Research · White Papers
Research & Publications
Exploring the mathematical foundations of efficient signal processing and AI model compression. Join the waitlist for updates on our latest research.
Research Focus Areas
Our research explores fundamental challenges in sparse signal processing, deterministic algorithm design, and certification frameworks for production systems.
Efficient Spectral Analysis
Investigating efficient algorithms for identifying and reconstructing sparse frequency components in high-dimensional signals across various domains.
Deterministic Algorithms
Developing verification-ready signal processing frameworks with guaranteed reproducibility for production AI and high-reliability applications.
Computational Optimization
Advancing computational efficiency for frequency domain analysis through optimized processing and intelligent resource allocation.
Validation & Benchmarking
Establishing comprehensive benchmarking methodologies and validation frameworks for comparing signal processing implementations across diverse use cases.
Technical Papers
SparseTech technical papers covering deterministic sparse FFT engines, sublinear data discovery, and memory-compute workload modeling. PDF available for each.
Sparse FFT as a Memory-Compute Workload: FFTW Benchmarking and Traffic/Energy Modeling
Aaron R. Flouro, Shawn P. Chadwick
Published: May 12, 2026
eess.SPcs.ARcs.PF
We benchmark a production Rust implementation of a Four-View GATED CRT sparse FFT against FFTW and evaluate its suitability for near-memory sparse spectral processing. The sparse arithmetic core scales as $O(k \log k)$, while input acquisition remains streaming $O(N)$. On synthetic on-grid sparse signals, the…
SparseDSP: System-Level Evaluation of Deterministic Sparse FFT Engine Routing across Synthetic, Impaired, and Curated Real-Payload Workloads
Aaron R. Flouro, Shawn P. Chadwick
Published: May 10, 2026
eess.SPcs.DScs.AR
We present SparseDSP, a regime-adaptive deterministic sparse FFT engine routing system evaluated against Dense FFT across on-grid, off-grid, and curated real-payload workloads. SparseDSP estimates input sparsity internally, then dispatches to an exact engine drawn from a complexity-class family spanning $O(k \log k)$,…
SparseDSP: System-Level Evaluation of Deterministic Sparse FFT for 5G/6G-Relevant Wideband Spectrum Sensing
Aaron R. Flouro, Shawn P. Chadwick
Published: May 11, 2026
eess.SPcs.ITcs.NI
We present SparseDSP, a regime-adaptive deterministic sparse FFT system evaluated against dense FFT baselines for transform-stage bin identification in 5G/6G-relevant wideband sensing regimes. SparseDSP estimates effective sparsity internally and dispatches among deterministic sparse recovery engines spanning…
SparseDSP: System-Level Evaluation of Deterministic Sparse FFT for Radar, Sonar, and LiDAR
Aaron R. Flouro, Shawn P. Chadwick
Published: April 19, 2026
eess.SPcs.AR
We present SparseDSP, a regime-adaptive deterministic sparse FFT system evaluated against Dense FFT across radar, sonar, electronic warfare, and LiDAR operating points. SparseDSP estimates signal sparsity internally, then dispatches to an exact engine selected by its internal dispatch policy from an internal family of…
SparseDSP: Sublinear Data Discovery for Large-Scale Computational Pipelines
Aaron R. Flouro, Shawn P. Chadwick
Published: April 19, 2026
cs.DScs.LGcs.IR
Large-scale data processing pipelines spend substantial time on discovery: selecting relevant subsets from large data stores before downstream computation begins. This discovery stage, which includes dense scans, FFT-based analysis, and exhaustive top-$k$ selection, scales linearly with data size regardless of…
SparseTech Publications
Deterministic Sparse FFT via Keyed Multi-View Gating with $O(\sqrt{N} \log k)$ Expected Time
Aaron R. Flouro, Shawn P. Chadwick
Published: May 5, 2026
eess.SPcs.DScs.IT
We introduce a deterministic sparse Fourier transform framework based on a keyed multi-view gating mechanism that leverages 2-of-3 Chinese Remainder Theorem (CRT) agreement to reduce candidate frequency pairs from $O(k^2)$ to $Θ(k)$ under sparse-regime assumptions. Unlike prior approaches that rely on randomized…
Safety-Certified CRT Sparse FFT: $Ω(k^2)$ Lower Bound and $O(N \log N)$ Worst-Case
Aaron R. Flouro, Shawn P. Chadwick
Published: April 20, 2026
eess.SPcs.DScs.IT
Computing Fourier transforms of k-sparse signals, where only k of N frequencies are non-zero, is fundamental in compressed sensing, radar, and medical imaging. While the Fast Fourier Transform (FFT) evaluates all N frequencies in $O(N \log N)$ time, sufficiently sparse signals should admit sub-linear complexity in N.…
Post-Training Probability Manifold Correction via Structured SVD Pruning and Self-Referential Distillation
Aaron R. Flouro, Shawn P. Chadwick
Published: January 30, 2026
cs.LGcs.AIcs.CL
Large language models are expensive to deploy. We introduce Sparse Knowledge Distillation (SparseKD), a post-training method that compresses transformer models by combining structured SVD pruning with self-referential knowledge distillation. The key insight is simple: instead of using an external teacher, the model…
Adaptive Weighting in Knowledge Distillation: An Axiomatic Framework for Multi-Scale Teacher Ensemble Optimization
Aaron R. Flouro, Shawn P. Chadwick
Published: January 25, 2026
cs.LG
Knowledge distillation with multiple teachers is increasingly used to improve robustness, efficiency, and safety, yet existing approaches rely largely on heuristic or implementation-specific weighting schemes. This paper develops an operator-agnostic axiomatic framework for adaptive weighting in multi-teacher knowledge…
Recursive Meta-Distillation: An Axiomatic Framework for Iterative Knowledge Refinement
Aaron R. Flouro, Shawn P. Chadwick
Published: January 19, 2026
cs.LG
Recent work in probability-domain knowledge distillation has established axiomatic frameworks for temperature scaling, multi-teacher aggregation, and bias-variance trade-offs in single-stage settings. However, the mathematical behavior of recursive or multi-generation distillation remains poorly understood, with prior…
Multi-Teacher Ensemble Distillation: A Mathematical Framework for Probability-Domain Knowledge Aggregation
Aaron R. Flouro, Shawn P. Chadwick
Published: January 14, 2026
cs.LG
Building on the probability-domain distillation framework of Sparse-KD, we develop an axiomatic, operator-theoretic framework for multi-teacher ensemble knowledge distillation. Rather than prescribing a specific aggregation formula, we define five core axioms governing valid knowledge aggregation operators,…
Hallucinations Live in Variance
Aaron R. Flouro, Shawn P. Chadwick
Published: January 11, 2026
cs.LGcs.AI
Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can trigger cascading failures in multi-step execution. Yet this form of…
Sparse Knowledge Distillation: A Mathematical Framework for Probability-Domain Temperature Scaling and Multi-Stage Compression
Aaron R. Flouro, Shawn P. Chadwick
Published: January 6, 2026
cs.LG
We develop a unified theoretical framework for sparse knowledge distillation based on probability-domain softening operators. While the equivalence $p^{1/T} \propto \mathrm{softmax}(z/T)$ is well known, our contribution is an operator-level analytical framework built on this foundation rather than the equivalence…
Foundational Readings
Curated academic papers that inform our research directions.
Note: These are external publications from arXiv, not SparseTech publications. We share them as context for the mathematical foundations underlying our work.
Showing 747,678 results
QGPINNs: A Physics-Informed Neural Network Framework for Nonlocal Differential Equations on Quantum Graphs
Vaibhav Mehandiratta, Saket Ramchandra
Published: August 28, 2026
cs.LGmath.NA
We propose QGPINNs, a physics-informed neural network framework developed in PyTorch for the numerical solution of nonlocal differential equations on quantum graphs. The framework is designed as a general computational implementation in which the solution on each edge of the graph is approximated by a neural network,…
Aero Hand Open: A Simulation-Ready Tendon-Driven Hand for Dexterous Manipulation Learning
Nan Wang, Mohit Yadav, Jonathan Wulff +5 more
Published: August 28, 2026
cs.ROcs.AIcs.LG
Tendon-driven hands are anthropomorphic, and moving the actuators off the joints is what makes a hand of this capability affordable to build. Two effects produce that saving. Routing force through a cable removes the requirement that a motor fit inside the joint it drives, so smaller and cheaper motors suffice, and one…
Learning a Size-Weight Frontier for Synthetic-Augmented Inference
Chengpiao Huang, Kaizheng Wang
Published: August 28, 2026
stat.MEcs.AIcs.LG
Synthetic data can improve statistical inference when real data are scarce, but naively treating synthetic samples as real data can introduce bias and lead to unreliable inference. We develop a general framework for synthetic-augmented inference across a population of related tasks. It characterizes synthetic…
SignRR: Retrieve and Refine Real Motion for Sign Language Production
Fidel Omar Tito Cruz, Angie Sanchez Marquina, Summy Farfan +1 more
Published: August 28, 2026
cs.CV
Sign language production (SLP) aims to generate continuous signing motion from spoken language, often through gloss-to-pose generation. Prior work mainly follows two paradigms. Generative models synthesize motion from a learned prior or from noise, without reference to an observed signing instance, making rare hand…
GeBDA: Building Damage Assessment as Text-Based Sequence Prediction
Olivier Dietrich, Krishna Sapkota, Konrad Schindler +1 more
Published: August 28, 2026
cs.CV
Conventionally, Building Damage Assessment (BDA) is tackled either with dedicated network architectures or by fine-tuning geospatial image foundation models. In this work, we ask whether a general-purpose Vision-Language Model (VLM) can localize buildings and grade their damage through autoregressive sequence…
On two proofs of $d^2$ mixing of weighted Dikin walks
Yuansi Chen, Yunbum Kook
Published: August 28, 2026
cs.DScs.LGmath.OC
We study the mixing time of weighted Dikin walks for sampling from exponential distributions on polytopes and truncated positive-semidefinite (PSD) cones. Our first result gives a general total-variation mixing bound under strong self-concordance, $\barν$-symmetry, and mixed-trace regularity on the local metric. The…
Learning between the peaks: sharp asymptotics for kernel ridge regression under power-law anisotropy
Lorenzo Rizzi, Arie Wortsman Zurich, Bruno Loureiro
Published: August 28, 2026
stat.MLcs.LG
We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $α\geq 0$ for polynomial inner-product kernels. We derive asymptotically sharp expressions for the kernel spectrum and the generalization error in the polynomial high-dimensional regime…
A Formal Limitation on Learning Human Language From Textual Corpora
Emily Cheng, Ryan Cotterell
Published: August 28, 2026
cs.CL
Can a listener recover what a speaker means from the form of an utterance alone? We answer this question information-theoretically, and for a listener given by any featurizer of text, including the hidden states of contemporary large language models. Modeling language use as a joint distribution over meanings,…
Blog: Survey of Optimizers
Ruoran Xu
Published: August 28, 2026
cs.LGcs.AI
Neural-network optimization in 2025-2026 is no longer well described as a succession of new Adam variants. The design space has expanded from coordinates to matrices and layers, from fixed training horizons to policies over time, and from mathematical update rules to state representations that must survive sharding and…
A Complete Characterization of Tensorizable $f$-divergences
Rodrigo Cruz, Flavio P. Calmon, Qian Yu
Published: August 28, 2026
cs.ITmath.PRmath.ST
Csiszar's formulation of the $f$-divergence introduced a vast family of functionals for quantifying dissimilarity between probability distributions. However, many applications in statistics and information theory rely only on a few $f$-divergences, such as the Kullback-Leibler divergence, the $χ^2$-divergence, and the…
Logos: An Agent Harness on a Cross-Process Bus
Hanzhang Jia, Liheng Zeng, Hao Cheng +2 more
Published: August 28, 2026
cs.AIcs.MA
Modern agent systems assemble capabilities at runtime, and this dynamic composition has recently received a complete formal treat ment in the spatiotemporal-composability calculus, in which a capability is a component carrying a tracked inverse, and agents are assembled as plugins. This plugin form is carried by a…
Advancing Interaction-Sensitive Feature Selection: Novel Relief-Based Algorithms, Expanded Comparisons, and Recommendations for Biomedical Data Mining
Kia Kazemi-Nia, Harsh Bandhey, Philip J. Freda +1 more
Published: August 28, 2026
cs.LG
As a precursor to high-dimensional biomedical data modeling, reliable feature selection can reduce computational expense, improve modeling performance, and yield simpler, more interpretable models. However, most filter-based feature selection methods struggle to detect feature interactions, while wrapper or embedded…
Video Generative Models as Geometry Learner
Haosen Yang, Jifei Song, Zhensong Zhang +2 more
Published: August 28, 2026
cs.CVcs.AI
Recent generative approaches to geometry estimation adapt pretrained image diffusion models and treat the task as image-conditioned generation. Leveraging off-the-shelf image diffusion models, they either (i) train task-specific geometry models (for depth and surface normal estimation) independently, losing the…
DARTS: Decoder-Aware Representation Tuning via Surgery for Model Merging
Aaryan Ajay Sharma, Sai Nishanth Padala, Seganrasan Subramanian
Published: August 28, 2026
cs.LG
Model merging combines multiple task-specific fine-tuned LLMs into a single multi-task model without additional training. However, merged models are known to suffer from representation bias: systematic drift between the merged model's hidden states and those of each individual source model. Prior work (Yang et al.,…
Closest Normal Matrix Found Again Using Riemannian Optimization
Vanni Noferini, Matvei Zhukov
Published: August 28, 2026
math.NA
We propose an approach based on Riemannian optimization to compute a nearest normal matrix to a given one. The problem can be formulated as the minimization of a smooth function either on the manifold $U(n)$ of unitary matrices of size n or on the flag manifold $U (n)/U (1)^n$. The flag manifold is particularly…
An Enclosed Mode Is a Gauge Choice: Topology Relative to Reach in Certified Code World Models
Javier Aguilar Martín
Published: August 28, 2026
cs.LGcs.AI
A code world model accepted by a sampling gate can be exactly right on everything the gate can see and arbitrarily wrong beyond it. We characterize what a certified model can know, and what its errors can cost, when the omission is an annular freeze mode enclosing an unreachable interior. The gate quotient makes the…
Analysis of Polynomial Threshold Functions on Random Regular Graphs: Computational Complexity of Detecting Noisy Random Lift
Xifan Yu
Published: August 28, 2026
math.COcs.CCcs.DS
In this work, we present the first analysis of low degree polynomial threshold functions for the natural hypothesis testing problem of detecting the noisy random lift of a base $d$-regular graph from a uniformly random $d$-regular graph. Along the way, we obtain a new result for the distribution of short cycle counts…
InstructMesh: Selective Refinement of Generative 3D Models for Fabrication
Faraz Faruqi, Ahmed Katary, Demircan Tas +10 more
Published: August 28, 2026
cs.AI
Recent advances in generative AI allow users to create 3D models from text or images. However, these models prioritize visual plausibility over geometric accuracy, often generating results with flaws that compromise their intended use post-fabrication. We present InstructMesh, an interactive post-generation refinement…
Texture Image Classification Using DWT AlexNet Feature Fusion and Deep Neural Networks
Arun D. Kulkarni
Published: August 28, 2026
cs.CVcs.AI
Texture image classification plays a significant role in computer vision applications, including industrial inspection, medical image analysis, remote sensing, and object recognition. Handcrafted features can capture local texture characteristics but may have limited capability to represent complex visual patterns. In…
When Robots Mishear Us: Mapping the Safety Risks of Voice-Controlled Embodied AI
Sihan Jia, Oliver Lemon
Published: August 28, 2026
cs.AIcs.CLcs.RO
We investigate whether automatic speech recognition (ASR) errors in user input can lead to unsafe outputs from Embodied AI (EAI) models. We find that ASR errors can lead to harmful instructions being accepted and executed by EAI models, thereby reducing safety. We simulate ASR errors and combine them with existing…
Learning the Target Priors Before Image Translation: A Decoupled Training Paradigm for Cross-Modal Image Translation in Remote Sensing
Keyan Hu, Mingtao Wang, Ziyu Zhou +4 more
Published: August 28, 2026
cs.CV
Cross-modal image translation in remote sensing must preserve source-observed content while matching the target-domain distribution. Existing methods jointly learn the target prior and cross-modal dependence from scarce paired data, overlooking a key asymmetry: only the latter intrinsically requires cross-modal…
Conformal Uncertainty Quantification Guarantees for Neural Operators
Tom Stent, Nicolas Boullé
Published: August 28, 2026
math.NAcs.AImath.PR
Neural operators provide fast surrogate models for approximating operators between function spaces, but their predictions often lack uncertainty quantification. We develop a split conformal framework to guarantee that a calibrated pointwise band around the neural operator output contains the true solution on at least a…
Quadratic Probing Insertions Are $ε^{-(1+o(1))}$
Yang Hu, William Kuszmaul, Jingxun Liang +3 more
Published: August 28, 2026
cs.DS
First proposed in 1968, quadratic probing has stood for more than half a century as one of the simplest and most widely used hash-table designs in computer science. It is conjectured that, at load factor $1 - ε$, the hash table achieves $O(ε^{-1})$ expected insertion time. But even proving a bound of the form…
Training Communication-Efficient Mixture-of-Experts Language Models with Layer Re-Configuration
Simeng Sun, Roger Waleffe
Published: August 28, 2026
cs.AI
When training Mixture-of-Experts (MoE) language models with expert parallelism, all-to-all token dispatch and combine collectives can consume a substantial fraction of end-to-end training time. In this work, we study communication-efficient MoE models (CE-MoE), in which we adopt a heterogeneous layer pattern that…