Papers

We tackle the question of how to scale more efficiently across the many, ever-growing stages of current LLM training pipelines. Our guiding intuition stems from the fact that the dynamics of later stages of the pipeline, e.g. post-training, can be used to inform earlier stages such as pre-training. To this end, we propose Introspective Training (or IXT), inspired by offline reward-conditioned reinforcement learning and applicable to any stage of training. IXT uses a thinking reward model to annotate data with natural language critique based feedback, enabling quality aware training from the earliest stages of the pipeline. Models are then trained by prefix-conditioning the data with the generated feedback – ensuring that not all tokens are treated equally starting much earlier in training than usual. Comprehensive experiments on 7.5-12B transformer-based dense LLMs trained from scratch all the way up to 18 Trillion tokens seen show that our method: bends scaling curves resulting in up to 2.8x more compute efficiency generally; and reaches performance levels unachievable for models trained otherwise in domains such as math and code.

Industrial anomaly detection has been significantly advanced by Large Multimodal Models (LMMs), enabling diverse human instructions beyond detection, particularly through visually grounded reasoning for better image understanding. However, LMMs lack domain-specific knowledge, which limits their ability to generate accurate responses in complex industrial scenarios. In this work, we present JUDO, Juxtaposed Domain-Oriented Multimodal Reasoner, a framework that efficiently incorporates domain knowledge and context in visual and textual reasoning. Through visual reasoning, our model segments the defect region by juxtaposing query images with normal images as visual domain context, enabling a fine-grained visual comparative inspection. Furthermore, we inject domain knowledge through supervised fine-tuning (SFT) to enhance context understanding and subsequently guide domain reasoning through reinforcement learning (GRPO) with tailored rewards, opting for a domain-oriented reasoning process. Experimental results demonstrate that JUDO achieves superior performance on the MMAD benchmark, surpassing models such as Qwen2.5-VL-7B and GPT-4o. These results highlight the importance of enhancing domain knowledge and context for effective reasoning in anomaly understanding.

We develop a unified microeconomic and monetary theory of artificial intelligence inference costs and their pass-through to inflation, welfare, and optimal monetary policy. We introduce the Inference-Cost Phillips Curve (ICPC), an augmented New Keynesian Phillips curve in which firm-level marginal costs of producing differentiated goods include a non-trivial AI inference component lambda-bar, and prove a closed-form structural slope kappa*_inf = lambda-bar * kappa, where kappa is the standard Calvo-Yun slope. We derive a welfare-relevant Hicks-Kaldor decomposition of consumer welfare under inference-cost shocks, prove a generalized Taylor principle for the inference-augmented economy, and characterize the optimal monetary policy response coefficient psi*_inf = (1 + phi*rho) * lambda-bar * kappa under commitment. A second-order welfare loss formula closes the model in closed form. We confront the theory with U.S. monthly data 2022:M01-2026:M04 using a two-step GMM estimator with Newey-West HAC standard errors and Hansen J-test, recovering an empirical slope kappa-hat_inf = 0.087 (HAC s.e. 0.021) which lies within one standard error of the structural prediction. A scaling regression over 50 rolling-window subwindows yields b-hat = 0.987 (R^2 = 0.998), consistent with a near-unit-elasticity pass-through. A G7 reduced-form panel with Driscoll-Kraay HAC standard errors yields b-hat^G7 = 0.094 (s.e. 0.026), and a Wald test fails to reject cross-country homogeneity (p = 0.78). The framework provides a single equilibrium scaffold for the joint study of AI inference cost dynamics, monetary policy under generative-AI shocks, and the welfare cost of inference-driven inflation.

Generative artificial intelligence is rapidly transforming the supply side of training data: an increasing share of new tokens, images, and structured records is produced by previous-generation models rather than by human originators. Recursive training on such synthetic content induces a measurable and often irreversible loss of distributional fidelity, a phenomenon known as model collapse. We develop the first unified microeconomic theory of synthetic data markets under model collapse. We introduce the Synthetic Data Contamination Equilibrium (SDCE), prove existence and generic uniqueness, derive a welfare decomposition W = W_prod + W_cons - L_coll - L_info, establish a Wasserstein-gradient-flow mean-field collapse limit, prove an impossibility of information-constrained implementation, and obtain closed-form expressions for the welfare-maximizing provenance subsidy s* = KL(q||p)/(2 kappa) and the welfare-maximizing watermark strength w* = (1 - psi) KL(q||p)/(2 kappa psi). We prove an information-theoretic Cramer-Rao lower bound on any provenance estimator using only producer-side observations and show that the Provenance-Market Iterative Retraining (PMIR) algorithm attains this bound up to constants while converging to an epsilon-SDCE in O(epsilon^-2 log T) iterations. A reduced-form OLS estimation on a C4-synthetic benchmark over ten retraining generations yields a collapse-rate coefficient b-hat = 0.181 (HAC s.e. 0.024), within one standard error of the structural prediction 0.183. Calibrated experiments raise generation-ten model quality by 23.1 percent over the unregulated benchmark while lowering the 2-Wasserstein drift on a held-out diversity probe from 0.318 to 0.142. Scaling experiments over generations t in {1,...,10} recover a logarithmic-in-t collapse law log Q_t = log Q_0 - 0.183 t rho^2 with R^2 = 0.962.

Long-form image captioning exposes a reward granularity problem in RL: captions are judged as whole sequences, while the important errors occur at the level of individual visual claims. A good dense caption should be both faithful and informative, avoiding hallucination without omitting salient details. Yet pairwise preferences, reference-based metrics, and holistic scalar rewards compress these local errors into a single sequence-level signal, obscuring the tradeoff between factuality and coverage. We introduce ClaimDiff-RL, a framework that uses reference-conditioned atomic claim differences as the reward unit for caption RL. Given an image, an actor caption, and a reference caption, a multimodal judge enumerates visually grounded differences, verifies each difference against the image, assigns open-vocabulary error types and severity levels, and produces per-difference statistics for reward composition. This makes hallucinated claims and omitted salient facts separately measurable and tunable. Experiments show that holistic scalar rewards can reduce hallucination by increasing missing facts, while ClaimDiff-RL exposes this faithfulness and coverage tradeoff and enables more balanced operating points. On a 160-image human-labeled diagnostic benchmark, public captioning benchmarks, and VQA benchmarks, ClaimDiff-RL improves the hallucination–missing-fact balance, preserves general capability, and even surpasses Gemini-3-Pro-Preview on several fine-grained Capability dimensions such as object counting, spatial relations, and scene recognition. These results suggest that typed, verifiable claim differences are an effective reward unit for fine-grained and diagnosable caption RL.

The global deployment of edge intelligence operates across heterogeneous legal frameworks. While some regions permit centralized learning (CL) via cloud data aggregation, others enforce strict data localization, necessitating federated learning (FL). This operational dichotomy introduces two incompatible optimization regimes (i.e., unbiased global gradients yet coupled with internal covariate shift in CL versus biased, drift-prone local updates in FL), resulting in that any naive integration of the two lacks rigorous theoretical guarantees. To fill this gap, we propose OmniISR, a unified framework that fuses pure CL, pure FL, and hybrid CL-FL training modes via equipping intermediate supervision and regularization (ISR) signals at multiple hidden layers. Specifically, we propose (i) to use mutual-information (MI) as intermediate supervision to align shifting internal covariate in CL and client-drifting representations in FL, and (ii) to adopt negative-entropy (NE) as intermediate regularizer to penalize overconfident prediction, preserve representational uncertainty, and avoid device-specific collapse. On the theory side, we derive (i) a unified, ISR-agnostic, and non-asymptotic O(1/sqrt(T)) convergence bound that shows the introduced ISR does not violate standard SGD convergence, (ii) a federated drift-bound that quantifies the ISR-reduced client drift, (iii) a gradient-alignment guarantee that ensures non-conflicting CL and FL updates under mild bias, and (iv) an explicit escape-time bound that indicates that CL-FL hybrid mixing enlarges effective stochasticity and accelerates escape from strict saddles. Extensive experiments demonstrate that OmniISR consistently improves model performance in both centralized and federated paradigms, reduces the CL-FL gap by 22.60%, and yields 37/48 paired metric wins across multiple FL algorithms.

Online model editing for multimodal large language models (MLLMs) requires assimilating a stream of corrections under tight compute and memory budgets. Yet editors developed for text-only LLMs often degrade on MLLMs: visually dominant activations skew the statistics that shape updates, causing cross-modal conflict, while sequential writes become entangled in a shared edit space and amplify long-horizon interference, causing inter-edit interference. To address these, we propose M-ORE, a modality-decoupled online recursive editor for lifelong MLLM adaptation. M-ORE is derived from a unified proximal-projection formulation and admits a closed-form update with a Sherman-Morrison recursion, yielding constant per-edit overhead. It maintains module-wise locality statistics for the text stack and the visual projector to avoid visually dominated update shaping and performs continual updates in a fixed orthogonal low-rank edit subspace via a Sherman-Morrison recursion to mitigate long-horizon interference. Experiments on multiple MLLM backbones and online editing benchmarks show that our M-ORE method consistently improves reliability, generality, and locality over strong baselines, while achieving favorable quality-efficiency scaling. Our code is publicly available at https://github.com/lab-klc/M-ORE.

While humans readily generalize abstract concepts to more complex or larger tasks, building Reinforcement Learning (RL) systems with this ability remains elusive. Here, we present the first theoretical model of how such Out-of-Distribution (OOD) generalization can be achieved in RL agents. Our approach considers Partially Observable Markov Decision Processes (POMDPs) and assumes that an intelligent agent uses an abstraction function to determine which experiences can be treated as equivalent and which must be distinguished. First, we extend the existing state abstraction framework and proof techniques to POMDPs. Then, we define a successor-weighted model reduction, a model reduction variant that enables compression into smaller abstract spaces than prior definitions allow. We derive a bound on the agent's OOD test performance, thereby defining the conditions under which OOD generalization is achievable. This bound decomposes an agent's performance loss into approximation and estimation errors, revealing how reducing an agent's abstract state space size improves test performance and OOD generalization. Our analysis suggests that constraining an agent to operate over a small, finite set of abstract states is necessary for achieving generalization to more complex tasks. Our results motivate further research into learning RL architectures that scale across tasks of varying complexity levels.

Learning universal representations from electroencephalogram (EEG) signals is a cutting-edge approach in the field of neuroinformatics and brain-computer interfaces (BCIs). Conventionally, EEG is treated as a multivariate temporal signal, where time- or frequency-domain features are extracted for representation learning. This paper investigates a simple yet effective EEG representation, i.e., microstates. Microstates represent the building blocks of brain activity patterns at a microscopic time scale. We build a universal microstate tokenizer from a large medical EEG dataset by clustering continuous EEG signals into sequences of discrete microstates. The microstate tokenizer is then adopted universally across a series of downstream tasks, including sleep staging, emotion recognition, and motor imagery classification. Experimental results show that EEG representation learning with microstates outperforms traditional time-domain and frequency-domain features under different models and across different tasks. Further analysis shows that microstates offer greater interpretability and scalability, thereby opening up applications in both cognitive neuroscience and clinical research.

Advanced image editing software enables easy creation of highly convincing image manipulations, which has been made even more accessible in recent years due to advances in generative AI. Manipulated images, while often harmless, could spread misinformation, create false narratives, and influence people's opinions on important issues. Despite this growing threat, there is limited research on detecting advanced manipulations across different visual domains. Thus, we introduce Analysis Under Domain-shifts, qualIty, Type, and Size (AUDITS), a comprehensive benchmark designed for studying axes of analysis in image manipulation detection. AUDITS comprises over 530K images from two distinct sources (user and news photos). We curate our dataset to support analysis across multiple axes using recent diffusion-based inpaintings, spanning a diverse range of manipulation types and sizes. We conduct experiments under different types of domain shift to evaluate robustness of existing image manipulation detection methods. Our goal is to drive further research in this area by offering new insights that would help develop more reliable and generalizable image manipulation detection methods.

Every spring, flash floods strike the haor wetlands of northeast Bangladesh just before the boro rice harvest, and one flood can erase a family's entire crop in days. Warning people in time is hard here for a structural reason: the Sunamganj Haor is a flat, bowl-shaped basin that fills at once from local rain, domestic rivers, and the Barak River in India, while fewer than twelve working gauges cover its 8,000 km2. Existing models add a quieter problem of their own, because they train on raw temperature, which simply follows the season, so they learn the calendar instead of the flood, and none of them delivers a warning to a farmer. HaorFloodAlert answers both problems with free data alone: Sentinel-1 radar that sees through storm clouds, rainfall records and forecasts, soil moisture, and a modeled upstream Barak signal worth about 36 hours of lead time. A monthly climatological anomaly then removes the seasonal bias, cutting the temperature-label correlation from r=0.570 to r=-0.031. Tested by leave-one-out cross-validation on 77 events with real Sentinel-1 images (2014-2024), the Random Forest and XGBoost ensemble reaches 90.9% accuracy, 89.2% F1-score, and AUC 0.939, and these labels hold up against 12.3 years of official gauge records. The same system then ran live for ten days in May-June 2026 and raised a high-risk alert about three days before the river neared its danger level. Warnings go out in Bengali by SMS, e-mail, and WhatsApp, and every number here can be regenerated from our public, seeded pipeline.

Non-destructive testing of aerospace SiC/SiC composites via X-ray computed tomography (XCT) relies on expert visual assessment, with current workflows offering limited traceability for accept/reject decisions. Deep convolutional networks can automate defect detection, yet their black-box nature conflicts with the transparency that industrial inspection practice demands. To close this gap, we introduce p-ResNet-50, a convolutional framework extended with a prototype layer that couples high detection accuracy with case-based explanations. Six learned prototypes are explicitly aligned with expert-defined semantic categories-healthy matrix, matrix–air interfaces, pores, line-like defects, and mixed morphologies-so that every classification is traceable to a physically meaningful reference. Two novel regularisation terms, anchor-based and medoid-based, tether prototypes to expert-selected patches and prevent prototype collapse, addressing a known limitation of prototype networks. Latent-space analysis via UMAP delineates semantically coherent sub-domains and maps zones of uncertainty where misclassifications concentrate, giving inspectors an explicit picture of where the model is-and is not-reliable. The framework is validated on an XCT patch dataset of approximately 12,000 patches extracted from four defect-rich SiC/SiC laboratory specimens. Taking a black-box ResNet-50 as a baseline (ROC-AUC = 0.991), the prototype extension achieves comparable performance (accuracy 0.957 vs. 0.959; ROC-AUC 0.994 vs. 0.993) while trading a slight reduction in sensitivity for higher precision and specificity. Each decision is backed by representative evidence patches, and the model explicitly flags its uncertainty regions. Beyond defect mapping, the framework establishes a reusable methodology for embedding domain-expert knowledge into prototype networks, applicable to other XCT inspection scenarios requiring traceable, auditable decisions.

Music streaming fraud, where bad actors artificially inflate stream counts to manipulate chart rankings and royalty payments, poses a significant threat to streaming services and legitimate content creators. Traditional fraud detection approaches struggle with a critical challenge: many legitimate edge cases, including super-fans and sleep-music sessions, exhibit activity patterns that closely mimic those of coordinated fraud. We present SAGE, a novel counterfactual-aware negative harvesting approach that combines SimHash-based stratified sampling with a modular gating ensemble for confident negative identification from unlabeled data. Our ensemble architecture employs pluggable statistical gates (currently instantiated with Mahalanobis distance and k-NN density) with configurable voting thresholds enabling adaptive precision-recall trade-offs. This addresses the representation bias problem in Positive-Unlabeled learning by ensuring comprehensive coverage of rare behavioral cohorts through floor-constrained sampling. Evaluation demonstrates strong precision and recall on held-out data. The approach generalizes across fraud detection domains, achieving strong performance on both customer-level and artist-level fraud without modification to the core methodology.

The proliferation of generative artificial intelligence has given rise to an interactive learning environment, where model parameters are continuously updated using not only data generated by natural processes, but also synthetic outputs produced by other models. This paradigm introduces two major challenges: (1) training data are no longer drawn exclusively from the target population, undermining a core assumption of classical statistical learning, and (2) model training processes become inherently correlated, as models interact with one another through repeated exposure to each other's synthetic outputs in a potentially complex manner. Establishing reliable statistical inference in such structured interactive learning environments therefore remains an important open problem. In particular, there is growing concern about model collapse, a phenomenon in which the performance of generative models progressively degrades as they are trained on synthetic data produced by earlier model generations. Prior work on model collapse primarily focuses on a single model trained on its own output, failing to capture model performance in multi-model interactive settings. In this work, we fill this gap by investigating the performance of generative models in an interactive learning environment with general interaction patterns. In particular, we formalize model interactions using directed graphs and show that the occurrence of model collapse depends critically on the topology of the interaction graph. We further derive an explicit necessary and sufficient condition characterizing when model collapse occurs, and establish finite-sample results for linear regression and asymptotic guarantees for general M-estimators. We support our theoretical findings through extensive numerical experiments.

Gaussian process (GP) predictive distributions are commonly used in Bayesian optimization (BO) to guide the selection of evaluation points for expensive objective functions. The choice of kernel and hyperparameters has a strong influence on the exploration–exploitation trade-off. For minimization, sampling criteria such as expected improvement (EI) depend on both the probability mass below the current best value and the shape of the predictive distribution in this region. This article studies goal-oriented calibration of GP predictive distributions below a low threshold $t$ in the noiseless setting, for standard GP models with hyperparameters selected by maximum likelihood. We consider two complementary forms of calibration below $t$ for inputs distributed according to a reference measure $\mu$: occurrence calibration over the design space and thresholded $\mu$-calibration on sublevel sets of the form $\{x\in\mathbb{X}, f(x)\le t\}$. We propose tcGP, a post-hoc method that combines these two forms of calibration for GP predictive distributions below $t$. With fixed GP hyperparameters, the exact EI sampling criterion based on tcGP generates a sequence of evaluation points that is dense in the design space. Experiments on standard benchmarks show improved lower-tail calibration and BO performance relative to standard GP models and globally calibrated GP models.

Learning generalizable trajectory representations from raw GPS traces remains difficult because the data is continuous, noisy, and irregularly sampled. Spatial tokenization is also challenging: fine grids yield sparse cells with weak embeddings, while coarse grids merge heterogeneous movement patterns into the same token. We present TrajTok, a trajectory encoder with a simple pretraining recipe for transferable trajectory embeddings. TrajTok first learns a multi-resolution hexagonal cell partition from the spatial distribution of GPS points, converting noisy GPS sequences into discrete cell tokens. To capture both geometry and kinematics, it uses a factorized transformer encoder with early per-modality self-attention blocks, cross-attention fusion layers, and spatiotemporal rotary position embeddings, ST-RoPE, to encode where and when each token occurs. TrajTok is pretrained with masked-token modeling that recovers both geometric structure and kinematic patterns from partial trajectory observations. On the Porto dataset, a frozen TrajTok encoder with lightweight task adapters achieves strong performance across trajectory similarity search, classification, estimated time of arrival, and full travel-time regression, outperforming multiple task-specific methods. The same frozen encoder supports both geometry-dominated and kinematics-dominated tasks, suggesting that TrajTok learns transferable trajectory structure rather than task-specific shortcuts. These results indicate that learned multi-resolution spatial tokenization combined with masked-token pretraining is a promising direction for general-purpose trajectory foundation models.

Distributed acoustic sensing (DAS) systems generate continuous, ultra-high-channel-count data streams at rates that exceed the capabilities of conventional batch-oriented analysis frameworks. As a result, essential tasks such as interactive exploration of long-duration recordings, scalable event annotation, and real-time algorithm-in-the-loop monitoring remain inadequately supported by workflows built around manually selected data segments and offline processing. This paper presents FiLark (Fiber Lark), a Python framework that applies a streaming-first principle uniformly across data access, signal processing, visualization and monitoring for DAS. Instead of operating on manually selected data segments, FiLark presents any DAS sources-including continuous multi-file recordings-as a unified stream and builds all system components around that abstraction. An OpenGL-based ring-buffer renderer enables interactive browsing and visualization of arbitrarily long recordings with constant memory usage. An integrated annotation interface supports event labeling directly within continuous data streams, facilitating the creation of reproducible machine-learning-ready labeled datasets without offline preprocessing. The signal processing library includes temporal, spatial, spectral, and decomposition-based operators, with both CPU implementations and GPU-accelerated variants via PyTorch, alongside stateful chunked execution that preserves processing continuity and application semantics across segment boundaries. A standardized monitor interface further integrates streaming detectors and learning-based models into the visualization workflow. By sharing a common streaming abstraction across all layers, FiLark allows processing configurations and workflows developed interactively to transfer directly to scalable production pipelines without modification.

Artificial vision models are often evaluated against the human visual cortex by measuring how accurately their internal representations predict brain responses. However, prediction accuracy alone does not indicate which dimensions of the target brain's response space are recovered. Here, we introduce a unified framework for evaluating both model-brain and brain-brain alignment by identifying the response dimensions recovered by prediction. Using repeated fMRI measurements, we first identify target-brain response dimensions that can be reproducibly predicted across independent trial splits. We then predict target-brain responses from either another subject's brain responses or a vision model's internal representations, and quantify how strongly each of these reproducible response dimensions is recovered. Applying this framework to a subset of the Natural Scenes Dataset, in which eight subjects viewed the same natural images during fMRI, we find that the early-to-intermediate visual-cortex responses contain a low-dimensional set of reproducible dimensions. Brain-to-brain comparisons identify which of these dimensions are consistently recoverable from other subjects' brains, providing a diagnostic human reference rather than only a scalar benchmark. In some cases, pretrained and randomly initialized models achieve similar prediction accuracy while showing distinct recovery profiles across these response dimensions. These results show that prediction accuracy alone can mask model-brain mismatches. By making explicit which reproducible brain response dimensions are recovered by prediction, our framework provides a more diagnostic evaluation of alignment between artificial vision models and the human visual cortex.

Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately, even in lower dimensional Euclidean space problems $\left( d \in \{2,3\} \right)$, algorithms for Wasserstein distance computation with approximate or exact precision guarantees scale poorly in the runtime as a function of $n$ and the desired precision. In response, we consider the computational-statistical runtime, where the goal is to estimate from samples the Wasserstein distance between potentially smooth measures up to $\epsilon$-additive error in expectation with respect to the sampling; we allow $O(1)$ computational cost for collecting a sample. Towards this, we develop a Sample-Sketch-Solve paradigm where we introduce a regular cartesian grid sketch of the samples. We show that (especially under $\alpha$-Hölder smooth distributions) this can compress the data without increasing asymptotic error, and also regularizes the structure which enables faster exact algorithms. Ultimately, we approximate $W_2^2(P,Q)$ within $\epsilon$ error in $\epsilon^{-\max(2,\frac{d+1+o(1)}{1+\alpha})}$ time for $0 < \alpha < 1$ Hölder smooth distributions $P,Q$ on $(0,1)^{d}$; an optimal $\Theta(\epsilon^{-2})$ for $\alpha > 1/2$ when $d=2$ and nearly optimal as $\alpha \to 1$ when $d = 3$.

We show that time series foundation models scale: a single training recipe produces reliable forecast-quality improvements from 4M to 2.5B parameters. We release Toto 2.0, a family of five open-weights forecasting models trained under this recipe. The Toto 2.0 family sets a new state of the art on three forecasting benchmarks: BOOM, our observability benchmark; GIFT-Eval, the standard general-purpose benchmark; and the recent contamination-resistant TIME benchmark. This report describes our experimental results and details the design decisions behind Toto 2.0: its architecture and training recipe, training data, and the u-muP hyperparameter transfer pipeline. All five base checkpoints are released under Apache 2.0.

While conventional (k=1) discrete-time barrier certificate conditions impose strict safety constraints by requiring the function to be non-increasing at every step, k-inductive barrier certificates relax this by allowing a temporary increase – up to k-1 times, each within a threshold $\epsilon$ – while maintaining overall safety, and improving flexibility. This paper leverages neural networks and constructs k-inductive neural barrier certificates (k-NBCs) for (partially) unknown nonlinear systems. While neural networks offer scalability in the design process, they lack formal guarantees, requiring additional approaches such as counterexample-guided inductive synthesis (CEGIS) with satisfiability modulo theories (SMT) for verification. However, the CEGIS-SMT framework requires knowledge of system dynamics, which is unavailable in practical settings. To address this, we leverage the generalization of the Willems et al.'s fundamental lemma, using a single state trajectory, to construct a data-driven representation of (partially) unknown models for SMT verification without sacrificing accuracy. Additionally, CEGIS-SMT further removes the constraint of restricting barrier certificates to specific function classes, such as sum-of-squares, enabling greater flexibility in their design. We validate our approach on three nonlinear case studies with (partially) unknown dynamics.

JEPAs often regularize one-view embeddings toward an isotropic Gaussian, implicitly baking Euclidean symmetry into the representation. We show that this is not merely a benign default. For a known structured downstream geometry $H\succ0$, the minimax and maximum-entropy covariance under a Hamiltonian energy budget is $(c/d)H^{-1}$, and Euclidean isotropy incurs a closed-form price of isotropy. More importantly, when the downstream geometry is unknown, no geometry-independent fixed marginal target is canonical: every fixed covariance shape can be maximally misaligned for some structured geometry. We further show that even oracle one-view marginals do not identify the JEPA view-to-view predictive coupling. Within continuous linear phase-space flows, stationarity of the lifted oracle law, momentum reversal, and fixed-unit kinematics uniquely select Hamiltonian dynamics. These results suggest that the structural bias in JEPAs should enter the cross-view coupling rather than a fixed encoder marginal. We instantiate this principle with HamJEPA, which encodes each view as a phase-space state $(q,p)$ and predicts view-to-view transitions with a learned Hamiltonian leapfrog map, while non-isotropic scale and spectral floors discourage collapse. In a deliberately headless token protocol, HamJEPA improves over SIGReg on CIFAR-100 by $+4.89$ kNN@20 and $+3.52$ linear-probe points at 30 epochs, and, over two training seeds at 80 epochs, by $+7.24$ kNN@20 and $+9.67$ linear-probe points relative to the full 2048-dimensional SIGReg representation. Matched non-symplectic and non-reversible controls retain the gain, so the experiments do not identify either property as individually necessary. On ImageNet-100, HamJEPA-$q$ improves by $+4.82$ kNN@20 and $+7.52$ linear-probe points at 45 epochs.

Learning to generalise from limited data is a fundamental challenge for both artificial and biological systems. A common strategy is to extract reusable structure from abundant unlabelled data, enabling efficient adaptation to new tasks from limited labelled data. This two-stage paradigm is now standard in modern training pipelines, where pretraining is followed by fine-tuning or linear probing. We provide an analytical model of this process: structure extraction is formalized as principal component analysis on unlabelled data, and downstream learning as linear regression on a separate labelled dataset. In the high-dimensional regime, we derive exact expressions for training and generalisation error showcasing their dependence on representation dimensionality, unlabelled and labelled sample sizes, and task alignment. Our results show that pretrained representations strongly influence downstream generalisation, and we characterize the optimal representation size as a function of task parameters: with abundant pretraining data but scarce downstream data, maximally compressed representations are optimal, whereas with limited pretraining data, higher-dimensional representations generalise better. Furthermore, we establish an exact trade-off between pretraining and supervision, quantifying how much unlabelled data is required to replace a single labelled sample. Beyond our idealised model, we observe similar phenomenology in autoencoders and pretrained LLMs. Altogether, we highlight that optimising representation size is critical, giving conditions for when compression during pretraining improves generalisation.

Speculative decoding (SD) accelerates large language model inference by leveraging a draft-then-verify paradigm. To maximize the acceptance rate, recent methods construct expansive draft trees, which unfortunately incur severe VRAM bandwidth and computational overheads that bottleneck end-to-end speedups. While dynamic-depth pruning can reduce this latency by removing marginal branches, it also discards potentially valid candidates, preventing the acceptance rate from reaching the upper bound of dense trees. In this paper, we identify a critical opportunity in resource allocation: the transition from dense to pruned drafting frees up significant computational budget. To break this Pareto tradeoff, we introduce Graft, a compensation framework that couples pruning and retrieval as mutually reinforcing operations. Pruning supplies sufficient budget for retrieval, while retrieval compensates for pruning-induced coverage loss and recovers accepted length. By employing a sequential `prune-then-graft' mechanism, Graft attaches highly predictive retrieved tokens into positions opened by pruning, filling the topological gaps with near-zero overhead. Graft is entirely training-free and lossless. Comprehensive evaluations show that Graft establishes a new Pareto frontier across practical deployment settings, including short-context generation, long-context generation, and large-scale models. On short-context benchmarks, it achieves up to 5.41$\times$ speedup and improves average speedup over EAGLE-3 by up to 21.8% on the large-scale Qwen3-235B. We also provide a preliminary exploration of applying Graft to the DFlash-style block drafting paradigm, offering initial evidence and insights for extending grafting beyond autoregressive draft trees.

Discovering shapelets – i.e., discriminative temporal patterns within time series – has been widely studied to address the inherent complexity of time-series classification (TSC) and to make model decision-making processes more transparent. However, existing methods primarily focus on population-level shapelets optimized across the entire dataset, which leads to two fundamental limitations: (i) population-level patterns often misalign with instance-specific features, resulting in suboptimal performance and potentially misleading interpretations, and (ii) most methods treat shapelets as independent entities, overlooking important temporal dependencies and interactions among multiple patterns. To address these limitations, we propose INSHAPE, an interpretable TSC framework that discovers variable-length, discriminative temporal patterns specific to each time series. INSHAPE identifies these patterns as non-overlapping segments and models their temporal dependencies, thereby providing clear instance-level interpretations while achieving strong predictive performance. Furthermore, INSHAPE bridges local and global interpretability through a bottom-up approach, aggregating instance-level shapelets into prototypical (population-level) shapelets. Extensive experiments on 128 UCR and 30 UEA benchmark datasets show that INSHAPE consistently outperforms state-of-the-art shapelet-based methods while providing more intuitive and interpretable insights.

Recent work pairs LLMs with evolutionary search to iteratively generate, modify, and select code using task-specific feedback. These systems have produced strong results in mathematical discovery and algorithm design, yet a fundamental question remains: what do they actually evolve? Progress is typically summarized by the best score a run reaches under a task-specific evaluator, but that score can reflect several different mechanisms: new algorithmic structure, re-tuning an existing strategy, recombining ideas already in the model's internal knowledge, or overfitting to the evaluator. Distinguishing these mechanisms requires inspecting the search process itself, not only its final outcome. We introduce EvoTrace, a dataset of evolutionary coding traces spanning four evolutionary frameworks, reasoning and non-reasoning models, and 16 tasks across mathematics and algorithm design. To analyze these traces, we develop EvoReplay, a replay-based methodology that reconstructs the local search states behind high-scoring solutions and tests controlled interventions, including adjusting constants, removing program components and substituting models or prompting contexts. We annotate every code edit in EvoTrace with one of nine recurring edit types using an LLM-as-judge pipeline validated against blind human re-annotation. Across EvoTrace, most score gains come from a small subset of these edit types. We further find a deterministic cycling pattern: about 30% of code lines added during search are byte-identical re-introductions of previously-deleted lines, present throughout nearly every run. These results show that benchmark gains in evolutionary coding agents can arise from qualitatively different mechanisms, only some of which correspond to new algorithmic structure. EvoTrace enables more diagnostic evaluation of evolutionary coding agents beyond final benchmark scores.

Diffusion and flow-based generative models dominate visual synthesis, with guidance aligning samples to user input and improving perceptual quality. However, Classifier-Free Guidance (CFG) and extrapolation-based methods are heuristic linear combinations of velocities/scores that ignore the generative manifold geometry, breaking probability conservation and driving samples off the learned manifold under strong guidance. We analyse guidance through the continuity equation and show its effect decomposes into a divergence term and a score-parallel term defined invariantly across parameterizations. We prove the divergence term blows up structurally as sampling approaches the data manifold, motivating a time-dependent schedule alongside score-parallel attenuation. The resulting plug-and-play rule, Adaptive Manifold Guidance (AdaMaG), targets both terms at no additional inference cost. Finally, we show that several existing saturation and manifold preserving heuristics can be read as acting on one of these two terms. On image generation benchmarks, AdaMaG improves realism, reduces visible artefacts, and induces controlled desaturation under strong guidance.

Distillation transfers knowledge from a large model trained on broad data to a smaller, more efficient model suitable for deployment. In structured prediction settings, prior knowledge about the task can guide the choice of a target architecture that is algorithmically aligned with the underlying problem. Building on recent learning-theoretic analyses of decision-tree (DT) distillation (Boix-Adsera, 2024), we study when distillation succeeds for combinatorial optimization tasks. We focus on the case where the target model is a graph neural network whose architecture is aligned with a dynamic programming (DP) algorithm for the task. Assuming that the source model is sufficiently rich, formalized through the linear representation hypothesis (LRH) (Elhage et al., 2022; Park et al., 2024), we show that the distillation problem can be solved efficiently in the complexity parameters of the DP transition function, represented as a DT. Our results provide a rigorous sufficient condition for successful distillation in the flavour of algorithmic alignment.

Competitive selection processes, from scientific funding to admissions and hiring, use evaluations to score candidates, and eventually choose a subset of them based on those scores. Recently, many organizations have adopted partial lotteries, which randomize selection based on evaluation scores. However, existing lottery designs are inherently unstable, as a small change to a single candidate's score can cause large shifts in their selection probabilities. This instability undermines a key goal of lotteries: reducing the influence of fine-grained score distinctions near the decision boundary. We propose smoothness as a design principle for partial lotteries, formalizing it as a Lipschitz condition on the mapping from review scores over candidates to selection probabilities. We introduce the Clipped Linear Lottery, a simple mechanism in which selection probabilities scale linearly with estimated quality between an upper threshold, above which we always accept, and a lower threshold, below which we always reject. We prove that the Clipped Linear Lottery's worst-case regret matches a lower bound for any smooth selection rule up to a factor of $(1 - k/n)$, where $k/n$ is the acceptance rate. We compare smooth selection to other stability notions like Individual Fairness and Differential Privacy, showing that the Clipped Linear Lottery achieves a better smoothness-regret tradeoff than alternatives. Experiments on real peer review data from ICLR 2025, NeurIPS 2024, and the Swiss National Science Foundation demonstrate that existing lottery designs are highly unstable in practice even under perturbations to a single score. Our experiments also confirm the tightness of our theoretical analysis and show that our proposed Clipped Linear Lottery achieves a better smoothness-utility tradeoff than alternatives in practice.

Standard generative models struggle with heavy-tailed data: Lipschitz architectures cannot produce power-law tails from Gaussian noise, and interpolating between heavy-tailed data and Gaussians is ill-posed. We propose a simple fix: apply the soft-log transform $\phi(x) = \mathrm{sign}(x) \cdot \log(1 + |x|)$ coordinate-wise to data before training, then exponentiate samples after generation. A Hill diagnostic decides per-coordinate whether to transform, leaving light-tailed margins untouched at no added complexity. This compresses heavy tails into a range where standard flow matching succeeds, without heavy-tailed base distributions or architectural modifications. We provide theoretical intuition for why this works: the log-transform maps Pareto tails to exponentials, and the induced dynamics implement a form of tail annealing via power transformations. On a 144-configuration multivariate benchmark (3 copulas, $d$ up to 100, 4 tail indices), Log-FM dominates specialized baselines on $W_1$, CVaR$_{99}$, and extreme-quantile metrics, and is the only method with zero severe divergences across 2{,}880 runs.