arXiv subjects

Sida Li

Publications and source records attributed to Sida Li.

At least 19 recordsLinked to original sources

arXiv2026

Bayesian Symbolic Regression with Entropic Reinforcement Learning

Symbolic regression is the problem of finding an algebraic expression describing a stochastic dependence of a target variable on a set of inputs. Unlike forms of regression that fit parameters assuming a fixed model structure, symbolic regression is a search problem over the space of expressions, represented, for example, as abstract syntax trees using a library of operators. Symbolic regression is typically used in settings with limited, noisy data in the natural sciences. However, searching for a single best-fitting expression fails to capture the epistemic uncertainty about the expression, which motivates a Bayesian perspective that enables uncertainty quantification and specification of natural priors to constrain the search space. In this work, we propose ERRLESS (Entropy-Regularized Reinforcement Learning for Expression Structure Sampling), a scalable approach for sampling from the posterior distribution over expressions given data using maximum-entropy reinforcement learning. ERRLESS learns a neural policy that constructs expressions sequentially by building up their abstract syntax trees. At convergence, the policy samples expressions from the posterior. At test time, expressions can be sampled by rollouts of this policy. We demonstrate that ERRLESS achieves competitive results on the Feynman benchmark while producing short and interpretable expressions. Additionally, we demonstrate that the mean of the posterior predictive approximated by ERRLESS achieves a high coefficient of determination ($R^2$) compared to an SMC baseline, highlighting the benefits of the Bayesian perspective in symbolic regression.

cs.LG↗

arXiv2026

A note on matchings and co-matchings in bipartite graphs

A class of bipartite graphs is said to have the strong Erd\H{o}s-Hajnal property if there exists $\varepsilon > 0$ such that every graph $((A, B), E)$ in the class contains a complete or empty induced subgraph with parts $X \subseteq A$, $Y \subseteq B$ where $|X| \ge \varepsilon|A|$ and $|Y| \ge \varepsilon|B|$. Scott, Seymour and Spirkl proved that it is enough to forbid a forest and the bipartite complement of a forest. In this paper, we provide quantitative bounds on $\varepsilon$ when we restrict to matchings.

math.CO↗

arXiv2026

Contemporary AI lacks the imagination to diverge or negate in science

Bold claims that AI will accelerate scientific discovery have raced ahead of evidence from working scientists, yet large-scale, scientist-in-the-loop evidence is scarce. Here we mount the largest evaluation to date, inviting authors of 121,640 recent preprints in biology, medicine, chemistry, and social science to judge large language model (LLM)-generated ideas derived from their own papers. 6,749 representative scientists returned 25,139 rating sets on novelty, feasibility, probability of being true, and favorability of adoption. Three patterns emerge. First, non-reasoning LLMs collapse into a narrow "hivemind" of similar ideas while reasoning models explore a wider hypothesis space, but no model spontaneously proposes null hypotheses, a move humans make more freely. Second, scientists reward ideas resembling their own and prize probability over novelty, though social scientists tolerate risk more than life scientists; senior social scientists are the harshest critics, and their skepticism is earned, as LLMs falter most in pluralistic fields demanding context-aware interpretation and evolving theories. Third, automated evaluators, including LLM-as-a-judge and state-of-the-art (SOTA) models, agree weakly with expert judgment. Retrieval augmentation and scientist persona prompting yield marginal gains. A Qwen3-14B reward model we post-trained on human ratings captures nuances of taste, beats SOTA models by up to 27%, and closes the gap to the consistency of human peer reviewers. An analysis of 39 million papers from 2010 to 2025 links survey findings to macro-level patterns: following ChatGPT's release, null claims are sharply suppressed and ideas contract. Agent-based simulations further suggest that saturated fields should especially prize human uniqueness. For all the hype, today's AI for science remains a collaborator whose imagination and judgment benefit from human grounding.

cs.CY↗

arXiv2026

Empirical Bayes Rebiasing

We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard debiasing approach, which subtracts the bias estimate from each biased estimate, inflates variance and yields long intervals. In this paper, we propose an empirical Bayes rebiasing strategy that starts from the fully debiased estimates and learns from data how much bias to reintroduce by estimating the unknown bias distribution. We provide convergence rates for the coverage of our intervals when the bias distribution is estimated using nonparametric maximum likelihood. Furthermore, we demonstrate substantial precision gains in prediction-powered inference, including pairwise LLM win-rate evaluations, as well as for inference of direct genetic effects in family-based GWAS.

stat.ME↗

arXiv2025

LLM-as-a-Prophet: Understanding Predictive Intelligence with Prophet Arena

Forecasting is not only a fundamental intellectual pursuit but also is of significant importance to societal systems such as finance and economics. With the rapid advances of large language models (LLMs) trained on Internet-scale data, it raises the promise of employing LLMs to forecast real-world future events, an emerging paradigm we call "LLM-as-a-Prophet". This paper systematically investigates such predictive intelligence of LLMs. To this end, we build Prophet Arena, a general evaluation benchmark that continuously collects live forecasting tasks and decomposes each task into distinct pipeline stages, in order to support our controlled and large-scale experimentation. Our comprehensive evaluation reveals that many LLMs already exhibit impressive forecasting capabilities, reflected in, e.g., their small calibration errors, consistent prediction confidence and promising market returns. However, we also uncover key bottlenecks towards achieving superior predictive intelligence via LLM-as-a-Prophet, such as LLMs' inaccurate event recalls, misunderstanding of data sources and slower information aggregation compared to markets when resolution nears.

cs.AI↗

arXiv2025

Mapping Overlaps in Benchmarks through Perplexity in the Wild

We introduce benchmark signatures to characterize the capacity demands of LLM benchmarks and their overlaps. Signatures are sets of salient tokens from in-the-wild corpora whose model token perplexity, reflecting training exposure, predicts benchmark performance. We extract them via stepwise forward selection with linear regression in a meta-evaluation spanning 32 LLMs and 89 benchmarks across diverse domains. We then analyze how these signatures relate to both the semantic similarity of benchmark questions and the correlation structure of model performance. While performance correlations are uniformly high and semantic overlaps stay in a narrow mid-range, benchmark signatures reveal more nuanced structure. For instance, they uncover substantial overlap between benchmarks in knowledge and reasoning tasks, whereas benchmarks in culture- and humanity-oriented domains show low similarity with each other. Unlike raw performance correlations, which are influenced by benchmark-orthogonal factors such as question formats, signatures are robust to such confounds. We further identify cross-functional overlaps between logic, math, language, instruction following, and cultural/world modeling, with coding emerging as the most isolated function, interacting only moderately with the ability of detecting missing information. Qualitative analysis shows that only the knowledge signature aligns with actual knowledge, suggesting that LLM semantic organization may differ from human conceptual structure. Together, these findings offer insights into benchmark validity, LLM sensitivities, and the landscape of interconnected LLM capacities. We have open-sourced the code and data in this https://github.com/siyangwu1/Benchmark-Signature-Repository.

cs.AI↗

arXiv2025

LLM Probability Concentration: How Alignment Shrinks the Generative Horizon

Despite their impressive capabilities, aligned large language models (LLMs) often generate outputs that lack diversity. What drives this consistency in the generation? We investigate this phenomenon through the lens of probability concentration in the model's output distribution. To quantify this concentration, we introduce the *Branching Factor* (BF) -- a token-invariant measure of the effective number of plausible next steps during generation. Our empirical analysis reveals two key findings: (1) BF often decreases as generation progresses, suggesting that LLMs become more predictable as they generate. (2) alignment tuning substantially sharpens the model's output distribution from the outset, reducing BF by a factor of 2-5 overall, and up to an order of magnitude (e.g., from 12 to 1.2) at the beginning positions. This stark reduction helps explain why aligned models often appear less sensitive to decoding strategies. Building on this insight, we find this consistency has surprising implications for complex reasoning. Aligned Chain-of-Thought (CoT) models (e.g., DeepSeek-distilled models), for instance, leverage this effect; by generating longer reasoning chains, they push generation into later, more deterministic (lower BF) stages, resulting in more stable outputs. We hypothesize that alignment tuning does not fundamentally change a model's behavior, but instead steers it toward stylistic tokens (e.g., "Sure") that unlock low-entropy trajectories already present in the base model. This view is supported by nudging experiments, which show prompting base models with such tokens can similarly reduce BF. Together, our findings establish BF as a powerful diagnostic for understanding and controlling LLM outputs - clarifying how alignment reduces variability, how CoT promotes stable generations, and how base models can be steered away from diversity.

cs.CL↗

arXiv2025

ShorterBetter: Guiding Reasoning Models to Find Optimal Inference Length for Efficient Reasoning

Recent models such as OpenAI o1 and DeepSeek-R1 have demonstrated strong performance on reasoning-intensive tasks by generating extended Chain-of-Thought (CoT) traces. While longer reasoning helps with thorough exploration of solution paths for complex problems, it also often leads to inefficient and redundant outputs--a phenomenon commonly described as overthinking. In this paper, we propose ShorterBetter, a simple yet effective reinforcement learning method that enables reasoning models to learn their own optimal CoT lengths without manual supervision. We define the Sample Optimal Length (SOL) as the length of the shortest correct response among multiple generations, which serves as a dynamic reward signal to guide the model toward efficient reasoning. Applied to DeepSeek-Distill-Qwen-1.5B/7B as base models, ShorterBetter achieves 50%-80% reduction in output lengths in both in-domain and out-of-domain reasoning tasks while maintaining accuracy. Our reasoning trace analysis shows that ShorterBetter refines the structure of the reasoning traces by reducing unnecessary repetition, excessive self-verification, and over-exploration of alternatives.

cs.AI↗

arXiv2025

Optimizing Multi-Round Enhanced Training in Diffusion Models for Improved Preference Understanding

Generative AI has significantly changed industries by enabling text-driven image generation, yet challenges remain in achieving high-resolution outputs that align with fine-grained user preferences. Consequently, multi-round interactions are necessary to ensure the generated images meet expectations. Previous methods enhanced prompts via reward feedback but did not optimize over a multi-round dialogue dataset. In this work, we present a Visual Co-Adaptation (VCA) framework incorporating human-in-the-loop feedback, leveraging a well-trained reward model aligned with human preferences. Using a diverse multi-turn dialogue dataset, our framework applies multiple reward functions, such as diversity, consistency, and preference feedback, while fine-tuning the diffusion model through LoRA, thus optimizing image generation based on user input. We also construct multi-round dialogue datasets of prompts and image pairs aligned with user intent. Experiments demonstrate that our method outperforms state-of-the-art baselines, significantly improving image consistency and alignment with user intent. Our approach consistently surpasses competing models in user satisfaction, especially in multi-turn dialogue scenarios.

cs.CV↗

arXiv2025

TimeChat-Online: 80% Visual Tokens are Naturally Redundant in Streaming Videos

The rapid growth of online video platforms, particularly live streaming services, has created an urgent need for real-time video understanding systems. These systems must process continuous video streams and respond to user queries instantaneously, presenting unique challenges for current Video Large Language Models (VideoLLMs). While existing VideoLLMs excel at processing complete videos, they face significant limitations in streaming scenarios due to their inability to handle dense, redundant frames efficiently. We introduce TimeChat-Online, a novel online VideoLLM that revolutionizes real-time video interaction. At its core lies our innovative Differential Token Drop (DTD) module, which addresses the fundamental challenge of visual redundancy in streaming videos. Drawing inspiration from human visual perception's Change Blindness phenomenon, DTD preserves meaningful temporal changes while filtering out static, redundant content between frames. Remarkably, our experiments demonstrate that DTD achieves an 82.8% reduction in video tokens while maintaining 98% performance on StreamingBench, revealing that over 80% of visual content in streaming videos is naturally redundant without requiring language guidance. To enable seamless real-time interaction, we present TimeChat-Online-139K, a comprehensive streaming video dataset featuring diverse interaction patterns including backward-tracing, current-perception, and future-responding scenarios. TimeChat-Online's unique Proactive Response capability, naturally achieved through continuous monitoring of video scene transitions via DTD, sets it apart from conventional approaches. Our extensive evaluation demonstrates TimeChat-Online's superior performance on streaming benchmarks (StreamingBench and OvOBench) and maintaining competitive results on long-form video tasks such as Video-MME and MLVU.

cs.CV↗

arXiv2025

Efficient Temporal Consistency in Diffusion-Based Video Editing with Adaptor Modules: A Theoretical Framework

Adapter-based methods are commonly used to enhance model performance with minimal additional complexity, especially in video editing tasks that require frame-to-frame consistency. By inserting small, learnable modules into pretrained diffusion models, these adapters can maintain temporal coherence without extensive retraining. Approaches that incorporate prompt learning with both shared and frame-specific tokens are particularly effective in preserving continuity across frames at low training cost. In this work, we want to provide a general theoretical framework for adapters that maintain frame consistency in DDIM-based models under a temporal consistency loss. First, we prove that the temporal consistency objective is differentiable under bounded feature norms, and we establish a Lipschitz bound on its gradient. Second, we show that gradient descent on this objective decreases the loss monotonically and converges to a local minimum if the learning rate is within an appropriate range. Finally, we analyze the stability of modules in the DDIM inversion procedure, showing that the associated error remains controlled. These theoretical findings will reinforce the reliability of diffusion-based video editing methods that rely on adapter strategies and provide theoretical insights in video generation tasks.

cs.CV↗

arXiv2025

TDRI: Two-Phase Dialogue Refinement and Co-Adaptation for Interactive Image Generation

Although text-to-image generation technologies have made significant advancements, they still face challenges when dealing with ambiguous prompts and aligning outputs with user intent.Our proposed framework, TDRI (Two-Phase Dialogue Refinement and Co-Adaptation), addresses these issues by enhancing image generation through iterative user interaction. It consists of two phases: the Initial Generation Phase, which creates base images based on user prompts, and the Interactive Refinement Phase, which integrates user feedback through three key modules. The Dialogue-to-Prompt (D2P) module ensures that user feedback is effectively transformed into actionable prompts, which improves the alignment between user intent and model input. By evaluating generated outputs against user expectations, the Feedback-Reflection (FR) module identifies discrepancies and facilitates improvements. In an effort to ensure consistently high-quality results, the Adaptive Optimization (AO) module fine-tunes the generation process by balancing user preferences and maintaining prompt fidelity. Experimental results show that TDRI outperforms existing methods by achieving 33.6% human preference, compared to 6.2% for GPT-4 augmentation, and the highest CLIP and BLIP alignment scores (0.338 and 0.336, respectively). In iterative feedback tasks, user satisfaction increased to 88% after 8 rounds, with diminishing returns beyond 6 rounds. Furthermore, TDRI has been found to reduce the number of iterations and improve personalization in the creation of fashion products. TDRI exhibits a strong potential for a wide range of applications in the creative and industrial domains, as it streamlines the creative process and improves alignment with user preferences

cs.CV↗

arXiv2025

Prediction-Powered Adaptive Shrinkage Estimation

Prediction-Powered Inference (PPI) is a powerful framework for enhancing statistical estimates by combining limited gold-standard data with machine learning (ML) predictions. While prior work has demonstrated PPI's benefits for individual statistical problems, modern applications require answering numerous parallel statistical questions. We introduce Prediction-Powered Adaptive Shrinkage (PAS), a method that bridges PPI with empirical Bayes shrinkage to improve the estimation of multiple means. PAS debiases noisy ML predictions within each task and then borrows strength across tasks by using those same predictions as a reference point for shrinkage. The amount of shrinkage is determined by minimizing an unbiased estimate of risk, and we prove that this tuning strategy is asymptotically optimal. Experiments on both synthetic and real-world datasets show that PAS adapts to the reliability of the ML predictions and outperforms traditional and modern baselines in large-scale applications.

stat.ML↗

arXiv2025

Strengthened upper bound on the third eigenvalue of graphs

Let $G$ be a graph on $n \ge 3$ vertices, whose adjacency matrix has eigenvalues $\lambda_1 \ge \lambda_2 \ge \dots \ge \lambda_n$. The problem of bounding $\lambda_k$ in terms of $n$ was first proposed by Hong and was studied by Nikiforov, who demonstrated strong upper and lower bounds for arbitrary $k$. Nikiforov also claimed a strengthened upper bound for $k \ge 3$, namely that $\frac{\lambda_k}{n} < \frac{1}{2\sqrt{k-1}} - \varepsilon_k$ for some positive $\varepsilon_k$, but omitted the proof due to its length. In this paper, we give a proof of this bound for $k = 3$. We achieve this by instead looking at $\lambda_{n-1} + \lambda_n$ and introducing a new graph operation which provides structure to minimising graphs, including $\omega \le 3$ and $\chi \le 4$. Then we reduce the hypothetical worst case to a graph that is $n/2$-regular and invariant under said operation. By considering a series of inequalities on the restricted eigenvector components, we prove that a sequence of graphs with $\frac{\lambda_{n-1} + \lambda_n}{n}$ converging to $-\frac{\sqrt{2}}{2}$ cannot exist.

math.CO↗

arXiv2025

Enhancing Low-Cost Video Editing with Lightweight Adaptors and Temporal-Aware Inversion

Recent advancements in text-to-image (T2I) generation using diffusion models have enabled cost-effective video-editing applications by leveraging pre-trained models, eliminating the need for resource-intensive training. However, the frame-independence of T2I generation often results in poor temporal consistency. Existing methods address this issue through temporal layer fine-tuning or inference-based temporal propagation, but these approaches suffer from high training costs or limited temporal coherence. To address these challenges, we propose a General and Efficient Adapter (GE-Adapter) that integrates temporal-spatial and semantic consistency with Baliteral DDIM inversion. This framework introduces three key components: (1) Frame-based Temporal Consistency Blocks (FTC Blocks) to capture frame-specific features and enforce smooth inter-frame transitions via temporally-aware loss functions; (2) Channel-dependent Spatial Consistency Blocks (SCD Blocks) employing bilateral filters to enhance spatial coherence by reducing noise and artifacts; and (3) Token-based Semantic Consistency Module (TSC Module) to maintain semantic alignment using shared prompt tokens and frame-specific tokens. Our method significantly improves perceptual quality, text-image alignment, and temporal coherence, as demonstrated on the MSR-VTT dataset. Additionally, it achieves enhanced fidelity and frame-to-frame coherence, offering a practical solution for T2V editing.

cs.CV↗

arXiv2025

On graphs with large third eigenvalue

Given a graph $G$, let $\lambda_3$ denote the third largest eigenvalue of its adjacency matrix. In this paper, we prove various results towards the conjecture that $\lambda_3(G) \le \frac{|V(G)|}{3}$, motivated by a question of Nikiforov. We generalise the known constructions that yield $\lambda_3(G) = \frac{|V(G)|}{3} - 1$ and prove the inequality holds for $G$ strongly regular, a regular line graph or a Cayley graph on an abelian group. We also consider the extended problem of minimising $\lambda_{n-1}$ on weighted graphs and reduce the existence of a minimiser with simple final eigenvalue to a vertex multiplication of a graph on 11 vertices. We prove that the minimal $\lambda_{n-1}$ over weighted graphs is at most $O(\sqrt{n})$ from the minimal $\lambda_{n-1}$ over unweighted graphs.

math.CO↗

arXiv2024

Testing the TDE Outflow Model for the Bipolar Sgr A Lobes at the Galactic Center

Sgr A lobes are a pair of 15-pc-sized bipolar bubbles with co-aligned major axes perpendicular to the Galactic plane found in X-ray and radio observations of the Galactic center (GC). Their elusive origin is a vital ingredient in understanding the ongoing high energy processes at the GC. Here we perform a suite of hydrodynamic simulations to explore the tidal disruption event (TDE) outflow model for the origin of the Sgr A lobes. By following the outflow evolution in the circumnuclear medium, we find that TDE outflows naturally produce bipolar lobes delimited by forward shocks, and the dense postshock shell contributes significantly to the lobe's X-ray emission. Our fiducial run reproduces the morphology, density, temperature, and X-ray surface brightness distribution of the observed Sgr A lobes reasonably well. The current lobe age is ~3300 yr. Our model further predicts that the uplifted wake flow breaks through the ejecta-induced shock front, producing a shock-enclosed head region which is relatively dim in X-rays compared to other lobe regions. Both the dim head region and the predicted limb-brightening feature of the lobes are slightly inconsistent with current X-ray observations, and may be used to further test our model with more sensitive future X-ray observations. While light narrow jets and massive wide winds from TDE events usually do not reproduce the observed oval-shaped morphology of the lobes, the TDE outflow in our fiducial run is massive and yet narrow. Whether it is a jet or wind remains uncertain and future simulations covering both the outflow acceleration region and its pc-scale evolution would be very helpful in determining whether the Sgr A lobes indeed originate from a pair of TDE jets or winds.

astro-ph.HE↗

arXiv2023

GFN-SR: Symbolic Regression with Generative Flow Networks

Symbolic regression (SR) is an area of interpretable machine learning that aims to identify mathematical expressions, often composed of simple functions, that best fit in a given set of covariates $X$ and response $y$. In recent years, deep symbolic regression (DSR) has emerged as a popular method in the field by leveraging deep reinforcement learning to solve the complicated combinatorial search problem. In this work, we propose an alternative framework (GFN-SR) to approach SR with deep learning. We model the construction of an expression tree as traversing through a directed acyclic graph (DAG) so that GFlowNet can learn a stochastic policy to generate such trees sequentially. Enhanced with an adaptive reward baseline, our method is capable of generating a diverse set of best-fitting expressions. Notably, we observe that GFN-SR outperforms other SR algorithms in noisy data regimes, owing to its ability to learn a distribution of rewards over a space of candidate solutions.

cs.LG↗