Algorithmic Simplification of Neural Networks with Mosaic-of-Motifs

Large-scale deep learning models are well-suited for compression. Methods like pruning, quantization, and knowledge distillation have been used to achieve massive reductions in the number of model parameters, with marginal performance drops across a variety of architectures and tasks. This raises the central question: \emph{Why are deep neural networks suited for compression?} In this work, we take up the perspective of algorithmic complexity to explain this behavior. We hypothesize that the parameters of trained models have more structure and, hence, exhibit lower algorithmic complexity compared to the weights at (random) initialization. Furthermore, that model compression methods harness this reduced algorithmic complexity to compress models. Although an unconstrained parameterization of model weights, $\mathbf{w} \in \mathbb{R}^n$, can represent arbitrary weight assignments, the solutions found during training exhibit repeatability and structure, making them algorithmically simpler than a generic program. To this end, we formalize the Kolmogorov complexity of $\mathbf{w}$ by $\mathcal{K}(\mathbf{w})$. We introduce a constrained parameterization $\widehat{\mathbf{w}}$, that partitions parameters into blocks of size $s$, and restricts each block to be selected from a set of $k$ reusable motifs, specified by a reuse pattern (or mosaic). The resulting method, $\textit{Mosaic-of-Motifs}$ (MoMos), yields algorithmically simpler model parameterization compared to unconstrained models. Empirical evidence from multiple experiments shows that the algorithmic complexity of neural networks, measured using approximations to Kolmogorov complexity, can be reduced during training. This results in models that perform comparably with unconstrained models while being algorithmically simpler.

On Representation Redundancy in Large-Scale Instruction Tuning Data Selection

Data quality is a crucial factor in large language models training. While prior work has shown that models trained on smaller, high-quality datasets can outperform those trained on much larger but noisy or low-quality corpora, systematic methods for industrial-scale data selection in instruction tuning remain underexplored. In this work, we study instruction-tuning data selection through the lens of semantic representation similarity and identify a key limitation of state-of-the-art LLM encoders: they produce highly redundant semantic embeddings. To mitigate this redundancy, we propose Compressed Representation Data Selection (CRDS), a novel framework with two variants. CRDS-R applies Rademacher random projection followed by concatenation of transformer hidden-layer representations, while CRDS-W employs whitening-based dimensionality reduction to improve representational quality. Experimental results demonstrate that both variants substantially enhance data quality and consistently outperform state-of-the-art representation-based selection methods. Notably, CRDS-W achieves strong performance using only 3.5% of the data, surpassing the full-data baseline by an average of 0.71% across four datasets. Our code is available at https://github.com/tdano1/CRDS.

On the Sparsifiability of Correlation Clustering: Approximation Guarantees under Edge Sampling

Correlation Clustering (CC) is a fundamental unsupervised learning primitive whose strongest LP-based approximation guarantees require $Θ(n^3)$ triangle inequality constraints and are prohibitive at scale. We initiate the study of \emph{sparsification--approximation trade-offs} for CC, asking how much edge information is needed to retain LP-based guarantees. We establish a structural dichotomy between pseudometric and general weighted instances. On the positive side, we prove that the VC dimension of the clustering disagreement class is exactly $n{-}1$, yielding additive $\varepsilon$-coresets of optimal size $\tilde{O}(n/\varepsilon^2)$; that at most $\binom{n}{2}$ triangle inequalities are active at any LP vertex, enabling an exact cutting-plane solver; and that a sparsified variant of LP-PIVOT, which imputes missing LP marginals via triangle inequalities, achieves a robust $\frac{10}{3}$-approximation (up to an additive term controlled by an empirically computable imputation-quality statistic $\overlineΓ_w$) once $\tildeΘ(n^{3/2})$ edges are observed, a threshold we prove is sharp. On the negative side, we show via Yao's minimax principle that without pseudometric structure, any algorithm observing $o(n)$ uniformly random edges incurs an unbounded approximation ratio, demonstrating that the pseudometric condition governs not only tractability but also the robustness of CC to incomplete information.

Linear Regression with Unknown Truncation Beyond Gaussian Features

In truncated linear regression, samples $(x,y)$ are shown only when the outcome $y$ falls inside a certain survival set $S^\star$ and the goal is to estimate the unknown $d$-dimensional regressor $w^\star$. This problem has a long history of study in Statistics and Machine Learning going back to the works of (Galton, 1897; Tobin, 1958) and more recently in, e.g., (Daskalakis et al., 2019; 2021; Lee et al., 2023; 2024). Despite this long history, however, most prior works are limited to the special case where $S^\star$ is precisely known. The more practically relevant case, where $S^\star$ is unknown and must be learned from data, remains open: indeed, here the only available algorithms require strong assumptions on the distribution of the feature vectors (e.g., Gaussianity) and, even then, have a $d^{\mathrm{poly} (1/\varepsilon)}$ run time for achieving $\varepsilon$ accuracy. In this work, we give the first algorithm for truncated linear regression with unknown survival set that runs in $\mathrm{poly} (d/\varepsilon)$ time, by only requiring that the feature vectors are sub-Gaussian. Our algorithm relies on a novel subroutine for efficiently learning unions of a bounded number of intervals using access to positive examples (without any negative examples) under a certain smoothness condition. This learning guarantee adds to the line of works on positive-only PAC learning and may be of independent interest.

Insights on Muon from Simple Quadratics

Muon updates weight matrices along (approximate) polar factors of the gradients and has shown strong empirical performance in large-scale training. Existing attempts at explaining its performance largely focus on single-step comparisons (on quadratic proxies) and worst-case guarantees that treat the inexactness of the polar-factor as a nuisance ``to be argued away''. We show that already on simple strongly convex functions such as $L(W)=\frac12\|W\|_{\text{F}}^2$, these perspectives are insufficient, suggesting that understanding Muon requires going beyond local proxies and pessimistic worst-case bounds. Instead, our analysis exposes two observations that already affect behavior on simple quadratics and are not well captured by prevailing abstractions: (i) approximation error in the polar step can qualitatively alter discrete-time dynamics and improve reachability and finite-time performance -- an effect practitioners exploit to tune Muon, but that existing theory largely treats as a pure accuracy compromise; and (ii) structural properties of the objective affect finite-budget constants beyond the prevailing conditioning-based explanations. Thus, any general theory covering these cases must either incorporate these ingredients explicitly or explain why they are irrelevant in the regimes of interest.

Solving PDEs in One Shot via Fourier Features with Exact Analytical Derivatives

Recent random feature methods for solving partial differential equations (PDEs) reduce computational cost compared to physics-informed neural networks (PINNs) but still rely on iterative optimization or expensive derivative computation. We observe that sinusoidal random Fourier features possess a cyclic derivative structure: the derivative of any order of $\sin(\mathbf{W}\cdot\mathbf{x}+b)$ is a single sinusoid with a monomial prefactor, computable in $O(1)$ operations. Alternative activations such as $\tanh$, used in prior one-shot methods like PIELM, lack this property: their higher-order derivatives grow as $O(2^n)$ terms, requiring automatic differentiation for operator assembly. We propose FastLSQ, which combines frozen random Fourier features with analytical operator assembly to solve linear PDEs via a single least-squares call, and extend it to nonlinear PDEs via Newton--Raphson iteration where each linearized step is a FastLSQ solve. On a benchmark of 17 PDEs spanning 1 to 6 dimensions, FastLSQ achieves relative $L^2$ errors of $10^{-7}$ in 0.07\,s on linear problems, three orders of magnitude more accurate and significantly faster than state-of-the-art iterative PINN solvers, and $10^{-8}$ to $10^{-9}$ on nonlinear problems via Newton iteration in under 9s.

Statistical Learning Analysis of Physics-Informed Neural Networks

We study the training and performance of physics-informed learning for initial and boundary value problems (IBVP) with physics-informed neural networks (PINNs) from a statistical learning perspective. Specifically, we restrict ourselves to parameterizations with hard initial and boundary condition constraints and reformulate the problem of estimating PINN parameters as a statistical learning problem. From this perspective, the physics penalty on the IBVP residuals can be better understood not as a regularizing term bus as an infinite source of indirect data, and the learning process as fitting the PINN distribution of residuals $p(y \mid x, t, w) q(x, t) $ to the true data-generating distribution $δ(0) q(x, t)$ by minimizing the Kullback-Leibler divergence between the true and PINN distributions. Furthermore, this analysis show that physics-informed learning with PINNs is a singular learning problem, and we employ singular learning theory tools, namely the so-called Local Learning Coefficient (Lau et al., 2025) to analyze the estimates of PINN parameters obtained via stochastic optimization for a heat equation IBVP. Finally, we discuss implications of this analysis on the quantification of predictive uncertainty of PINNs and the extrapolation capacity of PINNs.

Geometry-Aware Decoding with Wasserstein-Regularized Truncation and Mass Penalties for Large Language Models

Large language models (LLMs) must balance diversity and creativity against logical coherence in open-ended generation. Existing truncation-based samplers are effective but largely heuristic, relying mainly on probability mass and entropy while ignoring semantic geometry of the token space. We present Top-W, a geometry-aware truncation rule that uses Wasserstein distance-defined over token-embedding geometry-to keep the cropped distribution close to the original, while explicitly balancing retained probability mass against the entropy of the kept set. Our theory yields a simple closed-form structure for the fixed-potential subset update: depending on the mass-entropy trade-off, the optimal crop either collapses to a single token or takes the form of a one-dimensional prefix that can be found efficiently with a linear scan. We implement Top-W using efficient geometry-based potentials (nearest-set or k-NN) and pair it with an alternating decoding routine that keeps the standard truncation-and-sampling interface unchanged. Extensive experiments on four benchmarks (GSM8K, GPQA, AlpacaEval, and MT-Bench) across three instruction-tuned models show that Top-W consistently outperforms prior state-of-the-art decoding approaches achieving up to 33.7% improvement. Moreover, we find that Top-W not only improves accuracy-focused performance, but also boosts creativity under judge-based open-ended evaluation.

ECG-IMN: Interpretable Mesomorphic Neural Networks for 12-Lead Electrocardiogram Interpretation

Deep learning has achieved expert-level performance in automated electrocardiogram (ECG) diagnosis, yet the "black-box" nature of these models hinders their clinical deployment. Trust in medical AI requires not just high accuracy but also transparency regarding the specific physiological features driving predictions. Existing explainability methods for ECGs typically rely on post-hoc approximations (e.g., Grad-CAM and SHAP), which can be unstable, computationally expensive, and unfaithful to the model's actual decision-making process. In this work, we propose the ECG-IMN, an Interpretable Mesomorphic Neural Network tailored for high-resolution 12-lead ECG classification. Unlike standard classifiers, the ECG-IMN functions as a hypernetwork: a deep convolutional backbone generates the parameters of a strictly linear model specific to each input sample. This architecture enforces intrinsic interpretability, as the decision logic is mathematically transparent and the generated weights (W) serve as exact, high-resolution feature attribution maps. We introduce a transition decoder that effectively maps latent features to sample-wise weights, enabling precise localization of pathological evidence (e.g., ST-elevation, T-wave inversion) in both time and lead dimensions. We evaluate our approach on the PTB-XL dataset for classification tasks, demonstrating that the ECG-IMN achieves competitive predictive performance (AUROC comparable to black-box baselines) while providing faithful, instance-specific explanations. By explicitly decoupling parameter generation from prediction execution, our framework bridges the gap between deep learning capability and clinical trustworthiness, offering a principled path toward "white-box" cardiac diagnostics.

How well are open sourced AI-generated image detection models out-of-the-box: A comprehensive benchmark study

As AI-generated images proliferate across digital platforms, reliable detection methods have become critical for combating misinformation and maintaining content authenticity. While numerous deepfake detection methods have been proposed, existing benchmarks predominantly evaluate fine-tuned models, leaving a critical gap in understanding out-of-the-box performance -- the most common deployment scenario for practitioners. We present the first comprehensive zero-shot evaluation of 16 state-of-the-art detection methods, comprising 23 pretrained detector variants (due to multiple released versions of certain detectors), across 12 diverse datasets, comprising 2.6~million image samples spanning 291 unique generators including modern diffusion models. Our systematic analysis reveals striking findings: (1)~no universal winner exists, with detector rankings exhibiting substantial instability (Spearman~$ρ$: 0.01 -- 0.87 across dataset pairs); (2)~a 37~percentage-point performance gap separates the best detector (75.0\% mean accuracy) from the worst (37.5\%); (3)~training data alignment critically impacts generalization, causing up to 20--60\% performance variance within architecturally identical detector families; (4)~modern commercial generators (Flux~Dev, Firefly~v4, Midjourney~v7) defeat most detectors, achieving only 18--30\% average accuracy; and (5)~we identify three systematic failure patterns affecting cross-dataset generalization. Statistical analysis confirms significant performance differences between detectors (Friedman test: $χ^2$=121.01, $p<10^{-16}$, Kendall~$W$=0.524). Our findings challenge the ``one-size-fits-all'' detector paradigm and provide actionable deployment guidelines, demonstrating that practitioners must carefully select detectors based on their specific threat landscape rather than relying on published benchmark performance.