Geometric and Spectral Alignment for Deep Neural Network II

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.

What Did They Mean? How LLMs Resolve Ambiguous Social Situations across Perspectives and Roles

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.

From Pixels to Nucleotides: End-to-End Token-Based Video Compression for DNA Storage

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.

Analysis of Converged 3D Gaussian Splatting Solutions: Density Effects and Prediction Limit

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.

Efficient Post-Training Pruning of Large Language Models with Statistical Correction

Post-training pruning is an effective approach for reducing the size and inference cost of large language models (LLMs), but existing methods often face a trade-off between pruning quality and computational efficiency. Heuristic pruning methods are efficient but sensitive to activation outliers, while reconstruction-based approaches improve fidelity at the cost of heavy computation. In this work, we propose a lightweight post-training pruning framework based on first-order statistical properties of model weights and activations. During pruning, channel-wise statistics are used to calibrate magnitude-based importance scores, reducing bias from activation-dominated channels. After pruning, we apply an analytic energy compensation to correct distributional distortions caused by weight removal. Both steps operate without retraining, gradients, or second-order information. Experiments across multiple LLM families, sparsity patterns, and evaluation tasks show that the proposed approach improves pruning performance while maintaining computational cost comparable to heuristic methods. The results suggest that simple statistical corrections can be effective for post-training pruning of LLMs.

SCONE: A Practical, Constraint-Aware Plug-in for Latent Encoding in Learned DNA Storage

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.

Thinking Like Van Gogh: Structure-Aware Style Transfer via Flow-Guided 3D Gaussian Splatting

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.

TVC: Tokenized Video Compression with Ultra-Low Bitrate

Tokenized visual representations have shown great promise in image compression, yet their extension to video remains underexplored due to the challenges posed by complex temporal dynamics and stringent bitrate constraints. In this paper, we propose Tokenized Video Compression (TVC), the first token-based dual-stream video compression framework designed to operate effectively at ultra-low bitrates. TVC leverages the powerful Cosmos video tokenizer to extract both discrete and continuous token streams. The discrete tokens (i.e., code maps generated by FSQ) are partially masked using a strategic masking scheme, then compressed losslessly with a discrete checkerboard context model to reduce transmission overhead. The masked tokens are reconstructed by a decoder-only transformer with spatiotemporal token prediction. Meanwhile, the continuous tokens, produced via an autoencoder (AE), are quantized and compressed using a continuous checkerboard context model, providing complementary continuous information at ultra-low bitrate. At the Decoder side, both streams are fused using ControlNet, with multi-scale hierarchical integration to ensure high perceptual quality alongside strong fidelity in reconstruction. This work mitigates the long-standing skepticism about the practicality of tokenized video compression and opens up new avenues for semantics-aware, token-native video compression.

Stereo Image Coding for Machines with Joint Visual Feature Compression

2D image coding for machines (ICM) has achieved great success in coding efficiency, while less effort has been devoted to stereo image fields. To promote the efficiency of stereo image compression (SIC) and intelligent analysis, the stereo image coding for machines (SICM) is formulated and explored in this paper. More specifically, a machine vision-oriented stereo feature compression network (MVSFC-Net) is proposed for SICM, where the stereo visual features are effectively extracted, compressed, and transmitted for 3D visual task. To efficiently compress stereo visual features in MVSFC-Net, a stereo multi-scale feature compression (SMFC) module is designed to gradually transform sparse stereo multi-scale features into compact joint visual representations by removing spatial, inter-view, and cross-scale redundancies simultaneously. Experimental results show that the proposed MVSFC-Net obtains superior compression efficiency as well as 3D visual task performance, when compared with the existing ICM anchors recommended by MPEG and the state-of-the-art SIC method.

WTDUN: Wavelet Tree-Structured Sampling and Deep Unfolding Network for Image Compressed Sensing

Deep unfolding networks have gained increasing attention in the field of compressed sensing (CS) owing to their theoretical interpretability and superior reconstruction performance. However, most existing deep unfolding methods often face the following issues: 1) they learn directly from single-channel images, leading to a simple feature representation that does not fully capture complex features; and 2) they treat various image components uniformly, ignoring the characteristics of different components. To address these issues, we propose a novel wavelet-domain deep unfolding framework named WTDUN, which operates directly on the multi-scale wavelet subbands. Our method utilizes the intrinsic sparsity and multi-scale structure of wavelet coefficients to achieve a tree-structured sampling and reconstruction, effectively capturing and highlighting the most important features within images. Specifically, the design of tree-structured reconstruction aims to capture the inter-dependencies among the multi-scale subbands, enabling the identification of both fine and coarse features, which can lead to a marked improvement in reconstruction quality. Furthermore, a wavelet domain adaptive sampling method is proposed to greatly improve the sampling capability, which is realized by assigning measurements to each wavelet subband based on its importance. Unlike pure deep learning methods that treat all components uniformly, our method introduces a targeted focus on important subbands, considering their energy and sparsity. This targeted strategy lets us capture key information more efficiently while discarding less important information, resulting in a more effective and detailed reconstruction. Extensive experimental results on various datasets validate the superior performance of our proposed method.