Daily Papers

For the real part of the Cauchy-type integral that is known to be the logarithmic potential of the double layer, a necessary and sufficient condition for the continuous extension to the Ahlfors-regular boundary is established.

We introduce Meta Agents Research Environments (ARE), a research platform for scalable creation of environments, integration of synthetic or real applications, and execution of agentic orchestrations. ARE provides simple abstractions to build complex and diverse environments, each with their own rules, tools, content, and verifiers, helping to bridge the gap between model development and real-world deployment. We also propose Gaia2, a benchmark built in ARE and designed to measure general agent capabilities. Beyond search and execution, Gaia2 requires agents to handle ambiguities and noise, adapt to dynamic environments, collaborate with other agents, and operate under temporal constraints. Unlike prior benchmarks, Gaia2 runs asynchronously, surfacing new failure modes that are invisible in static settings. Our experiments show that no system dominates across the intelligence spectrum: stronger reasoning often comes at the cost of efficiency, and budget scaling curves plateau, highlighting the need for new architectures and adaptive compute strategies. Perhaps more importantly, ARE abstractions enable continuous extension of Gaia2 to other environments, empowering the community to rapidly create new benchmarks tailored to their domains. In AI's second half, progress increasingly depends on defining meaningful tasks and robust evaluations to drive frontier capabilities forward.

Extending discrete-time causal Prior-data Fitted Networks for time series to continuous time invites writing the mechanism as a stochastic differential equation (SDE) -- but if the SDE is integrated once per observation gap, the trajectory law depends on when it is observed, and the prior remains a discrete-time Markov model in SDE clothing. We propose a precise continuity criterion -- trajectory-law invariance to the observation schedule -- together with a three-tier taxonomy (discrete; naive observation-grid integration; fine-grid integration with decoupled observation) and a construction realising the top tier on a random DAG with OU or small-MLP nonlinear drifts, irregular observation schedules, and hard / soft / time-varying interventions. A 2 times 2 encoder times integrator ablation, run independently on a linear and a nonlinear prior, finds fine-grid integration beats naive on 8/8 cells (sign-consistency p < 1/256) with the gap growing as the eval grid refines; the encoder axis is null with fine integration but time-aware-leading with naive. We release the prior and a preliminary zero-shot protocol on pharmacokinetic and physical-system data.

Autoregressive models have demonstrated remarkable success in sequential data generation, particularly in NLP, but their extension to continuous-domain image generation presents significant challenges. Recent work, the masked autoregressive model (MAR), bypasses quantization by modeling per-token distributions in continuous spaces using a diffusion head but suffers from slow inference due to the high computational cost of the iterative denoising process. To address this, we propose the Fast AutoRegressive model (FAR), a novel framework that replaces MAR's diffusion head with a lightweight shortcut head, enabling efficient few-step sampling while preserving autoregressive principles. Additionally, FAR seamlessly integrates with causal Transformers, extending them from discrete to continuous token generation without requiring architectural modifications. Experiments demonstrate that FAR achieves 2.3times faster inference than MAR while maintaining competitive FID and IS scores. This work establishes the first efficient autoregressive paradigm for high-fidelity continuous-space image generation, bridging the critical gap between quality and scalability in visual autoregressive modeling.

Recursive Neural Networks (RvNNs), which compose sequences according to their underlying hierarchical syntactic structure, have performed well in several natural language processing tasks compared to similar models without structural biases. However, traditional RvNNs are incapable of inducing the latent structure in a plain text sequence on their own. Several extensions have been proposed to overcome this limitation. Nevertheless, these extensions tend to rely on surrogate gradients or reinforcement learning at the cost of higher bias or variance. In this work, we propose Continuous Recursive Neural Network (CRvNN) as a backpropagation-friendly alternative to address the aforementioned limitations. This is done by incorporating a continuous relaxation to the induced structure. We demonstrate that CRvNN achieves strong performance in challenging synthetic tasks such as logical inference and ListOps. We also show that CRvNN performs comparably or better than prior latent structure models on real-world tasks such as sentiment analysis and natural language inference.

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

We present GB-LSR (Global-Bandwidth Local Spectral Representation), a fixed-grid local spectral representation for continuous image reconstruction. The image domain is partitioned into non-overlapping square patches, each carrying coefficients for a truncated Fourier basis predicted from shared convolutional-encoder features. A single trainable scalar bandwidth is shared globally across all patches and images, and reconstruction at any continuous coordinate is a fixed-size basis contraction whose cost is independent of image size. We study three bandwidth-handling variants: a trainable global scalar (main), a fixed global scalar, and a per-patch bandwidth field. On a standardized native-reconstruction benchmark across Kodak, Set14, and Urban100, the main variant outperforms matched-budget amortized LIIF / LTE / WIRE re-implementations by 2.8-3.6 dB PSNR and 0.11-0.15 LPIPS, while running at roughly one-quarter of the slowest baseline's inference cost. The single global scalar suffices empirically: per-patch adaptive-bandwidth alternatives do not improve over it on either a closed-form locality diagnostic or an end-to-end ablation. In a separate arbitrary-scale super-resolution (ASR) extension, GB-LSR achieves competitive PSNR-Y under a canonical-style SR protocol and runs 1.44x faster than LIIF-RDN and 3.25x faster than LTE-SwinIR at x4; within the same extension, a variant trained and evaluated without 4-corner local-ensemble averaging gives a 1.77x speedup with 35% lower peak memory and negligible PSNR change, while additionally widening the RDN encoder from 64 to 96 channels gives a small positive PSNR shift with a 1.58x speedup and 31% lower peak memory. Native-reconstruction claims are scoped to the matched-budget amortized protocol, and ASR claims are scoped to a separate canonical-style SR protocol.

While on-policy distillation (OPD) effectively addresses sparse rewards and exposure bias in large language model post-training, its extension to flow models remains underexplored. To this end, we propose Flow Continuous Trajectory Supervision (FlowCTS), which matches subsequent student and reference trajectories initialized from the same student-visited state. Using the integral relation between trajectories and velocity fields, we derive a temporally weighted velocity-matching upper bound and discretize it into practical objectives parameterized by the number of supervision steps. Under a multi-reference setup, single-state FlowCTS-OPD outperforms vanilla KL-based OPD with faster convergence. FlowCTS-OPD improves GenEval from 0.90 to 0.93, OCR from 0.90 to 0.92, and PickScore from 22.75 to 23.06, while outperforming a mixed-reward RL baseline across all target metrics. Further analysis reveals a clear temporal supervision mismatch in vanilla KL-based OPD arising from its auxiliary SDE transition kernels. Beyond on-policy setting,FlowCTS also consistently outperforms vanilla SFT , particularly on OCR, while increasing supervision steps exhibit a trade-off between richer trajectory information and greater optimization difficulty.

Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent homology (PH) are being increasingly employed to augment the GNNs. We investigate the benefits of integrating these two paradigms. Specifically, we introduce TopNets as a broad framework that subsumes and unifies various methods in the intersection of GNNs/TNNs and PH such as (generalizations of) RePHINE and TOGL. TopNets can also be readily adapted to handle (symmetries in) geometric complexes, extending the scope of TNNs and PH to spatial settings. Theoretically, we show that PH descriptors can provably enhance the expressivity of simplicial message-passing networks. Empirically, (continuous and E(n)-equivariant extensions of) TopNets achieve strong performance across diverse tasks, including antibody design, molecular dynamics simulation, and drug property prediction.

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

Recently emerged Vision-and-Language Navigation (VLN) tasks have drawn significant attention in both computer vision and natural language processing communities. Existing VLN tasks are built for agents that navigate on the ground, either indoors or outdoors. However, many tasks require intelligent agents to carry out in the sky, such as UAV-based goods delivery, traffic/security patrol, and scenery tour, to name a few. Navigating in the sky is more complicated than on the ground because agents need to consider the flying height and more complex spatial relationship reasoning. To fill this gap and facilitate research in this field, we propose a new task named AerialVLN, which is UAV-based and towards outdoor environments. We develop a 3D simulator rendered by near-realistic pictures of 25 city-level scenarios. Our simulator supports continuous navigation, environment extension and configuration. We also proposed an extended baseline model based on the widely-used cross-modal-alignment (CMA) navigation methods. We find that there is still a significant gap between the baseline model and human performance, which suggests AerialVLN is a new challenging task. Dataset and code is available at https://github.com/AirVLN/AirVLN.

We revisit axion monodromy inflation in the context of UV-complete theories and point out that its cosmological observables are sensitive to heavy fields with masses far above the Hubble scale, such as the moduli of flux compactifications. By studying a string-inspired two-field extension of axion monodromy, we reveal that the oscillatory modulation of the axion potential leads to continuous excitation of heavy fields during inflation when the modulation frequency exceeds the field masses. This finding challenges the conventional single-field description, as heavy moduli cannot be simply integrated out. Using a full bootstrap analysis, we demonstrate that this mechanism produces cosmological collider signals that bypass the usual Boltzmann suppression for heavy masses. Specifically, we identify detectably large signatures of heavy moduli in the primordial bispectrum, offering a promising avenue for probing high-energy physics through cosmological observations.

In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are able to combine the efficient ordered nature of graph-based techniques, such as A*, with the anytime scalability of sampling-based algorithms, such as Rapidly-exploring Random Trees (RRT). BIT* uses a heuristic to efficiently search a series of increasingly dense implicit RGGs while reusing previous information. It can be viewed as an extension of incremental graph-search techniques, such as Lifelong Planning A* (LPA*), to continuous problem domains as well as a generalization of existing sampling-based optimal planners. It is shown that it is probabilistically complete and asymptotically optimal. We demonstrate the utility of BIT* on simulated random worlds in R^2 and R^8 and manipulation problems on CMU's HERB, a 14-DOF two-armed robot. On these problems, BIT* finds better solutions faster than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster anytime convergence towards the optimum, especially in high dimensions.

Denoising with a Joint-Embedding Predictive Architecture (D-JEPA), an autoregressive model, has demonstrated outstanding performance in class-conditional image generation. However, the application of next-token prediction in high-resolution text-to-image generation remains underexplored. In this paper, we introduce D-JEPAcdotT2I, an extension of D-JEPA incorporating flow matching loss, designed to enable data-efficient continuous resolution learning. D-JEPAcdotT2I leverages a multimodal visual transformer to effectively integrate textual and visual features and adopts Visual Rotary Positional Embedding (VoPE) to facilitate continuous resolution learning. Furthermore, we devise a data feedback mechanism that significantly enhances data utilization efficiency. For the first time, we achieve state-of-the-art high-resolution image synthesis via next-token prediction. The experimental code and pretrained models will be open-sourced at https://d-jepa.github.io/t2i.

We introduce the FRactional-Order graph Neural Dynamical network (FROND), a new continuous graph neural network (GNN) framework. Unlike traditional continuous GNNs that rely on integer-order differential equations, FROND employs the Caputo fractional derivative to leverage the non-local properties of fractional calculus. This approach enables the capture of long-term dependencies in feature updates, moving beyond the Markovian update mechanisms in conventional integer-order models and offering enhanced capabilities in graph representation learning. We offer an interpretation of the node feature updating process in FROND from a non-Markovian random walk perspective when the feature updating is particularly governed by a diffusion process. We demonstrate analytically that oversmoothing can be mitigated in this setting. Experimentally, we validate the FROND framework by comparing the fractional adaptations of various established integer-order continuous GNNs, demonstrating their consistently improved performance and underscoring the framework's potential as an effective extension to enhance traditional continuous GNNs. The code is available at https://github.com/zknus/ICLR2024-FROND.

We investigate the first-order differential calculus over extended metric-topological measure spaces. The latter are quartets mathbb X=(X,τ,{sf d},mathfrak m), given by an extended metric space (X,{sf d}) together with a weaker topology τ (satisfying suitable compatibility conditions) and a finite Radon measure mathfrak m on (X,τ). The class of extended metric-topological measure spaces encompasses all metric measure spaces and many infinite-dimensional metric-measure structures, such as abstract Wiener spaces. In this framework, we study the following classes of objects: - The Banach algebra {rm Lip}_b(X,τ,{sf d}) of bounded τ-continuous {sf d}-Lipschitz functions on X. - Several notions of Lipschitz derivations on X, defined in duality with {rm Lip}_b(X,τ,{sf d}). - The metric Sobolev space W^{1,p}(mathbb X), defined in duality with Lipschitz derivations on X. Inter alia, we generalise both Weaver's and Di Marino's theories of Lipschitz derivations to the extended setting, and we discuss their connections. We also introduce a Sobolev space W^{1,p}(mathbb X) via an integration-by-parts formula, along the lines of Di Marino's notion of Sobolev space, and we prove its equivalence with other approaches, studied in the extended setting by Ambrosio, Erbar and Savaré. En route, we obtain some results of independent interest, among which are: - A Lipschitz-constant-preserving extension result for τ-continuous {sf d}-Lipschitz functions. - A novel and rather robust strategy for proving the equivalence of Sobolev-type spaces defined via an integration-by-parts formula and those obtained with a relaxation procedure. - A new description of an isometric predual of the metric Sobolev space W^{1,p}(mathbb X).

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been extensively used in the most diverse types of problems, also motivating some respective generalizations. The present work addresses further generalizations of this index, including its modification into a coincidence index capable of accounting also for the level of relative interiority between the two compared entities, as well as respective extensions for sets in continuous vector spaces, the generalization to multiset addition, densities and generic scalar fields, as well as a means to quantify the joint interdependence between two random variables. The also interesting possibility to take into account more than two sets has also been addressed, including the description of an index capable of quantifying the level of chaining between three structures. Several of the described and suggested eneralizations have been illustrated with respect to numeric case examples. It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities, including as a measurement of clusters similarity or separation and as a resource for representing and analyzing complex networks.

We analyze various consequences in relation to the extension of operators T:Xto Y that are p-compact, as well as the extension of operators T:Xto Y whose adjoints T^*:Y^*to X^* are p-compact. In most cases, we discuss these extension properties when the underlying spaces, either domain or codomain, are P_lambda spaces. We also answer if these extensions are almost norm-preserving in such circumstances where the extension T of a T exists. It is observed that an operator can often be extended to a larger domain when the codomain is appropriately extended as well. Specific assumptions might enable us to obtain an extension of an operator that maintains the same range. Necessary and sufficient conditions are derived for a Banach space to be L_1-predual.

Extending the context window of large language models typically requires training on sequences at the target length, incurring quadratic memory and computational costs that make long-context adaptation expensive and difficult to reproduce. We propose EndPrompt, a method that achieves effective context extension using only short training sequences. The core insight is that exposing a model to long-range relative positional distances does not require constructing full-length inputs: we preserve the original short context as an intact first segment and append a brief terminal prompt as a second segment, assigning it positional indices near the target context length. This two-segment construction introduces both local and long-range relative distances within a short physical sequence while maintaining the semantic continuity of the training text--a property absent in chunk-based simulation approaches that split contiguous context. We provide a theoretical analysis grounded in Rotary Position Embedding and the Bernstein inequality, showing that position interpolation induces a rigorous smoothness constraint over the attention function, with shared Transformer parameters further suppressing unstable extrapolation to unobserved intermediate distances. Applied to LLaMA-family models extending the context window from 8K to 64K, EndPrompt achieves an average RULER score of 76.03 and the highest average on LongBench, surpassing LCEG (72.24), LongLoRA (72.95), and full-length fine-tuning (69.23) while requiring substantially less computation. These results demonstrate that long-context generalization can be induced from sparse positional supervision, challenging the prevailing assumption that dense long-sequence training is necessary for reliable context-window extension. The code is available at https://github.com/clx1415926/EndPrompt.

Adapting standard methods from geometric measure theory, we provide an example of a polynomial-valued measure mu on tame sets in R^d which satisfies many desirable properties. Among these is strict monotonicity: the measure of a proper subset is strictly less than the measure of the whole set. Using techniques from non-standard analysis, we display that the domain of mu can be extended to all subsets of R^d (up to equivalence modulo infinitesimals). The resulting extension is a numerosity function that encodes the i-dimensional Hausdorff measure for all iin N, as well as the i-th intrinsic volume functions.

Broad textual understanding and in-context learning require language models that utilize full document contexts. Due to the implementation challenges associated with directly training long-context models, many methods have been proposed for extending models to handle long contexts. However, owing to differences in data and model classes, it has been challenging to compare these approaches, leading to uncertainty as to how to evaluate long-context performance and whether it differs from standard evaluation. We implement a controlled protocol for extension methods with a standardized evaluation, utilizing consistent base models and extension data. Our study yields several insights into long-context behavior. First, we reaffirm the critical role of perplexity as a general-purpose performance indicator even in longer-context tasks. Second, we find that current approximate attention methods systematically underperform across long-context tasks. Finally, we confirm that exact fine-tuning based methods are generally effective within the range of their extension, whereas extrapolation remains challenging. All codebases, models, and checkpoints will be made available open-source, promoting transparency and facilitating further research in this critical area of AI development.

We present SetExpander, a corpus-based system for expanding a seed set of terms into amore complete set of terms that belong to the same semantic class. SetExpander implements an iterative end-to-end workflow. It enables users to easily select a seed set of terms, expand it, view the expanded set, validate it, re-expand the validated set and store it, thus simplifying the extraction of domain-specific fine-grained semantic classes.SetExpander has been used successfully in real-life use cases including integration into an automated recruitment system and an issues and defects resolution system. A video demo of SetExpander is available at https://drive.google.com/open?id=1e545bB87Autsch36DjnJHmq3HWfSd1Rv (some images were blurred for privacy reasons)

Addressing the challenge of effectively processing long contexts has become a critical issue for Large Language Models (LLMs). Two common strategies have emerged: 1) reducing the input length, such as retrieving relevant chunks by Retrieval-Augmented Generation (RAG), and 2) expanding the context window limit of LLMs. However, both strategies have drawbacks: input reduction has no guarantee of covering the part with needed information, while window extension struggles with focusing on the pertinent information for solving the task. To mitigate these limitations, we propose Chain-of-Agents (CoA), a novel framework that harnesses multi-agent collaboration through natural language to enable information aggregation and context reasoning across various LLMs over long-context tasks. CoA consists of multiple worker agents who sequentially communicate to handle different segmented portions of the text, followed by a manager agent who synthesizes these contributions into a coherent final output. CoA processes the entire input by interleaving reading and reasoning, and it mitigates long context focus issues by assigning each agent a short context. We perform comprehensive evaluation of CoA on a wide range of long-context tasks in question answering, summarization, and code completion, demonstrating significant improvements by up to 10% over strong baselines of RAG, Full-Context, and multi-agent LLMs.