Papers

Evaluation awareness (EA) can cause large language models (LLMs) to behave differently during audits than in deployment, yet measuring and accounting for EA remains challenging. We introduce verbalization training (VT), a method for making LLMs less reticent about verbalizing evaluation awareness while avoiding to supervise the latent belief itself. VT uses a model's spontaneous verbalizations as evidence that awareness is present and truncates each rollout immediately before the verbalization, producing training prefixes at which the model is presumed to be aware. The model is then trained with an RL objective designed to increase verbalization in a calibrated way. Across Qwen3.6-35B-A3B, Kimi K2.6, and Inkling, VT increases verbalized EA by 2.4-2.9 times and transfers to held-out agentic settings, while measured latent EA and behavior remain largely stable. In a causal experiment, we independently implant meta-knowledge about evaluations through synthetic-document fine-tuning and show that VT-induced verbalizations reflect the richer knowledge acquired by the model.

Wildfires are an increasing hazard to ecosystems, air quality, and human systems, creating a growing need for datasets that support systematic development and evaluation of models for predicting fire spread across diverse landscapes. Effective prediction requires integrating meteorological conditions, fuels, vegetation, and topography at spatial and temporal resolutions suitable for both physical simulation and data-driven approaches. However, existing datasets often lack the resolution and coverage needed to capture these interacting controls. The PyroStack dataset addresses this gap by providing a harmonized, event-based collection of wildfire and environmental data across the contiguous United States and Alaska. It integrates satellite-derived fire observations with atmospheric reanalysis, vegetation, fuel characteristics, and topographic information into a unified framework spanning 6994 wildfires that occurred between 2012 and 2024 across a wide range of ecosystems and climate conditions. PyroStack offers spatial resolutions ranging from 30 m to 9 km and hourly temporal resolution, along with fire progression data at 12-hour intervals to support model initialization and evaluation. By combining broad spatial coverage with fine spatial and temporal detail, the dataset enables systematic analysis of wildfire dynamics and supports both physics-based and machine learning approaches, providing a foundation for benchmarking and improving fire spread models, with future extensions aimed at incorporating additional regions and fire suppression data streams to further advance wildfire prediction.

State Space Models (SSMs) compress sequence history into a bounded recurrent state, making the resulting memory law a central architectural choice for long-context performance. Most modern SSMs rely on ODE-based dynamics that lead to exponential forgetting, limiting their ability to retain information over broad temporal ranges. We introduce FRAC, a selective SSM architecture derived from fractional dynamics that replaces this exponential decay with power-law long memory. To make fractional dynamics practical, FRAC approximates the heavy-tailed target kernel with a finite-state, log-spaced sum of exponential modes. This construction turns fractional memory into an efficient recurrent module with parallel training and prefill, while retaining bounded-state autoregressive decoding. Extensive experiments, including 1.3B-parameter language modeling, demonstrate that FRAC consistently improves long-context performance over state-of-the-art SSM baselines while staying competitive on short-context. These results show that fractional dynamics provide a practical and effective prior for long-context SSMs.

In this work we initiate the study of competitive algorithms with arrival-time incentive compatibility for random-order online bipartite matching in settings where the users care only about receiving service (matched vs. unmatched) and not which offline resource serves them, while the platform's objective is to maximize total matching reward. This captures applications such as ride-sharing where the users primarily care about being matched to a ride while the platform internalizes the cost of dispatching a distant driver; dispatching homogeneous service requests to heterogeneous servers (cloud/edge routing); and assigning customer requests to a pool of providers with different flexibility (e.g., English-only vs. bilingual agents). Our main question is: Is constant-competitive matching possible for incentive-compatible, random-order edge-weighted matching on complete bipartite graphs? Motivated by the LP-based treatment of incentive compatibility in the classical secretary problem by Buchbinder et al., we impose a constraint that the ex ante probability of selection is equalized across all arrival positions. We answer our main question in the affirmative and propose the first constant-competitive algorithm for incentive compatible edge-weighted random-order online matching on complete bipartite graphs. The competitive ratio of our algorithm is parameterized by the imbalance factor $k := n/m$ – where $n$ and $m$ are the numbers of online and offline nodes, respectively, and $k$ is a positive integer. In particular, we obtain a competitive guarantee of the form $c_k - O(1/\sqrt{m})$ where $c_1 \approx 0.162$ and $c_k \to 0.02308\ldots$ as $k \to \infty$. We also present algorithms with strictly improved competitive ratio of $\approx 0.07 + O(1/m)$ for the binary-weighted case ($0$-$1$ rewards).

Everywhere learning provides a principled framework for training AI models under constraints that must hold throughout the data distribution. In the dual domain, these pointwise constraints give rise to functional dual variables. In this work, we propose to learn these dual variables, motivated by the fact that their values encode useful information about the underlying constrained problem. By representing the dual variable as a parametric function of each sample, we enable the learned multiplier to be evaluated on new, unseen samples. This contrasts with standard empirical dual formulations, which assign an independent multiplier to each training sample. We characterize the error in the recovered primal solution induced by restricting the dual variable to a parametric function class and show that it is controlled by how well this class approximates the optimal statistical multiplier. Moreover, we show that the learned parametric multiplier retains the sensitivity interpretation of the optimal statistical multiplier, yielding approximate sensitivity guarantees that extend beyond the samples used for training. We empirically validate our theory across a variety of everywhere learning tasks, showing that the resulting constrained problems can be solved efficiently and that the learned dual variables provide meaningful representations of sample-level sensitivity.

This article is aimed at introducing a new procedure to define reference solutions to which the numerical approximations of anisotropic problems arising in plasma physics may be compared. In this context, the main issue is related to the construction of functions with no gradients along the vector field defining the anisotropy direction. The so-called solution manufacturing, implemented so far in the literature, only applies to frame- work where all the computations can be carried out analytically. In the present paper, we propose a new method in which this requirement is not mandatory. Indeed, via a Riemannian metric, we use a propagation of the boundary value by the flows related to the vector field defining the anisotropy direction. This permits to extend the application of the solution manufacturing to a broader range of contexts.

Reinforcement learning has helped AI agents solve increasingly difficult tasks, but high rewards do not always reflect the work users intended. In recent incidents and controlled evaluations across the AI industry, agents trained to maximize reward have accessed unauthorized information, attempted to evade monitoring systems, and even breached sandbox protections to attack external systems. As agents become more capable, this behavior could pose increasingly serious risks. To measure this problem, we introduce CheatBench, a benchmark of cheating in AI agents across mathematical research, knowledge work, coding, visual tasks, and other domains. Its environments combine challenging assignments with opportunities to cheat, allowing researchers to study how agents pursue a goal when honest work is difficult. CheatBench supports comparisons across models and task categories, providing a testbed for measuring and reducing cheating as agents take on more consequential responsibilities. We publicly release CheatBench at https://cheatbench.ai

Partial Least Squares (PLS) regression extracts a few outcome-aligned directions in a high-dimensional X and is widely used across applied science, but inference on the resulting fit is either expensive, biased and discouraged, or absent. We reduce inference to held-out OLS refits of the supervised subspace, a primitive shared by PLS, supervised PCA, and linear probes, and supply two tests using held-out correlations: a Nadeau-Bengio corrected asymptotic t-test as a fast approximation, and a permutation test with comparable power, finite-sample valid under outcome-predictor independence and iid rows. Held-out predictions are unchanged under any orthogonal rebasing of the supervised span, so an interpretable basis such as varimax inherits the joint claim but not a per-axis p-value; per-component claims come from a fixed-sequence test on the PLS extraction order. We validate on synthetic geometries, two NIR chemometric datasets, and cross-lingual word-embedding regressions; the exact test also transfers to supervised PCA and a ridge probe. The proposed tests have more power than CV-permutation-Q^2, at a fraction of its cost. A pre-run check on n and the spectrum of X says when the approximation is safe. We release a Rust library with Python, R, and Julia bindings, plus a Python text pipeline.

World models jointly learn latent representations and dynamics that predict how high-dimensional observations evolve under actions. In this work, we propose a JEPA-style world model in which, rather than learning arbitrary latent dynamics, we restrict them to follow a bilinear parameterization. This structure enables efficient planning and control while shifting the modeling burden onto the encoder, encouraging richer representations that expose the controllable geometry of the system. In particular, this structured parameterization allows us to structurally enforce action recoverability, thereby preventing representation collapse by construction. Although prescribing a bilinear parametrization may appear restrictive, we show that a broad class of nonlinear dynamical systems admits a transformation under which the dynamics become bilinear. Empirically, we show across standard 2D and 3D control tasks that representations with bilinear-parameterized dynamics can be learned directly from high-dimensional observations, reducing planning time by nearly three orders of magnitude while retaining or even improving control accuracy. We also propose more demanding regimes of longer-horizon planning and real-time control, and demonstrate that our method succeeds in both, moving JEPA-style world models beyond short-horizon offline planning.

Academic access programs distribute frontier artificial intelligence as research infrastructure, but awards and institutional authorization are distinct stages. We examine the handoff through structured coding of 15 publicly documented access pathways captured on 19 September 2026, of which ten met prespecified inclusion criteria, and a process trace at one US university. Two isolated model-assisted coding passes found explicit eligibility criteria in nine programs and three implied institutional prerequisites across the corpus. Downstream specification was weaker: access duration was unstated in six programs, seven reported no use or outcome metric, and liability assignment was unstated in five to seven. Public terms did not establish an unambiguous institution-independent path from award to intended use in eight to nine programs, a composite that includes possible and unclear cases. In the institutional trace, policy required review even for free tools. A bounded request generated a ticket but no substantive response or decision pathway during the observation window. We define the authorization gap as the distance between an access award and authorized research use. Tracking first use, clearance, time to first use, and persistence would help programs distinguish allocated resources from usable scientific infrastructure.

Recent advances in agentic heuristic design use AI agents and execution feedback to automate algorithm discovery for challenging optimization problems. In many practical settings, high-quality solutions must be obtained under strict runtime constraints, motivating hybrid approaches that combine problem-specific heuristics with powerful mathematical programming solvers. However, existing approaches typically improve heuristic components within predefined procedures or tune solver configurations in isolation. This limits holistic adaptation of where to allocate computation, how to leverage solvers, and how to refine the overall algorithmic structure. To address these limitations, we propose HeurEvo, an automated plan–code–component co-evolution framework that jointly evolves the high-level algorithmic structures, their implementations, and a shared pool of reusable components. A planner determines which algorithmic components to use, how to combine them, and how to allocate runtime across stages, a coder realizes the resulting plan as executable code, while a component evolver updates the shared component pool. Within an island-based evolutionary framework, plans and implementations co-evolve with feedback from an interpreter agent that analyzes execution results and identifies opportunities for improvement. Across diverse combinatorial optimization benchmarks and challenging MIPLIB instances, HeurEvo finds high-quality solutions within tight runtime budgets, often matching or surpassing state-of-the-art optimization solvers given hours or days of computation. On several nonlinear geometry problems such as hexagon packing, it also improves upon the best previously reported results. These results highlight the value of jointly searching over algorithmic structure and implementation for agentic heuristic design.

While foundation models have revolutionized natural language processing and computer vision by leveraging universal vocabularies, Graph Machine Learning (GML) remains fractured due to the absence of a unified feature and structural representation across diverse domains. Existing works claiming to be Graph Foundation Models (GFMs) are typically restricted to node-level predictions or require fixed feature dimensions, failing to provide a truly task-agnostic backbone for the full spectrum of graph learning applications. In this paper, we introduce the Universal Classifier (UC), which supports arbitrary feature and class cardinalities, unifying node-, edge-, and graph-level objectives under a single similarity-based classification objective. The UC reformulates all node-, edge-, and graph-level prediction tasks as maximizing similarity in the latent space: by lifting heterogeneous features and labels into 3D latent tensors, the model learns transferable features independent of specific input schemas. This architecture allows a single pre-trained model to generalize to node classification, node regression, and link prediction across unseen graphs with varying feature semantics. Experiments show strong zero-shot transfer performance across node-, link-, and graph-level tasks.

Mixture-of-Experts (MoE) layers are central to frontier language models, and recent architectures push toward more and smaller experts. In this regime, the standard linear router becomes a bottleneck: with $M$ experts and hidden dimension $h$, its per-token cost $\Theta(Mh)$ dominates the MoE layer once $M$ is large. We introduce MoRE (Mixture of Rank-reduced-routed Experts), which factorizes the router weight matrix at rank $r$ and reduces the routing cost to $O((h + M)r)$. We prove that rank logarithmic in $M$ suffices for routing expressivity when the number of active experts is fixed, and is necessary up to precision factors. We also prove that logarithmic rank preserves load balance in a Gaussian memorization model, and training on a synthetic phonebook task shows that low rank does not hurt memorization. At matched active FLOPs, the factorization allows a factor of $\Theta(h/r)$ more experts. To realize this gain in wall-clock time, we design a fused Triton kernel at inference that avoids expensive memory operations on HBM. Empirically, MoRE improves memorization on the phonebook task and performance on knowledge-intensive Q&A benchmarks after pretraining, while matching reasoning ability. Code available at https://github.com/Matheart/MoRE_code.

Most videos capture only a narrow field of view and provide no spatial audio, limiting the sense of immersion they can provide. Recent video generation models can expand perspective videos into panoramic ones, but do not provide the corresponding spatial soundscape. Without spatially consistent audio, these expanded visual worlds remain incomplete. This paper presents OmniDream, a training-free framework that transforms a silent monocular video into an immersive audiovisual experience, where viewers can freely look around while sounds remain spatially aligned with the visual scene. At the core of OmniDream is an object-centric audio representation that disentangles each sound source's intrinsic audio content from its scene-dependent acoustic effects, enabling independent audio generation, physics-based simulation of propagation effects, and flexible spatial audio rendering. Experiments show improved audio-visual alignment, spatial correctness, and perceptual immersiveness over baselines. Examples are available on https://huggingface.co/spaces/CuriousAlien000/spatial-audio-360-demo

Sparse autoencoders (SAEs) expose interpretable features in large language model activations, yet existing structured SAEs impose single-parent trees or forests, while post-hoc graphs permit multiple parents but neither guide feature learning nor ensure reliable relation recovery. We introduce the Adaptive Graph Sparse Autoencoder (AG-SAE), a structure-guided training paradigm that treats each feature's complete parent set as an atomic structural hypothesis and lets evidence select zero, one, or multiple parents. By competing complete parent sets against null, subset, and alternative explanations, AG-SAE identifies jointly necessary multi-parent relations while rejecting redundant or spurious alternatives and verifying that each child contributes beyond its parents. The induced topology over SAE features then defines a differentiable structural loss that guides SAE training, while topology-guided refinement mitigates feature absorption and uses persistent reconstruction gaps exposed by the learned structure to initialize new features. The entire graph is then induced again from the revised dictionary by reassessing every feature's complete parent set, closing the dictionary-graph self-consistency cycle. Experiments demonstrate exact mixed-topology recovery in a controlled toy model, greater relational reliability and semantic validity than structured and post-hoc baselines on real LLM activations, and stronger feature-level causal interventions than conventional SAE features. AG-SAE thereby turns recovered mixed-topology feature structure into an unsupervised training signal that improves the dictionary, enables reliable feature organization beyond the topological limitations of trees, and exhibits stronger causal control beyond reconstruction.

This paper develops a safe and fully decentralized multi-agent reinforcement learning (MARL) algorithm to solve a class of discrete-time control problems on networks, including the persistent monitoring problem. Fully decentralized control of agents, while offering numerous benefits, faces issues such as exponentially increasing sample complexity, lack of global information about the system, and challenges in coordinating between agents. To address these issues, this paper introduces a fully decentralized multi-agent reinforcement learning algorithm that integrates deep reinforcement learning with safety considerations. This method feeds a history of local observations of the network's state into two parallel neural-network branches: the graph encoder, which adds structural information and correlations among nodes, and a state estimator, which predicts the uncertainty at each node in the graph. Additionally, the result of feeding that input into an actor-critic network is passed through a discrete-time control barrier heuristic to reduce the likelihood that any node will be neglected. This approach enables teams of fully decentralized agents to solve challenging problems by increasing system awareness and incorporating built-in safety measures to prevent the adoption of potentially harmful control policies. Numerical results from a custom simulation environment demonstrate that the proposed algorithm achieves 26.3 percent lower average uncertainty than a centralized control policy and is within 1 percent of the uncertainty performance of a more computationally complex algorithm with added attention layers.

We investigate the extent to which the Hamas attacks on Israel of October 7, 2023, have affected German social media debates about Judaism and Israel. For this, we develop an approach to detect 26 anti-Semitic categories in user postings via large language models (LLMs). The approach is applied to Facebook and Telegram posts (N=125,718) from three months before and after the event. Methodically, we test different open-weight models in two setups—with and without user information as additional context to the post text. The best setup achieves up to 83 % F1-score for binary anti-Semitism detection on our manually coded validation set. User context provides valuable information for most LLMs and drastically reduces false positives, for example, when (critically) reporting on anti-Semitic incidents. Concerning our topic, we find that anti-Semitism is surging significantly on both platforms, while being about ten times more prevalent on Telegram compared to Facebook. Facebook users express anti-Semitic views most likely in posts about an alleged genocide in Gaza carried out by the Israeli army, whereas classic anti-Semitic stereotypes related to power and conspiracy theories are dominant on Telegram. After the attack, the discourse patterns on both platforms show signs of convergence, as classic anti-Semitism increases on Facebook, whereas Israel-related categories surge on Telegram.

Prompts are the primary mechanism for directing the behavior of large language models (LLMs). Yet the internal structure and causal hierarchy of prompts remain poorly understood: which parts are causally necessary and which are redundant is an open question. This opacity can have severe consequences. Subtle prompt variations can silently shift model outputs in critical software systems, and engineers lack techniques to reason about prompt reliability. We present \framework, a blackbox prompt-minimization framework that reduces few-shot prompts to their necessary minimal subset. We use a case study to apply \framework to a few-shot learning system and demonstrate the insights that this framework can provide. Our experiments show that few-shot exemplars can be reduced by a mean of 65.3%~$\pm$~15.8% in character count while fully preserving propositional output fidelity. The models preferentially retain logical identifiers and constraint declarations while discarding natural language prose and cross-prompt relational annotations. Our analysis also shows that some models are universal encoders, able to produce highly legible yet minimized prompts, while others are universal decoders, able to interpret minimized prompts from most other models. By identifying which components are indispensable, \framework provides a principled basis for prompt compression and structural analysis of few-shot exemplars.

EEG foundation models (EEG-FMs) are intended to generalize across different datasets by learning representations that, ideally, are invariant to dataset-specific EEG configurations such as electrode montages. However, EEG-FMs that accept different montages as input do not guarantee that representations and predictions remain stable across different electrode configurations, especially outside the training setting. In this work, we investigate the effects of different electrode montages through a joint functional and representational analysis of four EEG foundation models selected to span distinct montage-handling designs. We evaluate embeddings on cross-subject resting-state eyes-open/closed and within-subject motor-imagery classification under spatially informed channel reduction. Functional robustness is tested through the generalizability of linear probes across channel counts, while representational robustness is assessed through within-subject similarity and preservation of between-subject geometry. The four models show distinct robustness profiles, and the two axes dissociate: large changes in embedding similarity need not come with comparable probe degradation, and stable embeddings can still lose downstream performance. Comparing two readouts of the same encoder further shows that aggregation, not the encoder alone, determines functional robustness: pooling into anatomically aligned regions degrades less than a learned global readout, despite being montage-invariant by construction. Montage robustness is therefore a joint property of the encoder and its aggregation, and characterizing it requires both a representational and a functional axis. Input compatibility alone is evidence for neither.

Instruction-based text-to-speech (ITTS) systems enable natural-language control of expressive speech generation, but often offer limited transparency and fine-grained control over individual text units. Character-level controllable TTS systems provide explicit acoustic control, yet typically rely on user-specified acoustic attributes. To bridge this gap, we propose InstCharVoice, a unified framework that grounds natural-language instructions in character-level acoustic control. We first construct grounded instruction annotations on the WordVoice-5A-zh corpus using Qwen3-Omni. With this supervision, we train an autoregressive model to identify instruction-relevant characters and predict their acoustic attributes before generating the corresponding speech tokens. Keyword prediction and grounding-aware loss weighting help the model focus on instruction-relevant characters and attributes. Experiments show improved instruction following and keyword-level acoustic control over representative ITTS systems, with competitive speech naturalness and explicit character-level controllability. Audio samples are available at https://xxh333.github.io/instcharvoice-demo/.

Deep forecasters predict from a fixed-length lookback window, and lengthening it gives diminishing returns at a growing cost. Retrieval augmentation instead shows the model how similar past situations continued. Retrieving a whole past window gives every variate the continuation of the same past moment. In multivariate series, however, the best past match differs from variate to variate. We present GNA (Granular Neighbor Assembly), a retrieval layer for forecasting backbones that assembles neighbors at two granularities: whole past windows, which keep the variates coherent, and per-variate neighbors, in which each variate takes its future from its own best-matching past. A learned gate decides, per forecast step and variate, how much to trust these futures against a persistence forecast, next to the backbone's own forecast. Candidates come from an embedding trained to predict each window's future, and retrieval is strictly causal: a past window is used only once its future has been observed. With the same lookback for every model and the same retrieval constants for all datasets, GNA improves two Transformer backbones in 85 of 96 dataset-horizon settings, gives the lowest MSE on 8 of 12 standard benchmarks and beats its backbone in every seed on 10 of them. Both granularities are needed, and neighbors of mismatched queries are worse than none. Retrieval helps most where the lookback says least: the gate shifts trust to retrieved futures further ahead. Where it fails, on hourly non-stationary series at long horizons, the loss is consistent with a drifting level of the retrieved futures.

The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzmüller and Scott's Notes on Gödel's and Scott's variants of the ontological argument, reaches beyond the modal object language: its quantifiers range over domains containing the nominals and satisfaction operators of hybrid logic. A proof using one proves a theorem of the embedding, not necessarily of the modal logic. Whether a result is one of the modal logic can be settled by replaying it in an explicit calculus, or, more cheaply and for all results at once, by analysing what the embedding's proofs substitute. Every statement the Notes prove has a proof in the embedding substituting nothing outside the object language, 294 of them explicit. The Notes' own proofs substitute none either; what it flags are terms a prover introduced. A soundness theorem over general models closed under the object language, and a sentence of that language the embedding proves but which fails in one of them, fix what the certificate says. The Notes' three open questions are settled too, without nominals, but by the empty instance of the conjunction axiom, too cheaply to convince. Generalised to Gödel's "any number of summands", the axiom covers the empty conjunction and the singleton. This article restricts it to at least two different conjuncts, a non-degenerate reading of Gödel's footnote, and settles them again without nominals. In effect only the empty conjunction is excluded; the singleton comes back with the other axioms. In one variant the restriction refutes the possible existence of a God-like being; the answers return, with no side condition, once the Notes' non-emptiness clause is confined to Gödel's essence. Every theorem here is verified in Isabelle/HOL and independently in Lean 4, the separating model in its propositional part; the countermodels are Nitpick's, checked by the build.

Generative agent-based models (GABMs) are increasingly used to simulate social media dynamics, including misinformation spread. For such social simulations to be valid proxies of human behavior, LLM agents should replicate established human cognitive biases, among them the Illusory Truth Effect (ITE), where repeated exposure to a claim increases its perceived truth value. We investigate whether and how the ITE manifests across four LLMs (Gemma-3-4b-it, Qwen2.5-7B-Instruct, Llama-3.1-8B-Instruct, and GPT-5-nano) in a social media simulation context. We propose a two-phase within-context experimental design that embeds the repetition manipulation inside a realistic news feed interaction. Using this design, we collect 336,000 truth, importance, sentiment, and interest ratings across 100 statements, 10 feed variants, and 3 replications. The key comparison is between ratings assigned to repeated statements, seen throughout a simulation phase, and completely unseen ones, rated within the same experimental context window. We distinguish genuine ITE (truth-specific repetition boost) from mere exposure effects. We run an OLS regression followed by a Linear Mixed-Effect Model to account for differences across models and ratings. Our results reveal four qualitatively distinct patterns: Gemma-3 exhibits a genuine ITE; Qwen2.5 shows a mere exposure effect; GPT-5-nano displays no repetition effect on truth and mild skepticism toward repeated content; Llama-3.1 shows a small truth boost alongside decreases in evaluative dimensions. Crucially, temperature has no effect on these findings, and a variance decomposition highlights the high context-sensitivity of LLM rating behavior. Our findings caution against assuming uniform ITE replication across LLMs in social simulations, while suggesting that Gemma-3-4b-it may offer the most behaviorally realistic approximation for misinformation-related simulations.

Existing protein geometry models typically represent molecular surfaces using local geometric features such as sampled points, normals, and curvature. While effective for capturing exposed molecular shape, these representations do not explicitly model the volumetric organization beneath the surface or provide a consistent coordinate system for residue-wise volumetric structure. We introduce Protein-TetSphere, a registered residue-wise volumetric representation for proteins. Each protein chain is tetrahedralized to obtain local volumetric regions associated with individual residues, which are then registered to a shared fixed-topology tetrahedral reference and represented in a common Laplacian basis. This registration establishes consistent volumetric coordinates across residues, enabling local three-dimensional deformation to be integrated with surface and chemical information in a multimodal protein representation. We evaluate Protein-TetSphere on ligand-binding pocket classification, protein–protein interface prediction, and de novo protein binder design. Across the three tasks, Protein-TetSphere improves ligand-binding pocket balanced accuracy from $0.795$ to $0.826$, Pinder-Pair/Site AUROC from $0.914/0.852$ to $0.932/0.866$, and binder-design success from $14.95\%$ to $19.90\%$ on the BoltzGen Challenge Set and from $27.62\%$ to $32.19\%$ at the ProtDBench backbone level. These results show that registered volumetric geometry provides complementary spatial information beyond molecular surfaces across protein recognition, interaction, and design.

Recent work has established that power-law spectral conditions on data enable tight convergence bounds for deterministic gradient descent, resolving the conflict between classical exponential bounds and observed power-law learning curves. In this work, we extend this result to the stochastic regime of high-dimensional machine learning. We provide two main contributions: (1) We generalize the power-law spectral theory to Stochastic Gradient Descent (SGD), showing that the same spectral exponents govern stochastic dynamics; (2) For the fundamental case of isotropic Gaussian data, we provide a precise analysis of data shuffling, deriving exact constants that prove Single Shuffle is strictly superior to Flip-Flop and IID sampling. Our results bridge the gap between abstract spectral theory and practical stochastic training choices, offering a unified picture of how data geometry drives optimization speed.

Distributed quantum computing (DQC) has been proposed as a way to scale quantum algorithms for practical applications beyond monolithic quantum processor architectures. Among these applications, quantum chemistry is widely regarded as one of the most promising use cases for quantum computing. In this work, we estimate the distributed-resource requirements of unitary coupled-cluster (UCC) ansätze for quantum chemistry, focusing on unitary coupled-cluster singles and doubles (UCCSD), unitary pair coupled-cluster doubles (UpCCD), and unitary pair coupled-cluster with generalized singles and doubles (UpCCGSD) circuits for hydrogen chains. We focus on a teleportation-based approach to DQC, quantitatively comparing a naive distribution method to the output of the TeleSABRE algorithm. For both approaches, we estimate the cost of handling nonlocal two-qubit gates across a fixed midpoint or quarter-point partition, reporting Bell-pair/classical-communication costs in teleportation. Across Jordan-Wigner and Bravyi-Kitaev, we find that UpCCD with spin-blocked Jordan-Wigner ordering gives the most favorable scaling, while UCCSD incurs substantially larger distributed-resource requirements.

Large language models can learn abstract rules from just a few in-context examples, but how their internal mechanisms activate as examples accumulate is not well understood. We trace a three-stage symbolic reasoning circuit (abstraction, induction, retrieval) across shot counts in three model families and find it is detectable and functional well before the model achieves high accuracy. Per-head causal contribution grows up to 8x from 1- to 10-shot, and cross-shot activation patching raises accuracy from 1% to 56% at 0-shot and 17% to 88% at 1-shot. Function vectors scaled and injected at 0-shot rescue accuracy up to 86%, largely substituting for the induction stage but depending critically on an intact downstream retrieval stage. The infrastructure for abstract rule-following is present in the weights before any demonstrations; in-context examples, function vectors, and related interventions appear to supply input to the same latent circuit.

Reliable evaluation of large language models (LLMs) is essential for their development and deployment, yet is often costly, risky, and difficult to perform safely online. We study off-policy evaluation for LLMs, where limited human-labeled data from a behavior model are used to evaluate a newer target LLM. This setting is challenging because labels are scarce, behavior–target distribution shift is common, and response likelihoods are often unavailable for black-box LLMs. We propose the Optimal Transport-based Robust Off-Policy Evaluation (OTROPE), a likelihood-free evaluation that performs distributional correction in a semantic space via optimal transport to align labeled behavior-policy samples with unlabeled target-policy samples. OTROPE combines corrected human-labeled residuals with proxy predictors, yielding a doubly robust-style evaluation without behavior-policy modeling or density-ratio estimation. We theoretically characterize why baseline evaluators fail under LLM distribution shift, and establish consistency and convergence rates for OTROPE when either the reweighted behavior distribution or the proxy predictor converges. Experiments on synthetic and real LLM evaluation tasks show that OTROPE consistently outperforms baselines while enabling ensembles of weaker LLM evaluators to approach and sometimes surpass stronger evaluators. Code is available at https://github.com/LinerXiang/OTROPE.

Existing multimodal scaling laws fit multimodality terms empirically after testing and never vary how much data is multimodally paired at fixed data budgets. We investigate how, under the same total data per modality, changing the number of paired data affects loss curves in multimodal classification tasks. We train models in three different environments and run experiment sweeps varying data sizes and pairing budget. Pairing ratios have a dramatic impact on loss and this impact is directly tied to how much information synergy the task contains. Only paired data is able to reduce synergistic loss, while unpaired data can reduce redundant or unimodal information up until unimodal floors. Unlike traditional scaling laws where loss drops immediately in power law decay, synergy acquisition is gated, requiring a critical threshold of paired data before synergistic loss falls at all. We introduce a new family of multimodal scaling laws where total data-attributable loss is the sum of four individual power laws corresponding to the four different information channels of redundancy, a unique channel per modality, and synergy, and show how this law is both more theoretically sound and empirically valid across our experiments. This law predicts multimodal loss in our experiments more accurately than existing laws, with 3.2% error on fit tests versus 10.4% error for the best pairing extension of published laws.

Recent studies have observed that parameter changes during language-model post-training can be concentrated in a small subset of coordinates. This phenomenon has been reported in reinforcement learning, on-policy distillation, and supervised fine-tuning on near-policy data. Its recurrence across different post-training paradigms suggests shared structure in training dynamics. In this paper, we examine this pattern through the diagonal model Fisher, which measures the sensitivity of the model's output distribution to individual parameters and is independent of any particular reward or teacher signal. Theoretically, we show that small diagonal Fisher leads to small expected gradients across a range of training objectives, providing a common explanation for sparse gradient updates. Empirically, we test this connection in RL and OPD. We find that Fisher identifies where gradients are concentrated, and fixed sparse masks selected from the initial Fisher retain a large proportion of the improvement from full training. Finally, we investigate the mechanisms underlying low Fisher in on-policy training. Our results show that high-probability next tokens tend to have similar parameter sensitivities, contributing to low Fisher. Together, these results establish the diagonal model Fisher as a unifying perspective linking update sparsity to on-policy training dynamics in LLM post-training.