Cihan Ruan

Zhendong Wang, Cihan Ruan, Jingchuan Xiao et al.

We investigate what structure emerges in 3D Gaussian Splatting (3DGS) solutions from standard multi-view optimization. We term these Rendering-Optimal References (RORs) and analyze their statistical properties, revealing stable patterns: mixture-structured scales and bimodal radiance across diverse scenes. To understand what determines these parameters, we apply learnability probes by training predictors to reconstruct RORs from point clouds without rendering supervision. Our analysis uncovers fundamental density-stratification. Dense regions exhibit geometry-correlated parameters amenable to render-free prediction, while sparse regions show systematic failure across architectures. We formalize this through variance decomposition, demonstrating that visibility heterogeneity creates covariance-dominated coupling between geometric and appearance parameters in sparse regions. This reveals the dual character of RORs: geometric primitives where point clouds suffice, and view synthesis primitives where multi-view constraints are essential. We provide density-aware strategies that improve training robustness and discuss architectural implications for systems that adaptively balance feed-forward prediction and rendering-based refinement.

Cihan Ruan, Lebin Zhou, Rongduo Han et al.

DNA storage has matured from concept to practical stage, yet its integration with neural compression pipelines remains inefficient. Early DNA encoders applied redundancy-heavy constraint layers atop raw binary data - workable but primitive. Recent neural codecs compress data into learned latent representations with rich statistical structure, yet still convert these latents to DNA via naive binary-to-quaternary transcoding, discarding the entropy model's optimization. This mismatch undermines compression efficiency and complicates the encoding stack. A plug-in module that collapses latent compression and DNA encoding into a single step. SCONE performs quaternary arithmetic coding directly on the latent space in DNA bases. Its Constraint-Aware Adaptive Coding module dynamically steers the entropy encoder's learned probability distribution to enforce biochemical constraints - Guanine-Cytosine (GC) balance and homopolymer suppression - deterministically during encoding, eliminating post-hoc correction. The design preserves full reversibility and exploits the hyperprior model's learned priors without modification. Experiments show SCONE achieves near-perfect constraint satisfaction with negligible computational overhead (<2% latency), establishing a latent-agnostic interface for end-to-end DNA-compatible learned codecs.

Cihan Ruan, Lebin Zhou, Bingqing Zhao et al.

DNA-based storage has emerged as a promising approach to the global data crisis, offering molecular-scale density and millennial-scale stability at low maintenance cost. Over the past decade, substantial progress has been made in storing text, images, and files in DNA -- yet video remains an open challenge. The difficulty is not merely technical: effective video DNA storage requires co-designing compression and molecular encoding from the ground up, a challenge that sits at the intersection of two fields that have largely evolved independently. In this work, we present HELIX, the first end-to-end neural network jointly optimizing video compression and DNA encoding -- prior approaches treat the two stages independently, leaving biochemical constraints and compression objectives fundamentally misaligned. Our key insight: token-based representations naturally align with DNA's quaternary alphabet -- discrete semantic units map directly to ATCG bases. We introduce TK-SCONE (Token-Kronecker Structured Constraint-Optimized Neural Encoding), which achieves 1.91 bits per nucleotide through Kronecker-structured mixing that breaks spatial correlations and FSM-based mapping that guarantees biochemical constraints. Unlike two-stage approaches, HELIX learns token distributions simultaneously optimized for visual quality, prediction under masking, and DNA synthesis efficiency. This work demonstrates for the first time that learned compression and molecular storage converge naturally at token representations -- suggesting a new paradigm where neural video codecs are designed for biological substrates from the ground up.

Jingchuan Xiao, Xinyi Sui, Cihan Ruan

Alignment, the tendency of adjacent weight matrices in deep networks to develop compatible subspace orientations, underlies gradient flow, Neural Collapse, and representation similarity across architectures. Despite extensive empirical documentation, these phenomena have resisted unified theoretical treatment: existing explanations are post-hoc, each fitted to a specific observation with whatever mathematics is at hand. We reverse this direction by deriving the mathematical structure that layerwise alignment inherently demands. Using geometric invariant theory, we prove that alignment geometry has a canonical closed, polystable stratum given by a flag variety, and that subspace intersection dimension is its unique reparameterization-invariant observable, establishing that subspace metrics are not empirical conventions but mathematical necessities. This unified framework yields two dynamical consequences: ridge regularization drives subspace alignment at an exponential rate set by weight decay, whereas nonlinear activations induce a commutator obstruction to exact basis alignment, generically present in nonlinear networks and absent in linear ones. Together these give a geometric explanation of the Level-2/3 hierarchy in Neural Collapse from first principles rather than post-hoc analysis. The commutator magnitude and head subspace overlap further serve as weight-space windows into internal alignment structure, requiring no forward passes. Experiments on multilayer perceptrons, residual networks, and pretrained language models support the proposed diagnostics and delineate their scope.

Zhendong Wang, Lebin Zhou, Jingchuan Xiao et al.

In 1888, Vincent van Gogh wrote, "I am seeking exaggeration in the essential." This principle, amplifying structural form while suppressing photographic detail, lies at the core of Post-Impressionist art. However, most existing 3D style transfer methods invert this philosophy, treating geometry as a rigid substrate for surface-level texture projection. To authentically reproduce Post-Impressionist stylization, geometric abstraction must be embraced as the primary vehicle of expression. We propose a flow-guided geometric advection framework for 3D Gaussian Splatting (3DGS) that operationalizes this principle in a mesh-free setting. Our method extracts directional flow fields from 2D paintings and back-propagates them into 3D space, rectifying Gaussian primitives to form flow-aligned brushstrokes that conform to scene topology without relying on explicit mesh priors. This enables expressive structural deformation driven directly by painterly motion rather than photometric constraints. Our contributions are threefold: (1) a projection-based, mesh-free flow guidance mechanism that transfers 2D artistic motion into 3D Gaussian geometry; (2) a luminance-structure decoupling strategy that isolates geometric deformation from color optimization, mitigating artifacts during aggressive structural abstraction; and (3) a VLM-as-a-Judge evaluation framework that assesses artistic authenticity through aesthetic judgment instead of conventional pixel-level metrics, explicitly addressing the subjective nature of artistic stylization.

Ziran Liu, Wei Wang, Jinhao Wang et al.

This paper develops the angular and static-channel component of Geometric and Spectral Alignment for residual Jacobian chains. Starting from Cartan-coordinate rigidity and fitted effective-rank windows, we study how dominant singular subspaces are transported across adjacent layers and how the resulting finite matrices can be displayed in physical channel coordinates. The main results are deterministic, margin-verified results. We bound the error between full interface transport and its dominant-window truncation, add fitted-tail errors so that empirical spectra can be certified against the Gibbs--Cartan tail model, and distinguish source-mode incidence from fully physical input-output channel incidence. Given row groups and active supports, the Physical Alignment Matrix decomposes orthogonally as core plus overlap plus noise. Active-column gaps, pairwise overlap margins, and noise bounds combine into a static certificate radius under which the full transport and the truncated transport induce the same active supports, pairwise incidence graph, SRS sets, hub columns, and core/overlap/noise masks. The finer SC/SA/ST labels of the Invariant Channel Mapping require additional row-energy and profile-correlation margins, stated as explicit perturbation tests. The empirical section reports the matrices and block-energy heatmaps that measure these certificate quantities across CNNs, language models, and vision/diffusion backbones. The figures are interpreted as finite-dimensional measurements; complete membership in the Physical GSA certificate domain requires checking the numerical margin protocol stated in Section 10.

Ziran Liu, Wei Wang, Jinhao Wang et al.

Deep residual architectures are modeled as products of near-identity Jacobians. This paper proves deterministic quotient-geometric estimates for singular spectra of Frobenius-normalized layer factors, emphasizing a normalized top-radial Cartan coordinate and fitted power-law chart. Full-rank factors are mapped from $\mathrm{GL}(d)$ to the positive cone by $A\mapsto A^\top A$, then to ordered eigenvalue data. Under Frobenius normalization, exact power-law spectra form a trace-normalized Cartan orbit. This orbit is a Gibbs family on ranks, a Fisher information line, and a Bures--Wasserstein curve with line element $d/4$ times Fisher information. The main rigidity theorem is a slack-aware margin inequality: interface radial amplitude, non-backtracking slack, and signed residual variation control displacement of the fitted Cartan coordinate. In the exact-chart zero-slack case, a depth-$L$ budget gives exponent drift of order $(\log M)/L$; generally, slack and residual increments augment the bound. We separate scalar top-radial from full-Cartan spectral control, which also needs Bures/Hellinger residual variation. We prove approximate-power-law and metric-chart versions, converse lower bounds, Fisher--KL/Bures action estimates, and near-identity expansions for normalized residual chains. Near-identity results verify transport budgets; chart quality remains measurable. Effective rank is a spectral-energy quantile, giving finite-width power-law tail bounds and robust rank-window transition estimates. Empirical static-weight exponent profiles serve as diagnostics; full verification also requires interface budgets, slacks, and residuals for the same operator chain.

Qiming Yuan, Linyi Han, Nam Ling et al.

People increasingly turn to large language models (LLMs) to interpret ambiguous social situations: a delayed text reply, an unusually cold supervisor, a teacher's mixed signals, or a boundary-crossing friend. Yet in many such cases, no stable interpretation can be verified from the available evidence alone. We study how LLMs respond to these situations across four domains: early-stage romantic relationships, teacher--student dynamics, workplace hierarchies, and ambiguous friendships. Across 72 responses from GPT, Claude, and Gemini, only 9 (12.5\%) genuinely preserved uncertainty. The remaining 87.5% produced interpretive closure through recurring pathways including narrative alignment, narrative reversal, normative advice under uncertainty, and hedged language that still supported a single conclusion. We further find that narrator perspective shapes the path to closure: first-person accounts more often elicited alignment, while third-person accounts invited more detached interpretation, even when the underlying situation remained comparable. Together, these findings show that LLMs do not simply assist interpersonal sensemaking; they tend to resolve ambiguity into coherent and actionable narratives. These results suggest that the central risk is not only that LLMs may misinterpret social situations, but that they may make unresolved situations feel prematurely settled. We frame this tendency as a design challenge for uncertainty-preserving social AI.

Jinhao Wang, Cihan Ruan, Nam Ling et al.

Prior studies in learned image compression (LIC) consistently show that only a small subset of latent channels is critical for reconstruction, while many others carry limited information. Exploiting this imbalance could improve both coding and computational efficiency, yet existing approaches often rely on costly, dataset-specific ablation tests and typically analyze channels in isolation, ignoring their interdependencies. We propose a generalizable, dataset-agnostic method to identify and organize important channels in pretrained VAE-based LIC models. Instead of brute-force empirical evaluations, our approach leverages intrinsic parameter statistics-weight variances, bias magnitudes, and pairwise correlations-to estimate channel importance. This analysis reveals a consistent organizational structure, termed the Invariant Salient Channel Space (ISCS), where Salient-Core channels capture dominant structures and Salient-Auxiliary channels provide complementary details. Building on ISCS, we introduce a deterministic channel ordering and grouping strategy that enables slice-parallel decoding, reduces redundancy, and improves bitrate efficiency. Experiments across multiple LIC architectures demonstrate that our method effectively reduces bitrate and computation while maintaining reconstruction quality, providing a practical and modular enhancement to existing learned compression frameworks.