Papers

Learning reward functions from demonstrations assumes that demonstrations provide adequate supervision over all features – or task-relevant aspects of behavior. In practice, demonstrations are often imperfect: humans may under-emphasize certain features due to cognitive load or physical difficulty, or the training regime may fail to sufficiently cover all relevant situations. In either case, important features may be underspecified, leading to ambiguity in the learned reward function and misaligned behavior at deployment. We propose a framework that detects such underspecified features and actively solicits targeted corrective demonstrations. Our key insight is that demonstrations implicitly reveal which features are well specified: features that are consistently optimized show little variation across demonstrations, while features that are underspecified vary widely. We leverage this statistical signal to infer which features may have been insufficiently demonstrated. The robot then explains which features it is uncertain about in natural language and queries for demonstrations that explicitly address the identified gaps. We evaluate our approach in a simulated tabletop manipulation domain and in a user study with a real Franka robot. Targeted, explanation-guided queries significantly improve reward recovery compared to random querying and passive data collection, reducing ambiguity that would otherwise persist in learning from imperfect demonstrations.

Test-Time Training (TTT) is an emerging paradigm that enables models to adapt their parameters during inference, improving performance on tasks such as few-shot learning, retrieval-augmented generation, and complex reasoning. However, this dynamic adaptation introduces new vulnerabilities that adversaries can exploit to jailbreak models. We identify three threat models for TTT and demonstrate how attackers can leverage them to bypass safety filters. Our results show that TTT can significantly increase the Attack Success Rate (ASR) and the ASR over 10 generation trials (ASR@10). For example, under LoRA, the few-shot and generation-phase threat models achieve an average ASR@10 of 95% and 93% respectively, across models from different families and scales. These vulnerabilities transfer to production fine-tuning APIs. We also show that TTT-induced overfitting can produce degenerate outputs that inflate ASR under standard judges, and propose a validity-aware evaluation to correct for this. Our findings suggest that TTT exposes a new attack surface, strengthens attacks, and undermines existing safety guardrails. As a first step toward defense, we propose a lightweight provider-side detector that flags TTT requests via the perplexity shift on a private harmful holdout, but robust deployment will ultimately require dynamic alignment.

Fill-in-the-middle (FIM) is a pretraining objective widely used to equip causal language models with infilling ability, yet its effect on verbatim memorization remains underexplored. We study the memorization dynamics of FIM in a controlled setting by pretraining matched Llama 3.2 models with FIM and standard left-to-right (LTR) objectives on a FineWeb-Gutenberg corpus containing repeated Gutenberg excerpts. With prefix-based probes, FIM more often recovers short or partially matching spans, while LTR more often assigns high confidence to long exact continuations. We observe that verbatim extraction under FIM-training grows approximately linearly with repetitions over the tested range. Evaluating native FIM-format probes reveals that suffix context is not sufficient: verbatim recall under FIM-training remains strongly anchored in prefix context. Our results also show that evaluating only one span length or probing format can miss important nuances in memorization behavior.

Many novel unsupervised feature selection methods are proposed each year, yet their empirical evaluation is limited to supervised and unsupervised evaluation metrics computed on selected datasets, along with comparisons to existing methods. However, in the absence of an established evaluation baseline, it is difficult to determine the value added to the existing literature by each of these methods, and how effective their underlying approaches are. In this evaluation study, we are using random feature selection as a baseline for evaluating unsupervised feature selection methods. While a random selection of features might seem to be a rather weak baseline, we show in this evaluation study that many of the state-of-the-art methods in unsupervised feature selection are outperformed by random feature selection in both performance and efficiency. Accordingly, we emphasize the strict requirement of considering random feature selection as a baseline in the development process of novel unsupervised feature selection methods, and we encourage the community to develop better evaluation measures for feature selection. Both would help to ensure consistent improvement and realistic assessment.

Humans, animals, and modern machine learning models exhibit impressive abilities to learn complex behaviors and generalize these behaviors to unseen situations. This ability requires us to learn rules and regularities that allow for such generalizations. At the same time, in most complex environments, any rule will have its exceptions. How do learning systems balance between learning general regularities and memorizing exceptions? We argue that a lack of task paradigms has hindered the study of this essential ability. To address this gap, we introduce a novel task, transitive inference with exceptions, that tests for relational generalization and memorization of an exception to the relational rule. We then analytically characterize the behavior of a simple, theoretically tractable model of neural network learning (kernel ridge regression) across a broad family of representations and task parameters. We find that these models can balance between relational generalization and memorization, but unlike for transitive inference without an exception, successful generalization is sensitive to the specific representational geometry. We explain why this task is more challenging mechanistically by drawing on our analytical theory. Finally, we validate our theoretical insights in pretrained language models that are finetuned on ordered relations, finding that these models successfully generalize according to the transitive rule, but also make the kinds of systematic mistakes predicted by our theory. Overall, our theory shows how learning systems can balance between relational generalization and memorization, explains how this can go wrong, and emphasizes the need for new task paradigms designed to probe this ability.

Machine learning methods provide a methodological innovation that can help screen for cardiovascular disease through noninvasive and readily available measurement modalities. Recent investments in using electrocardiogram (ECG) data to screen for structural heart disease (SHD) are one example, where ECGs provide a low-cost, available modality for screening. This has led to the EchoNext dataset, a paired ECG-echocardiogram data repository for testing new methods of SHD detection. However, relatively few studies have investigated how more probabilistic classification through Bayesian inference may improve uncertainty quantification in this setting. Moreover, few studies have considered how triage systems can be developed to alleviate healthcare bottlenecks, such as the review of data from underserved, rural clinics by expert sonographers for SHD assessment. In this study, we leverage existing ECG-echocardiogram data to compare frequentist and Bayesian neural network classifiers. We show that the Bayesian approach is comparable or better than frequentist methods in SHD classification, and that they have a more robust uncertainty quantification attached to them. We provide an example of how this uncertainty-aware classification scheme can be used for screening SHD, providing a proof-of-concept for how machine learning can help with triage in getting individuals expert sonographer input when SHD is highly likely or measurements are highly uncertain.

When Masked Diffusion Models (MDMs) generate sequences through iterative refinement, the rich internal computation over masked positions is discarded, forcing every subsequent refinement step to recompute the valuable internal information stored as model representations. To avoid a hard reset between denoising rounds, we propose Learned Relay Representations (Relay), a method that allows MDMs to be forward-thinking when denoising by explicitly learning how to propagate latent information for the benefit of future denoising steps. Relay introduces a differentiable per-token channel that passes information between forward passes and is trained via truncated backpropagation through time (BPTT). We show that this framework can be scaled to state-of-the-art Diffusion Language Models (DLMs), and is seamlessly compatible with techniques like block diffusion and KV caching. We first provide a thorough justification of the design choices in Relay on a challenging Sudoku-based planning task. We then scale Relay to Fast-dLLM v2, a state-of-the-art DLM, outperforming standard supervised finetuning on coding tasks while reducing inference latency by up to 32%. Our empirical results demonstrate that state-of-the-art DLMs can be explicitly trained to relay latent information forward across decoding steps, advancing the performance-latency Pareto frontier. We provide code for all our experiments.

As state-of-the-art neural networks are deployed on reasoning and algorithmic tasks, exactness guarantees become increasingly important. However, high average-case accuracy can still mask inconsistent behaviors. This motivates exact certification, which asks for the smallest set of labeled examples needed to certify that a learned hypothesis equals the target. We show that while some hypotheses are easy to certify, even minimal overparametrization can make certification exponentially hard across several hypothesis classes. For threshold circuits of depth $\ge 2$, adding a single extra gate can force certificate sizes exponential in the input dimension. We show an analogous hardness result for log-precision Transformers with only constant architectural overhead. We also characterize approximate certification, showing that allowing only polynomially many mistakes still requires exponentially large certificates, whereas constant relative-error guarantees can hide exponentially many mistakes. Empirically, we study certification for constructed circuits and trained Transformers for recognizing binary addition. While the constructed circuits instantiate the exponential barrier for certification, the trained Transformer analysis shows that imperfect models can evade detection by large uniformly sampled certificate candidates.

Multi-center survival prediction can improve robustness and generalizability, yet privacy regulations and institutional governance often prevent pooling patient-level clinical and genomic data across institutions. In practice, deployment is further complicated by feature-space heterogeneity, in which sites collect different covariates or use different sequencing panels, resulting in only partially overlapping feature sets. We present FederatedRSF, a Python package that implements federated random survival forests, aggregating locally trained survival trees and redistributing only feature-compatible trees to each site, enabling inference with partial overlap without sharing raw data. We evaluate FederatedRSF on the GBSG2 breast cancer cohort distributed with the scikit-survival package, simulating feature heterogeneity across clients by withholding subsets of features, and assessing discrimination using Harrell's concordance index (C-Index) under repeated cross-validation and site-splits. The results demonstrated that the federated model can achieve performance comparable to that of the centralized training setting.

Score matching is an alternative to maximum likelihood estimation when the normalizing constant is unknown or too costly to evaluate. However, vanilla score matching has shown to be inefficient relative to maximum likelihood estimation for multimodal distributions with well-separated modes, which are commonly encountered in practical applications. We compare a novel diffusion-based denoising score matching estimator (DDSME) to the vanilla score matching estimator (SME) in this scenario. In particular, we prove statistical guarantees for both estimators, showing that the error bound for the vanilla SME worsens when the separation between the modes increases, which can be avoided in case of the DDSME with suitable hyperparameter tuning. This provides a novel theoretical explanation for the superior behavior of diffusion-based score matching over the vanilla version. We support our theoretical findings by numerical experiments.

When a coordinator compares answers from heterogeneous foundation models, self-reported confidence may have different meanings across responders and changing workloads. This paper presents MARGIN (Multi-Agent Runtime Grading via Incremental Normalisation), a runtime calibration method that learns model-specific confidence corrections from observed answer outcomes without retraining the models or requiring a held-out calibration set. MARGIN tracks recent accuracy and stated confidence within confidence bands, uses their ratio to correct reported confidence, and blends sparse-band corrections toward a model-level estimate. The corrected scores weight candidate answers in a collective decision. Evaluation covers code generation, question answering, and mathematics, using an 18-model pool and a nine-model subset for distribution-shift experiments. On BigCodeBench, model-mean confidence is negatively related to accuracy; among correct/incorrect response pairs, choosing the more confident responder performs below chance. Against five online calibration baselines receiving identical feedback and retaining their learned state across each transition, MARGIN achieves lower post-shift expected calibration error than all five in two code-generation transitions and than four in a question-answering transition; the remaining question-answering comparison is inconclusive. In separate code-generation coordination experiments, calibration improves the ranking of correct responses and increases answer-selection accuracy by 4.3 and 14.0 percentage points on two of three benchmarks relative to uncalibrated confidence weighting. These results support model-specific runtime calibration for coordination under changing workloads when correctness feedback is available for the participating responders.

Entropy reduction is not a safety criterion: it can leave predictions unchanged or accompany increasing risk for a protected group. We study entropy-regulated learning under separately specified task, risk, and intervention constraints. A noise-calibrated log-determinant functional yields an exact spectral force formula and a metric decomposition into observable and prediction-null velocities. For scalar feedback, we characterize the complete interval of coefficients preserving a task-descent fraction and meeting an entropy-rate request; restricting intervention to observable directions can make that interval empty. For several protected risks, we derive an exact minimax certificate of feasibility within a specified subspace and norm budget, an exact robust extension for uncertain constraint rows, and a cone-projection formula for the entropy reduction remaining after protection. These formulas use standard convex geometry but identify when apparently active entropy control has no admissible effect. Barrier comparisons, finite-step curvature and gradient-error margins, and fresh-data audits give distinct conditional guarantees for risk thresholds. Human authority enters through the specification and release policy; the mathematics does not identify compression with alignment or certify human well-being. A memorization counterexample separates fresh-input information from sample-level information, and a noisy sample-code assumption supports a conditional generalization bound. Reproducible mathematical checks and a small real-data experiment expose both feasible interventions and failures. The resulting theory characterizes admissible entropy regulation and its limitations, rather than asserting universal accuracy or safety improvements.

We aim to improve the reasoning capabilities of diffusion language models (DLMs). While SFT is a popular post-training recipe for autoregressive models, its use in DLMs faces challenges and can even hurt performance, though the underlying causes remain understudied. Our analysis reveals that vanilla SFT overlooks learnability, namely what and when tokens are learned. Specifically, rare tokens are difficult to learn when most of the input is masked, whereas it is straightforward and thus of little value to learn common tokens when most of the input is unmasked. Motivated by our analysis, we propose LIFT, an efficient SFT-based post-training algorithm for DLMs. LIFT learns easy tokens when most of the input is masked and hard tokens when more context is available, thus aligning the training with the information available at different diffusion time steps. Our results show that LIFT outperforms existing SFT baselines across six reasoning benchmarks, achieving up to a 3x relative gain on AIME'24 and AIME'25. Our code is publicly available at https://github.com/divelab/LIFT.

Serving personalized content on mobile devices has traditionally required pooling sensitive user data on centralized servers, a practice increasingly at odds with modern privacy expectations and geographical regulations. We present a two-stage federated recommendation system pipeline for mobile devices, built around a principled separation between non-sensitive user preference data and sensitive mobile context data that never leaves the device. The first stage runs a collaborative filtering model on non-sensitive app-context data in the cloud to generate a shortlist of relevant items. The second stage re-ranks these candidates on-device using sensitive mobile signals, with only model updates/gradients ever leaving the device. We validate the approach on MovieLens, UCI Human Activity Recognition, and a proprietary pilot dataset, and deliver a production-ready implementation as a Kotlin Multiplatform library deployable on Android and iOS.

Generative Vision-Language Models (VLMs) perform well on multimodal reasoning, but how visual inputs are transformed to text remains poorly understood. Existing interpretability work on VLMs uses Sparse Autoencoders (SAEs), which decompose static residual representations and miss the functional updates that drive cross-modal interaction. We adopt a function-centric framework based on Transcoders, sparse approximations of MLP sublayers that act as a causal proxy for layer-wise computation. Applied to Gemma 3-4B-IT, the framework decomposes the model into interpretable computational pathways linking image patches to directions in token generation. Transcoder attributions produce stronger and more stable effects on visually grounded tokens under patch ablation than SAE attributions, and align better with semantically relevant image regions. A False Visual Grounding counterfactual analysis confirms that the recovered pathways are specific to vision-language interaction.Finally, we perform a structural analysis of hallucinated generations, by extracting graph-based indicators from circuit traces produced by the transcoders. A logistic classifier over these mechanistic graph features predicts hallucinations at AUC $0.68$. These results show that function-centric circuit decomposition yields interpretable and predictive accounts of multimodal computation in VLMs.

Federated learning protocols face a structural trilemma: canonical server-based aggregation~\cite{mcmahan2017} creates a single point of failure and gradient inversion risk; decentralised ring-gossip alternatives~\cite{hu2019segmented} expose classification heads to semi-honest peers via uninformed uniform weights; and personalised methods~\cite{collins2021exploiting} reintroduce central aggregation. No existing protocol simultaneously achieves server-free operation, permanently private heads, ring topology, and principled asymmetric neighbour weighting. We propose FIRMA (FIbonacci Ring Model Aggregation), a family of three progressively enhanced federated learning protocols: 1) \fibfl\ establishes the foundation: server-free ring aggregation with Fibonacci-weighted neighbour blending and permanently private classification heads. 2) \fibflp\ augments this with accuracy-gated neighbour suppression, selectively down-weighting poorly-converged peers while preserving the Fibonacci directional bias. 3) \fibflpp, the full system, completes the family with a 2-opt ring permutation that maximises adjacent-client class diversity, global ring coverage via $K_g{=}\lceil N/2\rceil$ gossip passes, and cosine-annealed self-retention calibration. We establish a convergence rate bound and three supporting propositions governing normalisation, coverage, retention, and diversity optimality. Systematic experiments across 28 configurations – four benchmarks crossed with seven heterogeneity regimes – demonstrate that \fibflpp\ surpasses \fedavg\ in all 12 label-skew configurations, with a peak advantage of $+20.7$\,pp on CIFAR-10 at $K{=}1$. Under Dirichlet heterogeneity, \fibflpp\ is the Pareto-dominant method among all server-free protocols, achieving the highest accuracy in 17 of 28 configurations.

A persistent challenge in machine learning for scientific applications is jointly achieving prediction and understanding. Statistical models excel on structured data but operate as black boxes, while existing interpretability methods are largely inspective: they answer "which features matter?" but do not articulate how features interact or refine explanations iteratively alongside human understanding. Asking an LLM to predict the target directly forces it to search the entire output space; we instead anchor predictions with a base model and ask the LLM the narrower question of what that model is missing. We introduce Multi-Agent Residual In-Context Learning (MARICL), an agentic framework in which LLM agents analyze where a base-model fails, hypothesize missing structure from high-residual examples provided in context, and produce explicit correction terms refined through multi-turn textual gradient optimization. Across nine benchmarks spanning scientific, biomedical, socioeconomic, and synthetic settings, MARICL improves consistently over its base model on all datasets. To test whether these corrections reflect real structure or batch-specific noise, we freeze formulas learned on one experimental batch of the Cell-Free Protein dataset and apply them (with no retraining and no further LLM calls) to held-out batches. Within the same reagent protocol, the frozen formulas improve predictions in over 92% of cases; across a different protocol, they fail systematically. The success boundary aligns with the biochemistry, not the batch count; direct evidence of mechanistic generalization.

Vision-Language-Action (VLA) models have emerged as a promising paradigm for robotic manipulation by leveraging pre-trained vision-language representations. However, current VLA training methods suffer from two critical limitations: poor generalization to novel environments and low training efficiency requiring extensive demonstrations. We introduce Agentic-VLA, an agentic training framework that enables VLAs to efficiently adapt online through three key innovations: (1) Adaptive Reward Synthesis, which dynamically generates and adjusts reward functions based on the VLA's current capabilities and task complexity, decomposing complex tasks into learnable sub-goals for curriculum learning; (2) Language-Guided Exploration, where a critic model provides structured guidance for systematic exploration rather than random sampling; and (3) Experience Memory,which stores and retrieves task-relevant policy weights for warm-starting adaptation to similar tasks. We evaluate Agentic-VLA on the LIBERO benchmark, achieving substantial improvements: +12.3% on long-horizon tasks, +28.5% in 1-shot learning, and enabling cross-task transfer from 0% to 31.2% without task-specific demonstrations. Our framework also demonstrates 2.4x faster convergence compared to existing online adaptation methods. Beyond LIBERO, Agentic-VLA retains its advantage on the dual-arm RoboTwin 2.0 benchmark, including under its randomized Hard setting. These results establish Agentic-VLA as a significant step toward truly adaptive VLA systems capable of continuous learning in deployment.

Controlling physics-based humanoids from natural-language instructions is a critical step toward general-purpose embodied agents. However, existing methods remain constrained by a tension between semantic expressiveness and physical feasibility, often failing to jointly achieve faithful instruction following, high-quality motion, and stable long-horizon control. We propose SCRIPT, a scalable diffusion policy with a multi-stage training framework for language-driven physics-based humanoid control. The core of SCRIPT is a Joint Action-State-Text Diffusion Transformer (JAST-DiT), which represents actions, physical states, and text as dedicated token streams and couples them through joint attention, enabling direct interaction between language semantics and control dynamics. To stabilize autoregressive control, we introduce a nonlinear history conditioning mechanism, which preserves the dense recent context and samples increasingly sparse cues from long-term history. Beyond supervised imitation pre-training, we propose a post-training stage, further improving the performance using Reinforcement Learning with Hybrid Rewards (RLHR). By injecting learnable noise into the flow-sampling process, RLHR effectively improves motion quality and instruction following within closed-loop simulations using hybrid physical feedback and text rewards. Quantitative evaluations demonstrate that SCRIPT outperforms prior state-of-the-art methods, with gains across text alignment, motion quality, and physical realism metrics. Furthermore, scaling studies on the 1200-hour MotionMillion dataset demonstrate consistent performance gains with model scaling, highlighting SCRIPT's robust scalability for large-scale pre-training. Our code will be publicly available for future research.

We introduce a novel Longitudinal Focused Attention Meditation Electroencephalography (L-FAME) dataset and an accompanying benchmark, designed to foster research into the neural effects of various meditation practices and the evolution of these effects over a six-week training period. The dataset contains EEG recordings and psychological assessments from 74 healthy college participants, collected at two distinct time points: pre-intervention and post-intervention. Participants were randomly assigned to one of three distinct meditation groups: two mantra-based techniques (SA-TA-NA-MA and Hare Krishna) and one Breath Focus practice. Leveraging this unique longitudinal and comparative dataset, we propose a benchmark suite comprising three distinct classification tasks: (1) cognitive state decoding to distinguish between resting and meditation states, (2) fine-grained classification of the specific meditation techniques, and (3) cross-session adaptation to evaluate model generalization across the longitudinal time gap. We provide comprehensive baseline results for these tasks utilizing a range of classical machine learning algorithms and deep learning architectures. The complete dataset, preprocessing pipelines, and benchmark evaluation code will be publicly released, offering a valuable resource and a standardized framework for the development and comparison of new analytical methods in computational meditation research and EEG-based machine learning. The dataset is available at https://huggingface.co/datasets/L-FAME-Dataset-Benchmark/L-FAME

Modelling claim frequency and severity for non-life insurance pricing predominantly relies on generalised linear models (GLMs), with gradient-boosted machines as the leading machine learning alternative. Tabular foundation models (TFMs) present a fundamentally different inference paradigm. By pre-training on large collections of synthetic datasets, TFMs enable inference on new data through in-context learning, without any dataset-specific preprocessing, fitting, or hyperparameter tuning. This paper presents a first empirical evaluation of TabPFN for motor insurance pricing, benchmarking two versions of TabPFN against GLM and XGBoost on two publicly available motor third-party liability (MTPL) datasets. Our results show that TabPFN does not consistently outperform established baselines: it falls behind the GLM on claim frequency, where its performance depends on the size of the in-context training set, but it is competitive on claim severity, where data are scarcer. Its inference times are substantially longer. Although tabular foundation models are promising, particularly in data-scarce settings, TabPFN is not yet ready to replace established actuarial methods for claim frequency.

Evaluation in scientific reconstruction is dominated by pointwise metrics - RMSE, MAE, per-event resolution - under the implicit assumption that lower error means better reconstruction. We show that this assumption fails structurally for inverse problems with multimodal posteriors. By the law of total variance, point estimators trained to minimize MSE or MAE produce a marginal spectrum strictly narrower than the truth whenever the posterior has nonzero width. The resulting bias is independent of architecture, training, and dataset size, and it compresses precisely the spectral features - tails, modes, shapes - that downstream scientific measurements rely on. We propose a three-part evaluation protocol where each step targets a failure mode the others miss: per-event distributional accuracy via CRPS, population-level marginal accuracy via a spectrum-fidelity diagnostic, and uncertainty trustworthiness via coverage-based calibration. On a synthetic benchmark with an analytic posterior and on a realistic many-to-one inverse problem from particle physics, model rankings reverse between pointwise and distributional metrics, and calibration further separates architectures indistinguishable under CRPS. The evaluation protocol, not the model, determines the scientific conclusion.

AI-native wireless receivers based on deep learning exhibit remarkable performance under stationary channel conditions, yet their resilience to distributional shifts remains poorly characterized by conventional metrics such as bit error rate (BER). To overcome these limitations, this paper proposes a novel real-time metric, the Topological Resilience Index (TRI), grounded in persistent homology and persistence exponents. TRI quantifies the structural stability of a neural network receiver's parameter space during online adaptation to non-stationary channels. Specifically, TRI captures resilience through three complementary dimensions: (i) validation-loss resilience measuring model-channel mismatch, grounded in the topological persistence of loss-landscape sublevel sets; (ii) channel impulse response (CIR) distribution shift, tracking geometric drift of CIR vectors from the calibration reference distribution; and (iii) channel manifold topology, quantified by the spectral gap of the Gaussian kernel matrix normalized by the Olivier-Ricci curvature norm. We establish theoretical guarantees showing that TRI is bounded, monotonic under performance degradation, and Lipschitz-stable with respect to perturbations in channel distributions measured in Wasserstein distance. Simulation results for an OFDM deep-learning receiver adapting across ten ITU-R inter-environment transitions at three shift rates demonstrate that TRI provides a consistent mean warning lead of more than one OFDM symbol over gradient-norm and validation-loss baselines, whereas the gradient-norm baseline achieves zero lead in every scenario. Furthermore, the proposed TRI-guided burst re-adaptation reduces post-shift BER by 80% relative to no adaptation within 200 OFDM symbols.

Formal mathematics libraries are rapidly expanding, creating a growing need to refactor verified proofs for maintainability and to improve training data quality for neural provers. However, scalable proof optimization is hindered by heterogeneous and heuristically specified objectives, scarce data, and high training and inference costs. To overcome these challenges, we introduce ImProver 2, a neurosymbolic framework for automated proof optimization in Lean 4. ImProver 2 combines a data-efficient expert-iteration pipeline with a scaffold that exposes formal structure alongside lightweight informal abstractions. We further introduce a suite of metrics capturing structural proof properties. Using ImProver 2, we train a 7B-parameter model that outperforms orders-of-magnitude larger models within the same model family, and is competitive with mid-tier frontier models across metrics. We additionally demonstrate that our neurosymbolic scaffold significantly improves performance across both small and frontier models. We show that with proper scaffolding and training, small models can effectively restructure research-level proofs over complex and varied metrics, matching substantially larger systems and establishing proof optimization as a scalable, learnable task.

Autoregressive Transformer KV caches grow linearly with context length; sliding-window caching bounds memory but discards evicted tokens entirely, so relevant evidence outside the window becomes inaccessible. We introduce Tensor Cache, a two-level cache that pairs sliding-window softmax attention as a first-level cache (L1) with a fixed-size outer-product fast-weight memory as a second-level cache (L2) fed by KV pairs evicted from the window. Recent tokens remain in exact local attention; evicted pairs are compressed into a per-layer matrix $A$ and read by future queries through a single matrix multiplication, exploiting the linear-attention identity $q_t(k_i \otimes v_i)=\langle q_t,k_i\rangle v_i$. A learned scalar gate fuses the L1 and L2 outputs, and per-head decay and write-rate parameters are trained end-to-end. The outer-product memory and the read identity are well-known; our contribution is their use as an L2 cache fed exclusively by sliding-window evictions, plus identifying that the common chunked-mean training shortcut $A\!\leftarrow\!\lambda A\!+\!\eta(\bar k\!\otimes\!\bar v)$ silently introduces $C^2{-}C$ spurious cross-token outer products per chunk, and closing the gap with a parallel weighted-sum scan equivalent to per-token writes within float32 epsilon. Across systems scaling, controlled associative recall, long-context language modeling, and memory-capacity diagnostics, Tensor Cache improves the memory–quality frontier over bounded-state baselines.

Tokenisation is an integral part of the current NLP pipeline. Current tokenisation algorithms such as BPE and Unigram are greedy algorithms – they make locally optimal decisions without considering the resulting vocabulary as a whole. We instead formulate tokeniser construction as a linear program and solve it using convex optimisation tools, yielding a new algorithm we call ConvexTok. We find ConvexTok consistently improves intrinsic tokenisation metrics and the bits-per-byte (BpB) achieved by language models; it also improves downstream task performance, but less consistently. Furthermore, ConvexTok allows the user to certify how far their tokeniser is from optimal, with respect to a certain objective, via a lower bound, and we empirically find it to be within 1% of optimal at common vocabulary sizes.

We propose the Integrable Context-Dependent Demand Network (ICDN), a demand-first neural model for multiproduct retail demand. ICDN learns log-demand as a smooth, context-conditioned function of log-prices, allowing elasticities to be derived exactly from the learned demand surface. Across three retail datasets, the model achieves competitive out-of-sample prediction while producing analytically tractable, and economically regularized own- and cross-price responses.

Language models must now generalize out of the box to novel environments and work inside inference-scaling search procedures, such as AlphaEvolve, that select rollouts with a variety of task-specific reward functions. Unfortunately, the standard paradigm of LLM post-training optimizes a pre-specified scalar reward, often leading current LLMs to produce low-entropy response distributions and thus to struggle at displaying the diversity that inference-time search will require. We propose Vector Policy Optimization (VPO), an RL algorithm that explicitly trains policies to anticipate diverse downstream reward functions and to produce diverse solutions. VPO exploits that rewards are often vector-valued in practice, like per-test-case correctness in code generation or, say, multiple different user personas or reward models. VPO combines multi-answer prompting with a set-level reward to train the LLM to produce sets of solutions that specialize to different trade-offs in the vector reward space. Across four tasks, VPO matches or beats the strongest scalar RL baselines on test-time search (e.g. pass@k and best@k), with the gap widening as the search budget grows. For evolutionary search, VPO models unlock problems that GRPO models cannot solve at all. As test-time search becomes standard, diversity may need to become the default post-training objective.

Exploration is a prerequisite for learning useful behaviors in sparse-reward, long-horizon tasks, particularly within 3D environments. Curiosity-driven reinforcement learning addresses this via intrinsic rewards derived from the mismatch between the agent's predictive model of the world and reality. However, translating this intrinsic motivation to complex, photorealistic environments remains difficult, as agents can become trapped in local loops and receive fresh rewards for revisiting forgotten states. In this work, we demonstrate that this failure stems from a lack of spatial persistence and episodic context. We show that effective curiosity requires a model of the world that is persistent and continuously updated, paired with an agent that maintains an episodic trajectory history to navigate toward novel regions. We achieve this using an online 3D reconstruction as a persistent model of the world, while the agent policy is parameterized as a sequence model over RGB observations to maintain episodic context. This design enables effective exploration during training while allowing the agent to navigate using solely RGB frames at deployment. Trained purely via curiosity on HM3D, our agent outperforms RL-based active mapping baselines and generalizes zero-shot to Gibson and AI-generated worlds. Our end-to-end policy enables efficient adaptation to downstream tasks, such as apple picking and image-goal navigation, outperforming from-scratch baselines. Please see video results at https://recuriosity.github.io/.

Ordinary training optimises the task loss and then stops. It never pays for internal representation energy: Jacobians can stay large in directions that never helped the label, so even small label-preserving noise throws the model off—a design gap that classical noise-injection theory fixes at second order, but only when applied as default regularisation, which current practice does not do. We make that precise with a Matching Principle: name deployment directions (Sigma_task) and the training penalty Sigma', and ask whether the second covers the first. The no-thinking default is even-spread / isotropic penalty (Sigma' proportional to I)—classical Gaussian / Tikhonov at second order: no axis estimate, no architecture change, and—in a simple linear ridge model—strictly less deployment drift than task-only training, with no coverage miss by construction. When axes are known, matching is sharper; when they are missed, a residual floor remains. Across seven domains a named second-moment penalty beats unregularised training; a controlled illustration recovers match > even-spread > wrong-axis when axes are forced. The ridge theorems are proved; deep nets remain experiments under a specified perturbation. Design rule: fix internal energy by default (even-spread); match when axes are known; treat losses that control representation sensitivity as first-class design.