Papers

We formally introduce a class of models inspired by renormalization group (RG) theory, built on additive hierarchical expansions analogous to those appearing in functional ANOVA and mixed-effects models. Like ReLU convolutional neural networks, they are almost everywhere locally linear; unlike ReLU networks, their partition structure is explicit, interpretable, and easy to modify or constrain. In these models, one defines a multidimensional lattice partition of the input space and uses it to scaffold variations in regression parameters. Each dimension of the lattice corresponds to an attribute by which the statistics of the problem may vary. The parameters are themselves expressed in the form of an expansion, where each term captures variations relative to a lower (coarser) interaction scale. These models admit multiple equivalent interpretations: as piecewise GLMs, as hierarchical mixed-effects regressions, or as regression trees with structured parameter sharing. Since RG motivates the design of these models, we use techniques from statistical physics – specifically replica analysis – to study their generalization properties. Specifically, we analyze the behavior of the Watanabe-Akaike Information Criterion (WAIC) as a proxy for generalization loss. This analysis yields two practical results: (i) guidance on the lattice design as a function of dataset size and predictor dimensionality; and (ii) a principled scaling law for the regularization prior when adding higher-order terms to the expansion so that one can increase model complexity without an expected increase in generalization loss. We evaluate the methodology on public datasets and find performance competitive against both blackbox methods and other intrinsically interpretable approaches.

In the modern age of large-scale AI, federated learning has become an increasingly important tool for training large populations of AI agents; however, its computational and communication costs can rapidly fail to scale with the number of agents. This is precisely where decentralized agentic strategies shine: each agent acts autonomously, using only its own state together with a minimal summary of the ensemble, namely the mean-field. We derive the unique optimal decentralized policy in closed form. Optimality is characterized through a worst-client/minimax criterion: minimizing the under-performer regret, namely the maximal online cost incurred by the weakest agent in the ensemble. We further prove that the resulting decentralized policy asymptotically converges, in the large-population limit, to the Nash-optimal centralized policy, whose direct computation is not scalable. We use an online weighting mechanism to optimize the server-computed mixture of client predictions, thereby improving the mean prediction in addition to the previously optimized weakest-client prediction. Numerical experiments verify our theoretical guarantees and demonstrate that our decentralized policy typically outperforms natural greedy decentralized baselines.

We propose an architecture that augments the Flux Neural Operator (Flux NO), which combines the classical finite volume method (FVM) with neural operators, with ViT-based context injection. Our model is formulated as a hypernetwork: it extracts solution dynamics over a finite temporal window, encodes them with a recurrent Vision Transformer, and generates the parameters of a context-conditioned neural operator. This enables the model to infer and solve conservation laws without explicit access to the governing equation or PDE coefficients. Experimentally, we show that the proposed method preserves the robustness, generalization ability, and long-time prediction advantages of Flux NO over standard neural operators, while delivering reliable numerical solutions across a broad range of conservative systems, including previously unseen fluxes. Our code is available at https://github.com/xx257xx/CONTEXT_FLUX_NO.

We revisit a classic "chicken-and-egg" problem in reinforcement learning: to safely improve a policy, the value function must be accurate on the state-visitation distribution of the updated policy. That distribution over states is unknown and cannot be sampled for the purposes of training the value function. Conservative updates solve this problem, but at the cost of shrinking the policy update. This paper explores an alternative solution, Approximate Next Policy Sampling (ANPS), which addresses the problem by modifying the training distribution rather than constraining the policy update. ANPS is satisfied if the distribution of the training data approximates that of the next policy. To demonstrate the feasibility and efficacy of ANPS, we introduce Stable Value Approximate Policy Iteration (SV-API). SV-API modifies the standard approximate policy iteration loop to hold the target policy fixed while an iteratively updated behavioral policy gathers relevant experience. It only commits to a new policy once a convergence criterion has been met. If certain stability criteria are met, the update is guaranteed to be safe; otherwise, it remains no less safe than standard approximate policy iteration. Applying SV-API to PPO yields Stable Value PPO (SV-PPO), which matches or improves performance on high-dimensional discrete (Atari) and continuous control benchmarks while executing substantially larger target policy updates. These results demonstrate the viability of ANPS as a new solution to this classic challenge in RL.

The main post-hoc XAI methods for deep networks – GradCAM, SHAP, LIME, Integrated Gradients – originate from heterogeneous theoretical foundations and are not naturally comparable within a single representation. A recent benchmark also finds their coalition-based members (GradCAM, KernelSHAP, LIME) and gradient-based members (Integrated Gradients and variants) empirically complementary, each outperforming the other on different faithfulness metrics, with method selection as the only proposed remedy (Gevaert et al., 2022). This work presents GRALIS (Gradient-Riesz Averaged Locally-Integrated Shapley), which fuses these two mechanisms – a Shapley coalition weight and locality kernel, and a continuous Integrated-Gradients-style conditioned path – into a single estimator, and equips it with two certified guarantees neither mechanism supplies alone: an exact, closed-form completeness deficit (an order-d interaction is attributed at a factor 1/d of its true value under Shapley weights and a multilinear F) and a finite-sample bound, O(1/sqrt(m)) + O(1/k^2), for the actual self-normalized ratio the algorithm returns. This fusion is underpinned by a representation-theoretic result: every additive, linear, continuous attribution functional admits a unique canonical representation via the Riesz Representation Theorem, proved componentwise (feature by feature) rather than as one form shared across features or methods. This class includes SHAP, IG and LIME, but not nonlinear functionals such as standard GradCAM or attention maps. Seven theorems further establish an exact correspondence with Shapley Interaction Values, affine-regime correspondences with the Hoeffding/Sobol decomposition, and a minimum-variance multi-scale extension. A preliminary experimental illustration on breast histology imaging is included; extended validation is in a companion paper (Fanale, 2026).

Knowledge graphs automatically constructed from text are increasingly used in real-world applications. However, their inherent noise, fragmentation, and semantic inconsistencies significantly affect the performance of Graph Neural Networks (GNNs) on downstream tasks. Assessing their performance and robustness remains difficult, as it is often unclear whether observed results stem from the learning model or from the quality of the constructed graph itself. In this work, we introduce a dual-purpose benchmark designed to jointly evaluate (i) the performance of GNNs on noisy, text-derived graphs and (ii) the effectiveness of graph construction methods on a downstream task. The benchmark is built in the biomedical domain from a single textual corpus and includes two automatically constructed graphs generated using different extraction methods, alongside a high-quality reference graph curated by experts that serves as an upper performance bound. This design enables controlled comparison of construction methods and systematic evaluation of GNN robustness through semi-supervised node classification. We further provide a standardized, reproducible, and extensible evaluation framework, facilitating the integration of new graph extraction methods and learning models.

Graph Self-Supervised Learning (GSSL) offers a powerful paradigm for learning graph representations without labeled data. However, existing work assumes clean, manually curated graphs. Recent advances in NLP enable the large-scale automatic extraction of knowledge graphs from text, opening new opportunities for GSSL while introducing substantial real-world noise. This type of noise remains largely unexplored, as prior robustness studies typically rely on synthetic perturbations. To address this gap, we present the first comprehensive evaluation of GSSL methods on text-driven graphs for unsupervised term typing. We introduce Noise-Aware Text-Driven Graph GSSL (NATD-GSSL), a unified framework that combines automatic graph construction, graph refinement, and GSSL. Our evaluation follows a dual-graph protocol that contrasts a noisy graph derived from MedMentions with a clean Unified Medical Language System (UMLS) reference graph, aligned through a shared gold standard. Our results reveal variability in robustness across both pretext tasks and Graph Neural Network (GNN) architectures. Relation reconstruction is highly sensitive to noise and benefits from well-defined schemas, whereas feature reconstruction is considerably more robust, achieving performance comparable to clean-graph settings. Contrastive objectives are generally less affected by noise but depend strongly on alignment with downstream tasks. GNN architecture also plays a critical role: bidirectional relational message-passing designs are better suited to noisy, text-driven graphs, while unidirectional relational ones perform best on clean graphs. Overall, NATD-GSSL provides practical guidance for applying GSSL to real-world, noisy graphs and achieves up to a 7% improvement over pretrained language model baselines. All code and benchmarks are publicly available at https://github.com/OthmaneKabal/MC2GAE.

This work introduces PAS – Privacy Anchor Substitution, a structured mechanism for enabling user location privacy in spatial retrieval-augmented generation (RAG) systems. Unlike conventional differential privacy methods that directly perturb user locations, PAS represents location with relative anchor encoding consisting of an anchor, direction bin, and distance bin, allowing seamless integration with modern RAG pipelines. We evaluate PAS on a synthetic urban dataset and show that it achieves impressive coarse privacy guarantees, with approximately 370-400m adversarial location error, while retaining more than half of the baseline retrieval performance. Despite the slight drop in retrieval performance, the downstream generation quality under PAS remains comparatively robust, indicating that large language models can compensate for imperfect spatial retrieval. Furthermore, we provide empirical analysis showing that PAS exhibits non-monotonic privacy-utility relationship with respect to privacy parameters. We attribute this to geometric bias induced by anchor discretization, making it different from continuous noise mechanisms such as geo-indistinguishability. Our results show that structured spatial representations offer a practical approach to privacy in location based reasoning in RAG systems.

Nonconvex methods have emerged as a dominant approach for low-rank matrix estimation, a problem that arises widely in machine learning and AI for learning and representing high-dimensional data. Existing analyses for these methods often require additional regularization to mitigate nonconvexity, even though such regularization is often unnecessary in practice. Moreover, most analyses rely on problem-specific arguments that are difficult to generalize to more complex settings. In this paper, we develop a theoretical framework for studying nonconvex procedures across a broad class of low-rank matrix estimation problems. Rather than focusing on a specific model, we reveal a fundamental mechanism that explains why nonconvex procedures can behave well in low-rank estimation. Our key device is a benign regularizer that does not alter the original update rule, but yields an equivalent locally strongly convex formulation of the algorithm. This perspective uncovers a disguised convexity inherent in the nonconvex procedure and provides a new route to theoretical guarantees for nonconvex low-rank matrix estimation.

Standard fine-tuning of transformer models on causal reasoning tasks leads to catastrophic model collapse, where models learn trivial solutions such as always predicting "Yes" or "No" regardless of input structure. We demonstrate that fine-tuning Gemma 270M on transitivity and d-separation tasks without semantic loss results in 100% collapse rate, with models achieving misleadingly high accuracy (73.9%) while learning no causal reasoning. We propose a semantic loss function with graph-based logical constraints and dynamic lambda scheduling that prevents this collapse. Our approach achieves 70.4% accuracy on transitivity tasks and 68.6% on d-separation tasks with stable, context-dependent predictions, representing a 42.7% improvement over collapsed baselines. Adversarial evaluation on 1,000 structural reasoning samples shows semantic models achieve 67-70% accuracy while collapsed models fail catastrophically at 43-71%. We validate our findings through comprehensive benchmarking on 200,000+ evaluation samples across five model variants, demonstrating that semantic loss is essential and not optional, for stable causal reasoning in transformers.

Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization – connecting it to an equivalent penalty that augments the learning objective. However, modern deep learning systems are complex, carrying modifications to the training procedure and architecture (e.g. early stopping, minibatching, dropout) whose effects are not always directly interpretable. Although estimating the resulting implicit regularization could aid theorists in algorithm design and practitioners in interpreting their hyperparameter choices, this problem has received little direct attention. It is also tractable: regularization makes weight updates deviate from loss gradients, promising a signal for identifying implicit bias. Here we provide gradient matching methods that can be used to empirically estimate the implicit regularization. Our method works on networks with known regularization, recovering popular explicit penalties like $\ell_1$ and $\ell_2$. It also replicates known implicit effects, like the quadratic weight penalty induced by early stopping in gradient descent, demonstrating that it can be used to test theories of implicit regularization. Crucially, because our method is empirical, it can handle implicit regularization in arbitrary networks. We demonstrate this use by characterizing implicit $\ell_2$ effects of dropout in deep networks. Our work shows that practitioners can use gradient matching to understand regularization in networks with implicit biases that are too complicated to derive analytically.

Generative compressed sensing uses the range of a pretrained generator as a nonlinear model for recovering structured signals from limited measurements. We study a conditional version of this problem for image recovery from subsampled Fourier measurements using prompt-conditioned generative models. Our framework separates two roles of conditioning: the prompt used to design the sampling distribution and the prompt used to define the recovery model. For ReLU and Lipschitz conditional generators, we prove stable recovery bounds showing that prompt-matched Christoffel sampling retains the same Christoffel complexity constant as existing near-optimal generative compressed sensing theory, while prompt mismatch incurs an explicit compatibility penalty. Experiments with Stable Diffusion show that prompts meaningfully reshape Christoffel sampling distributions and influence image recovery. Overall, our results suggest treating prompts as design variables for sensing, approximation, and recovery, opening new directions for the practical use of conditional generative models in compressed sensing, where conditioning, sampling, and optimization must be considered jointly.

We study nonparametric estimation of Schrödinger bridge (SB) drifts from i.i.d.\ data observed on a single time interval. Starting from the conditional-ratio form of the Schrödinger bridge time-series (SBTS) drift formula, we analyze a direct Nadaraya–Watson plug-in estimator built from kernelized numerator and denominator terms. Unlike recent SB analyses based on entropic-OT potentials, Sinkhorn iterations, or iterative bridge solvers, our approach works directly at the drift level and isolates statistical error from optimization, approximation, and discretization error. Under Hölder regularity, a marginal-density floor, and bounded support, we prove a uniform non-asymptotic bound for admissible bandwidth pairs, a pointwise CLT under genuine undersmoothing, and an adaptive bandwidth selector satisfying an oracle inequality. We also prove a pivot-local minimax lower bound which, through an explicit uniform pivot, yields a global minimax lower bound under transparent compatibility conditions; hence the adaptive selector is minimax-rate optimal up to logarithmic factors. Synthetic experiments provide theorem-targeted diagnostics for finite-sample scaling, Gaussian approximation, and adaptive behavior.

Large language models (LLMs) remain vulnerable to adversarial prompting despite advances in alignment and safety, often exhibiting harmful behaviors under novel attack strategies. While adversarial training can improve robustness, existing approaches are computationally expensive and difficult to scale. Recent continuous adversarial training methods, such as Continuous adversarial training (CAT) and Continuous Adversarial Preference Optimization (CAPO), address this challenge by leveraging gradient-based perturbations in the embedding space, enabling more efficient and expressive attacks. Building on this paradigm, we propose WARDEN, a distributionally robust adversarial training framework for LLMs that dynamically reweights adversarial examples through an f -divergence ambiguity set around the empirical training distribution. Our method optimizes the worst-case adversarial loss within a divergence ball around the empirical data distribution, automatically emphasizing harder adversarial examples. Using the convex dual formulation, the objective reduces to a log-sum-exp form under the KL divergence, with a dynamical parameter controlling the strength of reweighting. This study leads to a new class of information-theoretic objectives that significantly reduce attack success rates while maintaining model utility. Across multiple LLMs and attack settings, WARDEN substantially reduces attack success rates with computational and utility costs comparable to CAT-, CAPO-, and MixAT-based baselines, making it a practical approach for scalable robust alignment.

Differential-algebraic equations (DAEs) with state-dependent events arise in systems whose continuous dynamics are constrained by algebraic equations and interrupted by mode changes, switching logic, impacts, or state reinitializations. Gradient-based parameter learning for such systems is challenging because algebraic variables are implicitly defined, event times depend on the parameters, and reset maps introduce discontinuities. This paper studies differentiable parameter optimization for semi-explicit DAEs with events. We formulate the learning problem as a constrained least-squares problem with DAE dynamics, algebraic constraints, guard equations, and reset maps. We then develop two complementary gradient-computation strategies. The first is an automatic-differentiation-through-simulation method that solves algebraic variables inside the vector field, differentiates the algebraic solve using the implicit function theorem, and handles events through segmented differentiable integration. The second is an explicit discrete-adjoint method that represents the forward simulation as an event-split residual system and computes gradients by solving for the Lagrange multipliers of smooth-segment and event residuals. The formulation clarifies that residual terms in the adjoint method are equality constraints, not heuristic penalties. We compare the two approaches in terms of gradient interpretation, event-time handling, implementation complexity, and local validity. Both methods provide gradients for the event path selected by the forward simulation and are valid under fixed event ordering and transversal guard crossings.

Most neural methods for Vehicle Routing Problems (VRPs) are limited to Euclidean settings or simple graphs. In this work, we instead consider multigraphs, where parallel edges represent distinct travel options with varying trade-offs (e.g., distance vs. time). Multigraphs are highly relevant in practice, yet few neural methods are designed for them, and those that do exist face major scalability issues. We address these scalability issues with Node-Edge Policy Factorization (NEPF), which splits the routing policy into a node permutation stage and an edge selection stage. To enable the decomposition, we introduce a pre-encoding edge aggregation scheme and a non-autoregressive architecture for the edge stage, as well as a hierarchical reinforcement learning method to train the stages jointly. Our experiments across six VRP variants demonstrate that NEPF trains and runs up to orders of magnitude faster than prior neural multigraph methods and scales to considerably larger instances, while matching or improving on their solution quality.

We study zero-shot conditional sampling with pretrained diffusion models for linear inverse problems, including inpainting and super-resolution. In these problems, the observation determines only part of the unknown signal. The remaining degrees of freedom must be sampled according to the correct conditional data distribution. Existing projection-based samplers enforce measurement consistency by correcting the observed component during reverse diffusion. However, measurement consistency alone does not determine how probability mass should be distributed along the feasible set, and this can lead to biased conditional samples. We analyze this issue through a normal–tangent decomposition of the score function. For Gaussian noising, the observed-direction score is exactly determined by the measurement; only the tangent conditional score is unknown. We prove that the error from replacing this score by the unconditional tangent score is upper bounded by a dimension-free conditional mutual information between observed and unobserved components. This gives an information-theoretic decomposition into initialization and pathwise score-mismatch errors. Motivated by the theory, we propose a projected-Langevin initialization followed by guided reverse denoising, which outperforms a strong projection-based baseline in inpainting and super-resolution experiments.

Large language models increasingly operate in interactive settings where solving a task requires multiple rounds of information exchange with a user. However, most current systems treat dialogue reactively and lack a principled mechanism to reason about what information is missing. We propose BALAR (Bayesian Agentic Loop for Active Reasoning), a task-agnostic outer-loop algorithm that requires no fine-tuning and enables multi-turn interaction between an LLM agent and a user. BALAR maintains a structured belief over latent states, selects clarifying questions by maximizing expected mutual information, and dynamically expands its state representation when the current one proves insufficient. We evaluate BALAR on three diverse benchmarks: AR-Bench-DC (detective cases), AR-Bench-SP (thinking puzzles), and iCraft-MD (clinical diagnosis). BALAR outperforms all baselines across the three benchmarks, with 14.6% higher accuracy on AR-Bench-DC, 38.5% on AR-Bench-SP, and 30.5% on iCraft-MD. We further study whether BALAR can serve as a teacher for a questioning policy through supervised fine-tuning (SFT), direct preference optimization (DPO), and dense-reward reinforcement learning (RL). Across 18 iCraft-MD replications, distilling BALAR into a Llama-8B yields relative gains in frozen-Qwen final-answer accuracy of 8.1% with SFT, 10.9% with DPO, and 12.1% with RL over the untuned policy.

The optimisation of fed-batch (bio)chemical process recipes is subject to inherent, underlying, and unmeasurable fluctuations across batches, whose trajectories are difficult to model and costly to measure. Bayesian Optimisation (BayesOpt) is a powerful tool for sampling and optimisation of expensive-to-measure functions. Gaussian Processes (GPs), the surrogate models used in BayesOpt, are static, forecast poorly, and lack generalisation across experiments, limiting their applicability to time-varying batch processes with stochastic parameters, i.e., process fluctuations. This work investigates System-Aware Neural ODE Processes (SANODEP) as a meta-learning model to overcome the limitations of GPs and increase few-shot optimisation performance in BayesOpt. Using a penicillin batch production case study, we find that SANODEP outperforms GP-based BayesOpt in the low-data regime, resulting in improved objectives when few experimental runs are performed. These improvements are observed in both on- and off-distribution batches, highlighting the generalisation capabilities of SANODEP. Using this approach, batch process operators can accelerate the initial optimisation steps in BayesOpt by deploying meta-learning or optimise the process with fewer experiments when the experimental cost is high.

A key capability of intelligent agents is to act effectively under incomplete state observations. Recurrent policies address this by compressing observation histories into a hidden state. In this work, we show that the hidden state of a recurrent policy admits a control-theoretic interpretation: it plays the role of the co-state in Pontryagin's minimum principle, and the readout that maps it to actions implements control-Hamiltonian minimization. The hidden state thus tracks the gradient of the value function, encoding the optimality structure of the underlying control problem. We formalize this correspondence through a class of policies we refer to as co-state policies (CPs) and show that several modern recurrent cells implicitly realize this structure. The correspondence also allows for a co-state loss for actor-critic training, in which the critic's gradient serves as a target for the actor's hidden state. Empirically, we find that hidden states trained with the co-state loss encode co-state information beyond what is linearly decodable from the environment state alone, and that the loss improves policies both within and outside this class on challenging locomotion tasks, including the H1 and Berkeley humanoids. By connecting the minimum principle to recurrent memory, we provide a control-theoretic account of what hidden states compute in continuous control and a mechanism for shaping them toward optimality.

Drug discovery seeks molecules (ligands) that bind strongly and selectively to a target protein. However, fewer than 5% of candidate ligands pass the bar for even the early stages of drug discovery. Furthermore, we want methods that work for novel proteins for which we have no prior data. Starting from scratch, we have to iteratively select and test candidate ligands such that we find enough ligands of the desired quality in as few tests as possible. Our proposed algorithm, named SPADE, introduces a novel approach to ligand selection that requires only 40 tests on average to find 10 high-quality ligands. In one-vs-one comparisons, SPADE outperforms deep learning and Bayesian optimization methods on more proteins, achieving median improvements of 7%-32% in sample efficiency. SPADE is also 10x faster than its closest competitor at scoring candidate drugs. Dataset and code is available at https://anonymous.4open.science/r/SPADE_Fast_Drug_Discovery_by_Learning_from_Sparse_Data-F028/README.md

Given two GNNs that output node embeddings, how can we determine if they were trained independently? An adversary could have trained one GNN specifically to mimic the other GNN's embeddings. To obscure this relationship between the GNNs, the adversarial GNN might then transform its output embeddings. The two GNNs could have different architectures, weights, and embedding dimensions, and the adversary can transform the embeddings. Despite these stringent conditions, our algorithm (named CopyCop) can identify such copycat GNNs, unlike existing watermarking and fingerprinting methods. We also provide theoretical guarantees for CopyCop. Finally, experiments on 14 datasets and 5 GNN architectures demonstrate that CopyCop is accurate and robust against a broad class of adversarial attacks and transformations. Code is available at: https://anonymous.4open.science/r/CopyCop-Graph-Ownership-Verification-8143/README.md

Early-exiting neural networks enable adaptive inference by allowing inputs to exit at intermediate classifiers, reducing computation for easy samples while maintaining high accuracy. In practice, exits can be trained sequentially by incrementally adding them to a shared backbone; however, this sequential training can cause newly introduced exits to interfere with previously learned ones, degrading the performance of earlier classifiers. We address this problem by retaining the knowledge embedded in existing exits while allowing new ones to specialize. We propose two alternative approaches that operate at different levels of the model. The first constrains learning by protecting parameters that are important for previously trained exits, while the second preserves the output distributions of earlier exits as the network adapts. These alternatives directly reflect the stability-plasticity trade-off studied in continual learning. Accordingly, we leverage Elastic Weight Consolidation to constrain critical weights and Learning without Forgetting to preserve output distributions. Experiments on standard benchmarks show that our approaches consistently improve early-exit performance, achieving higher accuracy over existing sequential training methods and significant performance speedups at low computational budgets.

Service level agreements (SLAs) in data center colocation contracts define precise thresholds for power, temperature, and humidity, with tiered violation penalties expressed as credits against monthly recurring charges. Traditional reactive monitoring detects breaches only after they occur, limiting remediation opportunities. We present a framework that encodes SLA rules as structured JSON objects to generate training data without manual annotation. We train a per-customer multi-head transformer model in which each attention head specializes in one SLA rule, learning temporal dependencies that precede violations by 30 minutes. Post-training, the inference service emits structured prediction events transformed into three role-specific views: finance schemas exposing credit liability, operations schemas surfacing risk scores and recommended interventions, and compliance schemas bundling predictions with immutable telemetry signatures for audit. By aligning model architecture directly with contractual obligations, this framework enables operators to anticipate SLA breaches, prioritize corrective actions, and minimize financial penalties.

Sparse autoencoders (SAEs) are used to disentangle the dense, polysemantic internal representations of large language models (LLMs) into interpretable, monosemantic concepts. However, standard $\ell_1$-regularized SAEs suffer from feature starvation (dead neurons) and shrinkage bias, often requiring computationally expensive heuristic resampling and nondifferentiable hard-masking methods to bypass these challenges. We argue that feature starvation is not merely an empirical artifact of poor data diversity, but a fundamental optimization-geometric pathology of overcomplete dictionaries: the $\ell_1$-induced sparse coding map is unstable and fundamentally misaligned with shallow, amortized encoders. To address this structural instability, we introduce adaptive elastic net SAEs (AEN-SAEs), a fully differentiable architecture grounded in classical sparse regression. AEN-SAEs combine an $\ell_2$ structural term that enforces strong convexity and Lipschitz stability with adaptive $\ell_1$ reweighting that eliminates shrinkage bias and suppresses spurious features, thereby jointly controlling the curvature and interaction structure of the induced polyhedral geometry. Theoretically, we show that AEN-SAEs yield a Lipschitz-continuous sparse coding map and recover the global feature support under mild assumptions. Empirically, across synthetic settings and LLMs (Pythia 70M, Llama 3.1 8B), AEN-SAEs mitigate feature starvation without auxiliary heuristics while maintaining competitive reconstruction abilities.

Vision Transformer (ViT) autoencoders have emerged as compelling tokenizers for images, offering improved reconstruction over convolutional tokenizers. However, existing ViT tokenizers cannot explore this landscape as performance degrades outside training resolutions, and reliance on adversarial losses prevents stable scaling. ViTok (Hansen-Estruch et al., 2025) found that the compression ratio r mediates a reconstruction-generation trade-off where lower r means better reconstructions but harder generations, so improving tokenizer reconstruction is key to more Pareto-optimal tokenizers. We introduce ViTok-v2, which addresses these limitations with native resolution support via NaFlex for generalization across resolutions and aspect ratios, and a novel DINOv3 perceptual loss that replaces both LPIPS and GAN objectives for stable training at any scale. ViTok-v2 is trained on about 2B images and scaled to 5B parameters, the largest image autoencoder to date. ViTok-v2 matches or exceeds state-of-the-art reconstruction at 256p and outperforms all baselines at 512p and above. In joint scaling experiments with flow matching generators, we show that scaling both the autoencoder and the generator advances the Pareto frontier of this trade-off.

We introduce Graph Normalization (GN), a principled dynamical system on graphs that serves as a differentiable approximation engine for the NP-hard Maximum Weight Independent Set (MWIS) problem. MWIS encompasses many combinatorial challenges, including optimal assignment, scheduling, set packing, and MAP inference in discrete Markov Random Fields. Unlike Belief Propagation, we prove GN always converges to a binary indicator of a Maximum Independent Set. GN realizes a fast quasi-Newton descent through an exact Majorization-Minimization step, systematically improving the MWIS relaxed primal objective. We establish an equivalence between GN and the Replicator Dynamics of a nonlinear evolutionary game, where vertices compete for inclusion in an independent set. While a non-potential game, the GN game follows Fisher's Fundamental Theorem of Natural Selection, where the average fitness equals the MWIS primal objective and strictly increases. This connection leads to a weighted extension of the Motzkin-Straus theorem, showing MISes are in bijection with the local minima of a quadratic form over a tilted simplex. For the Assignment Problem, GN acts as a variant of the Sinkhorn algorithm that naturally converges to a hard assignment while generalizing to arbitrary constraint graphs. We demonstrate GN's performance as a fast binarization engine for the state-of-the-art Bregman-Sinkhorn relaxed MWIS solver. On real-world benchmarks with up to 1M edges, GN identifies solutions within 1% of the best known results in seconds on a CPU. GN opens new avenues for deep learning architectures requiring differentiable, "hard" decisions under constraints, with applications in structured sparse attention, dynamic network pruning, and Mixture-of-Experts. Beyond core AI, the GN framework enables end-to-end learning of constrained optimization in computer vision, computational biology, and resource allocation.

Safety policies define what constitutes safe and unsafe AI outputs, guiding data annotation and model development. However, annotation disagreement is pervasive and can stem from multiple sources such as operational failures (annotators misunderstand or misexecute the task), policy ambiguity (policy wording leaves room for interpretation), or value pluralism (different annotators hold different perspectives on safety). Distinguishing these sources matters. For example, operational failures call for quality control, ambiguity calls for policy clarification, and pluralism calls for deliberation about incorporating diverse perspectives. Yet understanding why annotators disagree is difficult. Directly asking annotators for their reasoning is costly, substantially increasing annotation burden, and can be unreliable for both human and LLM annotators as self-reported reasoning often fails to reflect actual decision processes. We introduce Annotator Policy Models (APMs), interpretable models that learn annotators' internal safety policies from labeling behavior alone, making annotator reasoning visible and comparable without additional annotation effort. We validate that APMs accurately model annotator safety policy (>80% accuracy), faithfully predict responses to counterfactual edits, and recover known policy differences in controlled settings. Applying APMs to LLM and human annotations, we demonstrate two core applications: (1) surfacing policy ambiguity by revealing how annotators interpret safety instructions differently, and (2) surfacing value pluralism by uncovering systematic differences in safety priorities across demographic groups. Together, these capabilities support more targeted, transparent, and inclusive safety policy design.

Large language models (LLMs) often suffer from catastrophic forgetting in continual learning: after learning new tasks sequentially, they perform worse on earlier tasks. Existing methods mitigate catastrophic forgetting by data replay, parameter freezing, or regularization. However, these methods lack understanding of LLM mechanisms and cannot distinguish which parameters store important knowledge from previous tasks and which parameters can be updated for new tasks. To address this, we propose the attribution-guided continual fine-tuning framework that leverages Layer-wise Relevance Propagation (LRP) to estimate parameter importance based on the internal computational process of LLMs. During continual learning, parameters critical to previous tasks are constrained to receive smaller updates, while less relevant parameters remain available for learning new tasks. Extensive experiments show that, compared with baseline methods, our approach reduces catastrophic forgetting while preserving adaptability to new tasks, highlighting the value of mechanistic attribution for continual fine-tuning of LLMs.

Evolutionary computation has long promised to deliver both high-performance optimization tools as well as rigorous scientific simulations of Darwinian evolution. However, modern algorithms frequently abandon evolutionary fidelity for physics-inspired heuristics or superficial biological metaphors. This paper derives a suite of advanced gradient-based optimization algorithms directly from evolutionary first principles. We introduce Darwinian Lineage Simulations (DLS) to prove that, in an asexual context, Fisher's and Wright's historically opposed views of evolution are actually formally equivalent; One can partition Fisher's deterministically-evolving total population into Wright's randomly-drifting sub-populations. We prove that proper bookkeeping requires introducing a specific kind of structured noise (the DLS noise relation). Crucially, any bookkeeping choices which satisfy this relation will yield a faithful simulation of evolution. Using this vast representational freedom, we prove that a broad family of battle-tested optimization algorithms are already perfectly compatible with evolutionary dynamics. These include: Stochastic Gradient Descent as well as many regularizations/approximations of Newton's method and Natural Gradient Descent. By simply adding DLS noise (i.e., evolutionarily faithful genetic drift), these algorithms become scientifically valid in silico simulations of Darwinian evolution. Finally, we demonstrate that even the state-of-the-art Adam optimizer can be brought into evolutionary compliance through a minor mathematical surgery.