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Dai Shi

Publications and source records attributed to Dai Shi.

At least 19 recordsLinked to original sources
arXiv2026

Feature Superposition in Neural Networks: From Theory to Practice

Superposition refers to neural networks representing more features than they have dimensions. It offers a possible explanation for polysemantic neurons and motivates methods for recovering interpretable features from neural activations. Theoretical models typically start with a given set of input features and assumptions about how their values vary across inputs, then study how a network encodes those values in a lower-dimensional hidden representation. Empirical work, by contrast, seeks to identify the features encoded in trained networks and determine their role in computation. In this survey, we review the geometry, learning, and computation of superposed representations, explaining how feature statistics and decoder choice affect the conclusions. To connect these theoretical accounts with evidence from trained networks, we compare practical methods for recovering and analyzing features and examine what their evaluations establish. Since accurate activation reconstruction alone does not establish feature identity or causal use, we discuss the methods' documented failures and applications in light of the evidence available for these different claims. Finally, we assess previously stated open problems and identify remaining theoretical and empirical questions about superposition in trained networks. We hope our work can pave the way for a deeper understanding of superposition and more reliable methods for interpreting neural networks.

cs.LG↗
arXiv2026

CoVer: Conflict-Aware Claim Verification

Social media fact-checking has long been challenged by evidence-level and aggregation-level conflicts, where erroneous evidence mimics authoritative news sources. To capture this challenge and support conflict verification tasks, we present ContraNote, a large-scale real-world dataset curated from X's Community Notes system. It includes 33,686 posts for evaluating evidence-level conflict resolution, and 54,474 instances for evaluating aggregation-level prioritization. Additionally, we propose CoVer, a factual adjudication framework with three-stage pipelines: evidence schema normalization, factual consensus and support verification. This prioritizes evidence over noise to prevent it from compromising the final verdict. Technical evaluations show that CoVer achieves strong performance compared with state-of-the-art baselines across ContraNote (86.0% Acc., 68.0% mac. F1, 64.5 bal. Acc. on Conflict; and 88.5% Acc., 88.5 mac. F1 and 89.2 bal. Acc. on Prioritization), CONFACT-HumC (88.4% Acc.) and CONFACT-ModC (89.4% Acc.).

cs.AI↗
arXiv2026

When the Canonical Completion Is Wrong: Formalizing and Measuring the Jump in Large Language Models

Whether large language models (LLMs) can perform the abductive leap from evidence to a new system of axioms, commonly referred to as a jump, has recently attracted considerable debate. A prominent position holds that LLMs are structurally incapable of such jumps, while recent studies challenge both its mechanism and empirical evidence. One of the main reasons why the debate remains open is the lack of a formal definition of the jump and of algorithms that test whether a jump appears. In this paper, we attempt to develop a formal account of the jump in four steps and measure the second. These steps ask what the default completion of partial data is, when abandoning it is forced, whether the abandonment is correct, and how successive jumps compound. We define a \emph{jump instance} as a finite extension problem constrained by excluding the canonical completion given by the Kan extensions and leave exactly one unique correct completion. Under such an environment, a model offers a jump when it produces the correct completion, and fails to jump when it keeps the canonical default. We tested four frontier models on nine instances, where the Kan-default rate is zero in all 248 constrained trials, suggesting that the models can jump at least in this step. We further formalize the third and fourth steps, where a test of the jump is still wanted. We hope our work paves the path for formalizing and measuring the full jump in the future. The code of the paper is available at https://github.com/EEthanShi/kan-jump-test.

cs.CL↗
arXiv2026

On Computational Hardness of Mistake-Bounded Language Generation: A Random-Oracle Query Separation

Generation in the limit guarantees eventual generation for every countable collection of infinite languages in the model of Kleinberg and Mullainathan [KM24], while closure dimension characterizes stronger information-theoretic guarantees [RLT25]. Neither restricts per-output computation. The cumulative-mistake objective in mistake-bounded generation makes finite failure prefixes quantitative [KPR26], and a per-output query budget exposes their computational source. Polynomial-time algorithms are known for parities, conjunctions, and monotone functions with polynomially many maxterms [JKO26]. We ask whether information-theoretic ease can coexist with bounded-access computational hardness. Relative to a random oracle $H$, we answer yes by constructing a countable collection $C^\star$ of infinite languages with closure dimension zero. Almost surely on the same $H$, an unbounded generator makes zero mistakes on every target and every complete distinct enumeration. Yet, writing $\lambda$ for the target-seed length, every fixed uniform generator $G$ with polynomially many oracle queries in $\lambda$ and the output index $i$ has a constant $c_G>0$ such that, for every sufficiently large $\lambda$, some target incurs more than $2^{c_G\lambda}$ expected mistakes within its first $2(\lceil 2^{c_G\lambda}\rceil+1)$ canonical outputs. Infinite accidental agreement enables exhaustive search; sparse queries hide fresh target values. Thus, in the random-oracle model, zero-mistake information-theoretic generation coexists with a generator-dependent exponential lower bound on worst-case expected mistakes under polynomial-query access.

cs.CC↗
arXiv2026

Flood and Harvest: The Provable Necessity of Trivia for Generating Valuable Mathematics via the Lens of Language Generation in the Limit

AI systems coupled to proof assistants now generate formal mathematics at scale, and the gap between what a checker can verify and what a mathematician would value has become the binding constraint. We model the generation of valuable mathematics as nested language generation in the limit: a verifiable formal language $F$, accessed through a membership oracle (the proof checker), contains an unknown valuable language $H \in \mathcal{H}$ revealed only through an adversarial enumeration of a core $C \subseteq H$ of exact density $\alpha$ (the literature). Every output is valuable ($\in H$), trivial ($\in F \setminus H$), or a hallucination ($\notin F$). We settle four questions. First, the verifier is not taste: the collections admitting generation with breadth are exactly those of the oracle-free model, characterized fiber-wise by Angluin's condition. Second, the verifier does buy sound coverage, covering all unseen valuable statements while asserting only valid ones: possible with it, impossible without it; it relocates unavoidable errors from false to trivial. Third, and centrally, a sharp dichotomy on the tight family: generators emitting finitely many trivia achieve optimal coverage $\alpha/2$, while any infinite trivia allowance, even at vanishing rate, jumps the optimum to $1-\alpha/2$ (both tight, for cores presented as the candidate intersection), and one generator attains both ends. The transition is in trivia count, not rate; the gap $1-\alpha$ is the unrecorded mass. Fourth, both regimes instantiate in a compression model of mathematics. A perfect verifier cannot substitute for taste: the unbounded stream of correct-but-worthless statements is not an engineering accident but a provable necessity, since covering unrecorded valuable mathematics requires an infinite, but asymptotically negligible, stream of certified trivia.

cs.LG↗
arXiv2026

CANote: Empowering Fact-checking Note Writing Through Scaffolded and Provenance-based Human-AI Collaboration

Crowdsourced fact-checking mechanisms, such as X's Community Notes, play a critical role in mitigating the spread of misinformation. However, drafting high-quality, evidence-based debunking notes imposes a substantial burden on contributors. We present CANote, an AI-assisted debunking note writing system featuring evidence correlation and structured co-drafting. CANote scaffolds the workflow by extracting subclaims from social media posts, providing provenance through explicit links between subclaims and retrieved evidence, and generating neutral, structural drafts to support human reasoning. We evaluated CANote against manual writing (N=52 fact-checkers, N=52 lay users) on simulated X platform, where we found CANote significantly improves note quality. Notably, CANote enables lay users to write notes that have comparable quality to those written by experts. While the task completion time and perceived cognitive load remain comparable to manual drafting, CANote significantly increases user satisfaction. However, this assistance introduces a trade-off, resulting in a reduced sense of user ownership and control over the debunking note.

cs.HC↗
arXiv2026

Learning Manifold and It\^o Dynamics with Branched Neural Rough Differential Equations

Neural rough differential equations (NRDEs) stay accurate under irregular sampling while taking far fewer integration steps than standard neural differential equations, summarising a finely sampled driver by its log-signature and advancing the hidden state over coarse intervals using the log-ODE method. This efficiency rests on the shuffle algebra, the algebraic counterpart of Stratonovich calculus. This reliance means NRDEs cannot expose the quadratic-variation terms It\^o dynamics require, nor the ordered covariant derivatives that govern It\^o flows on connection-equipped manifolds. Ameliorating this, we introduce Branched Neural Rough Differential Equations (B-NRDEs), a Hopf-algebraic framework that recasts the NRDE log-ODE step as geometric numerical integration on the state-space manifold, matching the driving algebra to the governing calculus: Grossman--Larson rooted trees for Euclidean It\^o dynamics, Munthe-Kaas--Wright planar rooted trees for ordered covariant derivatives on manifolds, and the shuffle algebra in the classical Stratonovich case. This yields intrinsic coarse-step dynamics that exactly preserve manifold constraints. Finally, we introduce a branched signature-kernel objective to enable It\^o-consistent law matching by making quadratic-variation terms visible during training. On rough Bergomi volatility, sim-to-real $\mathrm{SO}(3)$ dynamics forecasting, and SPD covariance dynamics, B-NRDEs offer a unified, effective approach to stochastic and manifold-valued dynamics beyond the Euclidean--Stratonovich setting.

cs.LG↗
arXiv2026

Towards Multi-Agent-Simulation-Based Community Note Evaluation

Community-based fact-checking that relies on cross-consensus is expanding rapidly on social media platforms. However, the delay and low-ratio of cross-consensus community fact-checks rated by human contributors remains a significant challenge. To address this, we first created ComRate, a large-scale dataset comprising 2.5 million community notes and over 209 million ratings sourced from $\mathbb{X}$. We then propose MultiCom, a persona-guided multi-agent rating framework for community note evaluation. MultiCom simulates diverse rater population by clustering contributors in a matrix-factorized rater space and prompting persona agents to generate structured assessments based on the official community notes rating schema. These agents output structured and explainable judgments, such as confidence, agreement signals and reasons. An out-of-fold calibrated aggregation algorithm combines features such as raw votes and diagnostic reason signals for reliable prediction. Extensive evaluations demonstrate that MultiCom outperforms alternative methods, achieving an average accuracy of 84.7% (balanced accuracy 68.3%, macro-F1 60.1%) on the evaluation set.

cs.SI↗
arXiv2026

S$^3$GNN: Efficient Global Mixing and Local Message Passing for Long-Range Graph Learning

Message-passing neural networks (MPNNs) often suffer from an information bottleneck when capturing long-range dependencies, leading to the oversquashing (OSQ) phenomenon. Alongside spatial connectivity enrichment (e.g., rewiring), recent studies have shown that spectral filtering can yield strong long-range learning outcomes, as spectral operators enable global information mixing that alleviates OSQ. These approaches achieve this either by stabilizing the Jacobian energies in deep propagation or by guaranteeing OSQ mitigation under strong theoretical assumptions. We revisit these conclusions and show that the associated Jacobian sensitivity lower bound is generally difficult to achieve in practice. We then propose S$^3$GNN, which mitigates OSQ without such restrictive assumptions by lightweightly reintroducing omitted components with substantially lower computational complexity, while standard stability constraints on feature transformations remain effective under our new dynamics. Extensive experiments across diverse domains (e.g., long-range benchmarks, KGQA, and mesh-based fluid dynamics) demonstrate that S$^3$GNN achieves up to an order-of-magnitude error reduction with up to 50\% fewer parameters. Our code can be found in https://github.com/EEthanShi/S3-GNN.git.

cs.LG↗
arXiv2026

EgoIntrospect: An Egocentric Dataset and Benchmark for User-Centric Internal State Reasoning

Despite extensive efforts on egocentric video datasets and benchmarks, understanding users' internal states, which is crucial for enabling seamless AI assistant experiences, remains largely overlooked. In this work, we introduce EgoIntrospect, the first egocentric dataset captured in user-driven scenarios with self-annotations that explicitly reveal users' interactive intentions with AI assistants. EgoIntrospect was collected using a cross-device setup, providing synchronized video, audio, gaze, motion, and physiological signals. It consists of 180 hours of recordings from 60 subjects, with an average recording duration of 3 hours per subject. Leveraging EgoIntrospect, we formalize a suite of tasks centered on user internal states, including affective experience, interactive intent, and cognitive memory. We further process the annotations to construct benchmarks that evaluate the ability of modern multimodal large language models to reason about users' internal states from egocentric observations. Experiments on our benchmark suggest that existing multimodal large language models struggle to effectively leverage multimodal signals to infer users' subjective internal states. The dataset and annotations will be made publicly available to advance research in egocentric vision and wearable AI assistants. Project page: https://ego-introspect.github.io/

cs.CV↗
arXiv2026

CogniFold: Always-On Proactive Memory via Cognitive Folding

Existing agent memory remains predominantly reactive and retrieval-based, lacking the capacity to autonomously organize experience into persistent cognitive structure. Toward genuinely autonomous agents, we introduce CogniFold, a brain-inspired "always-on" agent memory designed for the next generation of proactive assistants. CogniFold continuously folds fragmented event streams into self-emerging cognitive structures, bootstrapping progressively higher-level cognition from incoming events and accumulated knowledge. We ground this by extending Complementary Learning Systems (CLS) theory from two layers (hippocampus, neocortex) to three, adding a prefrontal intent layer. Emulating the prefrontal cortex as the locus of intentional control and decision-making, CogniFold achieves this through graph-topology self-organization: cognitive structures proactively assemble under the stream, merge when semantically similar, decay when stale, relink through associative recall, and surface intents when concept-cluster density crosses a threshold. We evaluate structural formation using CogEval-Bench, demonstrating that CogniFold uniquely produces memory structures that match cognitive expectations and concept emergence. Furthermore, across eight downstream benchmarks -- two probing long-term conversational memory (LoCoMo, LongMemEval) and six spanning other cognitive domains -- we validate that CogniFold simultaneously performs robustly on conventional memory tasks. Our code is available at https://github.com/OpenNorve/CogniFold.

cs.AI↗
arXiv2026

LOFT: Low-Rank Orthogonal Fine-Tuning via Task-Aware Support Selection

Orthogonal parameter-efficient fine-tuning (PEFT) adapts pretrained weights through structure-preserving multiplicative transformations, but existing methods often conflate two distinct design choices: the subspace in which adaptation occurs and the transformation applied within that subspace. This paper introduces LOFT, a low-rank orthogonal fine-tuning framework that explicitly separates these two components. By viewing orthogonal adaptation as a multiplicative subspace rotation, LOFT provides a unified formulation that recovers representative orthogonal PEFT methods, including coordinate-, butterfly-, Householder-, and principal-subspace-based variants. More importantly, this perspective exposes support selection as a central design axis rather than a byproduct of a particular parameterization. We develop a first-order analysis showing that useful adaptation supports should be informed by the downstream training signal, motivating practical task-aware support selection strategies. Across language understanding, visual transfer, mathematical reasoning, and multilingual out-of-distribution adaptation, LOFT recovers principal-subspace orthogonal adaptation while gradient-informed supports improve the efficiency-performance trade-off under matched parameter, memory, and compute budgets. These results suggest that principled support selection is an important direction for improving orthogonal PEFT.

cs.LG↗
arXiv2026

Wiener Chaos Expansion based Neural Operator for Singular Stochastic Partial Differential Equations

In this paper, we explore how our recently developed Wiener Chaos Expansion (WCE)-based neural operator (NO) can be applied to singular stochastic partial differential equations, e.g., the dynamic $\boldsymbol{\Phi}^4_2$ model simulated in the recent works. Unlike the previous WCE-NO which solves SPDEs by simply inserting Wick-Hermite features into the backbone NO model, we leverage feature-wise linear modulation (FiLM) to appropriately capture the dependency between the solution of singular SPDE and its smooth remainder. The resulting WCE-FiLM-NO shows excellent performance on $\boldsymbol{\Phi}^4_2$, as measured by relative $L_2$ loss, out-of-distribution $L_2$ loss, and autocorrelation score; all without the help of renormalisation factor. In addition, we also show the potential of simulating $\boldsymbol{\Phi}^4_3$ data, which is more aligned with real scientific practice in statistical quantum field theory. To the best of our knowledge, this is among the first works to develop an efficient data-driven surrogate for the dynamical $\boldsymbol{\Phi}^4_3$ model.

cs.LG↗
arXiv2026

Expanding the Chaos: Neural Operator for Stochastic (Partial) Differential Equations

Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with deep learning models promises fast solvers and new perspectives on classical learning tasks. In this work, we build on Wiener-chaos expansions (WCE) to design neural operator (NO) architectures for SDEs and SPDEs: we project driving noise paths onto orthonormal Wick-Hermite features and use NOs to parameterize the resulting chaos coefficients, enabling reconstruction of full trajectories from noise in a single forward pass. We also make the underlying WCE structure explicit for multi-dimensional SDEs and semilinear SPDEs by showing the coupled deterministic ODE/PDE systems governing these coefficients. Empirically, we achieve competitive accuracy across several tasks, including standard SPDE benchmarks and SDE-based diffusion one-step image sampling, topological graph interpolation, financial extrapolation, parameter estimation, and manifold SDE flood forecasting. These results suggest WCE-based neural operators are a practical and scalable approach to learning SDE/SPDE solution operators across domains.

cs.LG↗
arXiv2025

ACT as Human: Multimodal Large Language Model Data Annotation with Critical Thinking

Supervised learning relies on high-quality labeled data, but obtaining such data through human annotation is both expensive and time-consuming. Recent work explores using large language models (LLMs) for annotation, but LLM-generated labels still fall short of human-level quality. To address this problem, we propose the Annotation with Critical Thinking (ACT) data pipeline, where LLMs serve not only as annotators but also as judges to critically identify potential errors. Human effort is then directed towards reviewing only the most "suspicious" cases, significantly improving the human annotation efficiency. Our major contributions are as follows: (1) ACT is applicable to a wide range of domains, including natural language processing (NLP), computer vision (CV), and multimodal understanding, by leveraging multimodal-LLMs (MLLMs). (2) Through empirical studies, we derive 7 insights on how to enhance annotation quality while efficiently reducing the human cost, and then translate these findings into user-friendly guidelines. (3) We theoretically analyze how to modify the loss function so that models trained on ACT data achieve similar performance to those trained on fully human-annotated data. Our experiments show that the performance gap can be reduced to less than 2% on most benchmark datasets while saving up to 90% of human costs.

cs.LG↗
arXiv2025

ATOM: A Pretrained Neural Operator for Multitask Molecular Dynamics

Molecular dynamics (MD) simulations underpin modern computational drug discovery, materials science, and biochemistry. Recent machine learning models provide high-fidelity MD predictions without the need to repeatedly solve quantum mechanical forces, enabling significant speedups over conventional pipelines. Yet many such methods typically enforce strict equivariance and rely on sequential rollouts, thus limiting their flexibility and simulation efficiency. They are also commonly single-task, trained on individual molecules and fixed timeframes, which restricts generalization to unseen compounds and extended timesteps. To address these issues, we propose Atomistic Transformer Operator for Molecules (ATOM), a pretrained transformer neural operator for multitask molecular dynamics. ATOM adopts a quasi-equivariant design that requires no explicit molecular graph and employs a temporal attention mechanism, allowing for the accurate parallel decoding of multiple future states. To support operator pretraining across chemicals and timescales, we curate TG80, a large, diverse, and numerically stable MD dataset with over 2.5 million femtoseconds of trajectories across 80 compounds. ATOM achieves state-of-the-art performance on established single-task benchmarks, such as MD17, RMD17 and MD22. After multitask pretraining on TG80, ATOM shows exceptional zero-shot generalization to unseen molecules across varying time horizons. We believe ATOM represents a significant step toward accurate, efficient, and transferable molecular dynamics models.

cs.LG↗
arXiv2025

Fact-Checking Comments Precede Community Notes to Misleading Posts on X

Community-based fact-checking systems, such as X's Community Notes program, offer a potentially scalable approach against online misinformation diffusion. However, their efficacy is substantially undermined by the delay of fact-check delivery. To address this challenge, we investigated the promise of organic user comments as rapid corrective signals by analyzing a large-scale dataset of over 2.2 million comments directed to 1,841 community fact-checked misleading posts. We developed a high-performance language model pipeline to identify ``fact-checking (FC) comments'', i.e., comments that correct source posts with reasoning or evidence (91% accuracy). Using this pipeline, we find that 99.4% of misleading posts receive their first FC comments before the official community note is created. Notably, the median time to the initial FC comment is only 0.1 hours, while the creation of community notes has a median latency of 9.7 hours since the publication of misleading posts. Additionally, compared to random posts, those misleading posts with displayed notes have significantly more FC comments. This suggests that FC comments are a unique pattern for misleading posts. We further identified characteristics of FC comments' intensity and speed: (i) FC comments' volume is significantly associated with content richness and misinformation type, favoring multimedia content and missing-context scenarios; (ii) the speed of FC comments remains robust across diverse topics and emotional intensities. These results suggest that platforms could use FC comments as early-warning signals, and potential resource for complementing community notes or automated synthesis.

cs.HC↗
arXiv2025

SPDEBench: An Extensive Benchmark for Learning Stochastic PDEs

Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence flows, superconductors, and quantum dynamics. Although machine learning (ML)-based surrogate models have shown promise for efficiently approximating such dynamics, progress remains limited by the lack of a unified benchmark with controlled data generation and comprehensive evaluation. This gap is particularly significant for singular SPDEs, for which benchmark datasets are largely unavailable and reliable simulation requires numerically delicate schemes based on renormalization. Moreover, subtle differences in data-generation procedures, such as noise approximation, basis choice, and the inclusion of renormalization, can significantly affect the resulting datasets and, consequently, model evaluation. We introduce SPDEBench, the first unified benchmark for ML-based SPDE learning. SPDEBench provides ready-to-use datasets for physically and mathematically significant SPDEs on 1-3D domains with periodic or Dirichlet boundary condition. Both regular and singular SPDEs are taken into consideration. SPDEBench also incorporates representative ML baselines in operator learning, together with 7 evaluation metrics, including Sobolev and distributional metrics beyond the standard $L^2$-error. Supported by SPDEBench, we conduct systematic evaluations of model accuracy, robustness, and out-of-distribution generalization under controlled data variations. Our numerical results show that SPDE-aware architectures generally achieve stronger performance than generic operator-learning baselines. These findings establish SPDEBench as a reproducible and extensible resource, paving pathway for principled benchmarking and architecture design for stochastic spatio-temporal dynamics.

cs.LG↗