arXiv subjects

Siyu Lou

Publications and source records attributed to Siyu Lou.

12 recordsLinked to original sources

arXiv2026

Mathematical Principles and Experimental Discoveries of the Emergence of Symbolic Patterns in Artificial Neural Networks

Artificial Neural networks (ANNs) are often treated as black-box models, making explainability a central challenge in deep learning. Many engineering methods have been proposed to approximately explain the ANN from various perspectives, such as feature attribution and visualization. However, it remains a long-standing open question whether the complex inference logic of an ANN can be explained exhaustively and concisely as sparse symbolic patterns. This raises a deeper inquiry: does the emergence of symbolic patterns reflect a natural law rather than chance? Here, we show that across a broad class of ANNs trained on diverse tasks, their inference logic can indeed be reformulated as sparse symbolic interactions. We further prove that two common mathematical criteria, which are implicitly required across tasks, lead to the emergence of such sparse symbolic interactions. Empirical evidence confirms that the two criteria hold for the majority of input samples in diverse models. Furthermore, the faithfulness of these interactions is also demonstrated by their strong sample-to-sample and model-to-model transferability, as well as their ability to explain the overall generalization power of ANNs. Our theoretical analysis and extensive experiments provide a solid foundation for symbolic explanations of ANNs, and offer novel insights into the ANN's generalization power. Our findings also highlight the potential of communicative learning, a paradigm in which the inference logic of an ANN can be directly inspected and tuned at the level of symbolic patterns, thus complementing traditional end-to-end learning paradigm. Finally, the observed emergence of symbolic patterns in ANNs suggests that similar symbolic representations may also emerge in other types of black-box systems under certain conditions, because our proof does not depend on any specific ANN architecture.

cs.LG↗

arXiv2026

Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization

Discovering governing equations directly from observational data is a key step towards interpretable scientific machine learning. Current data-driven approaches typically operate on a single dataset, inherently limiting their performance when faced with restricted observations. In practice, multiple datasets are often available for the same physical system, distinguished only by distinct initial conditions or boundary configurations. Here, we present a competitive optimization framework designed to discover shared partial differential equations (PDEs) from multi-source datasets, termed MCO-PDE. The framework first trains independent neural surrogates for each data source, and then employs a soft-competitive weighting mechanism to dynamically assess dataset credibility and aggregate a consensus global coefficient. Integrated with a genetic algorithm for structural search, this approach simultaneously identifies the functional forms and parameters of the governing laws. We demonstrate that fusing as few as 50 observations per dataset across seven cases recovers canonical equations with high accuracy. The framework inherently handles two- and three-dimensional domains characterized by irregular boundaries and heterogeneous coefficients, and successfully extracts physically meaningful laws from real-world wave-tank experiments. Overall, this work establishes a promising route for automated scientific discovery via heterogeneous data fusion.

cs.LG↗

arXiv2026

Data-driven discovery of governing differential equations across physical systems

Differential equations play a critical role in scientific discovery because they provide a mathematical framework to describe the behaviour of physical phenomena. As a promising alternative to traditional first principles, data-driven differential equation discovery has attracted increasing attention for its ability to infer governing laws directly from experimental or simulated data, especially when the underlying physics is unclear. However, the field has expanded rapidly along diverse methodological directions, particularly with the emergence of AI-based approaches, and still lacks a clear organizing perspective. In this Review, we propose a problem-oriented perspective on data-driven differential equation discovery. We first introduce a two-dimensional phase diagram of equation discoverability, where discovery problems are organized according to structural complexity and coefficient complexity. This phase diagram shows how the field has moved from the discovery of sparse equations with simple coefficients toward more complex governing laws with richer structures and more flexible parameterizations. It also clarifies why different methodological families succeed or fail in different problem settings. We then present the representation-evaluation-optimization (REO) framework as a fundamental abstraction of the discovery process. By identifying the core problems of equation discovery that persist across algorithmic variations, REO shifts the discussion from individual algorithms to the fundamental principles that determine discoverability. We connect these perspectives to applications across physics and adjacent sciences, and argue that the next challenge is not merely recovering equations, but using them to revise existing theories, distil mechanisms and form new scientific concepts.

cs.LG↗

arXiv2026

Cross-LLM Consistency in Inference: Evidence from Shared Interactions

Large language models (LLMs) differ in architecture, training data, and optimization procedures, yet they may still develop similar internal inference patterns. In this paper, we examine this hypothesis using interaction-based explanations. We find that LLMs often share interaction patterns when predicting the same target token from the same prompt. This consistency is more pronounced among advanced LLMs. Shared interactions also tend to be lower-order and show weaker positive-negative cancellation than non-shared interactions. These results suggest that advanced LLMs may be implicitly optimized toward common inference patterns, even though the mechanisms that give rise to such cross-model consistency remain open.

cs.AI↗

arXiv2026

RRAttention: Dynamic Block Sparse Attention via Per-Head Round-Robin Shifts for Long-Context Inference

The quadratic complexity of attention mechanisms poses a critical bottleneck for large language models processing long contexts. While dynamic sparse attention methods offer input-adaptive efficiency, they face fundamental trade-offs: requiring preprocessing, lacking global evaluation, violating query independence, or incurring high computational overhead. We present RRAttention, a novel dynamic sparse attention method that simultaneously achieves all desirable properties through a head \underline{r}ound-\underline{r}obin (RR) sampling strategy. By rotating query sampling positions across attention heads within each stride, RRAttention maintains query independence while enabling efficient global pattern discovery with stride-level aggregation. Our method reduces complexity from $O(L^2)$ to $O(L^2/S^2)$ and employs adaptive Top-$\tau$ selection for optimal sparsity. Extensive experiments on natural language understanding (HELMET) and multimodal video comprehension (Video-MME) demonstrate that RRAttention recovers over 99\% of full attention performance while computing only half of the attention blocks, achieving 2.4$\times$ speedup at 128K context length and outperforming existing dynamic sparse attention methods.

cs.CL↗

arXiv2024

Defining and Extracting generalizable interaction primitives from DNNs

Faithfully summarizing the knowledge encoded by a deep neural network (DNN) into a few symbolic primitive patterns without losing much information represents a core challenge in explainable AI. To this end, Ren et al. (2024) have derived a series of theorems to prove that the inference score of a DNN can be explained as a small set of interactions between input variables. However, the lack of generalization power makes it still hard to consider such interactions as faithful primitive patterns encoded by the DNN. Therefore, given different DNNs trained for the same task, we develop a new method to extract interactions that are shared by these DNNs. Experiments show that the extracted interactions can better reflect common knowledge shared by different DNNs.

cs.LG↗

arXiv2024

Quantifying In-Context Reasoning Effects and Memorization Effects in LLMs

In this study, we propose an axiomatic system to define and quantify the precise memorization and in-context reasoning effects used by the large language model (LLM) for language generation. These effects are formulated as non-linear interactions between tokens/words encoded by the LLM. Specifically, the axiomatic system enables us to categorize the memorization effects into foundational memorization effects and chaotic memorization effects, and further classify in-context reasoning effects into enhanced inference patterns, eliminated inference patterns, and reversed inference patterns. Besides, the decomposed effects satisfy the sparsity property and the universal matching property, which mathematically guarantee that the LLM's confidence score can be faithfully decomposed into the memorization effects and in-context reasoning effects. Experiments show that the clear disentanglement of memorization effects and in-context reasoning effects enables a straightforward examination of detailed inference patterns encoded by LLMs.

cs.LG↗

arXiv2024

Physics-constrained robust learning of open-form partial differential equations from limited and noisy data

Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise evaluations, which in turn result in redundant function terms or erroneous equations. This study proposes a framework to robustly uncover open-form partial differential equations (PDEs) from limited and noisy data. The framework operates through two alternating update processes: discovering and embedding. The discovering phase employs symbolic representation and a novel reinforcement learning (RL)-guided hybrid PDE generator to efficiently produce diverse open-form PDEs with tree structures. A neural network-based predictive model fits the system response and serves as the reward evaluator for the generated PDEs. PDEs with higher rewards are utilized to iteratively optimize the generator via the RL strategy and the best-performing PDE is selected by a parameter-free stability metric. The embedding phase integrates the initially identified PDE from the discovering process as a physical constraint into the predictive model for robust training. The traversal of PDE trees automates the construction of the computational graph and the embedding process without human intervention. Numerical experiments demonstrate our framework's capability to uncover governing equations from nonlinear dynamic systems with limited and highly noisy data and outperform other physics-informed neural network-based discovery methods. This work opens new potential for exploring real-world systems with limited understanding.

cs.LG↗

arXiv2024

Empowering Machines to Think Like Chemists: Unveiling Molecular Structure-Polarity Relationships with Hierarchical Symbolic Regression

Thin-layer chromatography (TLC) is a crucial technique in molecular polarity analysis. Despite its importance, the interpretability of predictive models for TLC, especially those driven by artificial intelligence, remains a challenge. Current approaches, utilizing either high-dimensional molecular fingerprints or domain-knowledge-driven feature engineering, often face a dilemma between expressiveness and interpretability. To bridge this gap, we introduce Unsupervised Hierarchical Symbolic Regression (UHiSR), combining hierarchical neural networks and symbolic regression. UHiSR automatically distills chemical-intuitive polarity indices, and discovers interpretable equations that link molecular structure to chromatographic behavior.

cs.LG↗

arXiv2023

Bayesian Neural Networks Avoid Encoding Complex and Perturbation-Sensitive Concepts

In this paper, we focus on mean-field variational Bayesian Neural Networks (BNNs) and explore the representation capacity of such BNNs by investigating which types of concepts are less likely to be encoded by the BNN. It has been observed and studied that a relatively small set of interactive concepts usually emerge in the knowledge representation of a sufficiently-trained neural network, and such concepts can faithfully explain the network output. Based on this, our study proves that compared to standard deep neural networks (DNNs), it is less likely for BNNs to encode complex concepts. Experiments verify our theoretical proofs. Note that the tendency to encode less complex concepts does not necessarily imply weak representation power, considering that complex concepts exhibit low generalization power and high adversarial vulnerability. The code is available at https://github.com/sjtu-xai-lab/BNN-concepts.

cs.LG↗

arXiv2023

HarsanyiNet: Computing Accurate Shapley Values in a Single Forward Propagation

The Shapley value is widely regarded as a trustworthy attribution metric. However, when people use Shapley values to explain the attribution of input variables of a deep neural network (DNN), it usually requires a very high computational cost to approximate relatively accurate Shapley values in real-world applications. Therefore, we propose a novel network architecture, the HarsanyiNet, which makes inferences on the input sample and simultaneously computes the exact Shapley values of the input variables in a single forward propagation. The HarsanyiNet is designed on the theoretical foundation that the Shapley value can be reformulated as the redistribution of Harsanyi interactions encoded by the network.

cs.LG↗

arXiv2022

Audio-text Retrieval in Context

Audio-text retrieval based on natural language descriptions is a challenging task. It involves learning cross-modality alignments between long sequences under inadequate data conditions. In this work, we investigate several audio features as well as sequence aggregation methods for better audio-text alignment. Moreover, through a qualitative analysis we observe that semantic mapping is more important than temporal relations in contextual retrieval. Using pre-trained audio features and a descriptor-based aggregation method, we build our contextual audio-text retrieval system. Specifically, we utilize PANNs features pre-trained on a large sound event dataset and NetRVLAD pooling, which directly works with averaged descriptors. Experiments are conducted on the AudioCaps and CLOTHO datasets, and results are compared with the previous state-of-the-art system. With our proposed system, a significant improvement has been achieved on bidirectional audio-text retrieval, on all metrics including recall, median and mean rank.

cs.SD↗