Papers

Most time series forecasting benchmarks remain numerical-centric and provide limited support for evaluating contextual information that shapes real-world temporal dynamics. Existing multimodal benchmarks also suffer from limited data and context coverage, fragmented evaluation settings, and overreliance on aggregate evaluation. In this paper, we propose MUSE-Bench, a unified benchmark for multimodal time series forecasting with heterogeneous context. It comprises fourteen datasets across eight domains and six types of context: metadata, events, holidays, news, images, and numerical covariates. We evaluate diverse forecasting paradigms, including statistical, data-specific, foundation, multimodal, and general-purpose LLM forecasting methods under shared non-overlapping forecast windows, common target observations, and consistent point and probabilistic metrics. Extensive experiments yield three main findings. First, numerical time series foundation models dominate the overall ranking, while Aurora, the evaluated multimodal foundation model, trails the leading numerical TSFMs but outperforms all evaluated data-specific models. Second, ablations show that external context improves the four evaluated context-aware models, whereas incorrect or temporally misaligned context degrades performance. Third, general-purpose LLMs perform poorly as direct forecasters, and LLM-guided refinement does not yield consistent improvements. MUSE-Bench enables systematic evaluation of how forecasting models utilize context and provides a foundation for future multimodal forecasting research.

The maximin share (MMS) is a central fairness benchmark for allocating indivisible items, but it need not be simultaneously attainable even under additive preferences. While extensive work has developed approximation guarantees, quantitative impossibility bounds have received comparatively little attention. We establish improved asymptotic and constant impossibility bounds for both goods and chores. For every sufficiently large number $n$ of agents, we construct additive goods instances in which every allocation gives some agent at most a $1-\Omega((\log n)^{-2})$ fraction of her MMS. This strengthens the $1/n^4$ shortfall of Feige, Sapir, and Tauber (2021) to an inverse-polylogarithmic shortfall. For chores, we construct instances in which every allocation gives some agent cost at least a $1+\Omega((\log n)^{-2})$ factor of her MMS. Consequently, for every fixed $\varepsilon>0$, guarantees of $1-O(n^{-\varepsilon})$ for goods and $1+O(n^{-\varepsilon})$ for chores are impossible. Both asymptotic constructions use $n+O(\log n)$ items. Together with concurrent existence results of Feige (2026), this determines the threshold $n+\Theta(\log n)$ for guaranteed MMS existence under additive preferences, for both goods and chores. We also give four-agent, eleven-item instances that improve the universal impossibility bounds from $39/40$ to $20/21$ for goods and from $44/43$ to $31/30$ for chores.

We present shape calculus techniques and a scalable automatic shape differentiation framework for multi-phase topology optimisation on unfitted discretisations defined by several level-set functions. First we establish general, exact shape calculus expressions in the discrete case for multi-phase systems by leveraging concepts from convex geometry. To complement this theoretical foundation, we introduce an open-source multi-phase automatic shape differentiation framework based on polytopal cutting. This computational framework is validated against both finite differences and our established exact expressions, matching the latter to near machine precision. Furthermore, the proposed automatic shape differentiation is scalable across distributed computing environments, demonstrating near ideal weak scaling up to 1.65 billion finite elements across 13,824 computer cores. We demonstrate our implementation by solving unfitted multi-phase topology optimisation problems for anisotropic diffusion, linear elasticity, and fluid–structure interaction. Together, these theoretical and computational contributions provide a robust and accessible foundation for advancing multi-phase topology optimisation using unfitted finite element methods. In particular, the methods enable the solution of topology optimisation problems involving multi-phase and multi-physics systems with non-trivial boundary conditions. The open-source software is available at https://github.com/zjwegert/GridapTopOpt.jl.

Mixed-curvature representation learning seeks to capture rich geometric structures that cannot be adequately modeled by a single curvature regime. Existing approaches largely rely on product manifolds, which require manually specifying how different curvature spaces are combined and separate their curvature contributions across factors. We introduce the $\mathbb{SL}(n)$ space, a representation geometry defined by the simple $\det(A)=1$ constraint and a left invariant Schatten-$p$ Finsler structure. Despite this minimal construction, $\mathbb{SL}(n)$ exhibits pointwise negative, zero, and positive flag curvature around a common flagpole, while its mixed-curvature and curvature-coupling capacities are asymptotically maximal relative to the intrinsic geometric upper bound. Beyond geometry, its noncommutative group structure provides inherent order sensitivity, and its non-nilpotent Lie algebra admits nonzero nested Lie brackets at arbitrary depth, enabling deep order-aware composition. Empirically, $\mathbb{SL}(n)$ consistently outperforms a broad range of representation manifold baselines across graph benchmarks at different scales. It reduces average distortion over the strongest baselines by $44.3\%$ on KEGG and $40.5\%$ on HumanCyc, and improves Hits@20 by $42.8\%$ on OGBL-PPA. Experiments on Flickr30k-Order further support its ability to capture higher order dependencies from ordered composition. Together, these results show how a seemingly simple structural constraint can yield unexpectedly rich geometry, capacity, and composition within a unified representation space.

Passive counterweights are simple gravity compensators, but a counterweight selected from a single pose is not generally optimal for the configurations and tasks a manipulator actually executes. This paper develops a task-distribution-aware synthesis framework in which the operating distribution $\rho(q)$ enters the design explicitly. For a counterweight moment $p=m_c r_c$ with gravity torque $-gp\phi(q)$, the weighted mean-square residual gravity torque has the closed-form minimizer $p^*=E_\rho[\tau_g\phi]/(gE_\rho[\phi^2])$. If payload gravity torque is affine in payload mass, the optimum is also affine: $p^*(m_p,\rho)=p_0^*(\rho)+m_pK_p(\rho)$. For fixed static moment, added counterweight inertia is $I_c=pr_c$ while mass is $m_c=p/r_c$, so mass-radius selection is underdetermined unless physical constraints are specified. A recovered three-link manipulator is used as a case study. At $r_c=0.20$ m, zero-payload equivalent optima are 0.672 kg for uniform joint-space operation, 0.683 kg for approximately uniform task-space operation, 0.713 kg for a representative pick-and-place family, and 0.952 kg for a high-gravity-biased distribution, a change of more than 40% caused solely by the operating distribution. Nondominated fronts show that preferred mass-radius pairs depend on declared engineering bounds. A rated-torque-referenced all-joint screen increases zero-payload feasible task-space coverage from 78.1% without compensation to 93.7% for the uniform-distribution design. A lumped point-mass trajectory study gives a provisional crossover from no counterweight at very aggressive motion to stronger compensation as motion slows. These actuator and dynamic results are engineering consequence studies rather than physical validation.

Multi-agent LLM architectures, such as LangChain and AutoGen, largely assume English as the lingua franca for internal inter-agent communication, even when the end-user task is non-English. We fill this gap by evaluating a two-agent extraction-answer core, with an additional back-translation agent in the English-forced condition, across four typologically diverse languages (Hindi, Chinese, Spanish, Arabic; n = 300 per language) using the Aya-23-8B model. We compare a native-language pipeline to an English-forced one (which incorporates a final back-translation step from English to the user's language). We discover a statistically significant English-Forcing Tax (surviving a strict Bonferroni correction) that isolates the cost of English routing from general multi-agent orchestration overhead. Forcing inter-agent communication through English reduces Exact Match accuracy by 13.0 percentage points (Spanish) up to 30.6 percentage points (Hindi) compared to native-language multi-agent execution. Using chrF scores as a diagnostic measure of English-reference lexical overlap, we find that lower overlap is strongly associated with pipeline failure, consistent with translation loss being an important contributor to the observed performance drop. These findings suggest a compelling case for native-language routing in agent frameworks when the source and target languages are typologically distant, reducing a compounding translation tax.

Vibe design agents translate natural-language requests into interfaces, yet repeated generations often converge on similar visual directions. We present an inference architecture that makes design exploration an explicit stage before implementation. A pre-pass proposes structured design specifications with typicality weights, an external policy samples a direction, and the generator implements it under fixed decoding settings. Candidate elicitation draws on Verbalized Sampling. Applied to UI themes and visual-asset prompts, this architecture provides direct control over aesthetic exploration without changing code-generation temperature. Across 168 benchmark prompts, theme sampling expands observed selection coverage from one option to nearly three and increases rendered visual variation. For visual-asset prompts, the strongest observed LLM-judge win/loss ratio is 1.32, with only a small change in whole-screen similarity. Localized aesthetic choices can thus influence judged preference even when the overall screen remains similar. We further evaluate joint theme and asset sampling in a randomized online study conducted over nearly two months, covering 3.39 million tasks and 87,416 labeled conversations. These studies show how explicit design specifications support exploration of alternative UI concepts and help us evaluate their effects on rendered interfaces, judged preference, and user interaction.

Molecular design is typically approached as a problem of finding molecules which can adopt a single bioactive conformation. In reality, molecules occupy a distribution over conformations, and many of the properties which determine whether a candidate is viable depend on that distribution rather than on any single conformer. We reframe molecular design as an optimisation of both the modes and properties of molecules' conformational ensembles, where modes can be represented as shapes, pharmacophore profiles or protein pockets, and properties are aggregate scalars computed over the whole distribution. To realise this we introduce ensemble-conditioned guidance, a framework which conditions 3D molecular generative models on both axes simultaneously. Mode conditions are composed adaptively at inference by combining the vector fields produced under each condition. Conditions may be targeted or avoided, mixed across modalities and combined in arbitrary numbers, allowing a wide range of design tasks to be expressed with a single trained model. We introduce adaptive symmetry learning to allow conditions from different reference frames to be composed, and extend our generative framework to enable flexible-size generation. We evaluate on new benchmarks for multi-mode conditioning and ensemble property optimisation, and apply the framework to two practical drug discovery tasks, dual-target binder design and active-state-selective agonist design, where in both cases conditioning on the additional state improves the desired outcome over single-state conditioning.

Methods of Branched Optimal Transport (BOT) mimic the economy and efficiency of natural tree-like structures, such as those found in rivers and biological systems. These methods are widely applicable for designing efficient networks in society, from river basins and blood vessels to mail and gas distribution systems. However, they remain understudied in the context of designing deep generative models, particularly at a large scale. Standard continuous-time generative models, such as the flow matching approach, fail to capture the inherent hierarchical and branching patterns present in real-world data. Current models provide no mechanism for flows to merge or share pathways to minimize total transport cost. Inspired by the "economy of scale" principle in BOT, we introduce a novel, scalable branched flow-matching algorithm designed to solve the branched optimal transport problem in high dimensions. Our method adapts the Benamou-Brenier continuous-time optimal transport formulation to learn branched generative flows. These flows allow probability mass to aggregate along common pathways before branching out to diverse targets. Parametrized by neural networks, our method effectively learns complex branched generative processes. We demonstrate its effectiveness on challenging high-dimensional tasks in biology and image generation.

The Komlós conjecture is a classic problem in discrepancy theory; it asks whether an absolute constant $K$ exists such that given any $n$ vectors $a_1,\ldots,a_n$ inside the $m$-dimensional Euclidean ball, regardless of how large $m,n$ are, there is always a selection of signs $\varepsilon_1,\ldots,\varepsilon_n$ guaranteeing $$\|\varepsilon_1a_1+\ldots+\varepsilon_na_n\|_\infty \leq K.$$ We show that if the $\varepsilon_i$'s are allowed to take not just the values of $\pm 1$ but any unit modulus complex number, which we refer to as complex discrepancy, then the above inequality holds for a finite, explicit constant $K_{\mathbb{C}}$. Here, the $\ell^\infty$ norm of the resulting vector in $\mathbb{C}^m$ is the largest modulus of its entries, and thus the complex discrepancy of real vectors is equivalent to their rank-$2$ vector discrepancy. This quantity provides an upper bound (modulo uniform constant prefactor) on Gaussian discrepancy – a discrepancy measure introduced by Chewi, Gerber, Rigollet and Turner. Thus, we also resolve the Komlós conjecture for Gaussian discrepancy. Our paper builds upon the recent work of Bansal and Jiang on the Beck-Fiala and Komlós conjectures, which we approach from the formalism of Burkholder and the Bellman function method from probability and harmonic analysis. Our work was in part motivated by the realization that the complex discrepancy of the columns of any unitary matrix is equal to 1, a fact that follows from a straightforward calculation based on Idel and Wolf's generalization of the Sinkhorn normal form for unitary matrices.

Diffusion Language Models (DLMs) generate text by iteratively denoising a masked sequence, independently predicting multiple tokens at each step. This conditional independence discards inter-token dependencies and degrades coherence-an issue that parallels the multi-modality problem in Non-Autoregressive Translation (NAT). Drawing on the Directed Acyclic Transformer (DAT), which tackles this problem in NAT via a Directed Acyclic Graph (DAG), we propose DA-DLM, a model that adapts DAG-based dependency modeling to DLMs' iterative setting through a position-oriented DAG design. The position-oriented DAG binds node groups to fixed output positions so that tokens fixed in earlier steps anchor neighboring predictions via learned transitions, and evolves with denoising to focus on remaining uncertainty as anchors accumulate. On language modeling, open-ended generation, and summarization, DA-DLM consistently outperforms Block Diffusion, especially under fewer denoising steps, and matches autoregressive models while preserving the parallel generation advantage. Our code is publicly available at https://github.com/jipy0222/DA-DLM.

Procedural audio has emerged as a viable source for transferable audio representation learning, but its design principles remain unclear.We revisit two questions: how a procedural source should be scaled, and whether training choices developed on natural audio should transfer unchanged to procedural data.Using a controlled source, we separate scale into formula-class coverage C and within-class rendering diversity I.Experiments with FDSL and AudioMAE show that these two forms of scale provide different benefits and depend on the learning formulation and downstream task. A matched AudioMAE study further shows that procedural audio favors low mask ratios (10%–25%), whereas AudioSet-28K favors 50%–75%. Shared-codebook analysis reveals lower patch diversity and stronger temporal predictability in procedural audio. These results motivate source-aware procedural pre-training, where source scaling and learning configuration are considered jointly.Code is available at https://github.com/Cross-Innovation-Lab/Formula-Bank.

We present Salesforce Koa, an enterprise language model built by post-training the open-weight Nemotron-3-Super-120B foundation model with reinforcement learning using Group Relative Policy Optimization (GRPO), and deployed in FP8 for production. Koa is trained only on public and synthetically generated data, and specialized for the agentic tool use that enterprise workflows demand: routing a request to the correct action, invoking the right tool with valid arguments, and completing multi-turn business tasks. The distinctive component of our pipeline is specification-driven task construction: declarative Agent Script specifications are expanded into persona-conditioned multi-turn environments whose rewards are grounded in successful tool use. Applied to enterprise CRM specifications, the same pipeline produces the in-domain training distribution on which Koa is specialized. On CRMAgentBench and the human-labeled production tool-calling set, Koa outperforms both its untuned open-weight base and GPT-4.1 and is competitive with the strongest frontier models. It reaches 87% Task Success Rate on CRMAgentBench (vs. GPT-4.1 at 82% and the base at 79%), is at or near the top of every metric on the human-labeled portion of an internal production benchmark, and preserves the base model's general capability on public benchmarks (Tau2Bench, BFCL). A controlled comparison with architecture and RL recipe held fixed shows that the additional in-domain RL stage improves argument accuracy and full tool-call success on the human-labeled enterprise benchmark.

Autonomous agents operating on multisensory data cannot assume that all sensory modalities remain consistently informative. In real environments, sensory streams are frequently corrupted by noise, missing data, or inter-modal incongruence, requiring adaptive arbitration between competing sensory hypotheses. While active inference provides a principled framework for uncertainty-guided inference, the role of dynamically inferred sensory precision in generative multimodal arbitration under sensory conflict remains comparatively underexplored. We propose a multimodal perceptual inference model in which latent beliefs and modality-specific sensory precisions are jointly updated through iterative free-energy minimization. In our proposed model, sensory precision dynamics not only reflect sensory uncertainty but actively shape the evolution of latent beliefs during multimodal conflict. In addition, we introduce a learned prior over sensory precisions that induces structured, class-dependent precision patterns and influences cross-modal inference dynamics. We evaluate the model using a synthetic multimodal MNIST dataset combining visual, auditory, and tactile representations of digit classes under controlled sensory noise and inter-modal incongruence. Results show that dynamic precision inference improves reconstruction robustness under corrupted sensory evidence, supports coherent latent inference from reduced sensory evidence, and enables stable arbitration between conflicting modalities. Furthermore, learned precision priors generate interpretable precision structures that shape inference dynamics and cross-modal latent structure. These findings support sensory precision inference as a mechanistic control process for adaptive multimodal belief formation under uncertainty, highlighting precision dynamics as a computational mechanism for robust and interpretable multisensory integration.

Reinforcement learning (RL) is widely utilized in large language model training to improve targeted capabilities, yet how RL reshapes a model remains poorly understood. Prior attempts to explain how RL works largely offer behavioral perspectives, leaving open what RL gives a model at the representation level: can RL create genuinely novel features, and which existing features does it enhance or suppress? Recent developments in mechanistic interpretability suggest sparse autoencoders (SAEs) as a promising lens to decompose internal activations into human-interpretable features; however, they cannot be directly applied to tracking change across training. In this work, we introduce Fixed-SAE Track, a framework that trains one shared SAE per considered layer on activations pooled across the base model and all RL checkpoints, holding every feature direction fixed so that representation shifts are rigorously defined through the activations of interpretable SAE latents, including the detection of emerging novel features. Validated across multiple datasets and RL algorithms, we find that RL-induced drift is small, gradual, concept specific, and concentrated in late layers, mainly enhancing the sampling rates of a small set of ladder tokens, formatting scaffolding such as step breaks and answer delimiters, rather than reshaping problem content. Steering these features into the base model recovers around 80% of RL's performance gain, suggesting that RL primarily elicits capabilities the model already possesses, much as steering does. We further design a synthetic benchmark with features known by construction to test whether RL can instill genuinely novel features. We believe Fixed-SAE Track provides a principled approach to tracking representation shifts and offers representational evidence for understanding how reinforcement learning changes the inner representation of LLMs.

A long-standing open question in query complexity asks whether there is a total Boolean function f with R(f) << C(f), where R(f) and C(f) denote its bounded-error randomized query complexity and certificate complexity, respectively. We construct a function with R(f) = O~(sqrt{C(f)}), which is optimal up to log factors. The same function also has $Q(f) = O~(C(f)^{1/4}), where Q(f) is the bounded-error quantum query complexity of f, which is also nearly optimal.

We determine the exact time exponent of space-optimal reversible pebbling on chains as $1.331742379256310\ldots$. The growth rate of space-optimal reach exists as a limit and admits a variational formula. The same exponent governs complete computations at minimal space, uniformly in the chain length.

Approximate nearest neighbor search (ANNS) retrieves the most similar vectors to a query vector in high-dimensional space. Label-filtering ANNS (LFANNS) extends ANNS with a label filter that the labels of base vectors must satisfy a set relation (e.g., equality, containment, or overlap) with the query labels. Existing LFANNS indices suffer from inconsistent performance across different filter types and degraded scalability under varying label scale and distribution. In this paper, we define label-stratified similarity graph (LSSG), where edges connect neighboring vectors whose label sets fall within stratified similarity thresholds. To implement LSSG efficiently, we design an incremental insertion algorithm to prune redundant edges in both vector and label spaces, and leverage a MinHash structure to ensure scalability for large-scale labels. We analyze stepwise probabilities under explicit label models and explain why stricter label tiers reduce ineffective in-filtering expansions. Benchmark experiments show that LSSG achieves ideal optimality for equality queries, and 1.06x-92.9x and 1.08x-84.1x faster than the best competing index for containment and overlap, respectively, in query speed with identical accuracy and 0.35x index size.

Deep learning has led to numerous proposed architectures for Automated Emotion Recognition (AER) from electrocardiogram (ECG) data, but inconsistencies in preprocessing, training, and evaluation make direct comparisons difficult. Most studies train and validate models on individual datasets collected under homogeneous conditions, limiting variability and raising concerns about generalizability. Cross-dataset validation is sometimes used but primarily assesses model adaptability rather than true generalization. This study presents a comparative analysis of prominent deep learning architectures in AER, emphasizing model generalization over dataset adaptability. To enable this benchmark, we introduce two open-source frameworks: Affective Research on Representations and Classifications (ARRC), a standardized benchmarking toolkit, and Affective Research Dataset Toolkit (ARDT), a framework for inter-dataset training and validation. Using ARDT, we consolidate three publicly available AER datasets, CUADS, ASCERTAIN, and DREAMER, into a single dataset, increasing variability in sensor types, recording conditions, and participant demographics. We then use ARRC to evaluate three widely studied deep learning models and two CNN baselines through hyperparameter optimization and 10-fold cross-validation. Our findings provide insights into the trade-offs between classification accuracy and model complexity, establishing a reproducible benchmark for AER research. All source code for ARRC, ARDT, and model evaluation is publicly available to ensure transparency and facilitate further research.

Multi-Agent (MA) systems are effective at solving complex tasks that demand planning, tool use, and the synthesis of evidence from multiple sources. Existing systems typically adopt Hierarchical Manager-Worker (HMW) or Router-based Message Passing (RMP) structures as their communication protocol. However, these designs restrict agent autonomy: Worker agents cannot directly consult specific "peers", and misrouted messages can propagate errors. Inspired by bus architectures in computer systems, we propose BusMA, a communication framework that allows any agent to address other agents through a shared channel, i.e., the Bus. It consists of agent registration, message routing, and shared memory management components. Worker agents, each equipped with tools, have their own local memory and can reason, act (tool usage), and communicate by posting shared messages with specific intents. We introduce four intents: discussion, challenge, guidance, and request for explanation, which support fine-grained communication among agents. A Chair agent monitors the shared memory to coordinate interactions and facilitate convergence among Workers. To evaluate the effectiveness of BusMA, we conduct extensive experiments with two frontier LLMs across 13 tasks spanning visual reasoning, mathematical reasoning, and knowledge retrieval. The results demonstrate that BusMA consistently outperforms state-of-the-art HMW and RMP methods.

Training prompts in online reinforcement learning (RL) differ substantially in how informative they are for the current policy: some are already saturated while others are too difficult to yield reliable learning signals, yet both receive equal rollout budget under standard training. We propose an exploration-guided prompt scaffolding framework that adapts the training prompt distribution dynamically throughout RL post-training of multimodal large language models (MLLMs). Central to our approach is the $\textit{Exploration Potential Score} (EPS)$, a lightweight rollout-based proxy for prompt utility derived from KL-regularized policy improvement theory, computable directly from on-policy rollout statistics without additional overhead. Rather than discarding low-utility prompts, we use a teacher model to generate scaffolded rewrites that preserve the original task intent while making subsequent training more informative, reframing teacher supervision as training-data refinement rather than output imitation. Integrated with GRPO on Geo3K and MMK12, our method consistently outperforms the baseline on both in-domain and out-of-distribution benchmarks, achieving up to 9.7% relative improvement in-domain and gains of 11.5% on MathVision and 11.1% on MMMU-Pro.

An ensemble can improve photovoltaic forecasts while adding components that contribute little or increase computation. We assess these effects through matched comparisons and ablations of a fixed heterogeneous predictor bank. Hourly experiments use GEFCom2014 and three additional public datasets, with chronological partitions and three seeds. Under retrospective ERA5 assistance, static fusion reduces scaled mean absolute error against matched boosting by 1.11%, 4.41%, and 1.63% on PVDAQ, OPSD, and Ausgrid; only OPSD remains supported after multiple-comparison correction. Weather gating offers no consistent incremental benefit. Exploratory member removals show group-level dependence alongside individual redundancy. A separate, previously inspected fifteen-minute case replaces one neural member with a tree predictor: normalized error falls by 1.72%, but measured inference is slower. These findings support component-wise evaluation with explicit limits on weather availability and test-set reuse.

Let $Y_s=\sqrt{s}X+Z$, where $Z$ is standard Gaussian and independent of the real random variable $X$. We prove that, under the square-exponential moment condition $\mathbb{E}e^{\beta X^2}<\infty$ for some $\beta>0$, the scalar minimum mean-square error $\operatorname{mmse}_X(s)$ is analytic at zero signal-to-noise ratio if and only if $X$ is Gaussian, with constant random variables included as degenerate Gaussians. The proof converts estimation in the Gaussian channel into a backward heat flow acting on the moment-generating function $M(z)=\mathbb{E}e^{zX}$. Under the stated tail condition, every non-Gaussian input forces $M$ to have a nonzero complex zero. We show that each zero cluster produces a finite singularity in its localized Borel transform at the action $\xi=z_0^2/2$. After removing the action scale, the Borel coefficients have a nonzero $n^{-1/2}$ prefactor for a simple zero. A zero of multiplicity $m\geq 2$ splits according to the roots of a Hermite polynomial and instead contributes a prefactor $n^{-m/2}e^{r_m\sqrt{2n}}$. A finite-disc localization and relative-cycle continuation argument then show that at least one such singularity survives in the full Borel transform. Thus, for every non-Gaussian input in the stated class, the formal zero-SNR expansion is Gevrey-1 but divergent. Rational-MMSE rigidity and the analogous analyticity criterion for mutual information follow as corollaries.

Xu, Vardi and Safran (ICML 2026) prove that over-parameterized ridge regression over an unstructured random Gaussian feature map groks, with the delay between memorization and generalization growing as $1/\lambda$ in the weight decay. We show that on a structured feature map the same delay does not appear. For a band-limited Fourier feature map over $\mathbb{Z}_p^2$ carrying a single-character target that lies inside the expressible class, enlarging the band at fixed positive weight decay drives peak held-out accuracy monotonically from $1.00$ to $0.07$, with no memorize-then-generalize regime anywhere along the sweep. The degradation is not an interpolation effect. It sets in at capacity ratio $q/n = 0.638$, far below the interpolation threshold, on separate grounds from the exact null space that appears above it. What does have a sharp boundary is the active support. Holding the nominal dimension fixed and masking the band back to $1089$ active modes restores held-out accuracy of $1.000$ with zero variance across seeds, while the full $4225$-mode band collapses to $0.185$. The number of active modes acts through the teacher-weighted spectrum of the empirical Gram matrix and not through the capacity ratio, which makes this a statement about feature geometry and not a restatement of double descent.

Personal health interfaces present wellbeing data through standardized dashboards that rarely fit how people interpret or act on it. Personalizing them to what people would like to see for themselves often requires design and technical expertise, a barrier that generative AI may potentially lower. Therefore, we ask what designs emerge and how it enables and constrains the design process. We conducted a co-design study where 14 participants redesigned Google and Apple Health interfaces using Figma Make. Participants reimagined interfaces that supported personal context, future planning, and interactive experiences, yet conversational AI designs converged around chat-window conventions. AI helped materialize loosely articulated ideas, but model defaults and generation latency shaped iteration. The process more readily operationalized interpretability and accountability than privacy, trust, and emotional safety. Generative co-design let participants create interfaces directly, blurring the boundary between intentions and model defaults. We discuss implications for preserving agency and flexible user-directed interfaces.

Prompt echoing is a recognized failure mode of instruct language models, in which a model instead of generating a response, mirrors the provided prompt, even though it did not receive a specific instruction to do so. Is this phenomenon a sign of the model leaking the content of its training dataset, or is it rather caused by a misaligned behavior of the internal induction/copying mechanisms? We investigate prompt echoing small language models from different families (Gemma, Llama, Qwen, SmolLM and OLMo) and show that echoing prompts are likely to have partial overlap with the training dataset but the phenomenon is primarily driven by the model's induction heads.

Data attribution seeks to quantify how individual training examples shape a model's predictions and underpins problems including data valuation, machine unlearning, and model interpretability. Despite having a long line of work, computationally scalable methods often struggle to predict the effect of removing training data in neural networks due to their non-convex nature. To overcome this challenge, metagradient-based methods such as MAGIC (Ilyas and Engstrom, 2025) differentiate each prediction through the entire training run and compute its exact influence with respect to the training data, but require a separate run for every prediction. To reduce this cost, we cast budgeted attribution as estimating a large influence matrix from a small number of measurements. We show that the measurements most appropriate for recovering this matrix differ from those best suited for attribution itself. We then present two algorithms, MAGE and SPELL, suited for reconstruction and attribution respectively, that run on existing metagradient machinery at no extra cost. Empirical studies demonstrate strong performance over existing baselines across training scales and measurement budgets.

User prompts provided to large language models (LLMs) may contain private information. One way to protect them is to execute the LLM inside a trusted execution environment (TEE). However, this results in slow inference times as current TEEs are significantly slower than GPUs for LLM inference. To circumvent this, Tramèr and Boneh (2019) proposed Slalom which splits neural network inference between a TEE and an untrusted GPU. They encrypt inputs to computations outsourced to the GPU. In this paper, we extend this split-inference architecture to LLM inference and instead protect intermediate inputs using differential privacy (DP). We first demonstrate that masking intermediate representations is necessary by showing an 80% accuracy on a prompt-reconstruction attack from these representations. Our main contribution is a global sensitivity analysis of key functions in LLM inference, which bounds the required scale of DP noise. Unlike encryption, DP avoids quantization, allowing the LLM to remain in the floating-point domain. We also derive an upper bound on the floating-point error from masking and subsequent noise cancellation as a function of the privacy parameter epsilon, keeping the same quality of the LLM response. We implement our architecture using the Intel TDX TEE and two LLMs: Llama-3.2-3B and Qwen3-4B. Our split execution is nearly twice as fast as fully TDX-based inference. Moreover, it is at most 43% faster than Slalom while achieving higher accuracy. Finally, we demonstrate that prompt reconstruction, even with knowledge of the DP mechanism, cannot recover more information than is contained in an unrelated prompt.

Language-model agents are increasingly used as synthetic people in surveys and social simulations, yet their apparent realism is often judged from population averages or distributional similarity. We tested what such evidence actually establishes by comparing Claude, Codex and Kimi under four prespecified prompt designs with matched farmer decisions from China and four African countries. Some configurations reproduced observed means and adoption rates. However, their person-level predictions were weak; their decisions clustered around typical values and policy-relevant extremes were largely missing. Most strikingly, a simple generator fitted only to the observed marginal dis- tribution, and given no information about any farmer, achieved greater distributional similarity than every language-model configuration. Prompt additions produced conditional gains rather than uni- versal improvement: results varied with model, outcome, population and validation target. We call this the average-farmer illusion: a synthetic population can look realistic while failing to repro- duce who does what or how behaviour varies. We provide a claim-matched validation framework and reusable modular prompts that turn prompt construction into an auditable experimental process. Population-level resemblance should therefore be treated as the start of validation, not as evidence of individual simulation.

Low-rank gradient projection reduces the optimizer-state memory cost of large language model (LLM) pretraining, but the steps and wall-clock time needed to reach a target quality remain a meaningful axis for improvement. We attribute this to two design choices in existing methods: the projection-rank budget is allocated uniformly across Transformer modules with heterogeneous projection sensitivity, and projecting a raw gradient attenuates its magnitude and direction jointly. We propose MoARa, which combines a static profiling-based module-aware projection-rank allocation with a block-wise magnitude-direction decomposition; the default block size is set in the neighborhood of the attention head dimension. Across five Transformer architectures spanning Llama, Qwen, and DeepSeek at 300M to 7B scales, GaLore with MoARa reaches standard GaLore's final perplexity in 37% fewer steps and 34% less wall-clock time on Llama 2 7B, with only 0.2% peak reserved memory overhead under standard graph compilation. Across the six low-rank pretraining methods we evaluate, module-aware rank allocation alone delivers directionally consistent step reductions on all six. On compatible hosts, the two-component design reaches up to 41.7% step reduction and 37.1% wall-clock reduction.