Daily Papers

Molecular dynamics (MD) is a central computational tool in physics, chemistry, and biology, enabling quantitative prediction of experimental observables as expectations over high-dimensional molecular distributions such as Boltzmann distributions and transition densities. However, conventional MD is fundamentally limited by the high computational cost required to generate independent samples. Generative molecular dynamics (GenMD) has recently emerged as an alternative, learning surrogates of molecular distributions either from data or through interaction with energy models. While these methods enable efficient sampling, their transferability across molecular systems is often limited. In this work, we show that incorporating auxiliary sources of information can improve the data efficiency and generalization of transferable implicit transfer operators (TITO) for molecular dynamics. We find that coarse-grained TITO models are substantially more data-efficient than Boltzmann Emulators, and that incorporating protein language model (pLM) embeddings further improves out-of-distribution generalization. Our approach, PLaTITO, achieves state-of-the-art performance on equilibrium sampling benchmarks for out-of-distribution protein systems, including fast-folding proteins. We further study the impact of additional conditioning signals -- such as structural embeddings, temperature, and large-language-model-derived embeddings -- on model performance.

We develop a general theory of semantic dynamics for large language models by formalizing them as Continuous State Machines (CSMs): smooth dynamical systems whose latent manifolds evolve under probabilistic transition operators. The associated transfer operator P: L^2(M,μ) to L^2(M,μ) encodes the propagation of semantic mass. Under mild regularity assumptions (compactness, ergodicity, bounded Jacobian), P is compact with discrete spectrum. Within this setting, we prove the Semantic Characterization Theorem (SCT): the leading eigenfunctions of P induce finitely many spectral basins of invariant meaning, each definable in an o-minimal structure over R. Thus spectral lumpability and logical tameness coincide. This explains how discrete symbolic semantics can emerge from continuous computation: the continuous activation manifold collapses into a finite, logically interpretable ontology. We further extend the SCT to stochastic and adiabatic (time-inhomogeneous) settings, showing that slowly drifting kernels preserve compactness, spectral coherence, and basin structure.

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to learning the transfer operator or the generator of the system, which in turn can be used for numerous tasks, such as forecasting and interpreting the system dynamics. We show that the search for a good representation can be cast as an optimization problem over neural networks. Our approach is supported by recent results in statistical learning theory, highlighting the role of approximation error and metric distortion in the learning problem. The objective function we propose is associated with projection operators from the representation space to the data space, overcomes metric distortion, and can be empirically estimated from data. In the discrete-time setting, we further derive a relaxed objective function that is differentiable and numerically well-conditioned. We compare our method against state-of-the-art approaches on different datasets, showing better performance across the board.

kooplearn is a machine-learning library that implements linear, kernel, and deep-learning estimators of dynamical operators and their spectral decompositions. kooplearn can model both discrete-time evolution operators (Koopman/Transfer) and continuous-time infinitesimal generators. By learning these operators, users can analyze dynamical systems via spectral methods, derive data-driven reduced-order models, and forecast future states and observables. kooplearn's interface is compliant with the scikit-learn API, facilitating its integration into existing machine learning and data science workflows. Additionally, kooplearn includes curated benchmark datasets to support experimentation, reproducibility, and the fair comparison of learning algorithms. The software is available at https://github.com/Machine-Learning-Dynamical-Systems/kooplearn.

Improving diesel engine efficiency, reducing emissions, and enabling robust health monitoring have been critical research topics in engine modelling. While recent advancements in the use of neural networks for system monitoring have shown promising results, such methods often focus on component-level analysis, lack generalizability, and physical interpretability. In this study, we propose a novel hybrid framework that combines physics-informed neural networks (PINNs) with deep operator networks (DeepONet) to enable accurate and computationally efficient parameter identification in mean-value diesel engine models. Our method leverages physics-based system knowledge in combination with data-driven training of neural networks to enhance model applicability. Incorporating offline-trained DeepONets to predict actuator dynamics significantly lowers the online computation cost when compared to the existing PINN framework. To address the re-training burden typical of PINNs under varying input conditions, we propose two transfer learning (TL) strategies: (i) a multi-stage TL scheme offering better runtime efficiency than full online training of the PINN model and (ii) a few-shot TL scheme that freezes a shared multi-head network body and computes physics-based derivatives required for model training outside the training loop. The second strategy offers a computationally inexpensive and physics-based approach for predicting engine dynamics and parameter identification, offering computational efficiency over the existing PINN framework. Compared to existing health monitoring methods, our framework combines the interpretability of physics-based models with the flexibility of deep learning, offering substantial gains in generalization, accuracy, and deployment efficiency for diesel engine diagnostics.

Agentic Variation Operators (AVO) are a new family of evolutionary variation operators that replace the fixed mutation, crossover, and hand-designed heuristics of classical evolutionary search with autonomous coding agents. Rather than confining a language model to candidate generation within a prescribed pipeline, AVO instantiates variation as a self-directed agent loop that can consult the current lineage, a domain-specific knowledge base, and execution feedback to propose, repair, critique, and verify implementation edits. We evaluate AVO on attention, among the most aggressively optimized kernel targets in AI, on NVIDIA Blackwell (B200) GPUs. Over 7 days of continuous autonomous evolution on multi-head attention, AVO discovers kernels that outperform cuDNN by up to 3.5% and FlashAttention-4 by up to 10.5% across the evaluated configurations. The discovered optimizations transfer readily to grouped-query attention, requiring only 30 minutes of additional autonomous adaptation and yielding gains of up to 7.0% over cuDNN and 9.3% over FlashAttention-4. Together, these results show that agentic variation operators move beyond prior LLM-in-the-loop evolutionary pipelines by elevating the agent from candidate generator to variation operator, and can discover performance-critical micro-architectural optimizations that produce kernels surpassing state-of-the-art expert-engineered attention implementations on today's most advanced GPU hardware.

Transformer-based neural operators have achieved substantial progress in solving Partial Differential Equations (PDEs) by projecting spatial observations into compact latent tokens and learning physical interactions in latent spaces. However, we reveal that existing learnable projection mechanisms cannot ensure stable and balanced assignments from observation points to latent tokens, causing some latent tokens to be over-assigned while others remain underutilized. This limitation further restricts the design of hierarchical architectures, as assignment imbalance is continuously inherited and amplified across latent spaces, eventually causing severe token collapse in deeper spaces. To address these issues, we propose MoNo (Multiscale Optimal Transport Neural Operator), a progressive multiscale neural operator that efficiently solves PDEs on general geometries through stable latent-space construction. At its core is CoTAP (Cross-scale Optimal Transport Assignment and Projection), a novel latent-space construction method that formulates cross-space assignment between adjacent spaces as an entropy-regularized optimal transport problem, thereby constructing balanced bidirectional projections and stable latent spaces. CoTAP also ensures stable information transfer across multiple latent spaces, further enabling multiscale architectures on general geometries, which in turn support more efficient learning of long-range physical interactions. Extensive experiments demonstrate that MoNo outperforms existing state-of-the-art neural operators in both prediction performance and computational efficiency. Code is available at https://github.com/ZijiangY1116/MoNo.

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.

Training large models from scratch usually costs a substantial amount of resources. Towards this problem, recent studies such as bert2BERT and LiGO have reused small pretrained models to initialize a large model (termed the ``target model''), leading to a considerable acceleration in training. Despite the successes of these previous studies, they grew pretrained models by mapping partial weights only, ignoring potential correlations across the entire model. As we show in this paper, there are inter- and intra-interactions among the weights of both the pretrained and the target models. As a result, the partial mapping may not capture the complete information and lead to inadequate growth. In this paper, we propose a method that linearly correlates each weight of the target model to all the weights of the pretrained model to further enhance acceleration ability. We utilize multi-linear operators to reduce computational and spacial complexity, enabling acceptable resource requirements. Experiments demonstrate that our method can save 76\% computational costs on DeiT-base transferred from DeiT-small, which outperforms bert2BERT by +12.0\% and LiGO by +20.7\%, respectively.

The dominant approach to unsupervised "style transfer" in text is based on the idea of learning a latent representation, which is independent of the attributes specifying its "style". In this paper, we show that this condition is not necessary and is not always met in practice, even with domain adversarial training that explicitly aims at learning such disentangled representations. We thus propose a new model that controls several factors of variation in textual data where this condition on disentanglement is replaced with a simpler mechanism based on back-translation. Our method allows control over multiple attributes, like gender, sentiment, product type, etc., and a more fine-grained control on the trade-off between content preservation and change of style with a pooling operator in the latent space. Our experiments demonstrate that the fully entangled model produces better generations, even when tested on new and more challenging benchmarks comprising reviews with multiple sentences and multiple attributes.

Despite recent progress in optimal hyperparameter transfer under model and dataset scaling, no unifying explanatory principle has been established. Using the Scion optimizer, we discover that joint optimal scaling across model and dataset sizes is governed by a single invariant: the operator norm of the output layer. Across models with up to 1.3B parameters trained on up to 138B tokens, the optimal learning rate/batch size pair (eta^{ast}, B^{ast}) consistently has the same operator norm value - a phenomenon we term norm transfer. This constant norm condition is necessary but not sufficient: while for each dataset size, multiple (eta, B) reach the optimal norm, only a unique (eta^{ast}, B^{ast}) achieves the best loss. As a sufficient condition, we provide the first measurement of (eta^{ast}, B^{ast}) scaling with dataset size for Scion, and find that the scaling rules are consistent with those of the Adam optimizer. Tuning per-layer-group learning rates also improves model performance, with the output layer being the most sensitive and hidden layers benefiting from lower learning rates. We provide practical insights on norm-guided optimal scaling and release our Distributed Scion (Disco) implementation with logs from over two thousand runs to support research on LLM training dynamics at scale.

Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly. However, most existing studies remain in 2D, while 3D turbulence has fundamentally different physics and is far more costly to simulate. Existing 3D resources also typically provide only one realization per configuration, making it difficult to distinguish learning the dynamics from fitting the statistics of a single flow. In this paper, we introduce TIDE (Turbulent Incompressible DNS Ensembles), a 256^3 DNS corpus and benchmark for 3D incompressible turbulence, with 15 configurations on eight controlled axes, independent ensembles, pressure fields, and equation-level verification. The benchmark includes five tasks, standardized learned baselines, controlled generalization splits, and physical-fidelity metrics alongside pointwise error. Across the main forecasting configurations, current learned models barely outperform persistence and still make about twice the error of a spectral solver given the true equations. Moreover, lower pointwise error can coincide with severely distorted small-scale dynamics, showing that accuracy alone does not ensure physical fidelity. Generalization results further show that most regime shifts reflect limited training coverage, whereas forced-to-decay transfer exposes a missing conditioning variable: operators trained under forcing continue to predict driven evolution when the external drive is removed. Closing these accuracy, fidelity, and conditioning gaps is the central open problem made measurable by TIDE.

Supervised fine-tuning (SFT) data selection is commonly formulated as instance ranking: score each example and retain a top-k subset. However, effective SFT training subsets are often produced through ordered curation recipes, where filtering, mixing, and deduplication operators jointly shape the final data distribution. We formulate this problem as fixed-pool data recipe search: given a raw instruction pool and a library of grounded operators, the goal is to discover an executable recipe that constructs a high-quality selected subset under a limited budget of full SFT evaluations, without generating, rewriting, or augmenting training samples. We introduce AutoSelection, a two-layer solver that decouples fixed-pool materialization based on cached task-, data-, and model-side signals from expensive full evaluation, using warmup probes, realized subset states, local recipe edits, Gaussian-process-assisted ranking, and stagnation-triggered reseeding. Experiments on a 90K instruction pool show that AutoSelection achieves the strongest in-distribution reasoning average across three base models, outperforming full-data training, random recipe search, random top-k, and single-operator selectors. Additional Out-of-distribution graph-reasoning results, search-stability analyses, structural ablations, and 1.5B-to-7B transfer checks further show that recipe structure matters beyond individual selection operators. Code is available at https://github.com/w253/AutoSelection.

Low Earth orbit (LEO) satellite constellations bring broadband internet and cellular service to the most remote locations on the planet. Unfortunately, many of these locations also host some of the world's best optical and radio astronomy (RA) observatories. With the number of LEO satellites expected to increase by an order of magnitude in the upcoming decade, satellite downlink radio frequency interference (RFI) is a growing concern in protected radio-quiet areas like the United States National Radio Quiet Zone. When these satellites transmit in the spectrum near protected RA bands, undesired out-of-band emission can leak into these protected bands and impact scientific observations. In this paper, we present a self-reporting system - Operational Data Sharing (ODS) - which enables mutual awareness by publishing radio telescopes' operational information to a protected database that is available to satellite operators through a representational state transfer application programming interface (REST API). Satellite operators can use the ODS data to adapt their downlink tasking algorithms in real time to avoid overwhelming sensitive RA facilities, particularly, through the novel Telescope Boresight Avoidance (TBA) technique. Preliminary results from recent experiments between the NRAO and the SpaceX Starlink teams demonstrate the effectiveness of the ODS and TBA in reducing downlink RFI in the Karl G. Jansky Very Large Array's observations in the 1990-1995 MHz and 10.7-12.7 GHz bands. This automated ODS system is beginning to be implemented by other RA facilities and could be utilized by other satellite operators in the near future.

At present, different deep learning models are presenting high accuracy on popular inference datasets such as SNLI, MNLI, and SciTail. However, there are different indicators that those datasets can be exploited by using some simple linguistic patterns. This fact poses difficulties to our understanding of the actual capacity of machine learning models to solve the complex task of textual inference. We propose a new set of syntactic tasks focused on contradiction detection that require specific capacities over linguistic logical forms such as: Boolean coordination, quantifiers, definite description, and counting operators. We evaluate two kinds of deep learning models that implicitly exploit language structure: recurrent models and the Transformer network BERT. We show that although BERT is clearly more efficient to generalize over most logical forms, there is space for improvement when dealing with counting operators. Since the syntactic tasks can be implemented in different languages, we show a successful case of cross-lingual transfer learning between English and Portuguese.

Transfer learning leverages feature representations of deep neural networks (DNNs) pretrained on source tasks with rich data to empower effective finetuning on downstream tasks. However, the pretrained models are often prohibitively large for delivering generalizable representations, which limits their deployment on edge devices with constrained resources. To close this gap, we propose a new transfer learning pipeline, which leverages our finding that robust tickets can transfer better, i.e., subnetworks drawn with properly induced adversarial robustness can win better transferability over vanilla lottery ticket subnetworks. Extensive experiments and ablation studies validate that our proposed transfer learning pipeline can achieve enhanced accuracy-sparsity trade-offs across both diverse downstream tasks and sparsity patterns, further enriching the lottery ticket hypothesis.

Transfer learning is a popular method for tuning pretrained (upstream) models for different downstream tasks using limited data and computational resources. We study how an adversary with control over an upstream model used in transfer learning can conduct property inference attacks on a victim's tuned downstream model. For example, to infer the presence of images of a specific individual in the downstream training set. We demonstrate attacks in which an adversary can manipulate the upstream model to conduct highly effective and specific property inference attacks (AUC score > 0.9), without incurring significant performance loss on the main task. The main idea of the manipulation is to make the upstream model generate activations (intermediate features) with different distributions for samples with and without a target property, thus enabling the adversary to distinguish easily between downstream models trained with and without training examples that have the target property. Our code is available at https://github.com/yulongt23/Transfer-Inference.

Transfer learning is a classic paradigm by which models pretrained on large "upstream" datasets are adapted to yield good results on "downstream" specialized datasets. Generally, more accurate models on the "upstream" dataset tend to provide better transfer accuracy "downstream". In this work, we perform an in-depth investigation of this phenomenon in the context of convolutional neural networks (CNNs) trained on the ImageNet dataset, which have been pruned - that is, compressed by sparsifying their connections. We consider transfer using unstructured pruned models obtained by applying several state-of-the-art pruning methods, including magnitude-based, second-order, re-growth, lottery-ticket, and regularization approaches, in the context of twelve standard transfer tasks. In a nutshell, our study shows that sparse models can match or even outperform the transfer performance of dense models, even at high sparsities, and, while doing so, can lead to significant inference and even training speedups. At the same time, we observe and analyze significant differences in the behaviour of different pruning methods.

In this work, we explore the possibility of utilizing transfer learning techniques to address the financial portfolio optimization problem. We introduce a novel concept called "transfer risk", within the optimization framework of transfer learning. A series of numerical experiments are conducted from three categories: cross-continent transfer, cross-sector transfer, and cross-frequency transfer. In particular, 1. a strong correlation between the transfer risk and the overall performance of transfer learning methods is established, underscoring the significance of transfer risk as a viable indicator of "transferability"; 2. transfer risk is shown to provide a computationally efficient way to identify appropriate source tasks in transfer learning, enhancing the efficiency and effectiveness of the transfer learning approach; 3. additionally, the numerical experiments offer valuable new insights for portfolio management across these different settings.

Working over infinite dimensional separable Hilbert spaces, residual results have been achieved for the space of contractive C_{0}-semigroups under the topology of uniform weak operator convergence on compact subsets of R_{+}. Eisner and Serény raised in 2009 the open problem: Does this space constitute a Baire space? Observing that the subspace of unitary semigroups is completely metrisable and appealing to known density results, we solve this problem positively by showing that certain topological properties can in general be transferred from dense subspaces to larger spaces. The transfer result in turn relies upon classification of topological properties via infinite games. Our approach is sufficiently general and can be applied to other contexts, e.g. the space of contractions under the pw-topology.

The residual stream mediates communication between transformer decoder layers via linear reads and writes of non-linear computations. While sparse-dictionary learning-based methods locate features in the residual stream, and activation patching methods discover circuits within the model, the mechanism by which features flow through the residual stream remains understudied. Understanding this dynamic can better inform jailbreaking protections, enable early detection of model mistakes, and their correction. In this work, we propose Activation Transport Operators (ATO), linear maps from upstream to downstream residuals k layers later, evaluated in feature space using downstream SAE decoder projections. We empirically demonstrate that these operators can determine whether a feature has been linearly transported from a previous layer or synthesised from non-linear layer computation. We develop the notion of transport efficiency, for which we provide an upper bound, and use it to estimate the size of the residual stream subspace that corresponds to linear transport. We empirically demonstrate the linear transport, report transport efficiency and the size of the residual stream's subspace involved in linear transport. This compute-light (no finetuning, <50 GPU-h) method offers practical tools for safety, debugging, and a clearer picture of where computation in LLMs behaves linearly.

Given a set of pre-trained models, how can we quickly and accurately find the most useful pre-trained model for a downstream task? Transferability measurement is to quantify how transferable is a pre-trained model learned on a source task to a target task. It is used for quickly ranking pre-trained models for a given task and thus becomes a crucial step for transfer learning. Existing methods measure transferability as the discrimination ability of a source model for a target data before transfer learning, which cannot accurately estimate the fine-tuning performance. Some of them restrict the application of transferability measurement in selecting the best supervised pre-trained models that have classifiers. It is important to have a general method for measuring transferability that can be applied in a variety of situations, such as selecting the best self-supervised pre-trained models that do not have classifiers, and selecting the best transferring layer for a target task. In this work, we propose TMI (TRANSFERABILITY MEASUREMENT WITH INTRA-CLASS FEATURE VARIANCE), a fast and accurate algorithm to measure transferability. We view transferability as the generalization of a pre-trained model on a target task by measuring intra-class feature variance. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. Compared to previous studies that estimate how discriminative the models are, intra-class variance is more accurate than those as it does not require an optimal feature extractor and classifier. Extensive experiments on real-world datasets show that TMI outperforms competitors for selecting the top-5 best models, and exhibits consistently better correlation in 13 out of 17 cases.

Transfer learning is a widely-used paradigm in deep learning, where models pre-trained on standard datasets can be efficiently adapted to downstream tasks. Typically, better pre-trained models yield better transfer results, suggesting that initial accuracy is a key aspect of transfer learning performance. In this work, we identify another such aspect: we find that adversarially robust models, while less accurate, often perform better than their standard-trained counterparts when used for transfer learning. Specifically, we focus on adversarially robust ImageNet classifiers, and show that they yield improved accuracy on a standard suite of downstream classification tasks. Further analysis uncovers more differences between robust and standard models in the context of transfer learning. Our results are consistent with (and in fact, add to) recent hypotheses stating that robustness leads to improved feature representations. Our code and models are available at https://github.com/Microsoft/robust-models-transfer .

In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural operator as follows: the output of the i-th neuron in a nonlinear operator layer is defined by mathcal O_i(u) = sigmaleft( sum_j mathcal W_{ij} u + mathcal B_{ij}right). Here, mathcal W_{ij} denotes the bounded linear operator connecting j-th input neuron to i-th output neuron, and the bias mathcal B_{ij} takes the form of a function rather than a scalar. Given its new universal approximation property, the efficient parameterization of the bounded linear operators between two neurons (Banach spaces) plays a critical role. As a result, we introduce MgNO, utilizing multigrid structures to parameterize these linear operators between neurons. This approach offers both mathematical rigor and practical expressivity. Additionally, MgNO obviates the need for conventional lifting and projecting operators typically required in previous neural operators. Moreover, it seamlessly accommodates diverse boundary conditions. Our empirical observations reveal that MgNO exhibits superior ease of training compared to other CNN-based models, while also displaying a reduced susceptibility to overfitting when contrasted with spectral-type neural operators. We demonstrate the efficiency and accuracy of our method with consistently state-of-the-art performance on different types of partial differential equations (PDEs).

One desired capability for machines is the ability to transfer their knowledge of one domain to another where data is (usually) scarce. Despite ample adaptation of transfer learning in various deep learning applications, we yet do not understand what enables a successful transfer and which part of the network is responsible for that. In this paper, we provide new tools and analyses to address these fundamental questions. Through a series of analyses on transferring to block-shuffled images, we separate the effect of feature reuse from learning low-level statistics of data and show that some benefit of transfer learning comes from the latter. We present that when training from pre-trained weights, the model stays in the same basin in the loss landscape and different instances of such model are similar in feature space and close in parameter space.

Neural operators learn to map initial conditions to the terminal solution of partial differential equations (PDEs), providing a surrogate for the full operator mapping. This enables rapid prediction across different input configurations. While recent neural operator architectures have demonstrated strong performance on diverse PDE tasks, their behavior under structured distribution shifts remains insufficiently understood. To investigate this, we study operator learning in a wave propagation setting governed by a one-dimensional variable-coefficient wave equation, using two representative architectures, the Fourier Neural Operator (FNO) and the Deep Operator Network (DeepONet). To examine their generalization under distribution shifts, we consider structured out-of-distribution (OOD) settings that independently vary input frequency and coefficient smoothness. The results show that under smoothness shifts, both models maintain stable performance, with FNO achieving lower error. In contrast, under frequency shifts, FNO exhibits a sharp increase in error under unseen high-frequency inputs, whereas DeepONet shows milder degradation despite higher overall error. Our analysis reveals that these differences arise from how each architecture represents and responds to variations in frequency structure. Together, these findings highlight a fundamental gap between strong in-distribution performance and generalization under distribution shifts in operator learning, underscoring the role of architectural representation bias in developing more reliable neural operators for physics-based PDE simulations beyond the training distribution.

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional machine learning to address issues such as data sparsity and overfitting in neural networks. In this work, we apply MTL to problems in science and engineering governed by partial differential equations (PDEs). However, implementing MTL in this context is complex, as it requires task-specific modifications to accommodate various scenarios representing different physical processes. To this end, we present a multi-task deep operator network (MT-DeepONet) to learn solutions across various functional forms of source terms in a PDE and multiple geometries in a single concurrent training session. We introduce modifications in the branch network of the vanilla DeepONet to account for various functional forms of a parameterized coefficient in a PDE. Additionally, we handle parameterized geometries by introducing a binary mask in the branch network and incorporating it into the loss term to improve convergence and generalization to new geometry tasks. Our approach is demonstrated on three benchmark problems: (1) learning different functional forms of the source term in the Fisher equation; (2) learning multiple geometries in a 2D Darcy Flow problem and showcasing better transfer learning capabilities to new geometries; and (3) learning 3D parameterized geometries for a heat transfer problem and demonstrate the ability to predict on new but similar geometries. Our MT-DeepONet framework offers a novel approach to solving PDE problems in engineering and science under a unified umbrella based on synergistic learning that reduces the overall training cost for neural operators.

Transfer learning is widely used for training deep neural networks (DNN) for building a powerful representation. Even after the pre-trained model is adapted for the target task, the representation performance of the feature extractor is retained to some extent. As the performance of the pre-trained model can be considered the private property of the owner, it is natural to seek the exclusive right of the generalized performance of the pre-trained weight. To address this issue, we suggest a new paradigm of transfer learning called disposable transfer learning (DTL), which disposes of only the source task without degrading the performance of the target task. To achieve knowledge disposal, we propose a novel loss named Gradient Collision loss (GC loss). GC loss selectively unlearns the source knowledge by leading the gradient vectors of mini-batches in different directions. Whether the model successfully unlearns the source task is measured by piggyback learning accuracy (PL accuracy). PL accuracy estimates the vulnerability of knowledge leakage by retraining the scrubbed model on a subset of source data or new downstream data. We demonstrate that GC loss is an effective approach to the DTL problem by showing that the model trained with GC loss retains the performance on the target task with a significantly reduced PL accuracy.

Transferability is the property of adversarial examples to be misclassified by other models than the surrogate model for which they were crafted. Previous research has shown that early stopping the training of the surrogate model substantially increases transferability. A common hypothesis to explain this is that deep neural networks (DNNs) first learn robust features, which are more generic, thus a better surrogate. Then, at later epochs, DNNs learn non-robust features, which are more brittle, hence worst surrogate. First, we tend to refute this hypothesis, using transferability as a proxy for representation similarity. We then establish links between transferability and the exploration of the loss landscape in parameter space, focusing on sharpness, which is affected by early stopping. This leads us to evaluate surrogate models trained with seven minimizers that minimize both loss value and loss sharpness. Among them, SAM consistently outperforms early stopping by up to 28.8 percentage points. We discover that the strong SAM regularization from large flat neighborhoods tightly links to transferability. Finally, the best sharpness-aware minimizers prove competitive with other training methods and complement existing transferability techniques.

Subliminal learning lets a student inherit a teacher's hidden trait from distillation data that never names it. We ask when such transfer can be audited before training. The answer is not model identity or scale alone, but channel location: the carrier through which the trait reaches the student. We find three regimes. In a controlled initialization-dependent body channel, a pre-training screen works. Coverage, the cosine between the student's initial distillation update and the teacher's fine-tuning displacement, predicts held-out transfer (Spearman ρapprox 0.95; AUROC 0.997). In pretrained language models, masked single-token traits instead ride convergent vocabulary geometry. This channel is initialization-independent, so initialization-alignment screens, including coverage, are not mechanistic; the useful handles are post-hoc detection and targeted mitigation. Even when a single-token named entity is removed from the loss, the student's held-out probability for that entity rises to 0.40 on average (sim 2500times), and a related semantic class transfers. In an untied-head model, orthogonalizing the trait's output row against entangled neighbours collapses leakage, while equal-size random-subspace edits do not. Thus removing a target string from distillation labels does not remove the corresponding preference: neighbouring tokens can carry it. Finally, conditional behaviours can route through the network body. For sycophancy, with agreement and correction markers masked from the loss, transfer reaches about 0.63 of the teacher's effect, localizes to body computation, and evades four audits across two model families. We scope this as masked transfer of a condition-present policy. Channel location is necessary for deciding which audits can be sound. It is not a deployment-ready screen: an audit used outside its carrier regime can give false assurance.

Transfer Learning (TL) is an efficient machine learning paradigm that allows overcoming some of the hurdles that characterize the successful training of deep neural networks, ranging from long training times to the needs of large datasets. While exploiting TL is a well established and successful training practice in Supervised Learning (SL), its applicability in Deep Reinforcement Learning (DRL) is rarer. In this paper, we study the level of transferability of three different variants of Deep-Q Networks on popular DRL benchmarks as well as on a set of novel, carefully designed control tasks. Our results show that transferring neural networks in a DRL context can be particularly challenging and is a process which in most cases results in negative transfer. In the attempt of understanding why Deep-Q Networks transfer so poorly, we gain novel insights into the training dynamics that characterizes this family of algorithms.

Transfer learning approaches have shown to significantly improve performance on downstream tasks. However, it is common for prior works to only report where transfer learning was beneficial, ignoring the significant trial-and-error required to find effective settings for transfer. Indeed, not all task combinations lead to performance benefits, and brute-force searching rapidly becomes computationally infeasible. Hence the question arises, can we predict whether transfer between two tasks will be beneficial without actually performing the experiment? In this paper, we leverage explainability techniques to effectively predict whether task pairs will be complementary, through comparison of neural network activation between single-task models. In this way, we can avoid grid-searches over all task and hyperparameter combinations, dramatically reducing the time needed to find effective task pairs. Our results show that, through this approach, it is possible to reduce training time by up to 83.5% at a cost of only 0.034 reduction in positive-class F1 on the TREC-IS 2020-A dataset.

Aligning foundation models is essential for their safe and trustworthy deployment. However, traditional fine-tuning methods are computationally intensive and require updating billions of model parameters. A promising alternative, alignment via decoding, adjusts the response distribution directly without model updates to maximize a target reward r, thus providing a lightweight and adaptable framework for alignment. However, principled decoding methods rely on oracle access to an optimal Q-function (Q^*), which is often unavailable in practice. Hence, prior SoTA methods either approximate this Q^* using Q^{pi_{sft}} (derived from the reference SFT model) or rely on short-term rewards, resulting in sub-optimal decoding performance. In this work, we propose Transfer Q^*, which implicitly estimates the optimal value function for a target reward r through a baseline model rho_{BL} aligned with a baseline reward rho_{BL} (which can be different from the target reward r). Theoretical analyses of Transfer Q^* provide a rigorous characterization of its optimality, deriving an upper bound on the sub-optimality gap and identifying a hyperparameter to control the deviation from the pre-trained reference SFT model based on user needs. Our approach significantly reduces the sub-optimality gap observed in prior SoTA methods and demonstrates superior empirical performance across key metrics such as coherence, diversity, and quality in extensive tests on several synthetic and real datasets.

Deepface generation has traditionally followed a task-driven paradigm, where distinct tasks (e.g., face transfer and hair transfer) are addressed by task-specific models. Nevertheless, this single-task setting severely limits model generalization and scalability. A unified model capable of solving multiple deepface generation tasks in a single pass represents a promising and practical direction, yet remains challenging due to data scarcity and cross-task conflicts arising from heterogeneous attribute transformations. To this end, we propose UniBioTransfer, the first unified framework capable of handling both conventional deepface tasks (e.g., face transfer and face reenactment) and shape-varying transformations (e.g., hair transfer and head transfer). Besides, UniBioTransfer naturally generalizes to unseen tasks, like lip, eye, and glasses transfer, with minimal fine-tuning. Generally, UniBioTransfer addresses data insufficiency in multi-task generation through a unified data construction strategy, including a swapping-based corruption mechanism designed for spatially dynamic attributes like hair. It further mitigates cross-task interference via an innovative BioMoE, a mixture-of-experts based model coupled with a novel two-stage training strategy that effectively disentangles task-specific knowledge. Extensive experiments demonstrate the effectiveness, generalization, and scalability of UniBioTransfer, outperforming both existing unified models and task-specific methods across a wide range of deepface generation tasks. Project page is at https://scy639.github.io/UniBioTransfer.github.io/

Training deep neural networks (DNNs) is computationally expensive, which is problematic especially when performing duplicated or similar training runs in model ensemble or fine-tuning pre-trained models, for example. Once we have trained one DNN on some dataset, we have its learning trajectory (i.e., a sequence of intermediate parameters during training) which may potentially contain useful information for learning the dataset. However, there has been no attempt to utilize such information of a given learning trajectory for another training. In this paper, we formulate the problem of "transferring" a given learning trajectory from one initial parameter to another one (learning transfer problem) and derive the first algorithm to approximately solve it by matching gradients successively along the trajectory via permutation symmetry. We empirically show that the transferred parameters achieve non-trivial accuracy before any direct training, and can be trained significantly faster than training from scratch.

Modern deep convolutional networks (CNNs) are often criticized for not generalizing under distributional shifts. However, several recent breakthroughs in transfer learning suggest that these networks can cope with severe distribution shifts and successfully adapt to new tasks from a few training examples. In this work we study the interplay between out-of-distribution and transfer performance of modern image classification CNNs for the first time and investigate the impact of the pre-training data size, the model scale, and the data preprocessing pipeline. We find that increasing both the training set and model sizes significantly improve the distributional shift robustness. Furthermore, we show that, perhaps surprisingly, simple changes in the preprocessing such as modifying the image resolution can significantly mitigate robustness issues in some cases. Finally, we outline the shortcomings of existing robustness evaluation datasets and introduce a synthetic dataset SI-Score we use for a systematic analysis across factors of variation common in visual data such as object size and position.

Transfer learning is an essential technique for many machine learning/AI models of complex structures such as large language models and generative AI. The essence of transfer learning is to leverage knowledge from resolved source tasks for a new target task, especially when the sample size m of the training data for the latter is low. In this work, we rigorously analyze the potential benefit of transfer learning in terms of sample efficiency. Specifically, taking an optimal transport viewpoint of transfer learning, we find that when the data dimension d is higher than 3, the sample complexity for transfer learning is O(m^{-(α+1)/d}), with α indicating the smoothness of the data distribution, as opposed to the O(m^{-p/d}) sample complexity for direct learning with p indicating the smoothness of the optimal target model. Our finding theoretically supports a better sample efficiency for transfer learning, when the target task is optimizing over a family of not-so-smooth models (i.e., highly complex networks with the possible use of non-smooth activation functions). Using image classification as an example, we numerically demonstrate the sample efficiency for transfer learning, that is, in the data hungry regime, the model performance can be significantly improved by transfer learning.

Transfer learning with a small amount of target data is an effective and common approach to adapting a pre-trained model to distribution shifts. In some situations, target data labels may be expensive to obtain, so we may only have access to a limited number of target data points. To make the most of a very small target dataset, we propose a lightweight, sample-efficient approach that learns a diverse set of features and adapts to a target distribution by interpolating these features. Our approach, Project and Probe (Pro^2), first learns a linear projection that maps a pre-trained embedding onto orthogonal directions while being predictive of labels in the source dataset. The goal of this step is to learn a variety of predictive features, so that at least some of them remain useful after distribution shift. Pro^2 then learns a linear classifier on top of these projected features using a small target dataset. Theoretically, we find that Pro^2 results in more sample-efficient generalization by inducing a favorable bias-variance tradeoff. Our experiments on four datasets, with multiple distribution shift settings for each, show that Pro^2 improves performance by 5-15% when given limited target data compared to prior methods such as standard linear probing.

Transfer of pre-trained representations improves sample efficiency and simplifies hyperparameter tuning when training deep neural networks for vision. We revisit the paradigm of pre-training on large supervised datasets and fine-tuning the model on a target task. We scale up pre-training, and propose a simple recipe that we call Big Transfer (BiT). By combining a few carefully selected components, and transferring using a simple heuristic, we achieve strong performance on over 20 datasets. BiT performs well across a surprisingly wide range of data regimes -- from 1 example per class to 1M total examples. BiT achieves 87.5% top-1 accuracy on ILSVRC-2012, 99.4% on CIFAR-10, and 76.3% on the 19 task Visual Task Adaptation Benchmark (VTAB). On small datasets, BiT attains 76.8% on ILSVRC-2012 with 10 examples per class, and 97.0% on CIFAR-10 with 10 examples per class. We conduct detailed analysis of the main components that lead to high transfer performance.

Current machine learning systems are brittle in the face of distribution shifts (DS), where the target distribution that the system is tested on differs from the source distribution used to train the system. This problem of robustness to DS has been studied extensively in the field of domain adaptation. For deep neural networks, a popular framework for unsupervised domain adaptation (UDA) is domain matching, in which algorithms try to align the marginal distributions in the feature or output space. The current theoretical understanding of these methods, however, is limited and existing theoretical results are not precise enough to characterize their performance in practice. In this paper, we derive new bounds based on optimal transport that analyze the UDA problem. Our new bounds include a term which we dub as entanglement, consisting of an expectation of Wasserstein distance between conditionals with respect to changing data distributions. Analysis of the entanglement term provides a novel perspective on the unoptimizable aspects of UDA. In various experiments with multiple models across several DS scenarios, we show that this term can be used to explain the varying performance of UDA algorithms.

Single-operator learning involves training a deep neural network to learn a specific operator, whereas recent work in multi-operator learning uses an operator embedding structure to train a single neural network on data from multiple operators. Thus, multi-operator learning is capable of predicting a range of operators within one model. In this work, we propose pretraining and fine-tuning strategies for solving PDEs using multi-operator learning. One key aspect is that by increasing the number of families of operators used in pretraining, a PDE foundation model can be fine-tuned to downstream tasks involving new PDEs with a limited number of samples, thus outperforming single operator neural networks. Specifically, a multi-operator learning model pre-trained with data from diverse PDE families can predict unseen operators after fine-tuning with only a limited number of operators from the new family, enabling them to serve as a data-free PDE solver. We also show that the proposed training and fine-tuning method is able to predict new operators in zero-shot prediction without samples. Additionally, we introduce a PDE-agnostic meta-learning algorithm to improve the adaptability of the model to various PDEs by providing a better parameter initialization process. To address the needs of applications with limited computing resources, we explore low-rank adaptation methods that reduce computational costs while enhancing solver accuracy. Lastly, by examining the scaling law with respect to the number of operator families, we establish and highlight its potential for broad adaptation in PDE-solving tasks.

On-policy distillation (OPD) transfers teacher capabilities by supervising trajectories sampled from the student's own policy, yet its generalization behavior remains poorly understood, as most studies evaluate OPD on a single domain and on benchmarks close to the training data. We present a controlled study that varies one generalization factor at a time, from in-domain distribution shifts to cross-domain transfer and the multi-teacher setting. We find that OPD transfers a teacher's reasoning behavior rather than its answers to particular problems: training difficulty barely matters, and even problems the teacher never solves are useful. Transfer depends strongly on the origin relationship between teacher and student: same-origin pairs bring the student close to the teacher across languages, reasoning horizons, and even other domains, whereas cross-origin pairs mostly fit the trained distribution. This broad reach is a double-edged sword: since routing prompts to domain experts cannot confine each teacher's influence, combining them yields a mixture-dependent seesaw among their capabilities. These results clarify when OPD generalizes and offer a useful perspective for diagnosing multi-teacher OPD.

A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically infinite-dimensional, deep learning has predominantly advanced through applications in computer vision and natural language processing that focus on mappings between finite-dimensional spaces. Such fundamental disparities in the nature of the data have limited neural networks from achieving a comparable level of success in scientific applications as seen in other fields. Neural operators are a principled way to generalize neural networks to mappings between function spaces, offering a pathway to replicate deep learning's transformative impact on scientific problems. For instance, neural operators can learn solution operators for entire classes of PDEs, e.g., physical systems with different boundary conditions, coefficient functions, and geometries. A key factor in deep learning's success has been the careful engineering of neural architectures through extensive empirical testing. Translating these neural architectures into neural operators allows operator learning to enjoy these same empirical optimizations. However, prior neural operator architectures have often been introduced as standalone models, not directly derived as extensions of existing neural network architectures. In this paper, we identify and distill the key principles for constructing practical implementations of mappings between infinite-dimensional function spaces. Using these principles, we propose a recipe for converting several popular neural architectures into neural operators with minimal modifications. This paper aims to guide practitioners through this process and details the steps to make neural operators work in practice. Our code can be found at https://github.com/neuraloperator/NNs-to-NOs

There is an increasing number of pre-trained deep neural network models. However, it is still unclear how to effectively use these models for a new task. Transfer learning, which aims to transfer knowledge from source tasks to a target task, is an effective solution to this problem. Fine-tuning is a popular transfer learning technique for deep neural networks where a few rounds of training are applied to the parameters of a pre-trained model to adapt them to a new task. Despite its popularity, in this paper, we show that fine-tuning suffers from several drawbacks. We propose an adaptive fine-tuning approach, called AdaFilter, which selects only a part of the convolutional filters in the pre-trained model to optimize on a per-example basis. We use a recurrent gated network to selectively fine-tune convolutional filters based on the activations of the previous layer. We experiment with 7 public image classification datasets and the results show that AdaFilter can reduce the average classification error of the standard fine-tuning by 2.54%.

Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that performs global convolutions in the Fourier space. However, such global operations are often prone to over-smoothing and may fail to capture local details. In contrast, convolutional neural networks (CNN) can capture local features but are limited to training and inference at a single resolution. In this work, we present a principled approach to operator learning that can capture local features under two frameworks by learning differential operators and integral operators with locally supported kernels. Specifically, inspired by stencil methods, we prove that we obtain differential operators under an appropriate scaling of the kernel values of CNNs. To obtain local integral operators, we utilize suitable basis representations for the kernels based on discrete-continuous convolutions. Both these approaches preserve the properties of operator learning and, hence, the ability to predict at any resolution. Adding our layers to FNOs significantly improves their performance, reducing the relative L2-error by 34-72% in our experiments, which include a turbulent 2D Navier-Stokes and the spherical shallow water equations.

Machine learning demand forecasts optimize statistical accuracy yet leave excess operational volatility that inflates safety stock and amplifies the Bullwhip effect. We introduce Contextual Deconvolution (CD), a two-stage estimator that reframes demand sensing as a convex decomposition: a kernel-modulated banded operator separates transient promotion-driven shocks from a smooth structural baseline, and hierarchical partial pooling enables catalog-scale deployment without per-SKU training. The operator is data-derived, not imposed---it reduces to the identity wherever the promotional response is impulsive (most of M5, all of Favorita) and contributes only where genuine multi-day carryover exists, so the gains rest on the structural decomposition itself. Evaluating strictly out-of-sample on 30,490 M5 SKUs and 2,845 Favorita items, with calendar-aware baselines given CD's identical future calendar, we anchor the contribution on a full inventory-cost accounting: CD lowers safety stock, holding cost, and order variance but under-provisions event spikes, reducing total cost only when holding costs exceed sim20\% of stockout costs (95\% CI [17%,25%]); otherwise it is an operational-stability and inventory-capital layer, not an expected-cost minimizer. Its accuracy contribution is reliability rather than central tendency: across eleven baselines, CD attains the lowest cross-sectional dispersion of per-SKU error and mis-forecasts by more than 200\% on 0.8\% of SKUs versus 9.9--20.6\% for every baseline, ranking first on both in all four M5 draws. Because the Variance Ratio and std-based safety stock are minimized by any sufficiently smooth forecast, we treat them as diagnostics, not objectives. A supporting analysis shows the learned demand operators are non-normal, yet CD's compact parametric kernel matches their operational performance interpretably.

Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets. Therefore, in order to expand the transfer learning scheme to regression tasks, we propose a novel transfer technique based on differential geometry, namely the Geometrically Aligned Transfer Encoder (GATE). In this method, we interpret the latent vectors from the model to exist on a Riemannian curved manifold. We find a proper diffeomorphism between pairs of tasks to ensure that every arbitrary point maps to a locally flat coordinate in the overlapping region, allowing the transfer of knowledge from the source to the target data. This also serves as an effective regularizer for the model to behave in extrapolation regions. In this article, we demonstrate that GATE outperforms conventional methods and exhibits stable behavior in both the latent space and extrapolation regions for various molecular graph datasets.

Transfer learning enables solving a specific task having limited data by using the pre-trained deep networks trained on large-scale datasets. Typically, while transferring the learned knowledge from source task to the target task, the last few layers are fine-tuned (re-trained) over the target dataset. However, these layers are originally designed for the source task that might not be suitable for the target task. In this paper, we introduce a mechanism for automatically tuning the Convolutional Neural Networks (CNN) for improved transfer learning. The pre-trained CNN layers are tuned with the knowledge from target data using Bayesian Optimization. First, we train the final layer of the base CNN model by replacing the number of neurons in the softmax layer with the number of classes involved in the target task. Next, the pre-trained CNN is tuned automatically by observing the classification performance on the validation data (greedy criteria). To evaluate the performance of the proposed method, experiments are conducted on three benchmark datasets, e.g., CalTech-101, CalTech-256, and Stanford Dogs. The classification results obtained through the proposed AutoTune method outperforms the standard baseline transfer learning methods over the three datasets by achieving 95.92%, 86.54%, and 84.67% accuracy over CalTech-101, CalTech-256, and Stanford Dogs, respectively. The experimental results obtained in this study depict that tuning of the pre-trained CNN layers with the knowledge from the target dataset confesses better transfer learning ability. The source codes are available at https://github.com/JekyllAndHyde8999/AutoTune_CNN_TransferLearning.

In modern large-scale deep learning, a prevalent and effective workflow for solving low-data problems is adapting powerful pre-trained foundation models (FMs) to new tasks via parameter-efficient fine-tuning (PEFT). However, while empirically effective, the resulting solutions lack generalisation guarantees to certify their accuracy - which may be required for ethical or legal reasons prior to deployment in high-importance applications. In this paper we develop a novel transfer learning approach that is designed to facilitate non-vacuous learning theoretic generalisation guarantees for downstream tasks, even in the low-shot regime. Specifically, we first use upstream tasks to train a distribution over PEFT parameters. We then learn the downstream task by a sample-and-evaluate procedure -- sampling plausible PEFTs from the trained diffusion model and selecting the one with the highest likelihood on the downstream data. Crucially, this confines our model hypothesis to a finite set of PEFT samples. In contrast to learning in the typical continuous hypothesis spaces of neural network weights, this facilitates tighter risk certificates. We instantiate our bound and show non-trivial generalization guarantees compared to existing learning approaches which lead to vacuous bounds in the low-shot regime.

Transfer learning has become a central paradigm in modern machine learning, yet it suffers from the long-standing problem of negative transfer, where leveraging source representations can harm rather than help performance on the target task. Although empirical remedies have been proposed, there remains little theoretical understanding of how to reliably avoid negative transfer. In this paper, we investigate a simple yet remarkably effective strategy: augmenting frozen, pretrained source-side features with a trainable target-side encoder that adapts target features to capture residual signals overlooked by models pretrained on the source data. We show this residual feature integration strategy is sufficient to provably prevent negative transfer, by establishing theoretical guarantees that it has no worse convergence rate than training from scratch under the informative class of target distributions up to logarithmic factors, and that the convergence rate can transition seamlessly from nonparametric to near-parametric when source representations are informative. To our knowledge, this is the first theoretical work that ensures protection against negative transfer. We carry out extensive numerical experiments across image, text and tabular benchmarks, and empirically verify that the method consistently safeguards performance under distribution shift, label noise, semantic perturbation, and class imbalance. We additionally demonstrate that this residual integration mechanism uniquely supports adapt-time multimodality extension, enabling a pretrained single-cell foundation model to incorporate spatial signals for lymph-node anatomical classification despite the source model being trained without them. Our study thus advances the theory of safe transfer learning, and provides a principled approach that is simple, robust, architecture-agnostic, and broadly applicable.

We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains. TNOs represent data as features defined on cells of varying dimension and model their interactions through Discrete Exterior Calculus, enabling explicit cross-dimensional coupling via gradient-, curl-, and divergence-type operators. The key design principle is to decouple where information flows, as governed by fixed topological operators, from how it is transformed (which is learned), yielding models that respect the geometric support of physical quantities and expose conservation and compatibility structure. We further propose Hierarchical TNOs (HTNOs), which incorporate learned coarse complexes to propagate long-range and topology-dependent information. Our framework subsumes existing NOs as a special case, providing a unified perspective on operator learning across discretizations. Across a range of PDE benchmarks, including irregular-geometry flow problems, TNOs and HTNOs improve accuracy; controlled studies further isolate the benefits of native higher-rank and topological structure. Project page: https://circle-group.github.io/research/TNO

Parameter-Efficient Transfer Learning (PETL) aims at efficiently adapting large models pre-trained on massive data to downstream tasks with limited task-specific data. In view of the practicality of PETL, previous works focus on tuning a small set of parameters for each downstream task in an end-to-end manner while rarely considering the task distribution shift issue between the pre-training task and the downstream task. This paper proposes a novel two-stage paradigm, where the pre-trained model is first aligned to the target distribution. Then the task-relevant information is leveraged for effective adaptation. Specifically, the first stage narrows the task distribution shift by tuning the scale and shift in the LayerNorm layers. In the second stage, to efficiently learn the task-relevant information, we propose a Taylor expansion-based importance score to identify task-relevant channels for the downstream task and then only tune such a small portion of channels, making the adaptation to be parameter-efficient. Overall, we present a promising new direction for PETL, and the proposed paradigm achieves state-of-the-art performance on the average accuracy of 19 downstream tasks.

In this work, we propose marginalized operators, a new class of off-policy evaluation operators for reinforcement learning. Marginalized operators strictly generalize generic multi-step operators, such as Retrace, as special cases. Marginalized operators also suggest a form of sample-based estimates with potential variance reduction, compared to sample-based estimates of the original multi-step operators. We show that the estimates for marginalized operators can be computed in a scalable way, which also generalizes prior results on marginalized importance sampling as special cases. Finally, we empirically demonstrate that marginalized operators provide performance gains to off-policy evaluation and downstream policy optimization algorithms.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

We consider the problem of training a deep neural network on a given classification task, e.g., ImageNet-1K (IN1K), so that it excels at both the training task as well as at other (future) transfer tasks. These two seemingly contradictory properties impose a trade-off between improving the model's generalization and maintaining its performance on the original task. Models trained with self-supervised learning tend to generalize better than their supervised counterparts for transfer learning; yet, they still lag behind supervised models on IN1K. In this paper, we propose a supervised learning setup that leverages the best of both worlds. We extensively analyze supervised training using multi-scale crops for data augmentation and an expendable projector head, and reveal that the design of the projector allows us to control the trade-off between performance on the training task and transferability. We further replace the last layer of class weights with class prototypes computed on the fly using a memory bank and derive two models: t-ReX that achieves a new state of the art for transfer learning and outperforms top methods such as DINO and PAWS on IN1K, and t-ReX* that matches the highly optimized RSB-A1 model on IN1K while performing better on transfer tasks. Code and pretrained models: https://europe.naverlabs.com/t-rex

Evasion attacks are a threat to machine learning models, where adversaries attempt to affect classifiers by injecting malicious samples. An alarming side-effect of evasion attacks is their ability to transfer among different models: this property is called transferability. Therefore, an attacker can produce adversarial samples on a custom model (surrogate) to conduct the attack on a victim's organization later. Although literature widely discusses how adversaries can transfer their attacks, their experimental settings are limited and far from reality. For instance, many experiments consider both attacker and defender sharing the same dataset, balance level (i.e., how the ground truth is distributed), and model architecture. In this work, we propose the DUMB attacker model. This framework allows analyzing if evasion attacks fail to transfer when the training conditions of surrogate and victim models differ. DUMB considers the following conditions: Dataset soUrces, Model architecture, and the Balance of the ground truth. We then propose a novel testbed to evaluate many state-of-the-art evasion attacks with DUMB; the testbed consists of three computer vision tasks with two distinct datasets each, four types of balance levels, and three model architectures. Our analysis, which generated 13K tests over 14 distinct attacks, led to numerous novel findings in the scope of transferable attacks with surrogate models. In particular, mismatches between attackers and victims in terms of dataset source, balance levels, and model architecture lead to non-negligible loss of attack performance.

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of PDEs. Here, we present novel adaptations for convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs. The resulting architecture, termed as convolutional neural operators (CNOs), is designed specifically to preserve its underlying continuous nature, even when implemented in a discretized form on a computer. We prove a universality theorem to show that CNOs can approximate operators arising in PDEs to desired accuracy. CNOs are tested on a novel suite of benchmarks, encompassing a diverse set of PDEs with possibly multi-scale solutions and are observed to significantly outperform baselines, paving the way for an alternative framework for robust and accurate operator learning. Our code is publicly available at https://github.com/bogdanraonic3/ConvolutionalNeuralOperator

Few-shot classification is a challenging problem due to the uncertainty caused by using few labelled samples. In the past few years, many methods have been proposed to solve few-shot classification, among which transfer-based methods have proved to achieve the best performance. Following this vein, in this paper we propose a novel transfer-based method that builds on two successive steps: 1) preprocessing the feature vectors so that they become closer to Gaussian-like distributions, and 2) leveraging this preprocessing using an optimal-transport inspired algorithm (in the case of transductive settings). Using standardized vision benchmarks, we prove the ability of the proposed methodology to achieve state-of-the-art accuracy with various datasets, backbone architectures and few-shot settings.