This paper investigates low-rank structure in the gradients of the training loss for two-layer neural networks while relaxing the usual isotropy assumptions on the training data and parameters. We consider a spiked data model in which the bulk can be anisotropic and ill-conditioned, we do not require independent data and weight matrices and we also analyze both the mean-field and neural-tangent-kernel scalings. We show that the gradient with respect to the input weights is approximately low rank and is dominated by two rank-one terms: one aligned with the bulk data-residue, and another aligned with the rank one spike in the input data. We characterize how properties of the training data, the scaling regime and the activation function govern the balance between these two components. Additionally, we also demonstrate that standard regularizers, such as weight decay, input noise and Jacobian penalties, also selectively modulate these components. Experiments on synthetic and real data corroborate our theoretical predictions.

Neural network architectures have a large impact in machine learning. However, in the specific case of reinforcement learning, network architectures have remained notably simple, as changes often lead to small gains in performance. This work introduces a novel encoder architecture for pixel-based model-free reinforcement learning. The Hadamax (\textbf{Hada}mard \textbf{max}-pooling) encoder achieves state-of-the-art performance by max-pooling Hadamard products between GELU-activated parallel hidden layers. Based on the recent PQN algorithm, the Hadamax encoder achieves state-of-the-art model-free performance in the Atari-57 benchmark. Specifically, without applying any algorithmic hyperparameter modifications, Hadamax-PQN achieves an 80\% performance gain over vanilla PQN and significantly surpasses Rainbow-DQN. For reproducibility, the full code is available on GitHub.

We resolve a 30-year-old open problem concerning the power of unlabeled data in online learning by tightly quantifying the gap between transductive and standard online learning. We prove that for every concept class $\mathcal{H}$ with Littlestone dimension $d$, the transductive mistake bound is at least $\Omega(\sqrt{d})$. This establishes an exponential improvement over previous lower bounds of $\Omega(\log \log d)$, $\Omega(\sqrt{\log d})$, and $\Omega(\log d)$, respectively due to Ben-David, Kushilevitz, and Mansour (1995, 1997) and Hanneke, Moran, and Shafer (2023). We also show that our bound is tight: for every $d$, there exists a class of Littlestone dimension $d$ with transductive mistake bound $O(\sqrt{d})$. Our upper bound also improves the previous best known upper bound of $(2/3) \cdot d$ from Ben-David et al. (1997). These results demonstrate a quadratic gap between transductive and standard online learning, thereby highlighting the benefit of advanced access to the unlabeled instance sequence. This stands in stark contrast to the PAC setting, where transductive and standard learning exhibit similar sample complexities.

Standard Retrieval-Augmented Generation (RAG) relies on chunk-based retrieval, whereas GraphRAG advances this approach by graph-based knowledge representation. However, existing graph-based RAG approaches are constrained by binary relations, as each edge in an ordinary graph connects only two entities, limiting their ability to represent the n-ary relations (n >= 2) in real-world knowledge. In this work, we propose HyperGraphRAG, the first hypergraph-based RAG method that represents n-ary relational facts via hyperedges. HyperGraphRAG consists of a comprehensive pipeline, including knowledge hypergraph construction, retrieval, and generation. Experiments across medicine, agriculture, computer science, and law demonstrate that HyperGraphRAG outperforms both standard RAG and previous graph-based RAG methods in answer accuracy, retrieval efficiency, and generation quality.

Current 3D/4D generation methods are usually optimized for photorealism, efficiency, and aesthetics. However, they often fail to preserve the semantic identity of the subject across different viewpoints. Adapting generation methods with one or few images of a specific subject (also known as Personalization or Subject-driven generation) allows generating visual content that align with the identity of the subject. However, personalized 3D/4D generation is still largely underexplored. In this work, we introduce TIRE (Track, Inpaint, REsplat), a novel method for subject-driven 3D/4D generation. It takes an initial 3D asset produced by an existing 3D generative model as input and uses video tracking to identify the regions that need to be modified. Then, we adopt a subject-driven 2D inpainting model for progressively infilling the identified regions. Finally, we resplat the modified 2D multi-view observations back to 3D while still maintaining consistency. Extensive experiments demonstrate that our approach significantly improves identity preservation in 3D/4D generation compared to state-of-the-art methods.

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point.

We study one of the most popular problems in **neurosymbolic learning** (NSL), that of learning neural classifiers given only the result of applying a symbolic component $\sigma$ to the gold labels of the elements of a vector $\mathbf x$. The gold labels of the elements in $\mathbf x$ are unknown to the learner. We make multiple contributions, theoretical and practical, to address a problem that has not been studied so far in this context, that of characterizing and mitigating *learning imbalances*, i.e., major differences in the errors that occur when classifying instances of different classes (aka **class-specific risks**). Our theoretical reveals a unique phenomenon: that $\sigma$ can greatly impact learning imbalances. This result sharply contrasts with previous research on supervised and weakly supervised learning, which only studies learning imbalances under data imbalances. On the practical side, we introduce a technique for estimating the marginal of the hidden gold labels using weakly supervised data. Then, we introduce algorithms that mitigate imbalances at training and testing time by treating the marginal of the hidden labels as a constraint. We demonstrate the effectiveness of our techniques using strong baselines from NSL and long-tailed learning, suggesting performance improvements of up to 14\%.

Existing Text Image Forgery Localization (T-IFL) methods often suffer from poor generalization due to the limited scale of real-world datasets and the distribution gap caused by synthetic data that fails to capture the complexity of real-world tampering. To tackle this issue, we propose Fourier Series-based Tampering Synthesis (FSTS), a structured and interpretable framework for synthesizing tampered text images. FSTS first collects 16,750 real-world tampering instances from five representative tampering types, using a structured pipeline that records human-performed editing traces via multi-format logs (e.g., video, PSD, and editing logs). By analyzing these collected parameters and identifying recurring behavioral patterns at both individual and population levels, we formulate a hierarchical modeling framework. Specifically, each individual tampering parameter is represented as a compact combination of basis operation-parameter configurations, while the population-level distribution is constructed by aggregating these behaviors. Since this formulation draws inspiration from the Fourier series, it enables an interpretable approximation using basis functions and their learned weights. By sampling from this modeled distribution, FSTS synthesizes diverse and realistic training data that better reflect real-world forgery traces. Extensive experiments across four evaluation protocols demonstrate that models trained with FSTS data achieve significantly improved generalization on real-world datasets.

Recent studies have demonstrated that fine-tuning language models with brain data can improve their semantic understanding, although these findings have so far been limited to English. Interestingly, similar to the shared multilingual embedding space of pretrained multilingual language models, human studies provide strong evidence for a shared semantic system in bilingual individuals. Here, we investigate whether fine-tuning language models with bilingual brain data changes model representations in a way that improves them across multiple languages. To test this, we fine-tune monolingual and multilingual language models using brain activity recorded while bilingual participants read stories in English and Chinese. We then evaluate how well these representations generalize to the bilingual participants' first language, their second language, and several other languages that the participants are not fluent in. We assess the fine-tuned language models on brain encoding performance and downstream NLP tasks. Our results show that bilingual brain-informed fine-tuned language models outperform their vanilla (pretrained) counterparts in both brain encoding performance and most downstream NLP tasks across multiple languages. These findings suggest that brain-informed fine-tuning improves multilingual understanding in language models, offering a bridge between cognitive neuroscience and NLP research. We make our code publicly available.

Zero-shot denoising aims to denoise observations without access to training samples or clean reference images. This setting is particularly relevant in practical imaging scenarios involving specialized domains such as medical imaging or biology. In this work, we propose the (ZS-NCD), a novel denoising framework based on neural compression. ZS-NCD treats a neural compression network as an untrained model, optimized directly on patches extracted from a single noisy image. The final reconstruction is then obtained by aggregating the outputs of the trained model over overlapping patches. Thanks to the built-in entropy constraints of compression architectures, our method naturally avoids overfitting and does not require manual regularization or early stopping. Through extensive experiments, we show that ZS-NCD achieves state-of-the-art performance among zero-shot denoisers for both Gaussian and Poisson noise, and generalizes well to both natural and non-natural images. Additionally, we provide new finite-sample theoretical results that characterize upper bounds on the achievable reconstruction error of general maximum-likelihood compression-based denoisers. These results further establish the theoretical foundations of compression-based denoising.