Point-to-Manifold Geometry: Flexibly Overcoming the Curse of Dimensionality in Neural Computational Units

Rohan Ghosh, Mehul Motani

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Statistical Mixing Guarantees for Contractive Echo State Networks

Pradeep Singh, Balasubramanian Raman

Sydney Poster Session 3, Wed, Dec 9, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Dimension Bounds for Contractive Reservoir Computing from Input Entropy

Pradeep Singh, Kishore Babu Nampalle, Balasubramanian Raman

Sydney Poster Session 1, Tue, Dec 8, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Temporal Smoothness Constraints on Efficient Neurobiological Codes Imply Temporal Specialization

John Vastola, Samuel J Gershman

Sydney Poster Session 2, Tue, Dec 8, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Looped Transformers with Layer Normalization Provably Learn the Power Method

Lyumin Wu, Chenyang Zhang, Yuan Cao

Sydney Poster Session 6, Thu, Dec 10, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Why Heavy-Tailed Weights Predict Model Quality

Joseph Wilson, Chris van der Heide, Liam Hodgkinson, Zhichao Wang and 2 more

Sydney Poster Session 2, Tue, Dec 8, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

On the Instability and Stabilization of Blockwise Muon

Yuanshi Liu, Weicheng Lin, Boyuan Jiang, Xin Tao and 2 more

Sydney Poster Session 6, Thu, Dec 10, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

NTK Regression under dual power-law model: Deterministic Equivalents via SDE and PDE Methods

Collin Cranston, Zhichao Wang, Todd Kemp

Paris Poster Session 5, Fri, Dec 11, 11:30 AM–1:30 PM, Paris Poster Hall · Published 2026

Elastic Representations via Hyperbolic Geometry

Arjun Ramesh Kaushik, Rudrasis Chakraborty, Nalini Ratha, Venu Govindaraju

Atlanta Poster Session 4, Thu, Dec 10, 4:30 PM–7:30 PM, Hall C1 · Published 2026

The Alternation Depth Principle for Neural Operator Design

Haoze Song, Zhilu Lai, Wei Wang

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Topological Invariance and Breakdown in Learning Dynamics

Yongyi Yang, Tomaso Poggio, Isaac Chuang, Liu Ziyin

Sydney Poster Session 1, Tue, Dec 8, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Synaptic Strength Controls Trainability and Structural Stability in Rank-Deficient RNNs

Fatih Dinc, Edouard Ponnat, Henrik Weyer, Yanin Guerra and 1 more

Sydney Poster Session 1, Tue, Dec 8, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Spectral Degeneration of Softmax Attention under Isotropic Score Geometry

Mengda Li, Jianfeng Yao

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Phase Kernel Lifts Capacity of Dense Associative Memory

Yifei Zhao, Ying Tang

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Spectral Identifiability for World Models: Polynomial Projectors, Resolvent Stability, and a Krylov Bottleneck

Phan Quoc Hung Mai, Duc H Nguyen, Luong Doan, Ngoc Mai Vu and 4 more

Sydney Poster Session 5, Thu, Dec 10, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

The Cost of Symmetry: Universality and Hardness for Permutation-Invariant Neural Networks

Dashiell Bhattacharyya

Sydney Poster Session 2, Tue, Dec 8, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Fast Approximate $\ell_p$ Chamfer Distance via Lopsided Embeddings and Structured JL

Ying Feng, David Woodruff

Atlanta Poster Session 5, Fri, Dec 11, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Compositional Generalization Certificates via the Van Kampen Theorem

Karen Sargsyan

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

FLIP: Fast and Accurate Global Lipschitz Estimation for Large Feedforward Networks

Hongbo Chen, Zihao Ren

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

The Optimal Control Foundation of Early Exits – Turnpikes and ResNets

Jens Püttschneider, Simon Heilig, Asja Fischer, Timm Faulwasser

Paris Poster Session 3, Thu, Dec 10, 12:30 PM–2:30 PM, Paris Poster Hall · Published 2026

Second-Order Complexity Theory for Neural Networks

Yoshihiro Maruyama

Sydney Poster Session 2, Tue, Dec 8, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

A Reproducible Evaluation Protocol for Quantum Non-Linearity in Variational Quantum Models

Pavel Sulimov, Claude Lehmann

Paris Poster Session 1, Wed, Dec 9, 12:30 PM–2:30 PM, Paris Poster Hall · Published 2026

Cauchy Scientific Networks: Loss–Architecture Alignment and Its Limit

Haonan Tan, Xin Li, juyi peng, Zhihong Xia and 2 more

Sydney Poster Session 2, Tue, Dec 8, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Spectral Re-Basin for Linear Mode Connectivity

Ya-Wei Eileen Lin, Thomas Dagès, Daniel Herbst, Daniel Cremers and 1 more

Paris Poster Session 2, Wed, Dec 9, 5:00 PM–7:00 PM, Paris Poster Hall · Published 2026

Foundations of Categorical Equivariant Deep Learning

Yoshihiro Maruyama

Sydney Poster Session 6, Thu, Dec 10, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Second-Order Complexity of Neural ODE Inference

Yoshihiro Maruyama

Sydney Poster Session 5, Thu, Dec 10, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Beyond Eigenfunctions: Divergence Principal Functions for Representation Learning

Ritabrata Ray, Sahil Dharod, Burak Varıcı, Nicholas Boffi and 1 more

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

A Hebbian Recurrent Neural Network Explains the Hierarchical Geometry of Sequence Memory

Zhitao FENG, Bo Ho, Huan Luo, xiaolong zou and 1 more

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

What the Geometry of Good Models Tells Us

Alexis Fox, Samuel Orellana Mateo, Krish Yadav, Yiyang Sun and 2 more

Sydney Poster Session 3, Wed, Dec 9, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

How are linear representations learned? Exact solutions to the dynamics of abstraction

William W Yang, Peter E Latham, Andrew Saxe

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Phase Space Attention: A Hairer Lift Resolves the Single-Layer Induction Obstruction

Kingsuk Maitra, Shagun Sood, Morteza Hosseini, Suman Gunnala and 1 more

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Surjective Pseudo-Invertible Neural Networks

Yamit Ehrlich, Amit Arad, Nimrod Berman, Assaf Shocher

Paris Poster Session 5, Fri, Dec 11, 11:30 AM–1:30 PM, Paris Poster Hall · Published 2026

Information bottleneck dynamics during learning across artificial and biological neural systems

Nikita Pospelov, Olga Ivashkina, Plusnin Viktor, Olga Rogozhnikova and 3 more

Sydney Poster Session 2, Tue, Dec 8, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Canonical Predictive Quotients: A Theory of Prediction under Hidden Predictive State Uncertainty with ICL Implications

Hiroyuki Kasai

Paris Poster Session 5, Fri, Dec 11, 11:30 AM–1:30 PM, Paris Poster Hall · Published 2026

Local-Interaction Learning Dynamics: A Markov Random Field Framework for Convergence of Deep Neural Network Learning

Wen Dong

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

What Makes a Good Path? Factoring Manifold Support and Path Geometry

Zhixuan Zhou, Tingting Dan, Guorong Wu

Atlanta Poster Session 1, Wed, Dec 9, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Emergence, Retention and Mitigation of Ill-conditioning due to Basis Lifting in KANs

Ferhat Arslan, Weihong Guo, Shuo Li

Atlanta Poster Session 3, Thu, Dec 10, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Understanding Double Descent through Universal Compression

Jiaxuan Cheng, Addison Spiegel

Atlanta Poster Session 2, Wed, Dec 9, 4:30 PM–7:30 PM, Hall C1 · Published 2026

Neural Spectral Capacity: An Architectural Quantity from Network Specification Alone

CHENYU ZHU, Ruoyu Zhao, Zhichao Lu

Sydney Poster Session 3, Wed, Dec 9, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

A Mahalanobis Margin \texorpdfstring{$\gamma_{\min}$}{gamma\_min} Bound on Task Confusion in Pretrained Class-Incremental Learning: From Infeasibility to Exponential Attenuation

Milad Khademi Nori, Guanghui Wang

Paris Poster Session 2, Wed, Dec 9, 5:00 PM–7:00 PM, Paris Poster Hall · Published 2026

Learning Modular Addition with Auxiliary Modulus

Hanato Kikuchi, Ryosuke Masuya, Kazuhiko Kawamoto, Hiroshi Kera

Sydney Poster Session 2, Tue, Dec 8, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Characterizing Learning in Deep Neural Networks using a Tractable Algorithmic Complexity Estimator

Pedram Bakhtiarifard, Sophia Natasha Wilson, Mahmoud H. A. Afifi, Jonathan Wenshøj and 1 more

Sydney Poster Session 1, Tue, Dec 8, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Memorization Is Folding: Topological Signatures of Noisy-Label Learning

Zhongtian Sun, Fan Mo, Prayag Tiwari, KELIN XIA

Sydney Poster Session 6, Thu, Dec 10, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

A Control-Theoretic Approximation to Predictive Coding Dynamics

Ryan Fayyazi, Kyle Daruwalla, Mitra Javadzadeh

Atlanta Poster Session 5, Fri, Dec 11, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Hard Attention Transformers and BSS-Machines

Lena Ehrmuth

Paris Poster Session 4, Thu, Dec 10, 5:30 PM–7:30 PM, Paris Poster Hall · Published 2026

Generalized Laplacian in Spectral Seriation on Manifold Data

Ruizi Wu, Wanjie Wang, Jinchi Lv

Sydney Poster Session 5, Thu, Dec 10, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

From Approximation to Computation: Universal Power of Deep Narrow Networks at Constant Width

Olivier Bournez, Johanne Cohen, Adrian Wurm

Paris Poster Session 1, Wed, Dec 9, 12:30 PM–2:30 PM, Paris Poster Hall · Published 2026

CP-MLPs: A Tensor-Rank Theory of Tied and Untied MLP Blocks

Md Rifat Arefin, Farzaneh Heidari, Irina Rish, Guillaume Rabusseau

Sydney Poster Session 1, Tue, Dec 8, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Spectral Estimation with Deformed Decompression

Siavash Ameli, Chris van der Heide, Liam Hodgkinson, Michael Mahoney

Sydney Poster Session 5, Thu, Dec 10, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Does Sparse Connectivity Improve Generalization? Convolutional Networks Below the Edge of Stability

Tongtong Liang, Esha Singh, Rahul Parhi, Alex Cloninger and 1 more

Atlanta Poster Session 3, Thu, Dec 10, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Sharpness of Minima in Deep Matrix Factorization

Anıl Kamber, Rahul Parhi

Atlanta Poster Session 2, Wed, Dec 9, 4:30 PM–7:30 PM, Hall C1 · Published 2026

Neural Expansion: A Unified Mechanism for How Deep Neural Network Generalize

Chashi Mahiul Islam, Samuel Jacob Chacko, Mao Nishino, Canlin Zhang and 1 more

Atlanta Poster Session 5, Fri, Dec 11, 10:00 AM–1:00 PM, Hall C1 · Published 2026

On Lipschitz Explosion in Deep Neural Networks with Normalization: Consequences for Optimization and Robustness

Ashkan Soleymani, Reyhaneh Hosseinpourkhoshkbari, Hadi Daneshmand, Patrick Jaillet

Atlanta Poster Session 4, Thu, Dec 10, 4:30 PM–7:30 PM, Hall C1 · Published 2026

A Theory of Spatial Continuous Attractors in Hopfield Energy Landscapes

Chong Li, Xiangyang Xue, Jianfeng Feng, Taiping Zeng

Sydney Poster Session 6, Thu, Dec 10, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Unrolled gradients in disguise: bridging interpolation-based and Jacobian regularization for stable neural dynamics

Maya Janvier, Etienne Meunier

Paris Poster Session 3, Thu, Dec 10, 12:30 PM–2:30 PM, Paris Poster Hall · Published 2026

Pattern-Based Matrix Analysis Under Permutations

Andrei Ermakov

Paris Poster Session 3, Thu, Dec 10, 12:30 PM–2:30 PM, Paris Poster Hall · Published 2026

Fast Sandwich Products in Clifford Algebra

Travis Pence, Daisuke Yamada, Jiaqi Mo, Chanyoung Moon and 2 more

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Comparing Linear Regions in ReLU-Type Networks: Theory and Monte Carlo Methods

Yuan Wang

Sydney Poster Session 5, Thu, Dec 10, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Geometric Analysis of Neural Regression Collapse via Intrinsic Dimension

George Andriopoulos, Zixuan Dong, Bimarsha Adhikari, Keith Ross

Sydney Poster Session 6, Thu, Dec 10, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

How I learned to stop worrying and love StopGrads: Stationarity, Convergence, and a case study on Flow Map Learning

A stopgrad regression principle characterizes stationary points of stopgrad objectives and proves convergence to true flow maps while halving training memory.

Mark Goldstein, Max Shen, Zichu Wang, Aahlad Manas Puli and 1 more

Sydney Poster Session 5, Thu, Dec 10, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

SGD Provably Prioritizes a Shortcut Spurious Feature in the XOR Model

SGD learns linear spurious correlations exponentially faster than XOR signals in two-layer ReLU networks, with dynamics that suppress true feature learning.

Tyler LaBonte, Vidya Muthukumar

Atlanta Poster Session 3, Thu, Dec 10, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Bifurcation Models: Learning Set-Valued Solution Maps with Weight-Tied Dynamics

Bifurcation models learn set-valued solution maps via weight-tied dynamics, representing multi-branch attractor landscapes with almost everywhere regular selectors and outperforming single-branch supervision, though diversity requires explicit encouragement.

Caleb Jore, Jialin Liu

Atlanta Poster Session 2, Wed, Dec 9, 4:30 PM–7:30 PM, Hall C1 · Published 2026

Random Neural Network Expressivity for Non-Linear Partial Differential Equations

Random neural networks approximate time-dependent Sobolev functions with dimension-free rate 1/2 and efficiently solve nonlinear porous medium and compressible Navier-Stokes equations.

Muhammed Ali Mehmood, Lukas Gonon

Sydney Poster Session 6, Thu, Dec 10, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Subcritical Signal Propagation at Initialization in Normalization-Free Transformers

Average partial Jacobian norms in transformers reveal subcritical signal growth in normalization-free architectures via tanh-like nonlinearities, explaining initialization sensitivity in DyT and Derf models.

Sergey Alekseev

Paris Poster Session 1, Wed, Dec 9, 12:30 PM–2:30 PM, Paris Poster Hall · Published 2026

On the Depth of Monotone ReLU Neural Networks and ICNNs

Monotone ReLU networks cannot compute or approximate maximum, ICNNs need depth n for it, and depth-k ICNNs cannot simulate some depth-2 ReLU networks.

Egor Bakaev, Florestan Brunck, Christoph Hertrich, Daniel Reichman and 1 more

Sydney Poster Session 1, Tue, Dec 8, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves

A Hilbert bundle convolutional framework defines HilbNets for infinite-dimensional manifold signals, proving discrete versions converge to continuous architectures and transfer across samplings.

Kartik Tandon, Julian J Gould, Tanishq Bhatia, Francesca Dominici and 2 more

Paris Poster Session 4, Thu, Dec 10, 5:30 PM–7:30 PM, Paris Poster Hall · Published 2026

Provable Quantization with Randomized Hadamard Transform

Dithered randomized Hadamard quantization is unbiased and achieves mean squared error asymptotically matching dense random rotations at O(d log d) cost.

Ying Feng, Piotr Indyk, Michael Kapralov, Dmitrii Krachun and 1 more

Atlanta Poster Session 6, Fri, Dec 11, 4:30 PM–7:30 PM, Hall C1 · Published 2026

Global Convergence of Four-Layer Matrix Factorization under Random Initialization

Gradient descent globally converges for randomly initialized four-layer matrix factorization with balanced regularization, avoiding saddles in polynomial time.

Minrui Luo, Weihang Xu, Xiang Gao, Maryam Fazel and 1 more

Atlanta Poster Session 1, Wed, Dec 9, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passing

Decoupled descent cancels data-reuse biases via approximate message passing so training error tracks test error, enabling zero-cost validation and shrinking the generalization gap versus gradient descent.

Max Lovig

Atlanta Poster Session 3, Thu, Dec 10, 10:00 AM–1:00 PM, Hall C1 · Published 2026

InfoFlow: A Framework for Multi-Layer Transformer Analysis

InfoFlow proves multi-layer Transformers exponentially beat single-layer ones on retrieval tasks and tracks information propagation to explain multi-layer approximation efficiency.

Penghao Yu, Haotian Jiang, Zeyu Bao, Qianxiao Li

Sydney Poster Session 3, Wed, Dec 9, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Learning Reveals Invisible Structure in Low-Rank RNNs

Deriving reduced ODEs for low-rank RNN learning reveals loss-invisible overlaps that encode training history and expose hidden connectivity differences.

Yoav Ger, Omri Barak

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Convergence Analysis of Newton's Method for Neural Networks in the Overparameterized Limit

Regularized Newton training of overparameterized neural networks converges to a deterministic NNTK limit with exponentially fast uniform convergence across all frequencies, avoiding gradient descent's spectral bias.

Konstantin Riedl, Justin Sirignano, Konstantinos Spiliopoulos

Sydney Poster Session 6, Thu, Dec 10, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Training-Induced Escape from Token Clustering in a Mean-Field Formulation of Transformers

Training a linear FFN in mean-field transformers drives token distributions to escape attention-induced clustering near final layers.

Noboru Isobe, Daisuke Inoue, Masaaki Imaizumi

Sydney Poster Session 5, Thu, Dec 10, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Quantifying Concentration Phenomena of Mean-Field Transformers in the Low-Temperature Regime

Mean-field transformers exhibit rapid token distribution concentration onto projection-driven limits with explicit Wasserstein bounds scaling in inverse temperature β and time t.

Albert Alcalde, Leon Bungert, Konstantin Riedl, Tim Roith

Paris Poster Session 4, Thu, Dec 10, 5:30 PM–7:30 PM, Paris Poster Hall · Published 2026

Optimal Representation Size: High-Dimensional Analysis of Pretraining and Linear Probing

High-dimensional analysis of pretraining via PCA and linear probing derives exact errors versus representation size, showing compression helps with abundant unlabeled but scarce labeled data.

Valentina Njaradi, Clémentine Dominé, Rachel A Swanson, Marco Mondelli and 1 more

Sydney Poster Session 1, Tue, Dec 8, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Fixed Universal Transformers

Fixed universal transformers simulate any target transformer via input embeddings with frozen internal parameters, and random initialization achieves universality almost surely.

Jingwen Liu, Alexandr Andoni, Daniel Hsu

Atlanta Poster Session 3, Thu, Dec 10, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Universal Approximation Theorems for Dynamical Systems with Infinite-Time Horizon Guarantees

Framework guarantees universal approximation for multistable dynamics with infinite-time horizon guarantees, linking topological properties to training metrics.

Ábel Ságodi, Memming Park

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Parameter symmetries determine representational geometry in overparameterized nonlinear networks

The poster argues parameter symmetries determine representational geometry in overparameterized nonlinear networks.

Marvin Theiss, Lukas Braun, Andrew Saxe, Erin Grant

Paris Poster Session 3, Thu, Dec 10, 12:30 PM–2:30 PM, Paris Poster Hall · Published 2026

Muon Dynamics as a Spectral Wasserstein Flow

Spectral Wasserstein distances unify normalized matrix flows, proving Muon dynamics are gradient flows with Benamou-Brenier equivalence for monotone norms.

Gabriel Peyré

Paris Poster Session 4, Thu, Dec 10, 5:30 PM–7:30 PM, Paris Poster Hall · Published 2026

Factual recall in linear associative memories: sharp asymptotics and mechanistic insights

Linear associative memory stores up to ~d² log p / 2 facts by raising correct scores above competing extremes, not via Hebbian broad fluctuations.

Alessio Giorlandino, Sebastian Goldt, Antoine Maillard

Paris Poster Session 3, Thu, Dec 10, 12:30 PM–2:30 PM, Paris Poster Hall · Published 2026

Theory of Optimal Learning Rate Schedules and Scaling Laws for a Random Feature Model

Optimal LR schedules for a solvable random feature model reveal easy-phase polynomial decay and hard-phase warmup-stable-decay regimes that improve scaling over constant or power-law schedules, with momentum and batch ramps further enhancing wall-clock time.

Blake Bordelon, Francesco Mori

Paris Poster Session 5, Fri, Dec 11, 11:30 AM–1:30 PM, Paris Poster Hall · Published 2026

Diffusion Models Observe Only Gradients: A Geometric Perspective on Score Matching Errors

Score errors decompose into visible gradient and invisible solenoidal parts, so L2 score error cannot bound distribution divergence and only gradient error matters for diffusion sampling quality.

Nail B Khelifa, Richard Turner, Ramji Venkataramanan

Paris Poster Session 2, Wed, Dec 9, 5:00 PM–7:00 PM, Paris Poster Hall · Published 2026

Statistical Convergence of Spherical First Hitting Diffusion Models

Spherical first-hitting diffusion models achieve near-minimax optimal convergence rates in total variation for Sobolev data on spheres, marking the first statistical optimality result for diffusion models using random generation times.

Simon Bienewald, Lukas Trottner

Paris Poster Session 2, Wed, Dec 9, 5:00 PM–7:00 PM, Paris Poster Hall · Published 2026

Most ReLU Networks Admit Identifiable Parameters

Deep ReLU networks with input and hidden widths ≥2 have open sets of identifiable parameters, yielding exact functional dimensions and generic depth hierarchies.

Moritz Grillo, Guido Montufar

Sydney Poster Session 2, Tue, Dec 8, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

The Symmetries of Three-Layer ReLU Networks

This paper characterizes generic parameter fibers of three-layer ReLU bottleneck networks via semi-algebraic descriptions, yielding polynomial-time functional equivalence tests and analyzing symmetry-induced gradient flow conservation laws.

Johanna Marie Gegenfurtner, Moritz Grillo, Guido Montufar

Sydney Poster Session 4, Wed, Dec 9, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Function graph transformers universally approximate operators between function spaces

Function graph transformers lift functions to graph measures to universally approximate nonlinear operators between function spaces via standard attention and MLPs.

Takashi Furuya, S D Mis, Ivan Dokmanić, Maarten V. de Hoop and 1 more

Atlanta Poster Session 5, Fri, Dec 11, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Training with (Swap) Regret Loss in a Single-Layer Self-Attention Model: A Case Study on the Probability Simplex

Single-layer self-attention trained with regret and swap-regret loss learns smoothed fictitious play and Blum-Mansour dynamics yielding coarse and correlated equilibria without supervised traces.

Chanwoo Park, Asuman Ozdaglar

Atlanta Poster Session 5, Fri, Dec 11, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Estimating the expected output of wide random MLPs more efficiently than sampling

Approximate layer-wise activation distributions via cumulants and Hermite expansions to estimate wide MLP expected outputs without sampling, reducing FLOPs versus Monte Carlo and improving rare-event estimates.

Wilson Wu, Victor Lecomte, Michael Winer, George Robinson and 2 more

Atlanta Poster Session 3, Thu, Dec 10, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Length Generalization for Transformers via Compression

Refining C-RASP via compressed strings yields polynomial transformer length generalization bounds for tasks with compressed-string solutions.

Georg Zetzsche, Hongjian Jiang, Andy J Yang, Pascal Bergsträßer and 3 more

Paris Poster Session 5, Fri, Dec 11, 11:30 AM–1:30 PM, Paris Poster Hall · Published 2026

Ordinary Least Squares as an Attention Mechanism

Ordinary least squares predictions are rewritten as restricted attention outputs, framing OLS as similarity-based prediction via learned embedding and decoding operations mapped onto query-key-value structures.

Philippe Goulet Coulombe

Atlanta Poster Session 5, Fri, Dec 11, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Conservation Laws for Diffusion Models

Conservation laws express diffusion cross-entropy via local information-theoretic derivatives along noise paths, unifying discrete and continuous likelihoods and reducing training to marginal posterior learning.

Ziv Aharoni, Henry Pfister

Atlanta Poster Session 6, Fri, Dec 11, 4:30 PM–7:30 PM, Hall C1 · Published 2026

Feature Learning Dynamics in Infinite-Depth Neural Networks

For one-layer ResNets under depth-μP scaling, reused-weight forward-backward coupling vanishes at initialization but SGD induces surviving correlations suppressed by depth, yielding a rigorous infinite-depth Neural Feature Dynamics limit.

Zihan Yao, Ruoyu Wu, Tianxiang Gao

Atlanta Poster Session 6, Fri, Dec 11, 4:30 PM–7:30 PM, Hall C1 · Published 2026

Bounding Global and Local Compression Error of Signal Parameterizations

A framework predicts reconstruction error of compressive signal parameterizations via scaled differences between model predictions at different compression levels without ground truth. It yields non-asymptotic, signal-specific bounds that closely track global errors and local error heatmaps across i

Quang Luong Nhat Nguyen, Sara Fridovich-Keil

Atlanta Poster Session 1, Wed, Dec 9, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation

Concept modulation models unify conditional latent variable model identifiability and extrapolation via attribute potentials and algebraic criteria for unseen attributes.

Soheun Yi, Yizhou Lu, Chandler Squires, Pradeep Ravikumar

Atlanta Poster Session 4, Thu, Dec 10, 4:30 PM–7:30 PM, Hall C1 · Published 2026

A Statistical Theory of Gated Attention through the Lens of Hierarchical Mixture of Experts

Gated attention represents attention matrices as hierarchical mixtures of experts and achieves polynomial sample complexity versus exponential for multi-head self-attention.

Viet Nguyen, Thinh Cao, Tuan M Pham, Tan Dinh and 3 more

Atlanta Poster Session 4, Thu, Dec 10, 4:30 PM–7:30 PM, Hall C1 · Published 2026

Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning

Neural LoFi frames deep training as iterative spectral low-degree filtering, predicting layer-wise feature selection, concept emergence, and compositional depth via low-degree correlation dynamics.

Yatin Dandi, Matteo Vilucchio, Luca Arnaboldi, Hugo Tabanelli and 1 more

Paris Poster Session 2, Wed, Dec 9, 5:00 PM–7:00 PM, Paris Poster Hall · Published 2026

Learning Orthogonal Multi-Index Models Beyond Small Initialization: Incremental Learning, Competitive Dynamics and Symmetry

Under standard initialization, two-layer networks learn orthogonal multi-index targets incrementally via competitive neuron dynamics, with lower-order Hermite components recovered before higher-order directions.

Mo Zhou, Weihang Xu, Simon Du, Maryam Fazel

Atlanta Poster Session 1, Wed, Dec 9, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Stability and Generalization in Looped Transformers

A fixed-point framework proves looped transformers need recall plus outer normalization for stable, input-dependent extrapolation, validated across chess, sudoku, and prefix-sums tasks.

Asher Labovich

Sydney Poster Session 3, Wed, Dec 9, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026

Generalization at the Edge of Stability

Stochastic optimizers at the edge of stability converge to low-dimensional fractal attractors, and a sharpness-dimension generalization bound reveals that chaotic training depends on the full Hessian spectrum.

Mario Tuci, Caner Korkmaz, Umut Simsekli, Tolga Birdal

Sydney Poster Session 5, Thu, Dec 10, 10:00 AM–1:00 PM, Hall 1-4 · Published 2026 · Code ★ 10

Uniform-in-Time Weak Propagation of Chaos in Shallow Neural Networks

Shallow neural networks trained via gradient descent exhibit uniform-in-time weak propagation of chaos, yielding poly(d/ε) neuron and sample complexity when mean-field loss decays faster than t^{-2}.

Margalit Glasgow, Joan Bruna

Atlanta Poster Session 5, Fri, Dec 11, 10:00 AM–1:00 PM, Hall C1 · Published 2026

Understanding Sample Efficiency in Predictive Coding

Predictive coding improves sample efficiency over backpropagation via higher target alignment, especially in deep, narrow, and pre-trained networks.

Gaspard Oliviers, Elene Lominadze, Rafal Bogacz

Sydney Poster Session 6, Thu, Dec 10, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

The Spectral Amplitude Principle for Dynamics of Quantum Neural Networks

Quantum neural networks follow spectral amplitude priority rather than frequency bias, enabling efficient high-frequency learning via large-amplitude components and outperforming classical networks.

Yihang Xu, Dan-Bo Zhang, Junchi Yan

Sydney Poster Session 2, Tue, Dec 8, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Isotropic Activation Functions Enable Deindividuated Neurons and Adaptive Topologies

Isotropic activation functions enable function-preserving diagonalization of network layers for adaptive topology restructuring and asymptotic 50% parameter sparsification.

George Bird

Sydney Poster Session 2, Tue, Dec 8, 5:00 PM–8:00 PM, Hall 1-4 · Published 2026

Learning Orthonormal Bases for Function Spaces

Neural networks parameterize orthonormal function-space bases via ODEs on orthogonal Lie manifolds driven by skew-adjoint generators, with rank-2 generators universally approximating any target basis.

Hamidreza Kamkari, Mohammad S Nabizadeh, Justin Solomon

Atlanta Poster Session 5, Fri, Dec 11, 10:00 AM–1:00 PM, Hall C1 · Published 2026