#01Nov 10, 2026
cs.LG
TorchCurves: Differentiable Parametric Curves
Alex Shtoff
We present TorchCurves, a PyTorch library that treats vector-valued parametric curves as learnable primitives. Its central operation maps batches of scalar inputs to points on curves represented in B-spline or Legendre polynomial bases, with differentiation through both inputs and coefficients. Curve coefficients can be optimized jointly with the surrounding model or produced by another network. The library provides trainable modules, reusable basis modules, and a functional interface, supporting applications ranging from continuous feature embeddings to Kolmogorov-Arnold networks and functional regression. Its implementation combines classical evaluation algorithms with vectorized PyTorch operations, emphasizing readability and maintainability without custom hardware kernels. Timing experiments compare curve evaluation against NumPy and SciPy and KAN training against EfficientKAN across a range of problem sizes. The results illustrate where this generality remains computationally practical and where overhead is substantial. Library is available on GitHub at https://github.com/alexshtf/torchcurves.
#02Nov 10, 2026
cs.CV
Measuring Robustness and Efficiency in a Connectome-Constrained Fly Visual System Model: Linking an Adversarial and a Perceptual Illusion
Alexandre Garcia-Duran, Alejandro Rodriguez-Garcia, Manuel Molano-Mazón and 3 more
Biological visual systems compute reliably under tight metabolic and wiring constraints, whereas artificial vision systems consume far more energy and can be sensitive to adversarial perturbations. Whether networks with brain-like wiring are more robust at lower computational cost is unclear. We address this by benchmarking a task-optimized, continuous-time recurrent neural network of the fly visual system constrained by its synaptic connectome (FlyNet) against artificial neural networks. We compare it against CNNs, RAFT, and continuous-time recurrent neural networks without detailed connectome constraints (sCTRNN, CTRNN) on a collision-detection task within a differentiable 3D rendering pipeline. FlyNet is adversarially vulnerable but, relative to its compute, more robust to common video corruptions than RAFT, while using up to five orders of magnitude fewer FLOPs. The CTRNNs remain more robust than FlyNet across almost all tested perturbations, suggesting that connectome constraints benefit efficiency, through their low edge count, over robustness. Recurrence improves robustness to white-box attacks in RAFT and temporal context improves robustness to common corruptions. FlyNet's position and velocity representations degrade under adversarial textures but recover under counterfactual textures that restore correct classification while staying equally far from training, ruling out unfamiliar textures as the cause of failure. The reverse-phi illusion similarly disrupts these representations and inverts the same low-level motion statistic as the adversarial textures. Optimizing this input statistic alone, without access to the network, suffices to induce classification failure, attributing both perturbations to the same circuit vulnerability. Connectome-constrained models can thus surface adversarial failure mechanisms as testable hypotheses about biological perceptual vulnerabilities.
#03Nov 10, 2026
cs.CV
UGG: Unified Generative Geometry Model
Amani Kiruga, Zhiyi Li, Ruojin Cai and 4 more
Understanding 4D scenes is a core challenge in visual intelligence, requiring models to jointly capture scene geometry, appearance, and dynamics from partial observations. However, existing approaches are subdivided into feedforward models for direct geometric prediction, and generative models for visual synthesis. We introduce UGG, a unified framework for 4D scene understanding that jointly models RGB video and geometric representations such as depth and camera pose. By assigning different noise levels across modalities and time, UGG formulates visual generation and geometric prediction as conditional completion within a single generative model. This flexible formulation enables the model to learn from diverse, heterogeneous datasets with different subsets of geometric and visual annotations. Furthermore, our generative formulation enables inference-time search over multiple plausible scene hypotheses, using geometric evidence extracted from observed RGB frames to improve geometric prediction without ground truth geometry. We demonstrate UGG's effectiveness over non-unified baselines across camera-controlled video generation, depth estimation, and camera pose prediction, including in challenging sparse observation settings. Code and visualizations are available at https://ugg-model.github.io/
#04Nov 10, 2026
math.AP
Bayesian inverse problems and epidemic-threshold uncertainty for a heterogeneous SIS reaction-diffusion model
Duc-Lam Duong
We study Bayesian inference of persistence from early observations of a heterogeneous susceptible--infected--susceptible (SIS) reaction--diffusion model with standard incidence. We show that the leading prevalence dynamics depend on the unknown coefficients only through the difference between the transmission and recovery rates and the infected diffusivity. The same pair determines the principal eigenvalue whose sign governs persistence, so early prevalence can inform the threshold even when the individual rates remain uncertain. We prove global weak well-posedness and quantitative parameter stability for the SIS system and use the resulting observation-map estimates to establish Bayesian well-posedness. For an initial infection of size $\varepsilon$, we derive a uniform second-order expansion that describes how the separate rates enter prevalence. Incidence depends explicitly on transmission at leading order. When the noise standard deviation is proportional to $\varepsilon$, we prove $O(\varepsilon)$ convergence in Hellinger distance of the nonlinear posteriors to their low-prevalence limits for both prevalence alone and joint prevalence and incidence data. We bound the principal eigenvalue using the growth rate of the infected $L^2$ norm between two times. This rate gives a lower bound for the full nonlinear system, and the upper bound separates spatial transients from nonlinear saturation. Uniform spectral estimates and bounds on infection size and measurement error give sufficient conditions for persistence and extinction. We also bound the error in posterior persistence probabilities under forward and eigenvalue approximation, accounting for posterior mass near the threshold. Numerical examples illustrate threshold inference and the predicted \(O(\varepsilon)\) convergence of the nonlinear posteriors to their low-prevalence limits in Hellinger distance.
#05Nov 10, 2026
cs.LG
Continual-ARC: Measuring Skill Acquisition over a Working Lifetime
Daniel Lenton
Agent harnesses have emerged as a promising mechanism for continual learning, alongside test-time parametric learning. However, the current benchmarks have several limitations: they generally focus on a single applied domain, serve each instance only once, and assume a single family of learner, so memory-based and weight-based systems are rarely compared on the same scale. We propose Continual-ARC, a lifelong stream built from the three ARC-AGI editions, whose tasks need no domain knowledge. The same tasks return after dormant gaps with fresh instances, while new tasks keep arriving. On each instance, the learner may pay for demonstrations, submit answers, or act inside the harness, with retries permitted on incorrect submissions, which are paid for. Each instance is scored based on the share of this feedback budget consumed. Since a learner may keep anything between instances, memory-based and weight-based systems are scored on the same scale. After the stream, the learner is frozen and tested on fresh instances of the tasks it met, which measures memorization, and on unseen tasks, which measures generalization. We run an agent harness with frozen weights, with and without persistence, on Qwen3.5-9B and GLM-5.3 Flash, comparing them with two prompting floors, a program-induction method and Qwen3.5-9B's weights trained to imitate GLM-5.3 Flash. Persistence in the harness generally does not improve memorization unless provided with explicit expert guidance. Most harness-based methods still learn less than a floor that simply caches each task's demonstrations, across all models we tested. No harness-based method gains on unseen tasks, whereas weight-based learning shows substantial gains. This opens the door to future weight-based continual learning that could teach models to drive harnesses in new domains.