arXiv subjects

Sam Zhang

Publications and source records attributed to Sam Zhang.

6 recordsLinked to original sources

arXiv2026

Graphs with connectivity $3/4 - \varepsilon$ are globally synchronizing

We study synchronization in the Kuramoto model on finite graphs. We prove that there is an absolute constant $\eta>0$ such that every finite simple graph $G$ on $n$ vertices with minimum degree at least $(3/4-\eta)n$ has no local minima of the Kuramoto energy other than the fully synchronized states. This strictly improves the previous $3/4$ upper bound and refutes a conjecture of Bandeira, Kireeva, Maillard, and R\"odder.

math.CO↗

arXiv2026

3D Primitives are a Spatial Language for VLMs

Vision-language models (VLMs) exhibit a striking paradox: they can generate executable code that reconstructs a 3D scene from geometric primitives with correct object counts, classes, and approximate positions, yet the same models fail at simpler spatial questions on the same image. We show that 3D geometric primitives (cubes, spheres, cylinders, expressed in executable code) serve as a powerful intermediate representation for spatial understanding, and exploit this through three contributions. First, we introduce \textbf{\textsc{SpatialBabel}}, a benchmark evaluating fourteen VLMs on primitive-based 3D scene reconstruction across six \emph{scene-code languages} (programming languages and declarative formats for 3D primitive scenes), revealing that a single model's object-detection F1 can vary by up to $5.7\times$ across languages. Second, we propose \textbf{Code-CoT} (Code Chain-of-Thought), a training-free inference strategy that routes spatial reasoning through primitive-based code generation. Code-CoT lifts the SpatialBabel-QA-Score by up to $+6.4$\% on primitive scenes and real-photo CV-Bench-3D accuracy by $+5.0$\% for VLMs with strong coding capabilities. Third, we propose \textbf{S$^{3}$-FT} (Self-Supervised Spatial Fine-Tuning), which self-supervisedly distills primitive spatial knowledge into general visual reasoning by parsing the model's own Three.js primitive-reconstructions into structured annotations and fine-tuning on the result, with \emph{no human labels and no teacher model}. Training on primitive images alone, S$^3$-FT improves Qwen3-VL-8B by $+4.6$ to $+8.6$\% on SpatialBabel-Primitive-QA, $+9.7$\% on CV-Bench-2D, and $+17$\% on HallusionBench; the recipe transfers across model families. These results establish geometric primitives in code as both a diagnostic and a transferable spatial vocabulary for VLMs. We will release all artifacts upon publication.

cs.CV↗

arXiv2025

Modeling Social Systems: Transparency, Reproducibility, and Responsibility

Mathematical models of complex social systems can enrich social scientific theory, inform interventions, and shape policy. From voting behavior to economic inequality and urban development, such models influence decisions that affect millions of lives. Thus, it is especially important to formulate and present them with transparency, reproducibility, and humility. Modeling in social domains, however, is often uniquely challenging. Unlike in physics or engineering, researchers often lack controlled experiments or abundant, clean data. Observational data is sparse, noisy, partial, and missing in systematic ways. In such an environment, how can we build models that can inform science and decision-making in transparent and responsible ways?

math.HO↗

arXiv2023

Scientific productivity as a random walk

The expectation that scientific productivity follows regular patterns over a career underpins many scholarly evaluations. However, recent studies of individual productivity patterns reveal a puzzle: the average number of papers published per year robustly follows the ``canonical trajectory'' of a rapid rise followed by a gradual decline, yet only about 20\% of individual productivity trajectories follow this pattern. We resolve this puzzle by modeling scientific productivity as a random walk, showing that the canonical pattern can be explained as a decrease in the variance in changes to productivity in the early-to-mid career. By empirically characterizing the variable structure of 2,085 productivity trajectories of computer science faculty at 205 PhD-granting institutions, spanning 29,119 publications over 1980--2016, we (i) discover remarkably simple patterns in both early-career and year-to-year changes to productivity, and (ii) show that a random walk model of productivity both reproduces the canonical trajectory in the average productivity and captures much of the diversity of individual-level trajectories, including the lognormal distribution of cumulative productivity observed by William Shockley in 1957. We confirm that these results generalize across fields by fitting our model to a separate panel of 22,952 faculty across 12 fields from 2011 to 2023. These results highlight the importance of variance in shaping individual scientific productivity, opening up new avenues for characterizing how systemic incentives and opportunities can be directed for aggregate effect.

stat.AP↗

arXiv2022

Labor advantages drive the greater productivity of faculty at elite universities

Faculty at prestigious institutions dominate scientific discourse, with the small proportion of researchers at elite universities producing a disproportionate share of all research publications. Environmental prestige is known to drive such epistemic disparity, but the mechanisms by which it causes increased faculty productivity remain unknown. Here we combine employment, publication, and federal survey data for 78,802 tenure-track faculty at 262 PhD-granting institutions in the American university system between 2008--2017 to show through multiple lines of evidence that the greater availability of funded graduate and postdoctoral labor at more prestigious institutions drives the environmental effect of prestige on productivity. In particular, we show that greater environmental prestige leads to larger faculty-led research groups, which drive higher faculty productivity, primarily in disciplines with research group collaboration norms. In contrast, we show that productivity does not increase substantially with prestige for either faculty papers published without group members, nor group members themselves. The disproportionate scientific productivity of elite researchers is thus largely explained by their substantial labor advantage, indicating a more limited role for prestige itself in predicting scientific contributions.

cs.DL↗

arXiv2022

Subfield prestige and gender inequality in computing

Women and people of color remain dramatically underrepresented among computing faculty, and improvements in demographic diversity are slow and uneven. Effective diversification strategies depend on quantifying the correlates, causes, and trends of diversity in the field. But field-level demographic changes are driven by subfield hiring dynamics because faculty searches are typically at the subfield level. Here, we quantify and forecast variations in the demographic composition of the subfields of computing using a comprehensive database of training and employment records for 6882 tenure-track faculty from 269 PhD-granting computing departments in the United States, linked with 327,969 publications. We find that subfield prestige correlates with gender inequality, such that faculty working in computing subfields with more women tend to hold positions at less prestigious institutions. In contrast, we find no significant evidence of racial or socioeconomic differences by subfield. Tracking representation over time, we find steady progress toward gender equality in all subfields, but more prestigious subfields tend to be roughly 25 years behind the less prestigious subfields in gender representation. These results illustrate how the choice of subfield in a faculty search can shape a department's gender diversity.

cs.CY↗