Inverse Design

The rapid evolution of generative video foundation models has propelled the field toward professional-grade cinematic synthesis. To achieve such demanding quality, the community transitions towards Reinforcement Learning (RL) and agentic workflows. However, reliable evaluation has emerged as a critical bottleneck. Existing benchmarks predominantly evaluate ''whether it is right'' (basic prompt-following) while fundamentally neglecting ''whether it is good'' (cinematic quality, acting, and aesthetics). Furthermore, current automated metrics lack the domain-specific rigor required to provide trustworthy signals, creating a severe credibility gap between human aesthetic perception and machine scoring. To bridge this gap, we introduce EvalVerse, a comprehensive, pipeline-aware, and expert-calibrated evaluation framework. We treat video generation assessment not merely as an engineering task, but as a core scientific problem: the systematic digitization of subjective cinematic expertise. First, we organize domain knowledge into an evaluation taxonomy aligned with the professional filmmaking workflow (pre-production, production, and post-production). Second, we distill human expert judgments into a curated dataset with large-scale human annotations. Third, we inject this knowledge into Vision-Language Models (VLMs) through an expert-calibrated fine-tuning strategy, enabling the VLM to perform explicit Chain-of-Thought reasoning. Compared to previous works, EvalVerse not only retains compatibility with foundational ''rightness'' metrics, but also significantly expands the criteria to ''goodness'' and broaden the task coverage to complex multi-shot sequencing and audio-visual integration. Consequently, by providing granular diagnostic signals, EvalVerse transcends a static leaderboard and establishes a fundamental infrastructure for future work, such as reward models and evaluator agent.

We document inverse scaling in LLMs on forecasting problems whose underlying time series exhibit superlinear growth and tail risk of regime change, a structure common in finance and epidemiology. On these tasks, more capable models produce worse distributional forecasts. The pattern appears on ForecastBench-Sim (FBSim), a contamination-free, simulated-world benchmark we release, in forecasting synthetic SIR epidemics with a matched linear control, and replicates in real-world datasets on COVID-19, measles, housing markets, and hyperinflation. A per-quantile decomposition shows the failure concentrates at the upper tail, which more capable models shift upward to track aggressive extrapolations of growth, while the lower tail stays put. A within-family study of Llama-3.1 shows that both model scale and post-training independently contribute to this effect. Domain knowledge does not reliably rescue calibration. This inverse scaling does not appear on single-threshold metrics common in LLM forecasting benchmarks, reversing the sign of the capability--accuracy relationship on identical outputs. Single-threshold scoring at conventional cutoffs misses the upper-tail cost; tail-inclusive scoring reverses the sign of the capability--accuracy relationship on the same outputs. We recommend that LLM forecasting evaluations use continuous (and unbounded) measures of accuracy alongside bounded binary threshold metrics.

Solving inverse partial differential equation (PDE) problems is a fundamental topic in scientific research due to its broad significance across a wide range of real-world applications. Inverse PDE problems arise across medical imaging, geophysics, materials science, and aerodynamics, where the goal is to infer hidden causes, design structures, or control physical states. In this paper, we provide a comprehensive review of recent advances in solving inverse PDE problems using artificial intelligence (AI). We first introduce the basic formulation, key challenges, and traditional numerical foundations of inverse PDE problems, and then organize it into three major categories: inverse problems, inverse design, and control problems. For each category, we further present a methodological paradigms, and review representative state-of-the-art approaches from recent years. We then summarize representative applications across scientific and industrial domains, including mechanical systems, aerodynamic problems, thermal systems, full-waveform inversion, system identification, and medical imaging. Finally, we discuss open challenges and future prospects, such as physics-informed architectures, limited real-world data, uncertainty quantification, and inverse foundation models. This survey aims to provide the first unified and systematic perspective on AI for inverse PDE problems, demonstrating how modern learning-based methods are reshaping inverse problems, inverse design, and control problems in PDE-governed systems.

We present VectraYX-Nano, a 41.95M-parameter decoder-only language model trained from scratch in Spanish for cybersecurity, with a Latin-American regional focus and native tool invocation via the Model Context Protocol (MCP). The model has four contributions. (i) Corpus: VectraYX-Sec-ES, a 170M-token Spanish corpus assembled by an eight-VM distributed pipeline at ~$25 USD of cloud compute and split into three curriculum phases (conversational 42M, cybersecurity 118M, offensive tooling 10M). (ii) Architecture: a 42M Transformer decoder with GQA, QK-Norm, RMSNorm, SwiGLU, RoPE and z-loss, paired with a domain-balanced 16,384-token byte-fallback BPE. (iii) Curriculum with replay across the three phases yields a monotonic loss descent (9.80 -> 3.17 -> 3.00 -> 2.16); after SFT (loss 1.74) the v2 bootstrap-ablation reference attains a conversational gate of 0.775 +/- 0.043 on B5 over N=4 seeds, and a controlled Phase-2 replay sweep over {0,5,10,25,50}% saturates B5 at >=25% replay. (iv) Two empirical findings, both N=4. A controlled bootstrap-corpus ablation across v2 (OpenSubs), v4 (mC4-ES), and v6 (60/25/15 OpenSubs/mC4/Wiki) exposes a loss-versus-register inversion: lower-perplexity bootstraps yield measurably worse conversational behavior (v2 > v4 > v6 on B5 at every paired seed). The B4 (tool-selection) floor of 0.000 is a corpus-density artifact, not a capacity gate: rebalancing the SFT mixture to tool-use ratio 1:21 yields VectraYX-Nano v7, the released headline configuration, reaching B4 = 0.230 +/- 0.052 at 42M while retaining B1 = 0.332 +/- 0.005 and B5 = 0.725 +/- 0.130; a LoRA replication on a 260M from-scratch mid-tier reaches 0.445 +/- 0.201. The released GGUF is 96 MB in F16, runs sub-second TTFT on commodity hardware under llama.cpp, and is, to our knowledge, the first published Spanish-native cybersecurity LLM with end-to-end MCP integration.

Recent advances in AI have been primarily driven by large-scale neural architectures that excel at function approximation, rather than by tailored inductive biases and inference or learning strategies that could be important for resource-efficient real-world perception and planning through the solution of inverse problems. In this work, we consider the possibility of enabling robust inversion of continuous forward processes $p \mapsto y$ by learning representations of $y$ that are bijectively aligned with $p$ while remaining insensitive to perturbations in $y$ caused by noise or model mismatch. We propose Twincher, a class of architectures based on stacks of structured diffeomorphic transformations and tailored adversarial training strategies that enable learning such bijective representations. We provide a public API for training and inference and empirically demonstrate the ability of the proposed architecture to efficiently learn bijective representations of synthetic systems, thereby enabling robust and efficient iterative inverse inference. Compared to a baseline inverse-modeling approach, the method exhibits improved data efficiency and robustness, providing initial evidence for the potential of bijective representation learning in robotics, vision, and physical AI.

Nonlinear inverse problems often trade inexpensive but fragile first-order updates against curvature-aware methods such as Gauss-Newton and Levenberg-Marquardt, which obtain stronger directions by repeatedly solving Jacobian-based linearized systems. We propose a learned alternative: amortize local inverse geometry into a reusable reverse operator. Our framework learns a bidirectional surrogate, Deceptron, and deploys it through D-IPG (Deceptron Inverse-Preconditioned Gradient), an iterative solver that pulls residual-corrected measurement-space proposals back to latent space. The key mechanism is a Jacobian Composition Penalty (JCP), which trains the reverse Jacobian to act as a local left inverse of the forward Jacobian; its runtime counterpart, RJCP, measures the same inverse-consistency error along optimization trajectories. We prove that D-IPG is first-order equivalent to damped Gauss-Newton under local pseudoinverse consistency, with deviation controlled by composition error and conditioning. Across seven PDE inverse-problem benchmarks, D-IPG outperforms standard baselines, achieves 94.8% mean success across the six-problem reliability suite, and reaches comparable or better recovery quality at up to 77x lower inference-time solve cost on the main benchmarks.

Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect settings. Typical definitions of stability encompass the notion of ''convergent regularization'', robustness to out-of-distribution data, and to inaccuracies in the forward operator or noise model. We evaluate these properties numerically. Furthermore, we benchmark generative approaches against modern optimization-based methods inspired by the widely used variational techniques. Our results give insights for which settings and applications generative priors can deliver state-of-the-art reconstructions, and on those in which they fall short or may even be problematic.

Machine learning-based simulators offer the potential to model the dynamics of complex systems more efficiently than classical approaches, while retaining differentiability, a key property for materials design. Graph neural network (GNN)-based simulators have shown strong performance across a range of physical domains, including molecular dynamics. However, their reliance on temporal context for accurate prediction limits their use in inverse design settings, where simulations must be initialized from a single static configuration. Moreover, inverse design requires robust out-of-distribution (OOD) generalization, as candidate structures typically lie outside the training domain. Here, we address both challenges by introducing two complementary strategies that enable stable and accurate structure-only initialization of GNN-based simulations. To directly target OOD generalization, we propose an inference-time physics-based optimization framework that constrains model predictions to remain physically consistent during rollout. In addition, we introduce a differentiable, GNN-based barostat that enables accurate tracking of system dimensions and pressure, critical for capturing macroscopic responses and supporting OOD generalization. We evaluate these approaches in the context of uniaxial compression of disordered elastic networks spanning a broad range of geometries, Poisson ratios, and microscopic behaviors. We find that, together, these methods substantially improve rollout stability and enable reliable OOD generalization, including regimes with distinct, more complex dynamics than those in the training data. These results show that, when properly initialized and constrained, GNN-based simulators can serve as efficient and generalizable tools for materials discovery and structural optimization, advancing their use in materials, molecular, and dynamical system design.

Programming the static friction of mechanical interfaces is critical for soft robotics, haptics, and precision gripping. Static friction is governed by the real contact area, and standard rough surfaces exhibit a linear area-load scaling inherent to classical Archard and Greenwood-Williamson models, severely restricting their functional range. Here, we propose a framework for the inverse design of tribological metainterfaces engineered for programmable contact behaviors. By utilizing general axisymmetric asperities, we unlock nonlinear macroscopic responses unattainable by standard Hertzian contacts. To solve the inverse problem, we embed a fully differentiable contact mechanics engine within a neural network and a quadratic optimizer. We leverage regularized physical gradients to automatically discover non-standard topographies that reproduce complex target friction laws, with only a few asperities in unit cells. The predicted designs are strictly validated against high-fidelity Boundary Element Method (BEM) simulations. This framework bridges data-driven optimization and rigorous physics, offering a scale-invariant pathway for discovering functional tribological surfaces.

Generative models are powerful tools for sampling from a learned distribution $\mathcal{P}(Y \mid X)$, and inverse-design methods invert this map to find an input $x$ that produces a desired point output $y^*$. However, many design goals are naturally distributional rather than pointwise, incorporating the inherent uncertainty of $Y$ and targeting a specific form for it, a task not addressed by standard inverse design. To address this issue we introduce Conditional Distribution Matching (CDM), a new inverse-design problem class in generative modeling: given a joint distribution $\mathcal{P}(X, Y)$ and a target distribution $\mathcal{G}(Y)$, find an input $x^*$ whose induced conditional distribution $\mathcal{P}(Y \mid X = x^*)$ matches $\mathcal{G}$. We formally define two variants: Conditional Distribution Matching Sampling (CDMS) and Conditional Distribution Matching Optimization (CDMO). To solve these problems, we propose MLGD-F (Matching-Loss Guided Diffusion with a Fast inner sampler), a plug-and-play inference-time algorithm that combines a pretrained score-based diffusion model with a pretrained fast conditional sampler, requiring no additional training or fine-tuning. By leveraging single-step conditional sampling, MLGD-F enables tractable gradient computation, making the estimation of $\mathcal{P}(Y \mid X)$ both memory-efficient and computationally lightweight. We validate MLGD-F on synthetic benchmarks, structured image transformations, and generative editing optimization, demonstrating reliable recovery of inputs whose conditional distributions match diverse user-specified targets, including discrete mixtures and continuous low-rank supports.

Inverse design of RF passive components from S-parameters is a high-dimensional, ill-posed problem, and prior generative approaches are limited to single-layer binary-metallization structures. This paper presents an inverse design approach that generates passive components from partial S-parameter inputs on an $8\times8$ mm board discretized at $64\times64$ pixels with sub-pixel grayscale metallization across 1-20 GHz. The framework generates two-layer copper layouts with vias, with hard physical constraints on feed locations enforced through annealed Langevin projection, flexible multi-modal conditioning on partial S-parameter specifications, port locations, dielectric properties, reference topology, and variable port placement. Candidate designs are generated in seconds, with surrogate-predicted S-parameters matching targets to within $0.77 \pm 1.28$ dB weighted mean absolute error. We validate the approach with two fabricated designs on RO4003C: a manufacturable alternative to a hairpin filter whose coupling gaps violate fabrication rules, and a combline bandpass filter designed from scratch given only target S-parameters.

This work presents a deeper analysis of the "irreversibility" property of PolyProtect, a biometric template protection method initially proposed for securing face embeddings. PolyProtect transforms embeddings into protected templates via multivariate polynomials, whose coefficients and exponents are distinct for each subject enrolled in the face recognition system. A polynomial is applied to consecutive sets of elements from a given embedding, where the amount of overlap between the sets is a tunable parameter. We begin our irreversibility analysis by demonstrating that PolyProtected templates are easier to invert using a numerical solver based on cosine distance, as opposed to Euclidean distance (used in the earlier PolyProtect work). To make this inversion more difficult, we then propose a "key selection algorithm", which tries to choose "keys" (coefficients and exponents of the PolyProtect polynomial) that enhance the irreversibility of PolyProtected templates, compared to when the keys are purely random. Our experiments show that this algorithm is effective at generating PolyProtected templates that are significantly more difficult to invert, and that it approximately equalises the irreversibility of PolyProtected templates generated using different "overlap" parameters. This allows for better control of the irreversibility versus accuracy trade-off, known to exist across different overlaps. We also show that accuracy in the PolyProtected domain can be affected by the range in which the embedding elements lie, but that this can be improved by normalizing the embeddings prior to applying PolyProtect. This work is reproducible using our open-source code.

Propagation-based X-ray phase-contrast imaging (PBI) enables high-contrast visualization of lung structures and holds strong medical potential. However, safe translation to the clinic will require a substantial radiation dose reduction, which inevitably increases image noise. Supervised convolutional-neural-network-based denoising can restore image quality but depends on paired low- and high-dose datasets, which are rarely available in practice. Self-supervised methods avoid this limitation, yet most are not well adapted to the inverse problem of PBI computed tomography (CT). We introduce Neighbor2Inverse, a self-supervised denoising framework designed for low-dose PBI-CT that generalizes to clinical CT. Building on the Neighbor2Neighbor principle, each noisy projection is subsampled into two variants that preserve structural information but contain independent noise realizations. These are reconstructed separately, and the resulting pairs are used to train a denoising network directly in the image domain. We benchmark the proposed method against established analytical and self-supervised denoising approaches. In region-of-interest PBI CT experiments, Neighbor2Inverse achieves superior noise suppression while preserving fine structural details, as demonstrated by improved contrast-to-noise ratio, spatial resolution, and composite image quality metrics. Competitive performance is also observed on clinical CT data under simulated low-dose conditions. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Code, data, and interactive figures are available at https://github.com/J-3TO/Neighbor2Inverse.

Nonlinear dynamical systems with regime transitions are typically described by ordinary differential equations with jumping parameters parameters. Traditional methods often treat change-point detection and parameter estimation as separate tasks, ignoring the inherent coupling between them. To address this, we propose residual-loss anomaly analysis of physics-informed neural networks, a unified framework that leverages dynamical consistency within the physics-informed learning paradigm. This approach jointly infers piecewise parameters and transition points under a single set of constraints. The method follows a two-stage strategy: First, local physical residuals are analyzed through overlapping subinterval decomposition. When a subinterval spans a true transition point, the residual exhibits a distinct structural elevation in noise-free conditions, which has a non-zero lower bound, enabling effective localization of potential transition intervals. Second, within our framework, change-point locations and piecewise parameters are integrated into a unified physical loss function for joint optimization, enabling simultaneous identification. Experiments on benchmark nonlinear dynamical systems, including Malthusian and logistic growth models, Van der Pol oscillator, Lotka-Volterra model and Lorenz system, demonstrate that the proposed method outperforms traditional decoupled approaches in both change-point localization and parameter estimation accuracy. This study provides an efficient, unified solution for structurally coupled inverse problems in nonlinear dynamical systems with regime switching.

Large (vision-)language models exhibit remarkable capability but remain highly susceptible to jailbreaking. Existing safety training approaches aim to have the model learn a refusal boundary between safe and unsafe, based on the user's intent. It has been found that this binary training regime often leads to brittleness, since the user intent cannot reliably be evaluated, especially if the attacker obfuscates their intent, and also makes the system seem unhelpful. In response, frontier models, such as GPT-5, have shifted from refusal-based safeguards to safe completion, that aims to maximize helpfulness while obeying safety constraints. However, safe completion could be exploited when a user pretends their intention is benign. Specifically, this intent inversion would be effective in multi-turn conversation, where the attacker has multiple opportunities to reinforce their deceptively benign intent. In this work, we introduce a novel multi-turn jailbreaking method that exploits this vulnerability. Our approach gradually builds conversational trust by simulating benign-seeming intentions and by exploiting the consistency property of the model, ultimately guiding the target model toward harmful, detailed outputs. Most crucially, our approach also uncovered an additional class of model vulnerability that we call para-jailbreaking that has been unnoticed up to now. Para-jailbreaking describes the situation where the model may not reveal harmful direct reply to the attack query, however the information that it reveals is nevertheless harmful. Our contributions are threefold. First, it achieves high success rates against frontier models including GPT-5-thinking and Claude-Sonnet-4.5. Second, our approach revealed and addressed para-jailbreaking harmful output. Third, experiments on multimodal VLM models showed that our approach outperformed state-of-the-art models.

Preference-based argumentation frameworks (PAFs) extend Dung's approach to abstract argumentation (AAFs) by encoding preferences over arguments. Such preferences control the transformation of attacks into defeats, and different approaches to doing so result in different reductions from a PAF to an AAF. In this paper we consider a PAF inverse problem which takes an argumentation graph, a labelling and a semantics as an input, and outputs a yes" or no" as to whether there is a preference relation between the arguments which can yield the desired labelling. This inverse problem has applications in areas including preference elicitation and explainability. We consider this problem in the context of the four most widely-used preference based reductions under the complete semantics. We show that in most cases, the problem can be answered in polynomial time.

We study the deep image prior (DIP) framework applied to photoacoustic tomography (PAT) as an unsupervised reconstruction approach to mitigate limited-view artifacts and noise commonly encountered in experimental settings. Efficient implementation is achieved by employing recently published fast forward and adjoint algorithms for circular measurement geometries. Initialization via a fast inverse and total variation (TV) regularization are applied to further suppress noise and mitigate overfitting. For comparison, we compute a classical TV reconstruction. Our experiments comprise simulated PAT measurements under limited-view geometries and varying levels of added noise as well as experimental measurements together with using a digital twin for quality assessment. Our findings suggest that DIP framework provides an effective unsupervised strategy for robust PAT reconstruction even in the challenging case of a limited view geometry providing improvement in several quantitative measures over total variation reconstructions.

Digital marketplaces processing billions of dollars annually represent critical infrastructure in sociotechnical ecosystems, yet their performance optimization lacks principled measurement frameworks that can inform algorithmic governance decisions regarding market efficiency and fairness from complex market data. By looking at orderbook data from double auction markets alone, because bids and asks do not represent true maximum willingnesses to buy and true minimum willingnesses to sell, there is little an economist can say about the market's actual performance in terms of allocative efficiency. We turn to experimental data to address this issue, `inverting' the standard induced value approach of double auction experiments. Our aim is to predict key market features relevant to market efficiency, particularly allocative efficiency, using orderbook data only -- specifically bids, asks and price realizations, but not the induced reservation values -- as early as possible. Since there is no established model of strategically optimal behavior in these markets, and because orderbook data is highly unstructured, non-stationary and non-linear, we propose quantile-based normalization techniques that help us build general predictive models. We develop and train several models, including linear regressions and gradient boosting trees, leveraging quantile-based input from the underlying supply-demand model. Our models can predict allocative efficiency with reasonable accuracy from the earliest bids and asks, and these predictions improve with additional realized price data. The performance of the prediction techniques varies by target and market type. Our framework holds significant potential for application to real-world market data, offering valuable insights into market efficiency and performance, even prior to any trade realizations.

Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches, which have primarily addressed denoising and, more recently, linear inverse problems. We address nonlinear inverse problems and introduce SPLIT (Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography), a self-supervised machine-learning framework for reconstructing images from nonlinear, incomplete, and noisy projection data without any samples of ground-truth images. SPLIT enforces cross-partition consistency and measurement-domain fidelity while exploiting complementary information across multiple partitions. Our main theoretical result shows that, under mild conditions, the proposed self-supervised objective is equivalent to its supervised counterpart in expectation. We regularize training with an automatic stopping rule that halts optimization when a no-reference image-quality surrogate saturates. As a concrete application, we derive SPLIT variants for multispectral computed tomography. Experiments on sparse-view acquisitions demonstrate high reconstruction quality and robustness to noise, surpassing classical iterative reconstruction and recent self-supervised baselines.

Text-driven inversion of generative models is a core paradigm for manipulating 2D or 3D content, unlocking numerous applications such as text-based editing, style transfer, or inverse problems. However, it relies on the assumption that generative models remain sensitive to natural language prompts. We demonstrate that for state-of-the-art native text-to-3D generative models, this assumption often collapses. We identify a critical failure mode where generation trajectories are drawn into latent ``sink traps'': regions where the model becomes insensitive to prompt modifications. In these regimes, changes to the input text fail to alter internal representations in a way that alters the output geometry. Crucially, we observe that this is not a limitation of the model's \textit{geometric} expressivity; the same generative models possess the ability to produce a vast diversity of shapes but, as we demonstrate, become insensitive to out-of-distribution \textit{text} guidance. We investigate this behavior by analyzing the sampling trajectories of the generative model, and find that complex geometries can still be represented and produced by leveraging the model's unconditional generative prior. This leads to a more robust framework for text-based 3D shape editing that bypasses latent sinks by decoupling a model's geometric representation power from its linguistic sensitivity. Our approach addresses the limitations of current 3D pipelines and enables high-fidelity semantic manipulation of out-of-distribution 3D shapes. Project webpage: https://daidedou.sorpi.fr/publication/beyondprompts

Inverse design aims to find design parameters $x$ achieving target performance $y^*$. Generative approaches learn bidirectional mappings between designs and labels, enabling diverse solution sampling. However, standard conditional flow matching (CFM), when adapted to inverse problems by pairing labels with design parameters, exhibits strong sensitivity to their arbitrary ordering and scaling, leading to unstable training. We introduce Diagonal Flow Matching (Diag--CFM), which resolves this through a zero-anchoring strategy that pairs design coordinates with noise and labels with zero, making the learning problem provably invariant to coordinate permutations. This yields substantially lower round-trip error than CFM and invertible neural network baselines across design dimensions up to $P{=}784$, including order-of-magnitude gains on several benchmarks. We develop two architecture-intrinsic uncertainty metrics, Zero-Deviation and Self-Consistency, that enable three practical capabilities: selecting the best candidate among multiple generations, abstaining from unreliable predictions, and detecting out-of-distribution targets; consistently outperforming ensemble and general-purpose alternatives across all tasks. We validate on airfoil, gas turbine combustor, scalable analytical benchmarks, a photonics inverse-design task, and an image-statistics benchmark.

Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of parameter-dependent high-dimensional dynamical systems is crucial in many applications in engineering and applied sciences. A popular class of projection-based ROMs projects the high-dimensional full-order model (FOM) dynamics onto a low-dimensional manifold. These projection-based ROMs approaches often rely on classical model reduction techniques such as proper orthogonal decomposition (POD) or, more recently, on neural network architectures such as autoencoders (AEs). In the case that the ROM is constructed by the POD, one has approximation guaranteed based based on the singular values of the problem at hand. However, POD-based techniques can suffer from slow decay of the singular values in transport- and advection-dominated problems. In contrast to that, AEs allow for better reduction capabilities than the POD, often with the first few modes, but at the price of theoretical considerations. In addition, it is often observed, that AEs exhibits a plateau of the projection error with the increment of the dimension of the trial manifold. In this work, we propose an invertible AE architecture, named inv-AE, that computationally improves upon the stagnation of the reconstruction error typical of traditional AE architectures. Inv-AE is composed of several invertible neural network layers that allows for gradually recovering more information about the FOM solutions the more we increase the dimension of the reduced manifold. Through the application of inv-AE to a 1-dimensional Burgers' equation, a 2-dimensional fluid flow around an obstacle with variable geometry, and a 3-dimensional Korteweg-de Vries, we show that (i) inv-AE mitigates the issue of the characteristic plateau of AEs and (ii) inv-AE can be combined with popular autoencoder-based ROM approaches, e.g., DL-ROM, to improve their accuracy.

Generalizing skill policies to novel conditions remains a key challenge in robot learning. Imitation learning methods, while data-efficient, are largely confined to the training region and consistently fail on input data outside it, leading to unpredictable policy failures. Alternatively, transfer learning approaches offer methods for trajectory generation robust to both changes in environment and tasks, but they remain data-hungry and lack accuracy in zero-shot generalization. We address these challenges in the context of task inversion learning and propose a novel joint learning approach to achieve accurate and efficient knowledge transfer. Our method constructs a common representation of the forward and inverse tasks, and leverages auxiliary forward demonstrations from novel configurations to successfully execute the corresponding inverse tasks, without any direct supervision. We demonstrate the extrapolation capabilities of our framework through ablation studies and experiments in simulated and real-world environments that require complex manipulation skills with a diverse set of objects and tools, where we outperform diffusion-based and multimodal VAE alternatives.

How does irrelevant information (i.e., distractors) affect test-time scaling in vision-language models (VLMs)? Prior work on text-only language models has shown that textual distractors can intensify inverse scaling, causing models to reason longer but less effective reasoning traces. In this work, we investigate whether similar phenomena arise in multimodal settings. We introduce Idis (Images with distractors), a visual question-answering dataset that systematically varies distractors along semantic and numerical dimensions. Our analyses reveal that visual distractors affect reasoning VLMs in a fundamentally different way from textual distractors: although inverse scaling still emerges, visual distractors reduce accuracy without increasing reasoning length. We further show that attribute counts extracted from reasoning traces provide key insights into how distractors interact with reasoning length and accuracy. As a sanity check, we propose a simple prompting strategy that mitigates distractor-driven predictions in reasoning vision-language models.

Understanding the internal representations of large language models (LLMs) is a central challenge in interpretability research. Existing feature interpretability methods often rely on strong structural assumptions--such as linearity or sparsity--that may not hold in practice. In this work, we introduce InverseScope, an assumption-light and scalable framework for interpreting neural activations via input inversion. Given a target activation, InverseScope characterizes its encoded information by generating natural-language inputs that produce nearby activations, grounding abstract internal states in concrete language. To overcome the prohibitive cost of sampling in high-dimensional activation spaces, we propose a novel control-layer conditioning architecture that substantially improves sample efficiency compared to prior token-prepending approaches. We demonstrate that InverseScope reveals rich geometric structure in LLM representation spaces, including sentence-level linear analogies. The framework scales to state-of-the-art open-source models of up to 14B parameters and generalizes to out-of-distribution inputs, enabling systematic analysis of activation neighborhoods.

We present a stroke design in which strokes are transport-coupled: each stroke deposits material of its own area and moves every earlier mark without changing its area, so later strokes deform earlier ones. We then solve the inverse problem under this design: given a target image, we optimise an ordered program of such strokes whose replay approximates it, with digital marbling as the motivating medium. The stroke is a capsule that continuously joins circular drops to drawn deposits; its transport is exactly area-preserving, with a closed-form inverse outside the deposit, and a variant with the same inverse differs from line-source potential flow by 8% of the mean displacement. A replay adjoint regenerates intermediate states instead of storing them and uses 8.7x less memory than checkpointed automatic differentiation; a fused implementation fits a 2000-stroke program at 1024x1024 in about four minutes on one GPU. On five marbled sheets the recovered programs are level with a published stroke-based fitter as rasters, replay across a fourfold resolution range, and support edits in program order and palette space that stay valid under transport.