Simplification

Parameterised graph theory studies how the complexity of graph-theoretic problems depends on structural parameters of the input graph. This perspective has proved useful in analysing tensor-network simulation (Markov and Shi, 2008). Its implications for tensor-network representations and tomography are less well understood. In particular, which graph parameters determine whether a tensor-network state (TNS) admits a tractable matrix product state (MPS) or tree tensor network (TTN) representation, and which control the complexity of learning the state? We address these questions using parameterised graph theory. First, we show that cutwidth and tree-cutwidth bound the bond dimension overhead required to represent a TNS as an MPS or TTN. In the TTN case, tree-cutwidth also bounds the local dimension of the grouped subsystems. The proofs are based on entanglement rerouting, a tensor-network analogue of rerouting information in a classical network. Second, we derive graph-dependent upper bounds on the sample and computational complexity of realisable TNS tomography, with exponents that depend on cutwidth, tree-cutwidth, and a new graph parameter, learning complexity, which we bound in terms of degree and treewidth. We obtain these results by extending the disentangling MPS learner of (Cramer et al., 2010), as analysed further in (Bakshi et al., 2025; Lin et al., 2025), to TTNs and to tensor networks on arbitrary known graphs. Finally, we extend the framework beyond the realisable setting. For an arbitrary input state, our agnostic learner outputs a pure state whose fidelity is within additive error $ε$ of the optimum over tensor-network states on the given graph with a given bond dimension, with explicit graph-dependent bounds on sample and computational complexity.

In regulated domains such as finance, a model that cannot be explained cannot be deployed, yet many interpretable classifiers defeat their own purpose by producing formulas with dozens of features that no regulator could read. We take the reverse direction. Starting from an interpretable classifier expressed as a single equation over the input features, we progressively simplify it into more readable forms, including a pruned monomial, a directional if--then rule, and the integer scorecards and tallies that finance already deploys. Because the equation is itself the predictive model rather than a post-hoc explanation we can directly quantify what is lost under each simplification. Across four financial datasets, we find that pruning is nearly free and that fidelity can erode faster than predictive performance, allowing simpler rules to remain effective classifiers without faithfully reproducing the original model. A human assessment shows that simplification improves perceived readability, while preferences for different representations vary by professional background. Beyond measuring these losses empirically, we show that some can be anticipated from the original model: we derive a bound on the change caused by pruning and predict how faithfully a rule retaining only the direction of each feature's effect preserves the original ranking.

Document-level text simplification requires large language models (LLMs) to rewrite complex documents while preserving meaning, readability, and discourse coherence. Although prompt-based LLMs have shown promising performance, they often produce inconsistent simplifications because textual instructions alone provide limited guidance for complex document-level transformations. We investigate whether retrieved document-simplification examples can improve document-level generation by augmenting prompts with examples selected from a parallel simplification corpus. This example-guided prompting approach enables LLMs to exploit relevant simplification patterns without task-specific fine-tuning. Experiments on the OneStopEnglish corpus using multiple state-of-the-art LLMs show that incorporating retrieved examples consistently improves simplification quality over prompt-only generation and achieves competitive or superior performance compared with representative supervised (T5) and planning-based (PlanSimp) document simplification systems. Furthermore, we find that the benefits of example-guided prompting vary across LLMs, suggesting that effective use of retrieved examples depends on a model's ability to integrate contextual information during generation.

We study the topology of learned representations in predictive coding networks (PCNs), a neuro-inspired bidirectional architecture, using a quantitative layer-wise persistent homology analysis. We train well-performing PCNs on a synthetic classification dataset ($\geq 99.9\%$ test accuracy) and on MNIST ($\geq 95\%$ test accuracy), and measure how topological features change across layers for different architectures and activation functions. We find that smaller PCNs collapse connected components across layers earlier than larger models (Spearman $\unicode{x1D70C} \in [0.72, 0.79]$ across activations), with model size measured as the sum of hidden-layer widths. We also observe a strong negative correlation ($\unicode{x1D70C} = -0.58$) between the depth at which simplification occurs and reconstruction error; i.e., architectures that simplify later reconstruct better. Finally, a seed-level bootstrap comparison across architectures and activations shows that PCNs consistently collapse connected components later than matched MLPs, with an average difference of $3.6$ layers. These results suggest that persistent homology offers a useful quantitative lens on the compression--reconstruction tradeoff in PCNs, and that both model capacity and the recurrent, bidirectional dynamics of predictive coding inference shape when this tradeoff is resolved across layers.

Interdisciplinary research is accelerating, yet scientific papers remain difficult to understand outside their home fields. We study large language model (LLM)-based simplification of scientific texts and present a human-in-the-loop workflow that transforms expert summaries into more accessible versions for non-specialists. Using SciSummNet as the source corpus, we first generate baseline simplifications with GPT-4o-mini. In Phase 1, readers from STEM fields outside computer science identify difficult sentences and phrases and compare the original and GPT-simplified summaries in terms of comprehensibility, naturalness, and simplicity. In Phase 2, computer science experts use this feedback to create expert-edited reference simplifications. We release the resulting corpus together with human judgments and automatic evaluation results. The Phase 1 judgments show a clear preference for the GPT-generated summaries in terms of comprehensibility and simplicity, while qualitative analysis of the Phase 2 edits highlights the importance of preserving domain-specific terminology and the strength of scientific claims. The resulting resource supports the training and benchmarking of simplification systems for cross-disciplinary scientific communication.

Symbolic regression (SR) aims to discover underlying mathematical expressions from data while preserving interpretability. Most existing learning-based SR methods primarily optimize expressions from observations without explicitly exploiting their structural mathematical properties. AI Feynman introduced a complementary paradigm that leverages such properties to recursively decompose complex expressions, but its decomposition criteria cover only restricted structural forms and its treatment of nested composition can require brute-force search over candidate sub-expressions. Building on this paradigm, we propose Deep Divide-and-Reduce in Symbolic Regression (DDRSR), a mathematically grounded framework that systematically generalizes expression decomposition and variable reduction. DDRSR extends translational symmetry to coefficient- and exponent-interfered forms, enables variable separation under overlapping variables and additive constant offsets, and generalizes the identification of nested compositional structures. We further characterize an intrinsic non-identifiability limitation of decomposition when no effective variable separation is induced. Experiments across multiple symbolic regression algorithms and benchmark datasets show that DDRSR identifies a broader range of decomposable structures than AI Feynman and overall improves downstream regression accuracy and exact-expression recovery.

We introduce the first dataset that jointly covers both lexical complexity prediction (LCP) annotations and lexical simplification (LS) for Romanian, along with a comparison of lexical simplification approaches. We propose a methodology for ordering simplification suggestions using a pairwise ranking approximation method, arranging candidates from simple to complex based on a separate set of human judgments. In addition, we provide human lexical complexity annotations for 3,921 word samples in context. Finally, we explore several novel pipelines for complexity prediction and simplification and present the first text simplification system for Romanian.

Despite recent advances in general-purpose robotic manipulation, real-world multi-object clutter remains challenging to handle for today's prevalent approaches. The problem scales in complexity due to more objects and collisions, more unpredictable contact physics, distractors, and task ambiguity. Bridging this gap to real-world deployment requires effective scene abstractions; yet today, producing such abstractions requires extensive task-specific manual engineering, which does not scale. These abstractions are costly to generate and difficult to adjust or fine-tune. We instead propose a plug-and-play fix to automatically generate scene-specific, task-specific, adaptively updating abstractions on top of existing planning and control stacks. LLM-guided Environment Simplification (LENS) produces a de-cluttered abstracted scene representation by merging (e.g., stacked objects) or pruning (e.g., distant objects) scene entities in a closed loop in response to task progress. These dynamic, task-relevant abstractions are versatile and easy to use. In our experiments, we show that LENS improves classical planning, model-based control, and a vision-language-action model, across a diverse set of highly cluttered manipulation scenes. Project website: https://lens-2026.github.io/.

Vision-Language Pre-training Models (VLPMs) are known to be vulnerable to adversarial attacks. Recent transferable attacks on VLPMs have followed a common pipeline with complicated loss functions or multi-stage text/image attacks. However, in this paper, we demonstrate that such a sophisticated attack pipeline can be simpler yet more successful. Specifically, we identify three previously overlooked issues caused by inappropriate cross-modal interactions and excessive operations. To address them, we propose the Simple Vision-Language Attack (SimVLA) pipeline, which observably improves transferability and efficiency. Experiments on four datasets and three downstream tasks validate the superiority of our pipeline. For instance, on Flickr30k text-image retrieval dataset, our SimVLA outperforms the SOTA baseline in R@1 transferability by 8.01%-14.71%, while consuming only about 35.73% of the time and 46.26% of the max VRAM. Overall, the superiority of our SimVLA highlights the importance of leveraging domain knowledge (e.g., our proposed cross-modal word identification), while blindly pursuing intricate operations (e.g, complex loss functions and redundant multi-stage designs) may even be harmful. We hope our SimVLA can serve as a simple yet effective backbone for future extensions. Code is available at https://github.com/RYC-98/SimVLA.

Medieval document transcribers have very different practices; on top of that, heterogeneous digitization policies have resulted in corpora where the character-set must be viewed as fluid. In this paper we address the problem of changing between character-sets in a flexible manner. We focus on one-to-one character mappings and train characterlevel one-to-one RNNs to undo them with self-supervision; recovering half the CER even with 20 text lines. We analyse the use of these one-to-one networks for HTR post-correction and we see that they obtain significant improvements while totally ignoring ins-dels. We then use the exact same networks with character-level alignment groundtruth compiled from parallel corpora in a training and inference mode we call Banded RNNs. We use such networks to successfully expand abbreviations in medieval charter transcriptions. Finally we introduce an elaborate heuristic which takes the characters of two arbitrary character-sets and defines a metric encapsulating what we consider to be semantic similarity of characters. We call the construction of such mappings letter lemmatization and present a rich Python library that efficiently performs all presented methods.

One-step image editing is important for making text-guided editing fast, practical, and easy to deploy, but its underlying mechanism is still not fully understood. We revisit ChordEdit through reproduction, ablation, and simplification. Our analysis shows that a) the chord window $δ$ largely acts as an effective timestep shift from $t$ to $t - δ$; b) chord transport acts on high-noise images and mainly performs low-frequency semantic editing; and c) proximal alignment acts on low-noise images and complements it by adding high-frequency target details. In this view, ChordEdit naturally decomposes editing into a coarse low-frequency transport stage and a fine high-frequency alignment stage. These findings suggest a path toward prompt-conditioned dynamic timestep selection for adaptive image editing. All code and results can be found at \href{https://github.com/Harvard-AI-and-Robotics-Lab/ChordEdit-Reproduction}{link}.

Injecting noise into the optimization process is a well-established technique for improving the training and generalization of deep neural networks. Yet, despite the breadth of existing approaches, it remains unclear which design choices truly matter in practice. In this work, we investigate parameter noise injection for stochastic gradient descent, focusing on two key questions: how to efficiently pair each training example with its own perturbation in mini-batch training, and whether sophisticated noise parameterizations or multi-sample gradient averaging yield meaningful gains over simpler alternatives. To address the first question, we leverage a distributional identity for linear layers that allows per-example noise injection without breaking batched computation. To address the second, we systematically compare several diagonal Gaussian parameterizations against an isotropic baseline across varying noise levels on CIFAR100. Our results consistently show that simple, lightweight strategies, isotropic noise with a single perturbed forward pass per update step, recover most of the benefit of more complex schemes. These findings suggest that simplicity suffices for parameter noise injection, and that practitioners need not resort to elaborate perturbation designs to reap the optimization and generalization benefits of noisy SGD.

What would it mean to have a scientific understanding of AI? Models are not static objects: they are snapshots of time-evolving processes shaped by data, objectives, architectures, and optimization dynamics. Yet much of AI research treats models as fixed artifacts, analyzing behaviors after training rather than asking why they emerge. This position paper argues that a science of AI must move beyond post-hoc fixes and study the training dynamics that produce model behavior. Such a science should support progressively stronger forms of understanding: predicting outcomes from early training signals, intervening when trajectories go wrong, and ultimately designing training procedures that more reliably produce desired properties. Scaling laws have made prediction routine for loss; the challenge is extending this success to capabilities, biases, robustness, and safety-relevant behaviors. We articulate requirements for such theories grounded in the history and philosophy of science, examine progress in mechanistic interpretability, fairness, memorization, and simplicity bias, and identify concrete open problems.

The deep neural network is a widely used framework in machine learning that has been widely applied in various fields. However, deep neural networks often involve a large number of parameters and inputs, many of which may be irrelevant to the goal or true output. These parameters and input variables not only increase computational complexity, but also contribute to additional computational cost. One solution to this problem is knockoff methods, which have proven successful in controlling false discovery rates in high-dimensional regression. Building on the knockoff methods and using the regularised neural network, this paper proposes three variable screening methods under the condition of controlling false discovery rates: one layer filter, multiple layers filter, and variable weight aggregation filter. In comparison with existing algorithms, we find that our algorithms show satisfactory performance.

Deep networks often exhibit a preference for "simple" solutions, and such a simplicity bias is widely believed to play a key role in generalization. Yet a broadly applicable, quantitative measure of simplicity remains elusive. We introduce polynomial representations as a distribution-aware, low-dimensional surrogate for neural functions: we approximate a network's predictive behavior along data-dependent interpolation paths using orthogonal polynomial bases, yielding a compact functional representation. We show that the effective degree of this representation serves as a practical simplicity metric that is predictive of generalization across tasks and architectures, and consistently outperforms existing generalization proxies such as sharpness. Finally, polynomial representations naturally yield a differentiable simplicity regularizer, which consistently improves generalization in image and text classification, fine-tuning contrastive vision-language models, and reinforcement learning.

Neural networks trained with gradient-based methods exhibit a strong simplicity bias: they learn simpler statistical features of their data before moving to more complex features. Previous analyses of this phenomenon have largely focused on settings with (quasi-)isotropic inputs. In this work, we study the simplicity bias from a Fourier perspective, which allows us to include two key features of natural images in the analysis: approximate translation-invariance and power-law spectra. We first show experimentally that simple neural networks trained on image classification tasks first rely on amplitude information -- related to pair-wise correlations between pixels -- before exploiting phase information, which encodes edges and higher-order correlations. In view of this, we introduce a synthetic data model for translation-invariant inputs that allows precise control over amplitudes and phases while remaining tractable. We rigorously establish that for isotropic and high-dimensional inputs, classification based on phase information alone is a genuinely hard task: online stochastic gradient descent (SGD) cannot distinguish the structured inputs from noise within $n \ll N^3$ steps, but needs at least $n \gg N^3 \log^2{N}$ steps. In contrast, we show both experimentally and theoretically that power-law spectra can dramatically accelerate the speed of learning phase information, even if the spectra do not help with classification. Simulations with two-layer networks trained on textures and with deep convolutional networks on ImageNet and CIFAR100 confirm this non-trivial interaction between amplitudes and phases, providing mechanistic insights into how deep neural networks can learn natural image distributions efficiently.

Self-attention serves as the core foundation of large-scale transformer pretraining, but its quadratic token interaction cost makes inference expensive. Replacing attention with simpler sequential modules is appealing, yet naive substitution is often lossy, especially at larger scales. This paper revisits attention replacement through the lens of sparsity. Based on the observation of diverse sparsity patterns across transformer layers, we posit that pretrained transformers decompose the complex token dependency across tokens into various sequence-to-sequence mappings of diverse complexities, where some layer functionalities can be approximated and replaced with much simpler sequential modules without loss. We evaluate this premise using a plug-and-play layer-wise distillation framework to approximate and replace attention functionalities in pretrained vision transformer models. Controlled group-wise replacements under a fixed training budget reveal a clear pattern: substituting layers with sparser attention incurs substantially smaller accuracy drops than replacing denser ones. We further impose explicit attention sparsity on the pretrained ViT via AViT-style token retention and perform sparsity-guided distillation for sequential replacing models, where we see increasing teacher sparsity consistently reduces the student-teacher gap. The proposed method achieves efficient attention replacement for reduced parameter size and latency through the guidance of attention sparsity.

Existing image simplification techniques often rely on Non-Photorealistic Rendering (NPR), transforming photographs into stylized sketches, cartoons, or paintings. While effective at reducing visual complexity, such approaches typically sacrifice photographic realism. In this work, we explore a complementary direction: simplifying images while preserving their photorealistic appearance. We introduce progressive semantic image simplification, a framework that iteratively reduces scene complexity by removing and inpainting elements in a controlled manner. At each step, the resulting image remains a plausible natural photograph. Our method combines semantic understanding with generative editing, leveraging Vision-Language Models (VLMs) to identify and prioritize elements for removal, and a learned verifier to ensure photorealism and coherence throughout the process. This is implemented via an iterative Select-Remove-Verify pipeline that produces high-quality simplification trajectories. To improve efficiency, we further distill this process into an image-to-video generation model that directly predicts coherent simplification sequences from a single input image. Beyond generating cleaner and more focused compositions, our approach enables applications such as content-aware decluttering, semantic layer decomposition, and interactive editing. More broadly, our work suggests that simplification through structured content removal can serve as a practical mechanism for guiding visual interpretation within the photorealistic domain, complementing traditional abstraction methods.

Text simplification plays a crucial role in improving the accessibility and comprehensibility of written information for diverse audiences, including language learners and readers with limited literacy. Despite its importance, large-scale, high-quality datasets for training and evaluating text simplification models remain scarce for languages other than English. This paper reports an experimental study on the collection and processing of crowd-sourced simplification data from comparable corpora to construct a corpus suitable for both training and testing text simplification systems across multiple languages (Catalan, English, French, Italian and Spanish). We report mechanisms for sentence-level alignment from document-level data. The resulting dataset of the aligned sentence pairs is publicly available.

Energy-based learning is a powerful framework for generative modelling, but its training is inherently non-convex, leading potentially to sensitivity to initialisation, poor local optima, and unstable gradient dynamics. We present a dynamical analysis of energy-based learning through the lens of the effective model, which can be interpreted as either a generalised Ising model with higher-order interactions or the Fourier expansion of the energy. Under sufficient expressivity, we show that the gradient flow induced by learning strictly positive distributions over binary variables admits two types of fixed points: data-consistent points, which exactly reproduce the target distribution, and spurious points, which satisfy stationarity without matching the target distribution. Around data-consistent points, we show that perturbations are either stable or neutral, with neutral directions leaving the effective model invariant. Finally, we show that gradient dynamics induce a hierarchy in which lower-order interactions are learned before higher-order ones. This provides a mechanistic explanation for the distributional simplicity bias and clarifies why fixed points that are not data-consistent at low orders are not observed in practice.

Out-of-distribution (OOD) detection is crucial for ensuring the reliability of deep learning models. Existing methods mostly focus on regular entangled representations to discriminate in-distribution (ID) and OOD data, neglecting the rich contextual information within images. This issue is particularly challenging for detecting near-OOD, as models with simplicity bias struggle to learn discriminative features in disentangled representations. The human visual system can use the co-occurrence of objects in the natural environment to facilitate scene understanding. Inspired by this, we propose an Object-Centric OOD detection framework that learns to capture Object CO-occurrence (OCO) patterns within images. The proposed method introduces a new OOD detection paradigm that understands object co-occurrence within an image by predicting disentangled representations for the test sample, then adaptively divides patterns into three scenarios based on object co-occurrence patterns observed in ID training data, and finally performs OOD detection in a divide-and-conquer manner. By doing so, OCO can distinguish near-OOD by considering the semantic contextual relationships present in their images, avoiding the tendency to focus solely on simple, easily learnable regions. We evaluate OCO through experiments across challenging and full-spectrum OOD settings, demonstrating competitive results and confirming its ability to address both semantic and covariate shifts. Code is released at https://github.com/Michael-McQueen/OCO.

When you read a paper about a new Vision-Language Model today, it can be easy to forget how strange this idea would have sounded not so long ago. Teaching machines to see was already hard. Teaching them to read and generate language was already hard. Asking them to do both at once - and then to reason, answer questions, follow instructions, and sometimes even surprise us - still carries a quiet trace of science fiction, even as it becomes routine. This book was born from a simple feeling: it is too easy to get lost. The field moves quickly, new model names appear constantly, and the gap between "I know the buzzwords" and "I actually understand how this works" can feel uncomfortably wide. I have felt that gap many times. If you are holding this book, you probably have too. My goal is not to provide an exhaustive catalog of every dataset, benchmark, and new model variant. Instead, I want to offer something more modest - and, I hope, more durable: a clear mental map of Vision-Language Models. Enough structure that you can read new papers with confidence; enough intuition that you can design your own systems without feeling as if you are assembling LEGO bricks blindly.

We evaluate an initial coding-agent system for ARC-AGI-3 in which the agent maintains an executable Python world model, verifies it against previous observations, refactors it toward simpler abstractions as a practical proxy for an MDL-like simplicity bias, and plans through the model before acting. The system is intentionally direct: it uses a scripted controller, predefined world-model interfaces, verifier programs, and a plan executor, but no hand-coded game-specific logic. The agent-facing prompts, workspace, and controller contain no game-specific code, game-specific prompts, hand-coded heuristics, hidden solutions, or other game-specific information; the same agent and prompts are used across games. Because the coding agent has broad system access, we audit unintended information channels, describe earlier vulnerable harnesses, and explain how the current harness closes observed leakage channels while reducing benchmark-specific information exposure. We report results on the 25 public ARC-AGI-3 games. Each playthrough starts from a fresh agent instance and clean workspace, with no access to files or conversation state from earlier playthroughs. With GPT-5.5 high reasoning effort, the agent fully solved 15 games and achieved a mean per-game RHAE of 58.12%. With GPT-5.4 high reasoning effort, it fully solved 8 games and achieved a mean per-game RHAE of 41.29%. Performance on the private validation set, which is not yet available to us, remains to be tested. Overall, the results provide preliminary evidence that verifier-driven executable world models are a promising approach for ARC-AGI-3 agents. Full run artifacts are released with the code at https://github.com/astroseger/arc-3-agents-baseline1.

Tree ensembles provide strong classification performance but usually behave as black-box models. Post-hoc interpretability techniques such as RuleCOSI+ extract a small ruleset that approximates the ensemble, but this simplification can leave the probabilities attached to the extracted rules unreliable. In particular, RuleCOSI+ assigns empirical class probabilities to the extracted rules and repeatedly uses those rule statistics during its greedy combination and simplification procedure. We present RCProb, a probabilistic extension that uses smoothed atomic class-conditional evidence for the expensive search stages and a support-adaptive mixture with an ensemble-informed m-estimate for the final rule probabilities. The method is evaluated on 18 binary and 5 multiclass datasets using random forest (RF) and gradient boosting machine (GBM) ensembles. Relative to RuleCOSI+, the median paired log-loss reduction is 71.9% for RF and 62.5% for GBM, with both differences remaining significant after Holm correction. The number of rules decreases by 38.7% for RF and 38.5% for GBM, while the primary tests do not detect a macro-F1 difference. Confidence-ECE also decreases for both ensembles, with statistical support for RF after correction. A separate controlled experiment with dedicated calibration data shows that native RCProb probabilities are competitive with RuleCOSI+ followed by temperature scaling, although additional post-hoc calibration can still improve RCProb. The results show that probability estimation is an important part of rule extraction and not only a post-processing step.

Operational phase unwrapping is the primary computational bottleneck in InSAR-based volcanic and seismic monitoring. We challenge the industry trend of adopting high-complexity computer vision architectures, such as attention mechanisms, without validating their suitability for physics-constrained geophysical regression. We present the first large-scale architectural ablation study on a global LiCSAR benchmark (20 frames, 39,724 patches, 651M pixels). Our results reveal a significant "complexity penalty": a vanilla U-Net (7.76M parameters) achieves $R^2=0.834$ and RMSE $= 1.01$ cm, outperforming 11.37M-parameter attention-based models by 34% in $R^2$ and 51% in RMSE. Power Spectral Density (PSD) analysis provides the physical justification: while attention excels at capturing sharp semantic edges in natural images, it injects unphysical high-frequency artifacts ($>0.3$ cycles/pixel) into geophysical fields, violating the fundamental smoothness constraints of elastic surface deformation. With a 2.92ms inference latency (a $2.5\times$ speedup), the vanilla U-Net is the only candidate to comfortably meet the sub-100ms requirement for operational early-warning systems. This work bridges the "publication-to-practice" gap by proving that convolutional locality outperforms modern complexity for smooth-field regression, advocating for physics-informed simplicity in ML4RS. Code available at https://github.com/prabhjotschugh/When-Less-is-More-InSAR-Phase-Unwrapping

Cross-Lingual Text Simplification (CLTS) aims to make content more accessible across languages by simultaneously addressing both linguistic complexity and translation. This study investigates the effectiveness of different prompting strategies for CLTS between English and French using large language models (LLMs). We examine five distinct prompting systems: a direct prompt instructing the LLM to perform both translation and simplification simultaneously, two Composition approaches that either translate-then-simplify or simplify-then-translate within a single prompt, and two decomposition approaches that perform the same operations in separate, consecutive prompts. These systems are evaluated across a diverse set of five corpora of different genres (Wikipedia and medical texts) using seven state-of-the-art LLMs. Output quality is assessed through a multi-faceted evaluation framework comprising automatic metrics, comprehensive linguistic feature analysis, and human evaluation of simplicity and meaning preservation. Our findings reveal that while direct prompting consistently achieves the highest BLEU scores, indicating meaning fidelity, Translate-then-Simplify approaches demonstrate the highest simplicity, as measured by the linguistic features.

Understanding social polarization requires integrating insights from psychology, sociology, and complex systems science. Agent-based modeling provides a natural framework to combine perspectives from different fields and explore how individual cognition shapes collective outcomes. This study introduces a novel agent-based model that integrates two cognitive and social mechanisms: the desire to be unique within a group (optimal distinctiveness theory) and the tendency to simplify complex information (cognitive compression). In the model, virtual agents interact in pairs and decide whether to adopt each other's opinions by balancing two opposing drives: maximizing opinion diversity within their local social group while simplifying the overall opinion landscape, with both evaluated using Shannon entropy. We show that the combination of these mechanisms can reproduce real-world patterns, such as the emergence of distinct heterogeneous opinion clusters. Moreover, unlike many existing models where opinions become fixed once opinion groups form, individuals in our model continue to adjust their opinions after clusters emerge, leading to ongoing variation within and between opinion groups. Computational experiments reveal that polarization emerges when local group sizes are moderate (consistent with Dunbar's number), while smaller groups cause fragmentation and larger ones hinder distinct cluster formation. Higher cognitive compression increases unpredictability, while lower compression produces more consistent group structures. These results demonstrate how simple psychological rules can generate complex, realistic social behavior and advance understanding of polarization in human societies.

The complexity of Vietnam's legal texts presents a significant barrier to public access to justice. While Large Language Models offer a promising solution for legal text simplification, evaluating their true capabilities requires a multifaceted approach that goes beyond surface-level metrics. This paper introduces a comprehensive dual-aspect evaluation framework to address this need. First, we establish a performance benchmark for four state-of-the-art large language models (GPT-4o, Claude 3 Opus, Gemini 1.5 Pro, and Grok-1) across three key dimensions: Accuracy, Readability, and Consistency. Second, to understand the "why" behind these performance scores, we conduct a large-scale error analysis on a curated dataset of 60 complex Vietnamese legal articles, using a novel, expert-validated error typology. Our results reveal a crucial trade-off: models like Grok-1 excel in Readability and Consistency but compromise on fine-grained legal Accuracy, while models like Claude 3 Opus achieve high Accuracy scores that mask a significant number of subtle but critical reasoning errors. The error analysis pinpoints \textit{Incorrect Example} and \textit{Misinterpretation} as the most prevalent failures, confirming that the primary challenge for current LLMs is not summarization but controlled, accurate legal reasoning. By integrating a quantitative benchmark with a qualitative deep dive, our work provides a holistic and actionable assessment of LLMs for legal applications.

3D Gaussian Splat (3DGS) enables high-fidelity, real-time novel view synthesis by representing scenes with large sets of anisotropic primitives, but often requires millions of Splats, incurring significant storage and transmission costs. Most existing compression methods rely on GPU-intensive post-training optimization with calibrated images, limiting practical deployment. We introduce \textbf{NanoGS}, a training-free and lightweight framework for Gaussian Splat simplification. Instead of relying on image-based rendering supervision, NanoGS formulates simplification as local pairwise merging over a sparse spatial graph. The method approximates a pair of Gaussians with a single primitive using mass preserved moment matching and evaluates merge quality through a principled merge cost between the original mixture and its approximation. By restricting merge candidates to local neighborhoods and selecting compatible pairs efficiently, NanoGS produces compact Gaussian representations while preserving scene structure and appearance. NanoGS operates directly on existing Gaussian Splat models, runs efficiently on CPU, and preserves the standard 3DGS parameterization, enabling seamless integration with existing rendering pipelines. Experiments demonstrate that NanoGS substantially reduces primitive count while maintaining high rendering fidelity, providing an efficient and practical solution for Gaussian Splat simplification. Our project website is available at \href{https://saliteta.github.io/NanoGS/}{https://saliteta.github.io/NanoGS/}.

While Adam has long been the ubiquitous default optimizer for deep neural networks, Muon has recently seen rapid adoption due to its superior training speed. Although much of the literature focuses on validating the benefits of Muon, our work investigates the potential downsides of the mechanism driving this speedup. On the theoretical front, we analyze the learning dynamics of simplified Muon on deep linear networks and linear attention. Our analysis reveals that Muon gains speed by avoiding saddle points, but does so at the expense of the simplicity bias characteristic of Gradient Descent (GD), where the complexity of the functional solution learned grows sequentially. Experiments demonstrate the consequences of losing the simplicity bias, showing that Muon struggles to uncover common underlying structure across tasks and may be prone to fitting spurious features. More broadly, this paper serves as a reminder that faster optimization is rarely a free lunch; improvements in optimization can come at the cost of changes in the inductive biases that shape generalization.

We propose a streamlined spectral algorithm for community detection in the two-community stochastic block model (SBM) under constant edge density assumptions. By reducing algorithmic complexity through the elimination of non-essential preprocessing steps, our method directly leverages the spectral properties of the adjacency matrix. We demonstrate that our algorithm exploits specific characteristics of the second eigenvector to achieve improved error bounds that approach information-theoretic limits, representing a significant improvement over existing methods. Theoretical analysis establishes that our error rates are tighter than previously reported bounds in the literature. Comprehensive experimental validation confirms our theoretical findings and demonstrates the practical effectiveness of the simplified approach. Our results suggest that algorithmic simplification, rather than increasing complexity, can lead to both computational efficiency and enhanced performance in spectral community detection.

Access control policies are reliability-critical configuration artifacts in cloud systems, yet administrators frequently struggle to verify that a policy permits exactly what they intend. This verification gap cannot be remedied by using LLMs to synthesize policies: we find that reasoning and non-reasoning LLMs fluently explain policy behavior but cannot reason about policy semantics with reliability-grade precision, even when the specification is the LLM's own explanation. We formulate this impasse as the Verifiable Synthesis Paradox: the verification gap persists regardless of how the policy was authored. To remedy this, we introduce PolicySummarizer, a neurosymbolic tool that pairs finite-state automata with an LLM-based simplification to generate precise human-readable characterizations of requests allowed by a policy. PolicySummarizer uses model counting to guarantee the fidelity of the generated characterization by rejecting characterizations that fall below a user-configured threshold in favor of the formally derived one. On 546 AWS, 100 Microsoft Azure, and 100 Google Cloud Platform policies, PolicySummarizer achieves a mean similarity score of 0.93 and a 2.7x improvement over an SMT-based baseline. In a user study, PolicySummarizer raised policy-change-review accuracy from 39% to 93% on the hardest sub-task while reducing self-reported mental demand. We release PolicySummarizer as an open-source tool.