Daily Papers

Hyper-Connections (HC) generalize residual connections into multiple streams, employing residual matrices for cross-stream feature mixing to enrich model expressivity. However, unconstrained mixing disrupts the identity mapping property intrinsic to the residual connection, causing unstable training. To address this, Manifold-Constrained Hyper-Connections (mHC) and its variant restrict these matrices to the Birkhoff polytope (doubly stochastic matrices) via Sinkhorn iterations or permutation-based parameterizations. We reveal three limitations of this polytope constraint: (1) identity degeneration, where learned matrices collapse around the identity and diminish cross-stream interactions, (2) an expressivity bottleneck, as the non-negativity constraint prevents subtractive feature disentanglement, and (3) parameterization inefficiencies, manifesting as unstable Sinkhorn iterations or the factorial-scaling overhead of permutation-based parameterizations. To overcome these flaws, we propose Spectral-Sphere-Constrained Hyper-Connections (sHC). By geometrically shifting the feasible set from a rigid polytope to a spectral norm sphere, sHC allows negative entries, unlocking subtractive interactions for selective feature diversification. This shift eliminates unstable Sinkhorn projections and factorial parameterization, enabling expressive, non-degenerate residual matrices while preserving training stability.

Mathematical programming formulations are routinely modified through algebraic reformulations, perturbations of constraint functions, and the addition or removal of constraints. Some of these modifications preserve the feasible set, whereas others reflect newly imposed modeling requirements and therefore change the optimization problem itself. This paper develops a metric framework for quantifying the robustness of formulation-dependent properties. Formulations are modeled as typed collections of constraint functions. Within each fixed typed-cardinality class, their distance is defined by optimally matching constraints of the same type and measuring the resulting discrepancies in a norm on the underlying function space. As a concrete demonstration of the framework, we study the Linear Independence Constraint Qualification (LICQ). We introduce the pointwise LICQ radius, defined as the distance from a feasible formulation to the set of formulations that remain feasible at a prescribed point but fail LICQ there. Under suitable assumptions, we derive an explicit formula for this radius and characterize the effect of adding a single equality or inequality constraint.

Increasing levels of renewable generation motivate a growing interest in data-driven approaches for AC optimal power flow (AC OPF) to manage uncertainty; however, a lack of disciplined dataset creation and benchmarking prohibits useful comparison among approaches in the literature. To instill confidence, models must be able to reliably predict solutions across a wide range of operating conditions. This paper develops the OPF-Learn package for Julia and Python, which uses a computationally efficient approach to create representative datasets that span a wide spectrum of the AC OPF feasible region. Load profiles are uniformly sampled from a convex set that contains the AC OPF feasible set. For each infeasible point found, the convex set is reduced using infeasibility certificates, found by using properties of a relaxed formulation. The framework is shown to generate datasets that are more representative of the entire feasible space versus traditional techniques seen in the literature, improving machine learning model performance.

Decision-focused learning (DFL) trains predictive models for downstream optimization, but existing methods largely assume centralized data. In cross-silo settings, federated learning offers a natural alternative, yet standard federated methods optimize prediction over decision quality and do not address heterogeneity in downstream objectives or feasible sets. This heterogeneity is especially challenging for DFL because small perturbations in polyhedral problems can cause discontinuous changes in optimal decisions, destabilizing client updates and aggregation. We propose FedRSPO+, a heterogeneity-aware framework for decision-focused federated learning, built on RSPO+, a regularized predict-then-optimize surrogate that smooths the decision map through projection. We show that RSPO+ upper bounds decision error and regret for the regularized decision and, under exact regularization and consistent LP solution selection, for the original LP decision. We further derive cross-client heterogeneity bounds that depend on both objective and feasible-set heterogeneity, vanish at homogeneity, and require no strong convexity. FedRSPO+ uses an annealed, modular training procedure compatible with standard federated personalization and aggregation methods. Experiments on synthetic knapsack, shortest-path, and real-world energy pricing tasks compare against prediction-only federated learning and DFL baselines under varying heterogeneity and communication budgets. Results suggest that smoothing is a useful ingredient for stable collaborative decision learning and provide a heterogeneity-aware foundation for federated DFL.

Large language model (LLM) inference is often bounded by memory footprint and memory bandwidth in resource-constrained deployments, making quantization a fundamental technique for efficient serving. While post-training quantization (PTQ) maintains high fidelity at 4-bit, it deteriorates at 2-3 bits. Fundamentally, existing methods enforce a shape-invariant quantization grid (e.g., the fixed uniform intervals of UINT2) for each group, severely restricting the feasible set for error minimization. To address this, we propose Bit-Plane Decomposition Quantization (BPDQ), which constructs a variable quantization grid via bit-planes and scalar coefficients, and iteratively refines them using approximate second-order information while progressively compensating quantization errors to minimize output discrepancy. In the 2-bit regime, BPDQ enables serving Qwen2.5-72B on a single RTX 3090 with 83.85% GSM8K accuracy (vs. 90.83% at 16-bit). Moreover, we provide theoretical analysis showing that the variable grid expands the feasible set, and that the quantization process consistently aligns with the optimization objective in Hessian-induced geometry. Code: github.com/KingdalfGoodman/BPDQ.

Text-conditioned motion generation is a promising interface for programming humanoid robots, yet current generators are often trained on human motion datasets retargeted to robot morphologies. Although such data provides rich semantic and kinematic priors, it fails to capture the nuances of whole-body tracking controllers, including balance, contact dynamics, actuation limits, and controller-specific failure modes. As a result, generated motions can be semantically plausible but difficult or impossible for the robot to execute. We introduce TEXEDO, a test-time scaling framework for humanoid motion generation that improves motion quality without requiring a stronger underlying generator. Given a text prompt, TEXEDO samples multiple candidate motions from a pretrained text-conditioned generator and selects the best motion that is both executable and task-aligned. The reward model combines a dynamic feasibility verifier, distilled from whole-body tracking rollouts to predict physical executability, with a semantic alignment verifier that measures text-motion alignment in a learned co-embedding space. Our pipeline treats dynamic feasibility as a hard constraint and semantic alignment as the selection objective within the feasible set. Through large-scale simulation studies and real-world deployment on a Unitree G1 humanoid robot, we show that TEXEDO consistently improves both tracking fidelity and text alignment. These results demonstrate that grounded verification is an effective path toward deployable language-guided humanoid motion generation. Project website: https://jianuocao.github.io/TEXEDO/

Multi-agent systems (MAS) increasingly solve complex tasks by orchestrating agents and tools selected from rapidly growing marketplaces. As these marketplaces expand, many candidates become functionally overlapping, making selection not just a retrieval problem: beyond filtering relevant agents, an orchestrator must choose options that are reliable, compatible with the current execution context, and able to cooperate with other selected agents. Existing recommender systems -- largely built for item-level ranking from flat user-item logs -- do not directly address the structured, sequential, and interaction-dependent nature of agent orchestration. We address this gap by formulating agent recommendation in MAS as a constrained decision problem and introducing a generic constrained recommendation framework that first uses retrieval to build a compact candidate set conditioned on the current subtask and context, and then performs utility optimization within this feasible set using a learned scorer that accounts for relevance, reliability, and interaction effects. We ground both the formulation and learning signals in historical calling trees, which capture the execution structure of MAS (parent-child calls, branching dependencies, and local cooperation patterns) beyond what flat logs provide. The framework supports two complementary settings: agent-level recommendation (select the next agent/tool) and system-level recommendation (select a small, connected agent team/subgraph for coordinated execution). To enable systematic evaluation, we construct a unified calling-tree benchmark by normalizing invocation logs from eight heterogeneous multi-agent corpora into a shared structured representation.

In this paper, we introduce a new projection-free algorithm for Online Convex Optimization (OCO) with a state-of-the-art regret guarantee among separation-based algorithms. Existing projection-free methods based on the classical Frank-Wolfe algorithm achieve a suboptimal regret bound of O(T^{3/4}), while more recent separation-based approaches guarantee a regret bound of O(κT), where κ denotes the asphericity of the feasible set, defined as the ratio of the radii of the containing and contained balls. However, for ill-conditioned sets, κ can be arbitrarily large, potentially leading to poor performance. Our algorithm achieves a regret bound of O(dT + κd), while requiring only O(1) calls to a separation oracle per round. Crucially, the main term in the bound, O(d T), is independent of κ, addressing the limitations of previous methods. Additionally, as a by-product of our analysis, we recover the O(κT) regret bound of existing OCO algorithms with a more straightforward analysis and improve the regret bound for projection-free online exp-concave optimization. Finally, for constrained stochastic convex optimization, we achieve a state-of-the-art convergence rate of O(σ/T + κd/T), where σ represents the noise in the stochastic gradients, while requiring only O(1) calls to a separation oracle per iteration.

Circuit cutting runs a quantum computation on processors smaller than the circuit, at the price of classical knitting whose cost grows exponentially with the number of cut gates. Keeping this cost affordable is necessary but not sufficient for an advantage, since knitting classically easy subcircuits is itself classically easy. We formulate three requirements for distributed quantum advantage under a stated budget: affordable knitting, classical difficulty that survives the cut, and, for variational circuits, resolvable gradients. We prove that under stated assumptions knitting stays affordable when subcircuits grow behind a bounded interface and becomes exponentially expensive when fixed-width subcircuits multiply. We turn the requirements into screening criteria and apply them to eighteen circuit families. We identify finite local-depth circuits with bounded interfaces as a setting in which the requirements can coexist, with hardness established only in the worst case. As a classically verifiable proof of principle, we knit one gate joining two field-perturbed toric-code patches on an IBM Nighthawk processor for up to 142 spins, and confirm that the reconstruction can at least resolve the contact correlation beyond independent execution for up to 98 qubits.

Optimizing objective functions subject to constraints is fundamental in many real-world applications. However, these constraints are often not readily defined and must be inferred from expert agent behaviors, a problem known as Inverse Constraint Inference. Inverse Constrained Reinforcement Learning (ICRL) is a common solver for recovering feasible constraints in complex environments, relying on training samples collected from interactive environments. However, the efficacy and efficiency of current sampling strategies remain unclear. We propose a strategic exploration framework for sampling with guaranteed efficiency to bridge this gap. By defining the feasible cost set for ICRL problems, we analyze how estimation errors in transition dynamics and the expert policy influence the feasibility of inferred constraints. Based on this analysis, we introduce two exploratory algorithms to achieve efficient constraint inference via 1) dynamically reducing the bounded aggregate error of cost estimations or 2) strategically constraining the exploration policy around plausibly optimal ones. Both algorithms are theoretically grounded with tractable sample complexity, and their performance is validated empirically across various environments.

Inverse reinforcement learning (IRL) denotes a powerful family of algorithms for recovering a reward function justifying the behavior demonstrated by an expert agent. A well-known limitation of IRL is the ambiguity in the choice of the reward function, due to the existence of multiple rewards that explain the observed behavior. This limitation has been recently circumvented by formulating IRL as the problem of estimating the feasible reward set, i.e., the region of the rewards compatible with the expert's behavior. In this paper, we make a step towards closing the theory gap of IRL in the case of finite-horizon problems with a generative model. We start by formally introducing the problem of estimating the feasible reward set, the corresponding PAC requirement, and discussing the properties of particular classes of rewards. Then, we provide the first minimax lower bound on the sample complexity for the problem of estimating the feasible reward set of order {Omega}Bigl( H^3SA{epsilon^2} bigl( log bigl(1{delta}bigl) + S bigl)Bigl), being S and A the number of states and actions respectively, H the horizon, epsilon the desired accuracy, and delta the confidence. We analyze the sample complexity of a uniform sampling strategy (US-IRL), proving a matching upper bound up to logarithmic factors. Finally, we outline several open questions in IRL and propose future research directions.

A declared task can sometimes certify a reduced source before a downstream encoder, codebook, rate, distortion target, or optimizer is chosen. This paper studies when one such reduction preserves the complete downstream problem family, a property termed Task-Sufficient Contraction. The reduced source is fixed by the task before the later operating point is selected. An exact contraction allows the later problem to be solved on that source with the same result as if the full source had been retained. For a machine with a fixed set of possible actions and a fixed loss, the paper identifies a consumer-specific source by merging states only when every available action has the same regret in both. For finite action sets, replacing the richer source by this reduced source preserves the complete one-step rate-regret curve, even though the reduction is fixed before the distortion target is chosen. A second result gives an exact characterization for quadratic loss on affine feasible-action sets: the canonical reduced source is the projection onto the directions in which feasible actions can differ. Under a fixed energy budget, this becomes centered load, while retaining only the optimal water-filled action is too coarse. Earlier Information Bottleneck, semantic rate-distortion, and goal-oriented quantization results are then used to distinguish exact, architecture-conditioned, approximate, failed, and corrected contractions. The framework suggests a way for heterogeneous machines to exchange what a receiving task needs without first aligning their full internal representations.

We study the online influence maximization problem in social networks under the independent cascade model. Specifically, we aim to learn the set of "best influencers" in a social network online while repeatedly interacting with it. We address the challenges of (i) combinatorial action space, since the number of feasible influencer sets grows exponentially with the maximum number of influencers, and (ii) limited feedback, since only the influenced portion of the network is observed. Under a stochastic semi-bandit feedback, we propose and analyze IMLinUCB, a computationally efficient UCB-based algorithm. Our bounds on the cumulative regret are polynomial in all quantities of interest, achieve near-optimal dependence on the number of interactions and reflect the topology of the network and the activation probabilities of its edges, thereby giving insights on the problem complexity. To the best of our knowledge, these are the first such results. Our experiments show that in several representative graph topologies, the regret of IMLinUCB scales as suggested by our upper bounds. IMLinUCB permits linear generalization and thus is both statistically and computationally suitable for large-scale problems. Our experiments also show that IMLinUCB with linear generalization can lead to low regret in real-world online influence maximization.

Adversarial optimization under a shared ell_1 budget requires deciding not only how much perturbation to use, but also where that limited budget should be spent. This allocation problem becomes particularly important when individual input coordinates are subject to local magnitude constraints, which restrict the extent to which perturbation can be concentrated on a small number of locations. We introduce an importance-guided allocation mechanism that uses a fixed clean-gradient prior to steer perturbation toward model-sensitive regions while leaving the feasible perturbation set unchanged. A centered allocation objective encourages perturbation at above-average importance locations and discourages unnecessary expenditure elsewhere, thereby redistributing rather than enlarging the available budget. Across ten robust model--dataset configurations under a common capacity-limited threat setting, the proposed method improves attack success over matched APGD- and PMA-based baselines by 2.52 to 17.70 percentage points. Allocation analysis shows that these gains are accompanied by substantially greater perturbation mass in high-importance regions without increased global ell_1 consumption. Mechanism ablations further show that centered non-uniform redistribution provides part of the benefit, while model-derived importance yields an additional improvement. These results identify perturbation allocation as a distinct and practically relevant dimension of adversarial optimization under shared-budget, locally constrained threat models.

When training neural rankers using Large Language Models, it's expected that a practitioner would make use of multiple GPUs to accelerate the training time. By using more devices, deep learning frameworks, like PyTorch, allow the user to drastically increase the available VRAM pool, making larger batches possible when training, therefore shrinking training time. At the same time, one of the most critical processes, that is generally overlooked when running data-hungry models, is how data is managed between disk, main memory and VRAM. Most open source research implementations overlook this memory hierarchy, and instead resort to loading all documents from disk to main memory and then allowing the framework (e.g., PyTorch) to handle moving data into VRAM. Therefore, with the increasing sizes of datasets dedicated to IR research, a natural question arises: s this the optimal solution for optimizing training time? We here study how three different popular approaches to handling documents for IR datasets behave and how they scale with multiple GPUs. Namely, loading documents directly into memory, reading documents directly from text files with a lookup table and using a library for handling IR datasets (ir_datasets) differ, both in performance (i.e. samples processed per second) and memory footprint. We show that, when using the most popular libraries for neural ranker research (i.e. PyTorch and Hugging Face's Transformers), the practice of loading all documents into main memory is not always the fastest option and is not feasible for setups with more than a couple GPUs. Meanwhile, a good implementation of data streaming from disk can be faster, while being considerably more scalable. We also show how popular techniques for improving loading times, like memory pining, multiple workers, and RAMDISK usage, can reduce the training time further with minor memory overhead.

Reinforcement learning (RL) has increasingly been applied to solve real-world planning problems, with progress in handling large state spaces and time horizons. However, a key bottleneck in many domains is that RL methods cannot accommodate large, combinatorially structured action spaces. In such settings, even representing the set of feasible actions at a single step may require a complex discrete optimization formulation. We leverage recent advances in embedding trained neural networks into optimization problems to propose SEQUOIA, an RL algorithm that directly optimizes for long-term reward over the feasible action space. Our approach embeds a Q-network into a mixed-integer program to select a combinatorial action in each timestep. Here, we focus on planning over restless bandits, a class of planning problems which capture many real-world examples of sequential decision making. We introduce coRMAB, a broader class of restless bandits with combinatorial actions that cannot be decoupled across the arms of the restless bandit, requiring direct solving over the joint, exponentially large action space. We empirically validate SEQUOIA on four novel restless bandit problems with combinatorial constraints: multiple interventions, path constraints, bipartite matching, and capacity constraints. Our approach significantly outperforms existing methods -- which cannot address sequential planning and combinatorial selection simultaneously -- by an average of 24.8\% on these difficult instances.

Auditing large language models for unexpected behaviors is critical to preempt catastrophic deployments, yet remains challenging. In this work, we cast auditing as an optimization problem, where we automatically search for input-output pairs that match a desired target behavior. For example, we might aim to find a non-toxic input that starts with "Barack Obama" that a model maps to a toxic output. This optimization problem is difficult to solve as the set of feasible points is sparse, the space is discrete, and the language models we audit are non-linear and high-dimensional. To combat these challenges, we introduce a discrete optimization algorithm, ARCA, that jointly and efficiently optimizes over inputs and outputs. Our approach automatically uncovers derogatory completions about celebrities (e.g. "Barack Obama is a legalized unborn" -> "child murderer"), produces French inputs that complete to English outputs, and finds inputs that generate a specific name. Our work offers a promising new tool to uncover models' failure-modes before deployment.

Live-streaming Novel View Synthesis (NVS) from unposed multi-view video remains an open challenge in a wide range of applications. Existing methods for dynamic scene representation typically require ground-truth camera parameters and involve lengthy optimizations (approx 2.67s), which makes them unsuitable for live streaming scenarios. To address this issue, we propose a novel viewpoint video live-streaming method (LiveStre4m), a feed-forward model for real-time NVS from unposed sparse multi-view inputs. LiveStre4m introduces a multi-view vision transformer for keyframe 3D scene reconstruction coupled with a diffusion-transformer interpolation module that ensures temporal consistency and stable streaming. In addition, a Camera Pose Predictor module is proposed to efficiently estimate both poses and intrinsics directly from RGB images, removing the reliance on known camera calibration information. Our approach enables temporally consistent novel-view video streaming in real-time using as few as two synchronized unposed input streams. LiveStre4m attains an average reconstruction time of 0.07s per-frame at 1024 times 768 resolution, outperforming the optimization-based dynamic scene representation methods by orders of magnitude in runtime. These results demonstrate that LiveStre4m makes real-time NVS streaming feasible in practical settings, marking a substantial step toward deployable live novel-view synthesis systems. Code available at: https://github.com/pedro-quesado/LiveStre4m

Large-scale humanoid motion-tracking controllers are commonly improved by reallocating training effort: difficult motions are sampled more often, isolated into smaller subsets, or assigned to specialized experts. We show that this view is incomplete. In strong whole-body-control baselines, a residual set of feasible training clips remains unsolved even under targeted training, especially for high-dynamic transitions and balance-critical motions. These failures arise not only from insufficient exposure, but from a mismatch between the motion demands and the effective capability induced by the default training recipe. We propose Athena-WBC, a compact teacher-student pipeline with capability-aligned policy experts for long-tail humanoid whole-body control. Dynamic experts use a tracking-focused, constraint-aware objective that removes conservative effort and temporal-control penalties while preserving physical feasibility constraints; balance experts use a gravity curriculum to improve early-training survivability. The resulting privileged teachers are motion-routed for DAgger distillation and then compressed into a single controller with deployable observations followed by RL fine-tuning. Experiments on a full-size humanoid show improved recovery of training-set long-tail motions and better held-out tracking than a strong SONIC-recipe baseline, using only a small number of experts.

Multi-agent trajectory prediction at signalized intersections is crucial for developing efficient intelligent transportation systems and safe autonomous driving systems. Due to the complexity of intersection scenarios and the limitations of single-vehicle perception, the performance of vehicle-centric prediction methods has reached a plateau. In this paper, we introduce an Infrastructure-to-Everything (I2X) collaborative prediction scheme. In this scheme, roadside units (RSUs) independently forecast the future trajectories of all vehicles and transmit these predictions unidirectionally to subscribing vehicles. Building on this scheme, we propose I2XTraj, a dedicated infrastructure-based trajectory prediction model. I2XTraj leverages real-time traffic signal states, prior maneuver strategy knowledge, and multi-agent interactions to generate accurate, joint multi-modal trajectory prediction. First, a continuous signal-informed mechanism is proposed to adaptively process real-time traffic signals to guide trajectory proposal generation under varied intersection configurations. Second, a driving strategy awareness mechanism estimates the joint distribution of maneuver strategies by integrating spatial priors of intersection areas with dynamic vehicle states, enabling coverage of the full set of feasible maneuvers. Third, a spatial-temporal-mode attention network models multi-agent interactions to refine and adjust joint trajectory outputs.Finally, I2XTraj is evaluated on two real-world datasets of signalized intersections, the V2X-Seq and the SinD drone dataset. In both single-infrastructure and online collaborative scenarios, our model outperforms state-of-the-art methods by over 30\% on V2X-Seq and 15\% on SinD, demonstrating strong generalizability and robustness.

The success of large language models (LLMs) can be attributed in part to their ability to efficiently store factual knowledge as key-value mappings within their MLP parameters. Recent work has proposed explicit weight constructions to build such fact-storing MLPs, providing an improved understanding of LLM fact storage mechanisms. In this paper, we introduce an MLP construction framework that improves over previous constructions in three areas: it 1) works for all but a measure-zero set of feasible input-output pairs, 2) achieves asymptotically optimal parameter efficiency matching information-theoretic bounds for some embeddings, and 3) maintains usability within Transformers for factual recall. Through our improvements, we 1) discover a metric on value embeddings that characterizes facts-per-parameter scaling for both constructed and gradient-descent-trained MLPs, 2) identify a simple encoder-decoder mechanism that empirically matches gradient-descent MLP facts-per-parameter asymptotics across all the inputs and outputs we test, and 3) uncover a fundamental tradeoff between an MLP's fact-storage capacity and its usability within Transformers. Finally, we demonstrate a proof-of-concept application of fact-storing MLPs: modular fact editing on one-layer Transformers by replacing entire MLPs at once.

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance on every individual data point. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.

This paper presents an equivalence between feasible kinodynamic planning and optimal kinodynamic planning, in that any optimal planning problem can be transformed into a series of feasible planning problems in a state-cost space whose solutions approach the optimum. This transformation gives rise to a meta-algorithm that produces an asymptotically optimal planner, given any feasible kinodynamic planner as a subroutine. The meta-algorithm is proven to be asymptotically optimal, and a formula is derived relating expected running time and solution suboptimality. It is directly applicable to a wide range of optimal planning problems because it does not resort to the use of steering functions or numerical boundary-value problem solvers. On a set of benchmark problems, it is demonstrated to perform, using the EST and RRT algorithms as subroutines, at a superior or comparable level to related planners.

An important function of collaborative network intrusion detection is to analyze the network logs of the collaborators for joint IP addresses. However, sharing IP addresses in plain is sensitive and may be even subject to privacy legislation as it is personally identifiable information. In this paper, we present the privacy-preserving collection of IP addresses. We propose a single collector, over-threshold private set intersection protocol. In this protocol N participants identify the IP addresses that appear in at least t participant's sets without revealing any information about other IP addresses. Using a novel hashing scheme, we reduce the computational complexity of the previous state-of-the-art solution from O(M(N M/t)^{2t}) to O(t^2MN{t}), where M denotes the dataset size. This reduction makes it practically feasible to apply our protocol to real network logs. We test our protocol using joint networks logs of multiple institutions. Additionally, we present two deployment options: a collusion-safe deployment, which provides stronger security guarantees at the cost of increased communication overhead, and a non-interactive deployment, which assumes a non-colluding collector but offers significantly lower communication costs and applicable to many use cases of collaborative network intrusion detection similar to ours.

Most meta-learning methods assume that the (very small) context set used to establish a new task at test time is passively provided. In some settings, however, it is feasible to actively select which points to label; the potential gain from a careful choice is substantial, but the setting requires major differences from typical active learning setups. We clarify the ways in which active meta-learning can be used to label a context set, depending on which parts of the meta-learning process use active learning. Within this framework, we propose a natural algorithm based on fitting Gaussian mixtures for selecting which points to label; though simple, the algorithm also has theoretical motivation. The proposed algorithm outperforms state-of-the-art active learning methods when used with various meta-learning algorithms across several benchmark datasets.

Although self-supervised 3D anomaly detection assumes that acquiring high-precision point clouds is computationally expensive, in real manufacturing scenarios it is often feasible to collect a limited number of anomalous samples. Therefore, we study open-set supervised 3D anomaly detection, where the model is trained with only normal samples and a small number of known anomalous samples, aiming to identify unknown anomalies at test time. We present Open-Industry, a high-quality industrial dataset containing 15 categories, each with five real anomaly types collected from production lines. We first adapt general open-set anomaly detection methods to accommodate 3D point cloud inputs better. Building upon this, we propose Open3D-AD, a point-cloud-oriented approach that leverages normal samples, simulated anomalies, and partially observed real anomalies to model the probability density distributions of normal and anomalous data. Then, we introduce a simple Correspondence Distributions Subsampling to reduce the overlap between normal and non-normal distributions, enabling stronger dual distributions modeling. Based on these contributions, we establish a comprehensive benchmark and evaluate the proposed method extensively on Open-Industry as well as established datasets including Real3D-AD and Anomaly-ShapeNet. Benchmark results and ablation studies demonstrate the effectiveness of Open3D-AD and further reveal the potential of open-set supervised 3D anomaly detection.

Vision-Language Models (VLMs) show promise in medical image analysis, yet their capacity for structured reasoning in complex domains like dermatology is often limited by data scarcity and the high computational cost of advanced training techniques. To address these challenges, we introduce DermIQ-VLM, a VLM developed through a multi-stage, resource-efficient methodology designed to emulate a dermatologist's diagnostic process. Our primary contribution is a modified version of Grouped Relative Policy Optimization (GRPO), called GRPO++, which stabilizes the powerful but data-intensive GRPO framework. Our proposed training pipeline first employs GRPO++ for reasoning-oriented disease recognition, followed by supervised fine-tuning for conversational ability. To mitigate factual errors introduced during this step, we then align the model using Direct Preference Optimization (DPO), leveraging a Knowledge Graph-based system as a scalable proxy for expert preference. A preliminary evaluation on a curated dermatological dataset demonstrates that our proposed methodology yields notable performance gains over standard fine-tuning approaches. These findings validate the potential of our pipeline as a feasible pathway for developing specialized, reliable VLMs in resource-constrained environments.

Although LEGO sets have entertained generations of children and adults, the challenge of designing customized builds matching the complexity of real-world or imagined scenes remains too great for the average enthusiast. In order to make this feat possible, we implement a system that generates a LEGO brick model from 2D images. We design a novel solution to this problem that uses an octree-structured autoencoder trained on 3D voxelized models to obtain a feasible latent representation for model reconstruction, and a separate network trained to predict this latent representation from 2D images. LEGO models are obtained by algorithmic conversion of the 3D voxelized model to bricks. We demonstrate first-of-its-kind conversion of photographs to 3D LEGO models. An octree architecture enables the flexibility to produce multiple resolutions to best fit a user's creative vision or design needs. In order to demonstrate the broad applicability of our system, we generate step-by-step building instructions and animations for LEGO models of objects and human faces. Finally, we test these automatically generated LEGO sets by constructing physical builds using real LEGO bricks.

We study various machine learning based algorithms for performing accurate jet flavor classification on field-programmable gate arrays and demonstrate how latency and resource consumption scale with the input size and choice of algorithm. These architectures provide an initial design for models that could be used for tagging at the CERN LHC during its high-luminosity phase. The high-luminosity upgrade will lead to a five-fold increase in its instantaneous luminosity for proton-proton collisions and, in turn, higher data volume and complexity, such as the availability of jet constituents. Through quantization-aware training and efficient hardware implementations, we show that O(100) ns inference of complex architectures such as deep sets and interaction networks is feasible at a low computational resource cost.

We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To solve it, we propose a biconvex method that quickly produces an initial trajectory and iteratively refines it by solving two convex subproblems in alternation. This method is guaranteed to converge, returns a feasible trajectory even if stopped early, and does not require the selection of any line-search or trust-region parameter. Exhaustive experiments show that our method finds high-quality trajectories in a fraction of the time of state-of-the-art solvers for nonconvex optimization. In addition, it achieves runtimes comparable to industry-standard waypoint-based motion planners, while consistently designing lower-duration trajectories than existing optimization-based planners.

A safe action is not necessarily a viable one. A frozen vision-language-action (VLA) policy can favor a locally admissible move that leaves no policy-supported route to safe task completion. We call this the feasibility-likelihood gap: likelihood ranks the next move, while feasibility depends on the futures it leaves open. To bring those futures into the decision, we derive the exact next-block marginal of the history-conditioned policy-environment trajectory law restricted to safe task completion. The derivation reveals a candidate-dependent feasible-future mass: its support records whether safe completion remains possible under the frozen continuation process, while its magnitude measures how much weighted safe-completion mass remains. Since exact evaluation is impractical online, we develop a selective finite-candidate approximation and establish conditions for recovering the best retained viable candidate. Our alarm-triggered, training-free reranker VICS-G lowers mean cumulative safety cost by 1.9%-57.5% across six Safety-CHORES settings while remaining within 2.5 percentage points of policy sampling in success and 0.82 steps in mean episode length. Our approach offers a promising and practical path toward safer task completion, grounded in an exact policy-relative target yet requiring neither policy retraining nor online rollouts.

Benchmarking the hundreds of functional connectivity (FC) modeling methods on large-scale fMRI datasets is critical for reproducible neuroscience. However, the combinatorial explosion of model-data pairings makes exhaustive evaluation computationally prohibitive, preventing such assessments from becoming a routine pre-analysis step. To break this bottleneck, we reframe the challenge of FC benchmarking by selecting a small, representative core-set whose sole purpose is to preserve the relative performance ranking of FC operators. We formalize this as a ranking-preserving subset selection problem and propose Structure-aware Contrastive Learning for Core-set Selection (SCLCS), a self-supervised framework to select these core-sets. SCLCS first uses an adaptive Transformer to learn each sample's unique FC structure. It then introduces a novel Structural Perturbation Score (SPS) to quantify the stability of these learned structures during training, identifying samples that represent foundational connectivity archetypes. Finally, while SCLCS identifies stable samples via a top-k ranking, we further introduce a density-balanced sampling strategy as a necessary correction to promote diversity, ensuring the final core-set is both structurally robust and distributionally representative. On the large-scale REST-meta-MDD dataset, SCLCS preserves the ground-truth model ranking with just 10% of the data, outperforming state-of-the-art (SOTA) core-set selection methods by up to 23.2% in ranking consistency (nDCG@k). To our knowledge, this is the first work to formalize core-set selection for FC operator benchmarking, thereby making large-scale operators comparisons a feasible and integral part of computational neuroscience. Code is publicly available on https://github.com/lzhan94swu/SCLCS

Black-box machine learning models are now routinely used in high-risk settings, like medical diagnostics, which demand uncertainty quantification to avoid consequential model failures. Conformal prediction is a user-friendly paradigm for creating statistically rigorous uncertainty sets/intervals for the predictions of such models. Critically, the sets are valid in a distribution-free sense: they possess explicit, non-asymptotic guarantees even without distributional assumptions or model assumptions. One can use conformal prediction with any pre-trained model, such as a neural network, to produce sets that are guaranteed to contain the ground truth with a user-specified probability, such as 90%. It is easy-to-understand, easy-to-use, and general, applying naturally to problems arising in the fields of computer vision, natural language processing, deep reinforcement learning, and so on. This hands-on introduction is aimed to provide the reader a working understanding of conformal prediction and related distribution-free uncertainty quantification techniques with one self-contained document. We lead the reader through practical theory for and examples of conformal prediction and describe its extensions to complex machine learning tasks involving structured outputs, distribution shift, time-series, outliers, models that abstain, and more. Throughout, there are many explanatory illustrations, examples, and code samples in Python. With each code sample comes a Jupyter notebook implementing the method on a real-data example; the notebooks can be accessed and easily run using our codebase.

Learning neural subset selection tasks, such as compound selection in AI-aided drug discovery, have become increasingly pivotal across diverse applications. The existing methodologies in the field primarily concentrate on constructing models that capture the relationship between utility function values and subsets within their respective supersets. However, these approaches tend to overlook the valuable information contained within the superset when utilizing neural networks to model set functions. In this work, we address this oversight by adopting a probabilistic perspective. Our theoretical findings demonstrate that when the target value is conditioned on both the input set and subset, it is essential to incorporate an invariant sufficient statistic of the superset into the subset of interest for effective learning. This ensures that the output value remains invariant to permutations of the subset and its corresponding superset, enabling identification of the specific superset from which the subset originated. Motivated by these insights, we propose a simple yet effective information aggregation module designed to merge the representations of subsets and supersets from a permutation invariance perspective. Comprehensive empirical evaluations across diverse tasks and datasets validate the enhanced efficacy of our approach over conventional methods, underscoring the practicality and potency of our proposed strategies in real-world contexts.

Face recognition from image sets acquired under unregulated and uncontrolled settings, such as at large distances, low resolutions, varying viewpoints, illumination, pose, and atmospheric conditions, is challenging. Face feature aggregation, which involves aggregating a set of N feature representations present in a template into a single global representation, plays a pivotal role in such recognition systems. Existing works in traditional face feature aggregation either utilize metadata or high-dimensional intermediate feature representations to estimate feature quality for aggregation. However, generating high-quality metadata or style information is not feasible for extremely low-resolution faces captured in long-range and high altitude settings. To overcome these limitations, we propose a feature distribution conditioning approach called CoNAN for template aggregation. Specifically, our method aims to learn a context vector conditioned over the distribution information of the incoming feature set, which is utilized to weigh the features based on their estimated informativeness. The proposed method produces state-of-the-art results on long-range unconstrained face recognition datasets such as BTS, and DroneSURF, validating the advantages of such an aggregation strategy.

Recent advancements in Vision-Language-Action (VLA) models have shown promise for end-to-end autonomous driving by leveraging world knowledge and reasoning capabilities. However, current VLA models often struggle with physically infeasible action outputs, complex model structures, or unnecessarily long reasoning. In this paper, we propose AutoVLA, a novel VLA model that unifies reasoning and action generation within a single autoregressive generation model for end-to-end autonomous driving. AutoVLA performs semantic reasoning and trajectory planning directly from raw visual inputs and language instructions. We tokenize continuous trajectories into discrete, feasible actions, enabling direct integration into the language model. For training, we employ supervised fine-tuning to equip the model with dual thinking modes: fast thinking (trajectory-only) and slow thinking (enhanced with chain-of-thought reasoning). To further enhance planning performance and efficiency, we introduce a reinforcement fine-tuning method based on Group Relative Policy Optimization (GRPO), reducing unnecessary reasoning in straightforward scenarios. Extensive experiments across real-world and simulated datasets and benchmarks, including nuPlan, nuScenes, Waymo, and CARLA, demonstrate the competitive performance of AutoVLA in both open-loop and closed-loop settings. Qualitative results showcase the adaptive reasoning and accurate planning capabilities of AutoVLA in diverse scenarios.

Large language models (LLMs) are increasingly deployed in real-world applications that require careful balancing of multiple, often conflicting, objectives, such as informativeness versus conciseness, or helpfulness versus creativity. However, current alignment methods, primarily based on RLHF, optimize LLMs toward a single reward function, resulting in rigid behavior that fails to capture the complexity and diversity of human preferences. This limitation hinders the adaptability of LLMs to practical scenarios, making multi-objective alignment (MOA) a critical yet underexplored area. To bridge this gap, we propose Pareto Multi-Objective Alignment (PAMA), a principled and computationally efficient algorithm designed explicitly for MOA in LLMs. In contrast to computationally prohibitive multi-objective optimization (MOO) methods, PAMA transforms multi-objective RLHF into a convex optimization with a closed-form solution, significantly enhancing scalability. Traditional MOO approaches suffer from prohibitive O(n^2*d) complexity, where d represents the number of model parameters, typically in the billions for LLMs, rendering direct optimization infeasible. PAMA reduces this complexity to O(n) where n is the number of objectives, enabling optimization to be completed within milliseconds. We provide theoretical guarantees that PAMA converges to a Pareto stationary point, where no objective can be improved without degrading at least one other. Extensive experiments across language models ranging from 125M to 7B parameters demonstrate PAMA's robust and effective MOA capabilities, aligning with its theoretical advantages. PAMA provides a highly efficient solution to the MOA problem that was previously considered intractable, offering a practical and theoretically grounded approach to aligning LLMs with diverse human values, paving the way for versatile and adaptable real-world AI deployments.

Set representation has become ubiquitous in deep learning for modeling the inductive bias of neural networks that are insensitive to the input order. DeepSets is the most widely used neural network architecture for set representation. It involves embedding each set element into a latent space with dimension L, followed by a sum pooling to obtain a whole-set embedding, and finally mapping the whole-set embedding to the output. In this work, we investigate the impact of the dimension L on the expressive power of DeepSets. Previous analyses either oversimplified high-dimensional features to be one-dimensional features or were limited to analytic activations, thereby diverging from practical use or resulting in L that grows exponentially with the set size N and feature dimension D. To investigate the minimal value of L that achieves sufficient expressive power, we present two set-element embedding layers: (a) linear + power activation (LP) and (b) linear + exponential activations (LE). We demonstrate that L being poly(N, D) is sufficient for set representation using both embedding layers. We also provide a lower bound of L for the LP embedding layer. Furthermore, we extend our results to permutation-equivariant set functions and the complex field.

Motivated by baterryless IoT devices, we consider the following scheduling problem. The input includes n unit time jobs J = {J_1, ldots, J_n}, where each job J_i has a release time r_i, due date d_i, energy requirement e_i, and weight w_i. We consider time to be slotted; hence, all time related job values refer to slots. Let T=max_i{d_i}. The input also includes an h_t value for every time slot t (1 leq t leq T), which is the energy harvestable on that slot. Energy is harvested at time slots when no job is executed. The objective is to find a feasible schedule that maximizes the weight of the scheduled jobs. A schedule is feasible if for every job J_j in the schedule and its corresponding slot t_j, t_{j} neq t_{j'} if {j} j', r_j leq t_j leq d_j, and the available energy before t_j is at least e_j. To the best of our knowledge, we are the first to consider the theoretical aspects of this problem. In this work we show the following. (1) A polynomial time algorithm when all jobs have identical r_i, d_i and w_i. (2) A 1{2}-approximation algorithm when all jobs have identical w_i but arbitrary r_i and d_i. (3) An FPTAS when all jobs have identical r_i and d_i but arbitrary w_i. (4) Reductions showing that all the variants of the problem in which at least one of the attributes r_i, d_i, or w_i are not identical for all jobs are NP-Hard.

"Machine unlearning" is a popular proposed solution for mitigating the existence of content in an AI model that is problematic for legal or moral reasons, including privacy, copyright, safety, and more. For example, unlearning is often invoked as a solution for removing the effects of specific information from a generative-AI model's parameters, e.g., a particular individual's personal data or the inclusion of copyrighted content in the model's training data. Unlearning is also proposed as a way to prevent a model from generating targeted types of information in its outputs, e.g., generations that closely resemble a particular individual's data or reflect the concept of "Spiderman." Both of these goals--the targeted removal of information from a model and the targeted suppression of information from a model's outputs--present various technical and substantive challenges. We provide a framework for ML researchers and policymakers to think rigorously about these challenges, identifying several mismatches between the goals of unlearning and feasible implementations. These mismatches explain why unlearning is not a general-purpose solution for circumscribing generative-AI model behavior in service of broader positive impact.

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

Many machine learning algorithms are trained and evaluated by splitting data from a single source into training and test sets. While such focus on in-distribution learning scenarios has led to interesting advancement, it has not been able to tell if models are relying on dataset biases as shortcuts for successful prediction (e.g., using snow cues for recognising snowmobiles), resulting in biased models that fail to generalise when the bias shifts to a different class. The cross-bias generalisation problem has been addressed by de-biasing training data through augmentation or re-sampling, which are often prohibitive due to the data collection cost (e.g., collecting images of a snowmobile on a desert) and the difficulty of quantifying or expressing biases in the first place. In this work, we propose a novel framework to train a de-biased representation by encouraging it to be different from a set of representations that are biased by design. This tactic is feasible in many scenarios where it is much easier to define a set of biased representations than to define and quantify bias. We demonstrate the efficacy of our method across a variety of synthetic and real-world biases; our experiments show that the method discourages models from taking bias shortcuts, resulting in improved generalisation. Source code is available at https://github.com/clovaai/rebias.

Large language models (LLMs) face a dual challenge in creative capability evaluation: existing benchmarks (e.g., Story Cloze Test, HellaSwag) measure models' discriminative ability over narrative continuation using multiple-choice recognition paradigms, rather than directly measuring creative generation capability; rubric-based scoring and LLM-as-Judge methods rely on subjective dimension assessment or natural language model outputs, and cannot provide objective, automated scoring mechanisms. This paper proposes QUIET (Quality Understanding via Interlocked Evaluation Testing), a diagnostic benchmark for LLM creative capability based on multi-blank cascaded story cloze. QUIET sets N blanks (10-20) in a story with complete structure, with each blank accompanied by an explicit content constraint, and cascade dependency relationships between blanks -- the content filled into earlier blanks constrains the feasible solution space for later blanks. The evaluated model (or human participants) fills all blanks in open-ended generation mode; the results are scored by an information-theoretic automated scoring protocol without human grading. The scoring protocol directly operationalizes the "calibrated surprise" theoretical framework (Zou & Xu, 2026a). For each blank k, a composite score is computed: score = satisfy * (1 + lambda * surprise), where lambda = 1.0. Here, "satisfy" measures how well the blank filling satisfies the content constraint (objective logical reasoning judgment, not subjective aesthetic scoring), and "surprise" measures the degree of surprise given that the constraint is satisfied. Creative answers that do not satisfy the constraint score zero; answers that satisfy the constraint but are mediocre score low; answers that satisfy the constraint and are surprising score high.

Effectively configuring scalable large language model (LLM) experiments, spanning architecture design, hyperparameter tuning, and beyond, is crucial for advancing LLM research, as poor configuration choices can waste substantial computational resources and prevent models from realizing their full potential. Prior automated methods are designed for low-cost settings where repeated trial and error is feasible, but scalable LLM experiments are too expensive for such extensive iteration. To our knowledge, no work has addressed the automation of high-cost LLM experiment configurations, leaving this problem labor-intensive and dependent on expert intuition. Motivated by this gap, we propose AutoLLMResearch, an agentic framework that mimics how human researchers learn generalizable principles from low-fidelity experiments and extrapolate to efficiently identify promising configurations in expensive LLM settings. The core challenge is how to enable an agent to learn, through interaction with a multi-fidelity experimental environment that captures the structure of the LLM configuration landscape. To achieve this, we propose a systematic framework with two key components: 1) LLMConfig-Gym, a multi-fidelity environment encompassing four critical LLM experiment tasks, supported by over one million GPU hours of verifiable experiment outcomes; 2) A structured training pipeline that formulates configuration research as a long-horizon Markov Decision Process and accordingly incentivizes cross-fidelity extrapolation reasoning. Extensive evaluation against diverse strong baselines on held-out experiments demonstrates the effectiveness, generalization, and interpretability of our framework, supporting its potential as a practical and general solution for scalable real-world LLM experiment automation.

Large multimodal models (LMMs) have rapidly advanced in perception and reasoning; however, it remains unclear whether these capabilities generalize to discovering visually grounded solutions in open-ended environments, beyond pattern recognition. In such settings, intelligence requires more than answering well-posed questions: it involves identifying how elements in a scene can be repurposed in non-obvious yet physically feasible ways. This form of creative problem-solving is central to human intelligence, but remains largely untested in current benchmarks. To evaluate this ability, we introduce MM-CreativityBench, a benchmark for affordance-grounded creative tool use in visually rich, physically constrained environments. Each instance presents a scenario image with structured views of candidate entities and their parts, enabling fine-grained, interactive evaluation of how models iteratively inspect the scene, identify relevant affordances, and compose visually and physically grounded solutions. Our experiments show that current LMMs often fall short, not due to lack of generative capability, but because they do not sustain grounded exploration. Models often overlook relevant entities, under-examine critical parts, or hallucinate attributes not grounded in the image. Motivated by this failure mode, we propose affordance-grounded alignment, which casts creative tool use as a preference learning problem. Using Direct Preference Optimization, we encourage models to prefer attribute-affordance reasoning grounded in visual evidence over hallucinated alternatives. In addition, we incorporate supervision derived from an affordance knowledge base to guide broader entity exploration and multi-turn planning. Our results show consistent gains in selecting the correct entities and parts, while substantially reducing hallucination and grounding-related errors.

Large language models (LLMs) have demonstrated remarkable zero-shot generalization abilities: state-of-the-art chatbots can provide plausible answers to many common questions that arise in daily life. However, so far, LLMs cannot reliably solve long-horizon planning problems. By contrast, classical planners, once a problem is given in a formatted way, can use efficient search algorithms to quickly identify correct, or even optimal, plans. In an effort to get the best of both worlds, this paper introduces LLM+P, the first framework that incorporates the strengths of classical planners into LLMs. LLM+P takes in a natural language description of a planning problem, then returns a correct (or optimal) plan for solving that problem in natural language. LLM+P does so by first converting the language description into a file written in the planning domain definition language (PDDL), then leveraging classical planners to quickly find a solution, and then translating the found solution back into natural language. Along with LLM+P, we define a diverse set of different benchmark problems taken from common planning scenarios. Via a comprehensive set of experiments on these benchmark problems, we find that LLM+P is able to provide optimal solutions for most problems, while LLMs fail to provide even feasible plans for most problems.\footnote{The code and results are publicly available at https://github.com/Cranial-XIX/llm-pddl.git.

Searching for mathematical results remains difficult: most existing tools retrieve entire papers, while mathematicians and theorem-proving agents often seek a specific theorem, lemma, or proposition that answers a query. While semantic search has seen rapid progress, its behavior on large, highly technical corpora such as research-level mathematical theorems remains poorly understood. In this work, we introduce and study semantic theorem retrieval at scale over a unified corpus of 9.2 million theorem statements extracted from arXiv and seven other sources, representing the largest publicly available corpus of human-authored, research-level theorems. We represent each theorem with a short natural-language description as a retrieval representation and systematically analyze how representation context, language model choice, embedding model, and prompting strategy affect retrieval quality. On a curated evaluation set of theorem-search queries written by professional mathematicians, our approach substantially improves both theorem-level and paper-level retrieval compared to existing baselines, demonstrating that semantic theorem search is feasible and effective at web scale. The theorem search tool is available at https://huggingface.co/spaces/uw-math-ai/theorem-search{this link}, and the dataset is available at https://huggingface.co/datasets/uw-math-ai/TheoremSearch{this link}.

We present a tool-supported approach for the synthesis, verification and validation of the control software responsible for the safety of the human-robot interaction in manufacturing processes that use collaborative robots. In human-robot collaboration, software-based safety controllers are used to improve operational safety, e.g., by triggering shutdown mechanisms or emergency stops to avoid accidents. Complex robotic tasks and increasingly close human-robot interaction pose new challenges to controller developers and certification authorities. Key among these challenges is the need to assure the correctness of safety controllers under explicit (and preferably weak) assumptions. Our controller synthesis, verification and validation approach is informed by the process, risk analysis, and relevant safety regulations for the target application. Controllers are selected from a design space of feasible controllers according to a set of optimality criteria, are formally verified against correctness criteria, and are translated into executable code and validated in a digital twin. The resulting controller can detect the occurrence of hazards, move the process into a safe state, and, in certain circumstances, return the process to an operational state from which it can resume its original task. We show the effectiveness of our software engineering approach through a case study involving the development of a safety controller for a manufacturing work cell equipped with a collaborative robot.

We present a tool for exploring the design space of shaders using an interactive evolutionary algorithm integrated with the Unity editor, a well-known commercial tool for video game development. Our framework leverages the underlying graph-based representation of recent shader editors and interactive evolution to allow designers to explore several visual options starting from an existing shader. Our framework encodes the graph representation of a current shader as a chromosome used to seed the evolution of a shader population. It applies graph-based recombination and mutation with a set of heuristics to create feasible shaders. The framework is an extension of the Unity editor; thus, designers with little knowledge of evolutionary computation (and shader programming) can interact with the underlying evolutionary engine using the same visual interface used for working on game scenes.

Poisoning pretraining data can introduce harmful behaviors to LMs that are difficult to detect and mitigate. Prior work on poisoning pretraining data has largely exploited established data sources such as Wikipedia, which do not represent the large scale and heterogeneity typical of pretraining corpora, and has ignored the interaction between poisoned data and data curation pipelines. We demonstrate that poisoning attacks on pretraining data are feasible beyond this limited setting through an existing web-scale content injection mechanism: public discussion interfaces. Additionally, to measure whether malicious content is included after web crawling and data curation, we introduce HalfLife, a novel analysis for estimating adversarial content inclusion in web-crawl based LM training data. We use HalfLife to explore the feasibility of poisoning pretraining corpora at web scale through open discussion interfaces. Our analysis demonstrates the importance of estimating whether poison injections are included in pretraining data, and establishes third-party webpage content as a possible vector for attacking language model pretraining.

Natural-language feedback in interactive learning often explains why an action failed by pointing to violated requirements. Misinterpreting this feedback can lead an agent to rule out valid solutions. We study this setting by modeling user intent as latent constraints over an action space and formulating learning from language feedback as pure exploration over feasible regions. We introduce TRACE, an algorithm that organizes candidate constraints in a tree and tests each proposed refinement by generating actions that satisfy it. TRACE commits to the refinement only if the resulting feedback does not contradict it over repeated tests. We distinguish two ways of using the same feedback: (i) falsification, which detects contradictions to the constraint set currently being tested, and (ii) identification, which may additionally name a violated constraint. We prove high-probability coverage bounds with dependence on the candidate class size H for TRACE-Falsification. With reliable identification, TRACE-Identification can replace this dependence by K/p_{ext}, where K is the number of latent constraints and p_{ext} lower-bounds the probability of extracting a missing true constraint from informative feedback. We evaluate TRACE across six language-feedback tasks. On RecMovie, TRACE-Identification achieves 73% and 86% final-output success under caps of 20 and 60 evaluated outputs, compared with at most 42% and 48% for the evaluated prompting baselines given the same feedback and output caps. Controlled identity-corruption experiments further show greater robustness than direct accumulation when the falsification detector remains reliable.

We propose a novel application of prompting Pre-trained Language Models (PLMs) to generate analogies and study how to design effective prompts for two task settings: generating a source concept analogous to a given target concept (aka Analogous Concept Generation or ACG), and generating an explanation of the similarity between a given pair of target concept and source concept (aka Analogous Explanation Generation or AEG). We found that it is feasible to prompt InstructGPT to generate meaningful analogies and the best prompts tend to be precise imperative statements especially with a low temperature setting. We also systematically analyzed the sensitivity of the InstructGPT model to prompt design, temperature, and injected spelling errors, and found that the model is particularly sensitive to certain variations (e.g., questions vs. imperative statements). Further, we conducted human evaluation on 1.4k of the generated analogies and found that the quality of generations varies substantially by model size. The largest InstructGPT model can achieve human-level performance at generating meaningful analogies for a given target while there is still room for improvement on the AEG task.

Generative large vision-language models (LVLMs) have recently achieved impressive performance gains, and their user base is growing rapidly. However, the security of LVLMs, in particular in a long-context multi-turn setting, is largely underexplored. In this paper, we consider the realistic scenario in which an attacker uploads a manipulated image to the web/social media. A benign user downloads this image and uses it as input to the LVLM. Our novel stealthy Visual Memory Injection (VMI) attack is designed such that on normal prompts the LVLM exhibits nominal behavior, but once the user gives a triggering prompt, the LVLM outputs a specific prescribed target message to manipulate the user, e.g. for adversarial marketing or political persuasion. Compared to previous work that focused on single-turn attacks, VMI is effective even after a long multi-turn conversation with the user. We demonstrate our attack on several recent open-weight LVLMs. This article thereby shows that large-scale manipulation of users is feasible with perturbed images in multi-turn conversation settings, calling for better robustness of LVLMs against these attacks. We release the source code at https://github.com/chs20/visual-memory-injection

Visual Inspection with Acetic Acid (VIA) remains the most feasible cervical cancer screening test in resource-constrained settings of low- and middle-income countries (LMICs), which are often performed screening camps or primary/community health centers by nurses instead of the preferred but unavailable expert Gynecologist. To address the highly subjective nature of the test, various handheld devices integrating cameras or smartphones have been recently explored to capture cervical images during VIA and aid decision-making via telemedicine or AI models. Most studies proposing AI models retrospectively use a relatively small number of already collected images from specific devices, digital cameras, or smartphones; the challenges and protocol for quality image acquisition during VIA in resource-constrained camp settings, challenges in getting gold standard, data imbalance, etc. are often overlooked. We present a novel approach and describe the end-to-end design process to build a robust smartphone-based AI-assisted system that does not require buying a separate integrated device: the proposed protocol for quality image acquisition in resource-constrained settings, dataset collected from 1,430 women during VIA performed by nurses in screening camps, preprocessing pipeline, and training and evaluation of a deep-learning-based classification model aimed to identify (pre)cancerous lesions. Our work shows that the readily available smartphones and a suitable protocol can capture the cervix images with the required details for the VIA test well; the deep-learning-based classification model provides promising results to assist nurses in VIA screening; and provides a direction for large-scale data collection and validation in resource-constrained settings.

Automating tasks in outdoor agricultural fields poses significant challenges due to environmental variability, unstructured terrain, and diverse crop characteristics. We present a robotic system for autonomous pepper harvesting designed to operate in these unprotected, complex settings. Utilizing a custom handheld shear-gripper, we collected 300 demonstrations to train a visuomotor policy, enabling the system to adapt to varying field conditions and crop diversity. We achieved a success rate of 28.95% with a cycle time of 31.71 seconds, comparable to existing systems tested under more controlled conditions like greenhouses. Our system demonstrates the feasibility and effectiveness of leveraging imitation learning for automated harvesting in unstructured agricultural environments. This work aims to advance scalable, automated robotic solutions for agriculture in natural settings.

In this paper, we study the ideas of composition and decomposition in the context of vector spaces, graphs and matroids. For vector spaces V_{AB}, treated as collection of row vectors, with specified column set Auplus B, we define V_{SP}lrarv V_{PQ}, Scap Q= emptyset, to be the collection of all vectors (f_S,f_Q) such that (f_S,f_P)in V_{SP}, (f_P,f_Q)in V_{PQ}. An analogous operation G_{SP}lrarg G_{PQ}equivd G_{PQ} can be defined in relation to graphs G_{SP}, G_{PQ}, on edge sets Suplus P, Puplus Q, respectively in terms of an overlapping subgraph G_P which gets deleted in the right side graph (see for instance the notion of k-sum oxley). For matroids we define the `linking' M_{SP}lrarm M_{PQ} equivd (M_{SP}vee M_{PQ})times (Suplus Q), denoting the contraction operation by 'times'. In each case, we examine how to minimize the size of the `overlap' set P, without affecting the right side entity. In the case of vector spaces, there is a polynomial time algorithm for achieving the minimum, which we present. Similar ideas work for graphs and for matroids under appropriate conditions. Next we consider the problem of decomposition. Here, in the case of vector spaces, the problem is to decompose V_{SQ} as V_{SP}lrarv V_{PQ}, with minimum size P. We give a polynomial time algorithm for this purpose. In the case of graphs and matroids we give a solution to this problem under certain restrictions.

This document serves as a position paper that outlines the authors' vision for a potential pathway towards generalist robots. The purpose of this document is to share the excitement of the authors with the community and highlight a promising research direction in robotics and AI. The authors believe the proposed paradigm is a feasible path towards accomplishing the long-standing goal of robotics research: deploying robots, or embodied AI agents more broadly, in various non-factory real-world settings to perform diverse tasks. This document presents a specific idea for mining knowledge in the latest large-scale foundation models for robotics research. Instead of directly using or adapting these models to produce low-level policies and actions, it advocates for a fully automated generative pipeline (termed as generative simulation), which uses these models to generate diversified tasks, scenes and training supervisions at scale, thereby scaling up low-level skill learning and ultimately leading to a foundation model for robotics that empowers generalist robots. The authors are actively pursuing this direction, but in the meantime, they recognize that the ambitious goal of building generalist robots with large-scale policy training demands significant resources such as computing power and hardware, and research groups in academia alone may face severe resource constraints in implementing the entire vision. Therefore, the authors believe sharing their thoughts at this early stage could foster discussions, attract interest towards the proposed pathway and related topics from industry groups, and potentially spur significant technical advancements in the field.

We investigate a relatively under-explored class of hybrid neurosymbolic models that integrate symbolic learning with neural reasoning to construct data generators meeting formal correctness criteria. In Symbolic Neural Generators (SNGs), symbolic learners examine logical specifications of feasible data from a small set of instances -- sometimes just one. Each specification in turn constrains the conditional information supplied to a neural-based generator, which rejects any instance violating the symbolic specification. Like other neurosymbolic approaches, SNG exploits the complementary strengths of symbolic and neural methods. The outcome of an SNG is a pair (H, X), where H is a symbolic description of feasible instances constructed from data, and X a set of generated new instances that satisfy the description. We introduce a semantics for such systems, based on the construction of appropriate base and fibre partially-ordered sets combined into an overall partial order. We implement an SNG combining a restricted form of Inductive Logic Programming (ILP) with a large language model (LLM) and evaluate it on early-stage drug design. Our main interest is the description and the set of potential inhibitor molecules generated by the SNG. On benchmark problems -- where drug targets are well understood -- SNG performance is statistically comparable to state-of-the-art methods. On exploratory problems with poorly understood targets, generated molecules exhibit binding affinities on par with leading clinical candidates. Experts further find the symbolic specifications useful as preliminary filters, with several generated molecules identified as viable for synthesis and wet-lab testing.

Incorporating expert demonstrations has empirically helped to improve the sample efficiency of reinforcement learning (RL). This paper quantifies theoretically to what extent this extra information reduces RL's sample complexity. In particular, we study the demonstration-regularized reinforcement learning that leverages the expert demonstrations by KL-regularization for a policy learned by behavior cloning. Our findings reveal that using N^{E} expert demonstrations enables the identification of an optimal policy at a sample complexity of order mathcal{O}(Poly(S,A,H)/(varepsilon^2 N^{E})) in finite and mathcal{O}(Poly(d,H)/(varepsilon^2 N^{E})) in linear Markov decision processes, where varepsilon is the target precision, H the horizon, A the number of action, S the number of states in the finite case and d the dimension of the feature space in the linear case. As a by-product, we provide tight convergence guarantees for the behaviour cloning procedure under general assumptions on the policy classes. Additionally, we establish that demonstration-regularized methods are provably efficient for reinforcement learning from human feedback (RLHF). In this respect, we provide theoretical evidence showing the benefits of KL-regularization for RLHF in tabular and linear MDPs. Interestingly, we avoid pessimism injection by employing computationally feasible regularization to handle reward estimation uncertainty, thus setting our approach apart from the prior works.

The creation of practical deep learning data-products often requires parallelization across processors and computers to make deep learning feasible on large data sets, but bottlenecks in communication bandwidth make it difficult to attain good speedups through parallelism. Here we develop and test 8-bit approximation algorithms which make better use of the available bandwidth by compressing 32-bit gradients and nonlinear activations to 8-bit approximations. We show that these approximations do not decrease predictive performance on MNIST, CIFAR10, and ImageNet for both model and data parallelism and provide a data transfer speedup of 2x relative to 32-bit parallelism. We build a predictive model for speedups based on our experimental data, verify its validity on known speedup data, and show that we can obtain a speedup of 50x and more on a system of 96 GPUs compared to a speedup of 23x for 32-bit. We compare our data types with other methods and show that 8-bit approximations achieve state-of-the-art speedups for model parallelism. Thus 8-bit approximation is an efficient method to parallelize convolutional networks on very large systems of GPUs.

Self-Supervised Learning (SSL) is an effective paradigm for learning representations from unlabeled data, such as text, images, and videos. However, researchers have recently found that SSL is vulnerable to backdoor attacks. The attacker can embed hidden SSL backdoors via a few poisoned examples in the training dataset and maliciously manipulate the behavior of downstream models. To defend against SSL backdoor attacks, a feasible route is to detect and remove the poisonous samples in the training set. However, the existing SSL backdoor defense method fails to detect the poisonous samples precisely. In this paper, we propose to erase the SSL backdoor by cluster activation masking and propose a novel PoisonCAM method. After obtaining the threat model trained on the poisoned dataset, our method can precisely detect poisonous samples based on the assumption that masking the backdoor trigger can effectively change the activation of a downstream clustering model. In experiments, our PoisonCAM achieves 96\% accuracy for backdoor trigger detection compared to 3\% of the state-of-the-art method on poisoned ImageNet-100. Moreover, our proposed PoisonCAM significantly improves the performance of the trained SSL model under backdoor attacks compared to the state-of-the-art method. Our code, data, and trained models will be open once this paper is accepted.

Frontier AI developers are relying on layers of safeguards to protect against catastrophic misuse of AI systems. Anthropic guards their latest Claude 4 Opus model using one such defense pipeline, and other frontier developers including Google DeepMind and OpenAI pledge to soon deploy similar defenses. However, the security of such pipelines is unclear, with limited prior work evaluating or attacking these pipelines. We address this gap by developing and red-teaming an open-source defense pipeline. First, we find that a novel few-shot-prompted input and output classifier outperforms state-of-the-art open-weight safeguard model ShieldGemma across three attacks and two datasets, reducing the attack success rate (ASR) to 0% on the catastrophic misuse dataset ClearHarm. Second, we introduce a STaged AttaCK (STACK) procedure that achieves 71% ASR on ClearHarm in a black-box attack against the few-shot-prompted classifier pipeline. Finally, we also evaluate STACK in a transfer setting, achieving 33% ASR, providing initial evidence that it is feasible to design attacks with no access to the target pipeline. We conclude by suggesting specific mitigations that developers could use to thwart staged attacks.

In science and medicine, model interpretations may be reported as discoveries of natural phenomena or used to guide patient treatments. In such high-stakes tasks, false discoveries may lead investigators astray. These applications would therefore benefit from control over the finite-sample error rate of interpretations. We reframe black box model interpretability as a multiple hypothesis testing problem. The task is to discover "important" features by testing whether the model prediction is significantly different from what would be expected if the features were replaced with uninformative counterfactuals. We propose two testing methods: one that provably controls the false discovery rate but which is not yet feasible for large-scale applications, and an approximate testing method which can be applied to real-world data sets. In simulation, both tests have high power relative to existing interpretability methods. When applied to state-of-the-art vision and language models, the framework selects features that intuitively explain model predictions. The resulting explanations have the additional advantage that they are themselves easy to interpret.

Few Shot Class Incremental Learning (FSCIL) with few examples per class for each incremental session is the realistic setting of continual learning since obtaining large number of annotated samples is not feasible and cost effective. We present the framework MASIL as a step towards learning the maximal separable classifier. It addresses the common problem i.e forgetting of old classes and over-fitting to novel classes by learning the classifier weights to be maximally separable between classes forming a simplex Equiangular Tight Frame. We propose the idea of concept factorization explaining the collapsed features for base session classes in terms of concept basis and use these to induce classifier simplex for few shot classes. We further adds fine tuning to reduce any error occurred during factorization and train the classifier jointly on base and novel classes without retaining any base class samples in memory. Experimental results on miniImageNet, CIFAR-100 and CUB-200 demonstrate that MASIL outperforms all the benchmarks.

As Large Language Models quickly become ubiquitous, it becomes critical to understand their security vulnerabilities. Recent work shows that text optimizers can produce jailbreaking prompts that bypass moderation and alignment. Drawing from the rich body of work on adversarial machine learning, we approach these attacks with three questions: What threat models are practically useful in this domain? How do baseline defense techniques perform in this new domain? How does LLM security differ from computer vision? We evaluate several baseline defense strategies against leading adversarial attacks on LLMs, discussing the various settings in which each is feasible and effective. Particularly, we look at three types of defenses: detection (perplexity based), input preprocessing (paraphrase and retokenization), and adversarial training. We discuss white-box and gray-box settings and discuss the robustness-performance trade-off for each of the defenses considered. We find that the weakness of existing discrete optimizers for text, combined with the relatively high costs of optimization, makes standard adaptive attacks more challenging for LLMs. Future research will be needed to uncover whether more powerful optimizers can be developed, or whether the strength of filtering and preprocessing defenses is greater in the LLMs domain than it has been in computer vision.

We present an information retrieval based reverse dictionary system using modern pre-trained language models and approximate nearest neighbors search algorithms. The proposed approach is applied to an existing Estonian language lexicon resource, S\~onaveeb (word web), with the purpose of enhancing and enriching it by introducing cross-lingual reverse dictionary functionality powered by semantic search. The performance of the system is evaluated using both an existing labeled English dataset of words and definitions that is extended to contain also Estonian and Russian translations, and a novel unlabeled evaluation approach that extracts the evaluation data from the lexicon resource itself using synonymy relations. Evaluation results indicate that the information retrieval based semantic search approach without any model training is feasible, producing median rank of 1 in the monolingual setting and median rank of 2 in the cross-lingual setting using the unlabeled evaluation approach, with models trained for cross-lingual retrieval and including Estonian in their training data showing superior performance in our particular task.

Reservoir computing (RC) is among the most promising approaches for AI-based prediction models of complex systems. It combines superior prediction performance with very low CPU-needs for training. Recent results demonstrated that quantum systems are also well-suited as reservoirs in RC. Due to the exponential growth of the Hilbert space dimension obtained by increasing the number of quantum elements small quantum systems are already sufficient for time series prediction. Here, we demonstrate that three-dimensional systems can already well be predicted by quantum reservoir computing with a quantum reservoir consisting of the minimal number of qubits necessary for this task, namely four. This is achieved by optimizing the encoding of the data, using spatial and temporal multiplexing and recently developed read-out-schemes that also involve higher exponents of the reservoir response. We outline, test and validate our approach using eight prototypical three-dimensional chaotic systems. Both, the short-term prediction and the reproduction of the long-term system behavior (the system's "climate") are feasible with the same setup of optimized hyperparameters. Our results may be a further step towards the realization of a dedicated small quantum computer for prediction tasks in the NISQ-era.

Agent skills provide a lightweight mechanism for extending general-purpose agents, but their open format exposes them to skill-poisoning attacks. A practically dangerous injection must stay invisible: if executing the payload derails the user's legitimate task, the resulting failure signal invites inspection of the skill. We therefore evaluate attacks by Attack Success Rate, which requires the injected payload to execute and the user's task to still pass its verifier in the same trial. Prior skill-poisoning attacks face a reliability-stealth trade-off under this lens: YAML-header injections are reliably loaded but easily inspected, whereas stealthier body injections that place explicit malicious commands in the skill prose are less reliable because out-of-context commands invite the agent's own suspicion. We introduce POISE, a position-aware attack that compresses the trigger into a single, benign-looking body instruction, placing it at a feasible position and using a context-aware generator to blend it with nearby setup or prerequisite steps. On Skill-Inject with codex+gpt-5.2, POISE achieves an 89.3% ASR, 28.0 points above a random-placement body baseline and 2.6 points above a YAML-only baseline, while retaining the stealth advantage of body placement. That stealth is the decisive margin: because legitimate skill bodies naturally require privileged tool operations, LLM scanners are hyper-sensitive, falsely flagging 74.6% of clean skills on average across four judges and both benchmarks. Blending into these false alarms, POISE causes only 5.6% of poisoned variants to gain a new high-risk alert over their clean baselines, rendering current static defenses ineffective.

Mobile robots necessitate advanced natural language understanding capabilities to accurately identify locations and perform tasks such as package delivery. However, traditional visual place recognition (VPR) methods rely solely on single-view visual information and cannot interpret human language descriptions. To overcome this challenge, we bridge text and vision by proposing a multiview (360{\deg} views of the surroundings) text-vision registration approach called Text4VPR for place recognition task, which is the first method that exclusively utilizes textual descriptions to match a database of images. Text4VPR employs the frozen T5 language model to extract global textual embeddings. Additionally, it utilizes the Sinkhorn algorithm with temperature coefficient to assign local tokens to their respective clusters, thereby aggregating visual descriptors from images. During the training stage, Text4VPR emphasizes the alignment between individual text-image pairs for precise textual description. In the inference stage, Text4VPR uses the Cascaded Cross-Attention Cosine Alignment (CCCA) to address the internal mismatch between text and image groups. Subsequently, Text4VPR performs precisely place match based on the descriptions of text-image groups. On Street360Loc, the first text to image VPR dataset we created, Text4VPR builds a robust baseline, achieving a leading top-1 accuracy of 57% and a leading top-10 accuracy of 92% within a 5-meter radius on the test set, which indicates that localization from textual descriptions to images is not only feasible but also holds significant potential for further advancement, as shown in Figure 1.

Enterprises fine-tune language models on proprietary data that may later require removal due to privacy, contractual, or compliance obligations. Selective unlearning removes requested knowledge while preserving model utility, offering a practical alternative to full retraining, but existing methods treat the explicitly identified forget examples as the complete deletion scope. This is insufficient when target knowledge remains recoverable through paraphrases, aliases, or neighboring training examples. We propose GRAPHSU, a graph-guided controller that expands the deletion scope beyond forget seeds by constructing a weighted support-route graph, propagating deletion pressure through it, and applying graded forgetting strengths to high-risk neighbors. On the Task of Fictitious Unlearning (TOFU), a synthetic author-profile question-answering benchmark, and PISTOL, a structural-unlearning benchmark built around interconnected factual samples, with GPT-2 Medium and Llama-3.2-3B-Instruct, GRAPHSU achieves the lowest utility-feasible soft leakage across all deletion settings, reducing leakage by up to 49.5 percentage points over a matched seed-only baseline, demonstrating that effective enterprise unlearning requires controlling support routes, not just forget seeds.

Prediction sets have recently been shown to be a promising strategy for quantifying the uncertainty of deep neural networks in a way that provides theoretical guarantees. However, existing techniques have largely targeted settings where the space of labels is simple, so prediction sets can be arbitrary subsets of labels. For structured prediction problems where the space of labels is exponential in size, even prediction sets containing a small fraction of all labels can be exponentially large. In the context of code generation, we propose a solution that considers a restricted set of prediction sets that can compactly be represented as partial programs, which are programs with portions replaced with holes. Given a trained code generation model, our algorithm leverages a programming language's abstract syntax tree to generate a set of programs such that the correct program is in the set with high-confidence. Valuable applications of our algorithm include a Codex-style code generator with holes in uncertain parts of the generated code, which provides a partial program with theoretical guarantees. We evaluate our approach on PICARD (a T5 model for SQL semantic parsing) and Codex (a GPT model for over a dozen programming languages, including Python), demonstrating that our approach generates compact PAC prediction sets. This is the first research contribution that generates PAC prediction sets for generative code models.

We resolve a $1000 Erdős prize problem, complete with formal verification generated by a large language model. In over a dozen papers, beginning in 1976 and spanning two decades, Paul Erdős repeatedly posed one of his "favourite" conjectures: every finite Sidon set can be extended to a finite perfect difference set. We establish that {1, 2, 4, 8, 13} is a counterexample to this conjecture. During the preparation of this paper, we discovered that although this problem was presumed to be open for half a century, Marshall Hall, Jr. published a different counterexample three decades before Erdős first posed the problem. With a healthy skepticism of this apparent oversight, and out of an abundance of caution, we used ChatGPT to vibe code a Lean proof of both Hall's and our counterexamples.

Clustering in a big data setting is an intensively studied problem, with coresets emerging as one of the important paradigms in this line of work. Given a cost function cost(P,S) mapping input points P and a solution S to an objective value, a coreset is a typically weighted sketch Ωsubseteq P such that cost(Ω,S)approx cost(P,S). In practice, coreset sizes much smaller than those suggested by theoretical guarantees are often found to be sufficient. In this paper, we offer an explanation for this phenomenon. Smaller coreset sizes suffice if we only wish to preserve the costs of good solutions, i.e., solutions with low cost. We define and devise approximation-preserving coresets, which provide a weaker guarantee than strong coresets, which apply to all solutions, while providing stronger guarantees than weak coresets, which apply only to the optimum solution. We complement this result by showing that even a very small distortion in the approximation factor cannot admit coresets of this size.

Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains unresolved: beyond a few special dimensions, neither optimal packings nor tight upper bounds are known. Even a major breakthrough in dimension n=8, later recognised with a Fields Medal, underscores its difficulty. A leading technique for upper bounds, the three-point method, reduces the problem to solving large, high-precision semidefinite programs (SDPs). Because each candidate SDP may take days to evaluate, standard data-intensive AI approaches are infeasible. We address this challenge by formulating SDP construction as a sequential decision process, the SDP game, in which a policy assembles SDP formulations from a set of admissible components. Using a sample-efficient model-based framework that combines Bayesian optimisation with Monte Carlo Tree Search, we obtain new state-of-the-art upper bounds in dimensions 4-16, showing that model-based search can advance computational progress in longstanding geometric problems. Together, these results demonstrate that sample-efficient, model-based search can make tangible progress on mathematically rigid, evaluation limited problems, pointing towards a complementary direction for AI-assisted discovery beyond large-scale LLM-driven exploration.

Closed-loop decision-making systems (e.g., lending, screening, or recidivism risk assessment) often operate under fairness and service constraints while inducing feedback effects: decisions change who appears in the future, yielding non-stationary data and potentially amplifying disparities. We study online learning of a one-dimensional threshold policy from bandit feedback under demographic parity (DP) and, optionally, service-rate constraints. The learner observes only a scalar score each round and selects a threshold; reward and constraint residuals are revealed only for the chosen threshold. We propose Optimistic Feasible Search (OFS), a simple grid-based method that maintains confidence bounds for reward and constraint residuals for each candidate threshold. At each round, OFS selects a threshold that appears feasible under confidence bounds and, among those, maximizes optimistic reward; if no threshold appears feasible, OFS selects the threshold minimizing optimistic constraint violation. This design directly targets feasible high-utility thresholds and is particularly effective for low-dimensional, interpretable policy classes where discretization is natural. We evaluate OFS on (i) a synthetic closed-loop benchmark with stable contraction dynamics and (ii) two semi-synthetic closed-loop benchmarks grounded in German Credit and COMPAS, constructed by training a score model and feeding group-dependent acceptance decisions back into population composition. Across all environments, OFS achieves higher reward with smaller cumulative constraint violation than unconstrained and primal-dual bandit baselines, and is near-oracle relative to the best feasible fixed threshold under the same sweep procedure. Experiments are reproducible and organized with double-blind-friendly relative outputs.

We consider a fair division model in which agents have positive, zero and negative utilities for items. For this model, we analyse one existing fairness property - EFX - and three new and related properties - EFX_0, EFX^3 and EF1^3 - in combination with Pareto-optimality. With general utilities, we give a modified version of an existing algorithm for computing an EF1^3 allocation. With -alpha/0/alpha utilities, this algorithm returns an EFX^3 and PO allocation. With absolute identical utilities, we give a new algorithm for an EFX and PO allocation. With -alpha/0/beta utilities, this algorithm also returns such an allocation. We report some new impossibility results as well.

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s geq 3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analysis of higher-order phenomena based on local structures.

A coreset is a tiny weighted subset of an input set, that closely resembles the loss function, with respect to a certain set of queries. Coresets became prevalent in machine learning as they have shown to be advantageous for many applications. While coreset research is an active research area, unfortunately, coresets are constructed in a problem-dependent manner, where for each problem, a new coreset construction algorithm is usually suggested, a process that may take time or may be hard for new researchers in the field. Even the generic frameworks require additional (problem-dependent) computations or proofs to be done by the user. Besides, many problems do not have (provable) small coresets, limiting their applicability. To this end, we suggest an automatic practical framework for constructing coresets, which requires (only) the input data and the desired cost function from the user, without the need for any other task-related computation to be done by the user. To do so, we reduce the problem of approximating a loss function to an instance of vector summation approximation, where the vectors we aim to sum are loss vectors of a specific subset of the queries, such that we aim to approximate the image of the function on this subset. We show that while this set is limited, the coreset is quite general. An extensive experimental study on various machine learning applications is also conducted. Finally, we provide a ``plug and play" style implementation, proposing a user-friendly system that can be easily used to apply coresets for many problems. Full open source code can be found at https://github.com/alaamaalouf/AutoCoreset{https://github.com/alaamaalouf/AutoCoreset}. We believe that these contributions enable future research and easier use and applications of coresets.

In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing that the data set contains samples across the whole input space, or that the data set is balanced w.r.t. different classes. We present a formal approach for verifying a set of arbitrarily stated properties over a data set. The proposed approach relies on the transformation of the data set into a first order logic formula, which can be later verified w.r.t. the different properties also stated in the same logic. A prototype tool, which uses the z3 solver, has been developed; the prototype can take as an input a set of properties stated in a formal language and formally verify a given data set w.r.t. to the given set of properties. Preliminary experimental results show the feasibility and performance of the proposed approach, and furthermore the flexibility for expressing properties of interest.

In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets X_m of the set X_n (subset sum problem). Our algorithm has time complexity T=O(C_{n}^{k}) (k=[m/2], which significantly improves upon all known algorithms. This algorithm is applicable to all NP-complete problems. Moreover, the algorithm has memory complexity M=O(C_n^k), which makes our algorithm applicable to real-world problems. At first, we show how to use the algorithm for small dimensions m=4 ,5 ,6 ,7 ,8. After that we establish a general methodology for m>8. The main idea is to split the original set X_n (the algorithm becomes even faster with sorted sets) into smaller subsets and use parallel computing. This approach might be a significant breakthrough towards finding an efficient solution to NP-complete problems. As a result, it opens a way to prove the P versus NP problem (one of the seven Millennium Prize Problems).

Following the recent achievement of gold-medal performance on the IMO by frontier LLMs, the community is searching for the next meaningful and challenging target for measuring LLM reasoning. Whereas olympiad-style problems measure step-by-step reasoning alone, research-level problems use such reasoning to advance the frontier of mathematical knowledge itself, emerging as a compelling alternative. Yet research-level math benchmarks remain scarce because such problems are difficult to source (e.g., Riemann Bench and FrontierMath-Tier 4 contain 25 and 50 problems, respectively). To support reliable evaluation of next-generation frontier models, we introduce Soohak, a 439-problem benchmark newly authored from scratch by 64 mathematicians. Soohak comprises two subsets. On the Challenge subset, frontier models including Gemini-3-Pro, GPT-5, and Claude-Opus-4.5 reach 30.4%, 26.4%, and 10.4% respectively, leaving substantial headroom, while leading open-weight models such as Qwen3-235B, GPT-OSS-120B, and Kimi-2.5 remain below 15%. Notably, beyond standard problem solving, Soohak introduces a refusal subset that probes a capability intrinsic to research mathematics: recognizing ill-posed problems and pausing rather than producing confident but unjustified answers. On this subset, no model exceeds 50%, identifying refusal as a new optimization target that current models do not directly address. To prevent contamination, the dataset will be publicly released in late 2026, with model evaluations available upon request in the interim.

It is almost always easier to find an accurate-but-complex model than an accurate-yet-simple model. Finding optimal, sparse, accurate models of various forms (linear models with integer coefficients, decision sets, rule lists, decision trees) is generally NP-hard. We often do not know whether the search for a simpler model will be worthwhile, and thus we do not go to the trouble of searching for one. In this work, we ask an important practical question: can accurate-yet-simple models be proven to exist, or shown likely to exist, before explicitly searching for them? We hypothesize that there is an important reason that simple-yet-accurate models often do exist. This hypothesis is that the size of the Rashomon set is often large, where the Rashomon set is the set of almost-equally-accurate models from a function class. If the Rashomon set is large, it contains numerous accurate models, and perhaps at least one of them is the simple model we desire. In this work, we formally present the Rashomon ratio as a new gauge of simplicity for a learning problem, depending on a function class and a data set. The Rashomon ratio is the ratio of the volume of the set of accurate models to the volume of the hypothesis space, and it is different from standard complexity measures from statistical learning theory. Insight from studying the Rashomon ratio provides an easy way to check whether a simpler model might exist for a problem before finding it, namely whether several different machine learning methods achieve similar performance on the data. In that sense, the Rashomon ratio is a powerful tool for understanding why and when an accurate-yet-simple model might exist. If, as we hypothesize in this work, many real-world data sets admit large Rashomon sets, the implications are vast: it means that simple or interpretable models may often be used for high-stakes decisions without losing accuracy.

In this article, we study the parameterized complexity of the Set Cover problem restricted to semi-ladder-free hypergraphs, a class defined by Fabianski et al. [Proceedings of STACS 2019]. We observe that two algorithms introduced by Langerman and Morin [Discrete & Computational Geometry 2005] in the context of geometric covering problems can be adapted to this setting, yielding simple FPT and kernelization algorithms for Set Cover in semi-ladder-free hypergraphs. We complement our algorithmic results with a compression lower bound for the problem, which proves the tightness of our kernelization under standard complexity-theoretic assumptions.

We present a constructive lower bound of Ω(1/varepsilon) for Frank-Wolfe (FW) when both the objective and the constraint set are smooth and strongly convex, showing that the known uniform O(1/varepsilon) guarantees in this regime are tight. It is known that under additional assumptions on the position of the optimizer, FW can converge linearly. However, it remained unclear whether strong convexity of the set can yield rates uniformly faster than O(1/varepsilon), i.e., irrespective of the position of the optimizer. To investigate this question, we focus on a simple yet representative problem class: minimizing a strongly convex quadratic over the Euclidean unit ball, with the optimizer on the boundary. We analyze the dynamics of FW for this problem in detail and develop a novel computational approach to construct worst-case FW trajectories, which is of independent interest. Guided by these constructions, we develop an analytical proof establishing the lower bound.

We present new methods and results for constructing optimal Kobon triangle arrangements. First, we introduce a compact table notation for describing arrangements of pseudolines, enabling the representation and analysis of complex cases, including symmetrical arrangements, arrangements with parallel lines, and arrangements with multiple-line intersection points. Building on this, we provide a simple heuristic method and tools for recovering straight-line arrangements from a given table, with the ability to enforce additional properties such as symmetries. The tool successfully recovers arrangements for many previously known optimal solutions. Additionally, we develop a tool that transforms the search for optimal Kobon arrangement tables into a SAT problem, allowing us to leverage modern SAT solvers (specifically Kissat) to efficiently find new solutions or to show that no other solutions exist (for example, confirming that no optimal solution exists in the 11-line case). Using these techniques, we find new optimal Kobon arrangements for 23 and 27 lines, along with several other new results.

The standard quadratic program (StQP) minimizes a quadratic form over nonnegative variables that sum to one. We compose classical graph reductions with regularized Motzkin--Straus clique formulations to express discrete optimization problems in this continuous domain. The graph matrix has diagonal entries τ, zeros on edges, and ones on nonedges. For 0<τ<1, its minimum is τ/ω(G), where ω(G) is the clique number. Its strict local minimizers are precisely the uniform distributions on maximal cliques, and its global minimizers encode maximum cliques. At τ=1/2, integer scaling gives coefficients in {0,1,2} and minimum 1/ω(G), yielding an NP-complete StQP threshold problem with a restricted coefficient alphabet. We give explicit formulations for satisfiability, coloring, Hamiltonian cycles, independent set, vertex cover, set packing, three-dimensional matching, and graph isomorphism. A regularized weighted clique formulation combined with local-state compatibility graphs gives an exact compiler for finite-domain factor models specified by complete local tables, including QUBO, with at most four simplex coordinates per binary pair factor. The catalog covers Karp's 21 problems: twelve use direct graph formulations, and nine use factor-state formulations, including six obtained through binary-linear feasibility. For each route we record dimensions, coefficient structure, and recovery rules. We analyze interaction count, coefficient range, objective separation, perturbation tolerance, support recovery, and decoding overhead. The separation bounds quantify the effects of clique size, factor weights, and offsets. In the complete factor-state construction, every assignment, including each suboptimal assignment, is a strict local minimum.

Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain poorly understood, as universality is traditionally studied for models accepting inputs of a fixed size, defined on a compact subset of their domain. In sharp contrast, any-dimensional models can be viewed as sequences of functions defined on growing-sized inputs, and it is not clear in which sense they can be universal. We develop a systematic approach to establish any-dimensional universality, by identifying any-dimensional functions with a unique function taking inputs in a suitable infinite-dimensional limit space containing inputs of all finite sizes as well as their limits. Using the symmetries of these inputs and relations between inputs of different sizes, we show that this limit space admits a natural topology with rich families of compact sets on which any-dimensional universality can be established. We illustrate our approach by showing that several existing architectures fail to be universal, and we propose simple modifications that restore universality.

Magnitude of a finite metric space and the related notion of magnitude functions on metric spaces is an active area of research in algebraic topology. Magnitude originally arose in the context of biology, where it represents the number of effective species in an environment; when applied to a one-parameter family of metric spaces tX with scale parameter t, the magnitude captures much of the underlying geometry of the space. Prior work has mostly focussed on properties of magnitude in a global sense; in this paper we restrict the sets to finite subsets of Euclidean space and investigate its individual components. We give an explicit formula for the corrected inclusion-exclusion principle, and define a quantity associated with each point, called the moment which gives an intrinsic ordering to the points. We exploit this in order to form an algorithm which approximates the convex hull.

Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by the Andrews-Curtis conjecture, we propose algorithmic enhancements and a topological hardness measure with implications for a broad class of search problems. As part of our study, we also address several open mathematical questions. Notably, we demonstrate the length reducibility of all but two presentations in the Akbulut-Kirby series (1981), and resolve various potential counterexamples in the Miller-Schupp series (1991), including three infinite subfamilies.

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees, while achieving competitive empirical performance.

We study the problem of differentially private (DP) computation of coreset for the k-means objective. For a given input set of points, a coreset is another set of points such that the k-means objective for any candidate solution is preserved up to a multiplicative (1 pm α) factor (and some additive factor). We prove the first computational lower bounds for this problem. Specifically, assuming the existence of one-way functions, we show that no polynomial-time (ε, 1/n^{ω(1)})-DP algorithm can compute a coreset for k-means in the ell_infty-metric for some constant α> 0 (and some constant additive factor), even for k=3. For k-means in the Euclidean metric, we show a similar result but only for α= Θleft(1/d^2right), where d is the dimension.

A common assumption holds that enough observational and interventional data, given to a strong enough predictor, suffices. We report a failure mode that contradicts it. Across hundreds of structural causal models, on identified quantities a strong predictor and a Bayesian baseline both succeed, but on unidentified quantities (the couplings between counterfactual worlds) the predictor collapses to a point, on 28% of models to one no valid model can produce, while the truth is an admissible interval more data never narrows. The gap is structural: prediction cannot represent uncertainty over counterfactual couplings. We cast a world model as a single positive semidefinite coupling kernel K(T,T') over admissible worlds, whose diagonal is the ordinary posterior (what a predictor recovers) and whose off-diagonal is the cross-world coupling it cannot, which every counterfactual reads. The paper is the theory of that off-diagonal. It is real: two states with identical posteriors differ on a cross-world query, and the off-diagonal is the coupling that fixes counterfactuals. It can be bounded: positive semidefiniteness is partial-identifying information the marginals lack, and enforcing it bounds counterfactuals in polynomial time where the exact response-type program is intractable. Logical structure sharpens it: ontology axioms tighten the bound by up to a third, propagating to couplings they never touch. It can be acquired: targeted scars, constraints learned from encountered infeasibilities, close the gap several times faster than untargeted ones. Its full reconstruction is approximate counting of the admissible worlds, tractable below the Sly-Sun threshold and inapproximable above; we do not claim to beat the worst case.

Set theory is foundational to mathematics and, when sets are finite, to reasoning about the world. An intelligent system should perform set operations consistently, regardless of superficial variations in the operands. Initially designed for semantically-oriented NLP tasks, large language models (LLMs) are now being evaluated on algorithmic tasks. Because sets are comprised of arbitrary symbols (e.g. numbers, words), they provide an opportunity to test, systematically, the invariance of LLMs' algorithmic abilities under simple lexical or semantic variations. To this end, we present the SetLexSem Challenge, a synthetic benchmark that evaluates the performance of LLMs on set operations. SetLexSem assesses the robustness of LLMs' instruction-following abilities under various conditions, focusing on the set operations and the nature and construction of the set members. Evaluating seven LLMs with SetLexSem, we find that they exhibit poor robustness to variation in both operation and operands. We show -- via the framework's systematic sampling of set members along lexical and semantic dimensions -- that LLMs are not only not robust to variation along these dimensions but demonstrate unique failure modes in particular, easy-to-create semantic groupings of "deceptive" sets. We find that rigorously measuring language model robustness to variation in frequency and length is challenging and present an analysis that measures them independently. The code for reproducing the results of this paper, and for generating the SetLexSem Challenge dataset, is available at https://github.com/amazon-science/SetLexSem-Challenge{https://github.com/amazon-science/SetLexSem-Challenge}.

The sufficiently scattered condition (SSC) is a key condition in the study of identifiability of various matrix factorization problems, including nonnegative, minimum-volume, symmetric, simplex-structured, and polytopic matrix factorizations. The SSC allows one to guarantee that the computed matrix factorization is unique/identifiable, up to trivial ambiguities. However, this condition is NP-hard to check in general. In this paper, we show that it can however be checked in a reasonable amount of time in realistic scenarios, when the factorization rank is not too large. This is achieved by formulating the problem as a non-convex quadratic optimization problem over a bounded set. We use the global non-convex optimization software Gurobi, and showcase the usefulness of this code on synthetic data sets and on real-world hyperspectral images.

Finite unions of convex sets are a central object of study in discrete and computational geometry. In this paper we initiate a systematic study of complements of such unions -- i.e., sets of the form S=R^d setminus (cup_{i=1}^n K_i), where K_i are convex sets. In the first part of the paper we study isolated points in S, whose number is related to the Betti numbers of cup_{i=1}^n K_i and to its non-convexity properties. We obtain upper bounds on the number of such points, which are sharp for n=3 and significantly improve previous bounds of Lawrence and Morris (2009) for all n ll 2^d{d}. In the second part of the paper we study coverings of S by well-behaved sets. We show that S can be covered by at most g(d,n) flats of different dimensions, in such a way that each x in S is covered by a flat whose dimension equals the `local dimension' of S in the neighborhood of x. Furthermore, we determine the structure of a minimum cover that satisfies this property. Then, we study quantitative aspects of this minimum cover and obtain sharp upper bounds on its size in various settings.

The complexity of learning a concept class under Gaussian marginals in the difficult agnostic model is closely related to its L_1-approximability by low-degree polynomials. For any concept class with Gaussian surface area at most Γ, Klivans et al. (2008) show that degree d = O(Γ^2 / varepsilon^4) suffices to achieve an varepsilon-approximation. This leads to the best-known bounds on the complexity of learning a variety of concept classes. In this note, we improve their analysis by showing that degree d = tilde O (Γ^2 / varepsilon^2) is enough. In light of lower bounds due to Diakonikolas et al. (2021), this yields (near) optimal bounds on the complexity of agnostically learning polynomial threshold functions in the statistical query model. Our proof relies on a direct analogue of a construction of Feldman et al. (2020), who considered L_1-approximation on the Boolean hypercube.

Under ZF, we show that the statement that every subset of every R-vector space has a maximal convex subset is equivalent to the Axiom of Choice. We also study the strength of the same statement restricted to some specific R-vector spaces. In particular, we show that the statement for R^2 is equivalent to the Axiom of Countable Choice for reals, whereas the statement for R^3 is equivalent to the Axiom of Uniformization. We discuss the statement for some spaces of higher dimensions as well.

The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of DGP instances. In this paper, we study the Discretizable Molecular Distance Geometry Problem whose feasible solutions provide a discretization scheme for the DGP. We propose the first constraint programming formulations as well as a set of checks for proving infeasibility, domain reduction techniques, symmetry breaking constraints and valid inequalities. Our computational results indicate that our formulations outperform the state-of-the-art integer programming formulations, both for feasible and infeasible instances.

Utility functions or their equivalents (value functions, objective functions, loss functions, reward functions, preference orderings) are a central tool in most current machine learning systems. These mechanisms for defining goals and guiding optimization run into practical and conceptual difficulty when there are independent, multi-dimensional objectives that need to be pursued simultaneously and cannot be reduced to each other. Ethicists have proved several impossibility theorems that stem from this origin; those results appear to show that there is no way of formally specifying what it means for an outcome to be good for a population without violating strong human ethical intuitions (in such cases, the objective function is a social welfare function). We argue that this is a practical problem for any machine learning system (such as medical decision support systems or autonomous weapons) or rigidly rule-based bureaucracy that will make high stakes decisions about human lives: such systems should not use objective functions in the strict mathematical sense. We explore the alternative of using uncertain objectives, represented for instance as partially ordered preferences, or as probability distributions over total orders. We show that previously known impossibility theorems can be transformed into uncertainty theorems in both of those settings, and prove lower bounds on how much uncertainty is implied by the impossibility results. We close by proposing two conjectures about the relationship between uncertainty in objectives and severe unintended consequences from AI systems.

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. This class of functions includes monotone submodular functions as a sub-family. To understand the importance of this structure in optimization problems we consider the problem of maximizing function value under various types of constraints. To demonstrate the modeling power of submodular order functions we show applications in two different settings. First, we apply our results to the extensively studied problem of assortment optimization. While the objectives in assortment optimization are known to be non-submodular (and non-monotone) even for simple choice models, we show that they are compatible with the notion of submodular order. Consequently, we obtain new and in some cases the first constant factor guarantee for constrained assortment optimization in fundamental choice models. As a second application of submodular order functions, we show an intriguing connection to the maximization of monotone submodular functions in the streaming model. We recover some best known guarantees for this problem as a corollary of our results.

In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true one, with precision growing only with the square root of the batch size. A theoretical justification is with the help of stochastic approximation theory. However, the conditions for the validity of this theory are not satisfied in the usual learning rate schedules. Batch processing is also difficult to combine with efficient second-order optimization methods. This proposal is based on another hypothesis: the loss minimum of the training set can be expected to be well-approximated by the minima of its subsets. Such subset minima can be computed in a fraction of the time necessary for optimizing over the whole training set. This hypothesis has been tested with the help of the MNIST, CIFAR-10, and CIFAR-100 image classification benchmarks, optionally extended by training data augmentation. The experiments have confirmed that results equivalent to conventional training can be reached. In summary, even small subsets are representative if the overdetermination ratio for the given model parameter set sufficiently exceeds unity. The computing expense can be reduced to a tenth or less.

For nonconvex optimization in machine learning, this article proves that every local minimum achieves the globally optimal value of the perturbable gradient basis model at any differentiable point. As a result, nonconvex machine learning is theoretically as supported as convex machine learning with a handcrafted basis in terms of the loss at differentiable local minima, except in the case when a preference is given to the handcrafted basis over the perturbable gradient basis. The proofs of these results are derived under mild assumptions. Accordingly, the proven results are directly applicable to many machine learning models, including practical deep neural networks, without any modification of practical methods. Furthermore, as special cases of our general results, this article improves or complements several state-of-the-art theoretical results on deep neural networks, deep residual networks, and overparameterized deep neural networks with a unified proof technique and novel geometric insights. A special case of our results also contributes to the theoretical foundation of representation learning.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time (0,ε)-additive bicriteria approximation algorithm for finding optimal constrained policies across a broad class of recursively computable constraints, including almost-sure, chance, expectation, and their anytime variants. Matching lower bounds imply our approximation guarantees are optimal so long as P neq NP. The generality of our approach results in answers to several long-standing open complexity questions in the constrained reinforcement learning literature. Specifically, we are the first to prove polynomial-time approximability for the following settings: policies under chance constraints, deterministic policies under multiple expectation constraints, policies under non-homogeneous constraints (i.e., constraints of different types), and policies under constraints for continuous-state processes.

Let F_{k,d}(n) be the maximal size of a set {A}subseteq [n] such that the equation \[a_1a_2\dots a_k=x^d, \; a_1<a_2<\ldots<a_k\] has no solution with a_1,a_2,ldots,a_kA and integer x. Erdos, S\'ark\"ozy and T. S\'os studied F_{k,2}, and gave bounds when k=2,3,4,6 and also in the general case. We study the problem for d=3, and provide bounds for k=2,3,4,6 and 9, furthermore, in the general case, as well. In particular, we refute an 18 years old conjecture of Verstra\"ete. We also introduce another function f_{k,d} closely related to F_{k,d}: While the original problem requires a_1, ldots , a_k to all be distinct, we can relax this and only require that the multiset of the a_i's cannot be partitioned into d-tuples where each d-tuple consists of d copies of the same number.

For any integer d geq 2 and prime power q, we construct unexpectedly large induced matchings in the point-line incidence graph of F_{q}^{d} by leveraging a new connection with the Furstenberg-Sárközy problem from arithmetic combinatorics. In particular, we significantly improve the previously well-known baselines when q is prime, showing that F_{q}^{2} contains matchings of size q^{1.233} and F_{q}^{d} contains matchings of size q^{d-o_{d}(1)}. These results and their proofs have several applications. First, we also obtain new constructions for finite field Nikodym sets in dimension d geq 2, improving recent results of Tao by polynomial factors. For example, when q is prime, we show the existence of Nikodym sets in F_q^d of size q^d - q^{d - o_d(1)}. Second, we construct a new minimal blocking set in PG(2,q), solving a longstanding problem in finite geometry. Third, we obtain new constructions for the minimal distance problem (in R^{2} and also in higher dimensions), improving a recent result of Logunov-Zakharov. We also obtain analogous results for general finite fields with large characteristics. In particular, in one of our constructions we introduce a new special set of points inside the norm hypersurface in F_{q}^{d}, which directly generalizes the classical Hermitian unital and which may be of independent interest for applications.

With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics at the high-school, undergraduate, and graduate level, there are far fewer resources available that align with the level of difficulty and open endedness encountered by professional mathematicians working on open problems. To address this, we introduce a new collection of datasets, the Algebraic Combinatorics Dataset Repository (ACD Repo), representing either foundational results or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. Further differentiating our dataset collection is the fact that it aims at the conjecturing process. Each dataset includes an open-ended research-level question and a large collection of examples (up to 10M in some cases) from which conjectures should be generated. We describe all nine datasets, the different ways machine learning models can be applied to them (e.g., training with narrow models followed by interpretability analysis or program synthesis with LLMs), and discuss some of the challenges involved in designing datasets like these.

A major barrier to deploying current machine learning models lies in their non-reliability to dataset shifts. To resolve this problem, most existing studies attempted to transfer stable information to unseen environments. Particularly, independent causal mechanisms-based methods proposed to remove mutable causal mechanisms via the do-operator. Compared to previous methods, the obtained stable predictors are more effective in identifying stable information. However, a key question remains: which subset of this whole stable information should the model transfer, in order to achieve optimal generalization ability? To answer this question, we present a comprehensive minimax analysis from a causal perspective. Specifically, we first provide a graphical condition for the whole stable set to be optimal. When this condition fails, we surprisingly find with an example that this whole stable set, although can fully exploit stable information, is not the optimal one to transfer. To identify the optimal subset under this case, we propose to estimate the worst-case risk with a novel optimization scheme over the intervention functions on mutable causal mechanisms. We then propose an efficient algorithm to search for the subset with minimal worst-case risk, based on a newly defined equivalence relation between stable subsets. Compared to the exponential cost of exhaustively searching over all subsets, our searching strategy enjoys a polynomial complexity. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.

We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and orthomodular lattices. We prove a determinization lemma showing that lifting to sets or distributions yields a deterministic global dynamic, an ordinal stabilization theorem sending operator transforms to the fixed subspace by stage omega under normal spectral contraction, and a product of Riesz projections theorem for commuting layers. We establish a compositionality law for lifted maps, show closure of Phi packings, and present a quantitative application to sensory depletion that models tissue removal as a projection and derives strict decreases in the attainable fixed point under minimal monotonicity and positivity assumptions. We also state measurable conditions for probabilistic lifts, give explicit non normal and non commuting counterexamples, and provide finite dimensional and stochastic witnesses together with per theorem scope tables and a small reproducible code appendix.

A fundamental problem in combinatorial optimization is identifying equivalent formulations, which can lead to more efficient solution strategies and deeper insights into a problem's computational complexity. The need to automatically identify equivalence between problem formulations has grown as optimization copilots--systems that generate problem formulations from natural language descriptions--have proliferated. However, existing approaches to checking formulation equivalence lack grounding, relying on simple heuristics which are insufficient for rigorous validation. Inspired by Karp reductions, in this work we introduce quasi-Karp equivalence, a formal criterion for determining when two optimization formulations are equivalent based on the existence of a mapping between their decision variables. We propose EquivaMap, a framework that leverages large language models to automatically discover such mappings, enabling scalable and reliable equivalence verification. To evaluate our approach, we construct the first open-source dataset of equivalent optimization formulations, generated by applying transformations such as adding slack variables or valid inequalities to existing formulations. Empirically, EquivaMap significantly outperforms existing methods, achieving substantial improvements in correctly identifying formulation equivalence.

This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty quantification guarantees for machine learning systems. Much of the current interest in conformal prediction is due to its ability to integrate into complex machine learning workflows, solving the problem of forming prediction sets without any assumptions on the form of the data generating distribution. Since contemporary machine learning algorithms have generally proven difficult to analyze directly, conformal prediction's main appeal is its ability to provide formal, finite-sample guarantees when paired with such methods. The goal of this book is to teach the reader about the fundamental technical arguments that arise when researching conformal prediction and related questions in distribution-free inference. Many of these proof strategies, especially the more recent ones, are scattered among research papers, making it difficult for researchers to understand where to look, which results are important, and how exactly the proofs work. We hope to bridge this gap by curating what we believe to be some of the most important results in the literature and presenting their proofs in a unified language, with illustrations, and with an eye towards pedagogy.

We study sets of delta tubes in R^3, with the property that not too many tubes can be contained inside a common convex set V. We show that the union of tubes from such a set must have almost maximal volume. As a consequence, we prove that every Kakeya set in R^3 has Minkowski and Hausdorff dimension 3.

In this paper we present the Yale-CMU-Berkeley (YCB) Object and Model set, intended to be used to facilitate benchmarking in robotic manipulation, prosthetic design and rehabilitation research. The objects in the set are designed to cover a wide range of aspects of the manipulation problem; it includes objects of daily life with different shapes, sizes, textures, weight and rigidity, as well as some widely used manipulation tests. The associated database provides high-resolution RGBD scans, physical properties, and geometric models of the objects for easy incorporation into manipulation and planning software platforms. In addition to describing the objects and models in the set along with how they were chosen and derived, we provide a framework and a number of example task protocols, laying out how the set can be used to quantitatively evaluate a range of manipulation approaches including planning, learning, mechanical design, control, and many others. A comprehensive literature survey on existing benchmarks and object datasets is also presented and their scope and limitations are discussed. The set will be freely distributed to research groups worldwide at a series of tutorials at robotics conferences, and will be otherwise available at a reasonable purchase cost. It is our hope that the ready availability of this set along with the ground laid in terms of protocol templates will enable the community of manipulation researchers to more easily compare approaches as well as continually evolve benchmarking tests as the field matures.

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies can be achieved by reducing the input space if a minimal loss of information can be achieved. Clustering algorithms, in general, face two common problems: 1) these converge to different settings with different initial conditions and; 2) the number of clusters has to be arbitrarily decided beforehand. This problem has become critical in the realm of big data. Recently, clustering algorithms have emerged which can speedup computations using parallel processing over the grid but face the aforementioned problems. Goals: Our goals are to find methods to cluster data which: 1) guarantee convergence to the same settings irrespective of the initial conditions; 2) eliminate the need to establish the number of clusters beforehand, and 3) can be applied to cluster large datasets. Methods: We introduce a method that combines probabilistic and combinatorial clustering methods to produce repeatable and compact clusters that are not sensitive to initial conditions. This method harnesses the power of k-means (a combinatorial clustering method) to cluster/partition very large dimensional datasets and uses the Gaussian Mixture Model (a probabilistic clustering method) to validate the k-means partitions. Results: We show that this method produces very compact clusters that are not sensitive to initial conditions. This method can be used to identify the most 'separable' set in a dataset which increases the 'clusterability' of a dataset. This method also eliminates the need to specify the number of clusters in advance.

Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each vertex in the graph is a continuous decision variable constrained in a convex set, and the length of an edge is a convex function of the position of its endpoints. Problems of this form arise naturally in many areas, from motion planning of autonomous vehicles to optimal control of hybrid systems. The price for such a wide applicability is the complexity of this problem, which is easily seen to be NP-hard. Our main contribution is a strong and lightweight mixed-integer convex formulation based on perspective operators, that makes it possible to efficiently find globally optimal paths in large graphs and in high-dimensional spaces.

Prediction sets can wrap around any ML model to cover unknown test outcomes with a guaranteed probability. Yet, it remains unclear how to use them optimally for downstream decision-making. Here, we propose a decision-theoretic framework that seeks to minimize the expected loss (risk) against a worst-case distribution consistent with the prediction set's coverage guarantee. We first characterize the minimax optimal policy for a fixed prediction set, showing that it balances the worst-case loss inside the set with a penalty for potential losses outside the set. Building on this, we derive the optimal prediction set construction that minimizes the resulting robust risk subject to a coverage constraint. Finally, we introduce Risk-Optimal Conformal Prediction (ROCP), a practical algorithm that targets these risk-minimizing sets while maintaining finite-sample distribution-free marginal coverage. Empirical evaluations on medical diagnosis and safety-critical decision-making tasks demonstrate that ROCP reduces critical mistakes compared to baselines, particularly when out-of-set errors are costly.

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness requirements. These requirements can be imposed (with generalization guarantees) by formulating constrained learning problems that can then be tackled by dual ascent algorithms. Yet, though these algorithms converge in objective value, even in non-convex settings, they cannot guarantee that their outcome is feasible. Doing so requires randomizing over all iterates, which is impractical in virtually any modern applications. Still, final iterates have been observed to perform well in practice. In this work, we address this gap between theory and practice by characterizing the constraint violation of Lagrangian minimizers associated with optimal dual variables, despite lack of convexity. To do this, we leverage the fact that non-convex, finite-dimensional constrained learning problems can be seen as parametrizations of convex, functional problems. Our results show that rich parametrizations effectively mitigate the issue of feasibility in dual methods, shedding light on prior empirical successes of dual learning. We illustrate our findings in fair learning tasks.

Uncertainty learning and quantification of models are crucial tasks to enhance the trustworthiness of the models. Importantly, the recent surge of generative language models (GLMs) emphasizes the need for reliable uncertainty quantification due to the concerns on generating hallucinated facts. In this paper, we propose to learn neural prediction set models that comes with the probably approximately correct (PAC) guarantee for quantifying the uncertainty of GLMs. Unlike existing prediction set models, which are parameterized by a scalar value, we propose to parameterize prediction sets via neural networks, which achieves more precise uncertainty quantification but still satisfies the PAC guarantee. We demonstrate the efficacy of our method on four types of language datasets and six types of models by showing that our method improves the quantified uncertainty by 63% on average, compared to a standard baseline method.

In this paper, we propose a new mixed-integer linear programming (MILP) model ontology and a novel constraint typology of MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life scheduling, routing, planning, resource allocation, and timetabling optimization problems providing optimized business solutions for industry sectors such as manufacturing, agriculture, defence, healthcare, medicine, energy, finance, and transportation. Despite the numerous real-life Combinatorial Optimization Problems found and solved and millions yet to be discovered and formulated, the number of types of constraints (the building blocks of a MILP) is relatively small. In the search for a suitable machine-readable knowledge representation structure for MILPs, we propose an optimization modelling tree built based upon an MILP model ontology that can be used as a guide for automated systems to elicit an MILP model from end-users on their combinatorial business optimization problems. Our ultimate aim is to develop a machine-readable knowledge representation for MILP that allows us to map an end-user's natural language description of the business optimization problem to an MILP formal specification as a first step towards automated mathematical modelling.

Lattice-based planning techniques simplify the motion planning problem for autonomous vehicles by limiting available motions to a pre-computed set of primitives. These primitives are then combined online to generate more complex maneuvers. A set of motion primitives t-span a lattice if, given a real number t at least 1, any configuration in the lattice can be reached via a sequence of motion primitives whose cost is no more than a factor of t from optimal. Computing a minimal t-spanning set balances a trade-off between computed motion quality and motion planning performance. In this work, we formulate this problem for an arbitrary lattice as a mixed integer linear program. We also propose an A*-based algorithm to solve the motion planning problem using these primitives. Finally, we present an algorithm that removes the excessive oscillations from planned motions -- a common problem in lattice-based planning. Our method is validated for autonomous driving in both parking lot and highway scenarios.