Many high-impact machine learning tasks involve multi-dimensional data (e.g., images, volumetric medical scans, multivariate time-series). Yet, most neural architectures flatten inputs, discarding critical cross-dimension information. We introduce NdLinear, a novel linear transformation that preserves these structures without extra overhead. By operating separately along each dimension, NdLinear captures dependencies that standard fully connected layers overlook. Extensive experiments across convolutional, recurrent, and transformer-based networks show significant improvements in representational power and parameter efficiency. Crucially, NdLinear serves as a foundational building block for large-scale foundation models by operating on any unimodal or multimodal data in its native form. This removes the need for flattening or modality-specific preprocessing. Ndlinear rethinks core architectural priorities beyond attention, enabling more expressive, context-aware models at scale. We propose NdLinear as a drop-in replacement for standard linear layers -- marking an important step toward next-generation neural architectures.

We introduce the concept of programmable feature Our key motivation comes from a novel dynamical Ising-like engineering for time series modeling and propose model, the spin-gas Glauber dynamics, originated from a a feature programming framework. This newly debuted gas-like interaction that includes momentum framework generates large amounts of predictive and acceleration information. By using spin-gas Glauber features for noisy multivariate time series while dynamics as the fundamental model for time series generating allowing users to incorporate their inductive bias processes at the smallest time scale, we explore the with minimal effort. The key motivation of our potential of treating time series as the path-sum of infinitesimal framework is to view any multivariate time series increments generated by a series of Markovian coin as a cumulative sum of fine-grained trajectory tosses following the spin-gas Glauber dynamics. From such increments, with each increment governed by a a fine-grained perspective, a set of operators is motivated for novel spin-gas dynamical Ising model.