanings [2]. However, this mechanism is missing in most multi-agent systems [3, 4, 5, 6], restricting the communication efficiency and the capability of human-agent interaction. In this paper, we propose an algorithm, using which agents can spontaneously learn the ability to "read between lines" without any explicit hand-designed rules. We integrate the theory of mind (ToM) [7, 8] in a cooperative multi-agent pedagogical situation and propose an adaptive reinforcement learning (RL) algorithm to develop a communication protocol. ToM is a profound cognitive science concept, claiming that people regularly reason about other's mental states, including beliefs, goals, and intentions, to obtain performance advantage in competition, cooperation or coalition. With this ability, agents consider language as not only messages but also rational acts reflecting others' hidden states. Our experiments demonstrate the advantage of pragmatic protocols over non-pragmatic protocols. We also show the teaching complexity following the pragmatic protocol empirically approximates to recursive teaching dimension (RTD).