Science & Mathematics

We present a boundary integral method for evaluating electron repulsion integrals (ERIs) in dielectric environments of piecewise constant permittivity. This generalizes conventional bare-Coulomb ERIs by incorporating screening from structured dielectric surroundings, such as the substrates and/or encapsulating layers present in modern two-dimensional-material devices. We formulate the problem as a second-kind boundary integral equation for the induced surface charge on the dielectric interfaces, and discretize it with a Nyström method on adaptively refined panels. The incident potential generated by each smooth orbital source density is evaluated by a Fourier truncated-kernel method in or near to its source box, and by fast multipole method (FMM) accelerated quadrature farther away. The linear system is solved by a Krylov iteration also accelerated by the FMM. We focus on cuboidal device geometries, and retain efficiency at high aspect ratios via close-to-touching panel quadratures. We further develop a distributed pipeline that computes the full ERI tensor, comprising thousands of orbital pairs, embedded in a single dielectric geometry. We demonstrate the method on an effective three-layer graphene slab over a Si/SiO$_2$ heterojunction, focusing on the central graphene layer represented by $198$ $p_z$-like orbitals, retaining the $2613^2$ non-negligible entries of the $198^4$-sized ERI tensor. The model is resolved on $1.3$ million surface unknowns, achieving a relative error of $0.004\%$, at a cost of $22$ node-hours.

Protein language models (pLMs) are powerful tools for protein annotation and mutation-effect prediction, but progress has largely depended on scaling model size and data, making them expensive and prone to memorization. Test-time scaling offers a complementary path, but methods developed for autoregressive LLMs do not transfer directly: masked encoders lack a generation loop, and amino acids do not verbalize in a reasoning language. Instead, we adapt recursive pretraining to masked pLMs, where a weight-tied Transformer core refines residue-aligned hidden states over an adjustable number of cycles. We instantiate this recipe as recAMPLIFY, a pLM with 155M unique parameters trained on the same 2T tokens as AMPLIFY-350M. Despite 56% fewer parameters, it improves CASP contact recovery and three out of four supervised tasks, notably raising fold accuracy by 22.5%. Because optimal depth for recAMPLIFY varies across tasks and assays, we then introduce Gated Mixture Recurrence (GMR), a framework that decodes each protein from a probability-weighted mixture of hidden states visited during recursion. GMR employs a learned residual gate at scalar, low-rank, or per-dimension resolution to control how much of each cycle's proposed update is accepted into the state. This unifies halting and gating into a single adaptive computation objective while recovering PonderNet-style halting as a special case without gates. Layered on top of recAMPLIFY, GMR further reduces expected layer depth by up to 37%, although the accuracy trade-off varies by task. Mechanistic analyses show that residual gating controls recurrence stability beyond the trained depth and that halt depth tracks biological properties.

We show that gradient descent (GD) with step size $η$ can achieve $\varepsilon$ optimality gap on the multiclass logistic regression loss in a number of iterations $T$ that is independent of $\varepsilon$. To do so, the step size $η$ must be chosen large enough as a function of $\varepsilon$ (and properties of the linearly separable dataset), while $T$ is a constant that only depends on the data. The relevant properties of the data include the number of points and their margin (for $T$), and one additional quantity (for $η$) that turns out to be necessary in dimension $d \geq 3$. The proofs build on the known fact that, as $η\to \infty$, suitably rescaled GD becomes the perceptron algorithm, and the latter finds a perfect classifier in $T$ iterations. A similar claim was shown for two classes in dimension $d = 2$ using other proof techniques. This result adds to previous works that showed GD on the logistic regression loss can be accelerated by taking large step sizes. Those provoke a wild, oscillatory initial phase, followed by a stable phase. We provide results of this (qualitatively different) nature, too.

Adapting pre-trained continuous-time generative models to sequentially incoming data without forgetting earlier tasks is a central challenge in lifelong learning. A leading strategy, generative replay, uses a generative model trained on historical tasks to augment its own continual update with synthetic samples from experience. However, it requires full trajectory simulations at every training step, which accumulate discretization errors and can degrade the replayed historical distribution. Here, we propose trajectory replay, which bypasses sample generation by training an updated velocity field to match both a frozen historical velocity along its trajectories and the incoming task's velocity field, weighted by a stability-plasticity coefficient. Through the lens of continuous-time transport, we show the resulting optimum averages the two task velocities by their respective densities and generates the mixture of their probability paths. Combined with mean velocity distillation, trajectory replay accesses historical trajectories using only a few network evaluations per continual update. Empirically, it outperforms generative replay and distillation baselines on class-incremental image generation. In two biological case studies, trajectory replay extends generative perturbation models to new contexts and experimental batches across two data modalities while preserving treatment-effect prediction.

Recent embodied systems increasingly build on multimodal large language models (MLLMs) for their pretrained understanding and reasoning capabilities, but their perception of the physical world remains largely limited to basic modalities such as vision and audio. However, broadening MLLMs to more diverse sensory modalities from the physical environment is challenging: their representations are often weakly connected to the MLLM and vary substantially in structure and statistics, while their interpretation still requires shared high-level understanding and reasoning. We therefore propose Unisense, a unified embodied MLLM framework that supports diverse physical sensory modalities within a shared multimodal architecture. Unisense follows a two-stage training process: (i) aligning sensory representations with language to establish a language-accessible interface; and (ii) tuning modality-specific experts within the shared LLM to provide specialized processing for different sensory modalities. To support broad sensory learning, we curate Unisense-1M, a large-scale embodied sensory training corpus comprising 1M samples across 8 sensory modalities. We further evaluate Unisense on 12 benchmarks spanning depth, point cloud, IMU, tactile, thermal, radar, motion, and smell understanding. Across these heterogeneous sensing tasks, Unisense achieves strong performance and outperforms both generalist and specialized models on most benchmarks, demonstrating the potential of pretrained MLLMs as unified models for embodied sensory understanding.

Expert human readers process large inputs (e.g., code repositories and long documents) by skimming to closely read only what matters. On the other hand, language models process all input tokens through each model layer, resulting in significant processing costs for long-context inputs. We introduce TokenGate, a small, drop-in component that extends existing trained models to enable end-to-end learnable token pruning over long-context inputs for fast and memory-efficient prefill. To enable end-to-end learning despite the non-differentiable top-K operator for token pruning, we introduce token-gated attention, a mechanism inspired by Mixture-of-Experts that re-weights attention logits using token importance scores. Across diverse tasks, TokenGate achieves $1.4$-$11.3\times$ faster time-to-first token (TTFT) and $1.5$-$3.4\times$ lower peak memory at no accuracy degradation for prefill in transformers. Compared to the best-performing prior methods for token-pruning, TokenGate gives up to $6.4\times$ faster prefill and $2\times$ lower peak memory. TokenGate natively extends both standard transformers (e.g., Qwen3) and hybrid-attention models (e.g., Qwen3.5) with simple lightweight adaptation comparable to standard parameter-efficient fine-tuning. We make our code available at: https://github.com/tokengate-models/TokenGate.

Machine-learning models for metal-organic frameworks (MOFs) predominantly rely on atomic structures, whereas electron-density (ED) and electrostatic-potential (ESP) fields remain underexplored as scalable learning representations. These continuous fields encode complementary spatial and electronic information relevant to structure-property relationships, particularly pore geometry and guest-framework interactions, but costly first-principles calculations, storage requirements and the scarcity of systematically aligned datasets limit their broader use. Here we introduce MOFFieldBench, a multimodal benchmark comprising approximately 46,000 MOFs with one-to-one aligned crystallographic structures, ED fields and ESP fields. A unified workflow integrates field generation, error-controlled compression and sparse point-cloud representation, supporting field reconstruction, prediction of 13 material properties, multimodal property prediction and pairwise cross-modal retrieval. ED and ESP provide competitive representations for pore geometry, adsorption and separation properties. Multimodal fusion improves several prediction tasks relative to the best unimodal reference, supporting complementary predictive roles for atomic structures and electronic fields. Learned ED reconstruction closely approximates first-principles reference densities, while predicted-density initialization reduces self-consistent-field calculation time by 13.59\% on average in paired tests. These results support electronic fields as practical, informative learning modalities and establish MOFFieldBench as a resource for studying representation choice, multimodal learning and electronic-field-driven MOF modelling.

Reinforcement learning enables learning high-performance control policies, but its reliance on extensive interaction limits deployment on physical systems where data collection is costly, and failures are unsafe. We introduce Prior-Informed Adaptation (PIA), an offline-to-online model-based RL framework that uses structured simulation priors for rapid adaptation. PIA pretrains a world model on heterogeneous low- and high-fidelity simulated trajectories, then adapts it with limited target-domain interaction using uncertainty-regularized planning. Rather than requiring an accurate simulator for policy transfer, PIA treats simulated trajectories as biased priors whose residual mismatch is corrected during online adaptation. We evaluate PIA in autonomous racing using high-fidelity simulation and on a real full-size autonomous race car. In simulation, PIA adapts faster across track and surface shifts than strong baselines, achieving lower lap times and fewer failures. On hardware, PIA achieves reliable few-shot adaptation with less than one hour of on-vehicle interaction.

Indonesia's fragmented geography and uneven infrastructure pose persistent challenges for adopting new educational technologies. While national initiatives aim to mainstream AI in K-12 schools by 2025, policy readiness does not automatically mean teachers are ready for the classroom. This study surveys Indonesian K-12 teachers to examine: (1) their understanding of AI, (2) how they and their students use AI, and (3) their views on the acceptability of AI in learning activities. Through semi-automated thematic analysis, we identify common misconceptions and use cases. Our findings reveal a notable mismatch: while teachers find AI use in education acceptable and support it for the sake of efficiency, they remain fully aware of the risks to learning depth and academic honesty. We also find that this high level of acceptance is currently coupled with a poor understanding of how AI actually works.

Continuous in-hand rotation requires coordinated contact maintenance and renewal, linking manipulation performance to both hand geometry and tactile feedback. We investigate these relationships through rotational progress, finger participation, and fingertip loading on two versions of the low-cost LEAP Hand with anthropomorphic and symmetric finger arrangements. Both hands are integrated with TacTip vision-based tactile sensors and use a shared reinforcement learning framework. Simulation evaluates full tactile, binary touch, and proprioception-only observations on 12 unseen objects; hardware experiments evaluate full tactile policies on ten objects under multiple hand orientations. In simulation, full tactile observations increase mean normalized rotation per episode over proprioception alone by 94.8% for the anthropomorphic hand and 66.9% for the symmetric hand, with longer mean episode durations and lower mean total fingertip loads. Hardware contact measurements reveal more differentiated finger participation in the anthropomorphic hand, while cumulative loading is more evenly distributed across the symmetric hand's fingers. Overall, the symmetric hand achieves a 32.0% higher mean rotation count and a 25.8% higher aggregate rotation rate, together with longer manipulation duration. Additional hardware force recordings show a 19.9% lower mean total fingertip load for this layout. These findings relate finger arrangement to contact organization and load sharing, and show that richer tactile information supports greater task progress at lower mean loading in both simulated embodiments.

Learned image compression (LIC) has achieved promising rate-distortion performance, but most methods lack scalability for diverse platforms with varying computational and storage constraints. Existing slimmable LIC methods achieve flexible complexity via consecutive-channel activation but suffer from two limitations: forced consecutive-channel selection degrades narrow-model performance at low bitrates, and the lack of stable variable-rate control limits adaptability to varying bandwidth. We propose a channel-level mask-guided slimmable image compression method. A learnable channel-wise mask with sparsity-promoting regularization enables non-contiguous top-w channel selection, letting narrow models use the most informative channels. After training, mask merging and channel reordering convert the model into a standard slimmable network via Mask-to-Slimmable (M2S) conversion, enabling efficient inference without architectural changes. For variable-rate control, we combine lambda- and width-conditioned modulation with quantization-step scaling and a progressive training pipeline stabilized by a freeze-then-fine-tune strategy. Experiments on Kodak across E2E, Hyperprior, and Checkerboard backbones show superior rate-distortion performance across widths and bitrates, with large gains for narrow models at low bitrates. At w=48, it achieves up to 19.22%, 24.11%, and 22.76% BD-rate savings over the same-width Slimmable baseline on E2E, Hyperprior, and CKBD, respectively. A single VBR model replaces 40 independent models, reducing storage by 14.8x to 15.9x. Code: https://github.com/sjtu-tcloud/MGSIC.

We introduce DexOAK, a learning-based object-aware kinematic retargeting framework for generating contact-consistent robot hand references from human motion-capture data. DexOAK first minimizes an interaction-graph Laplacian objective over a joint hand-object graph, so the robot reproduces the demonstrated object-relative interaction geometry rather than the human hand pose alone. These per-frame solutions form seed retargeted references, from which a feed-forward network conditioned on human keypoints and object point clouds learns the retargeting function. Object-aware finetuning then refines the network under contact, non-penetration, and self-collision losses that position the fingers on the demonstrated contacts and reduce artifacts destabilizing physics-based refinement. Once trained, the network transfers to unseen data by inference alone, without per-frame optimization. DexOAK references improve dynamic retargeting over the state-of-the-art across bimanual tasks with rigid and articulated objects. On the Inspire hand, success rises from 39.5% to 48.4% on OakInk-v2, and ADD-AUC rises from 62.7% to 77.9% on ARCTIC. Ablations trace the gains to object-aware kinematic retargeting and the amortized network refined with contact losses. Trained on OakInk-v2, it transfers to ARCTIC zero-shot and nears in-domain performance after fine-tuning. On hardware, 46/56 open-loop replays succeed across five tasks, enabling dexterous robot data generation from human data. Visualizations and interactive results are at: https://fspinola.github.io/dexoak/.

Agents need reliable ways to validate their outputs, both when completing tasks and when filtering synthetic training data. We study verifier generation: from the instruction and environment available for solving a task, an agent writes an executable verifier that must accept every valid solution and reject invalid ones. We introduce VerifierBench, a benchmark of 222 tasks from six agent benchmarks spanning tool-call, state-based, and code verification, with 4,993 hidden test cases that include alternative valid solutions and attacks; Verifier4Verifier (V4V), a six-check audit, screens its source verifiers and test suites. Across 19 models in a common agent harness, normalized balanced accuracy ranges from 10.6 to 62.1, with generated verifiers consistently rejecting invalid solutions more reliably than they accept valid ones. This apparent strength can mask overly restrictive verification: most false rejections in the analyzed records come from verifiers that accept no tested solution to a task. Case studies reveal unsupported assumptions about solution formats, tool use, and code changes that exclude valid solutions. These errors survive self-testing because agents test solutions that share the verifier's mistaken assumptions, or submit verifiers without confirming that any correct solution passes. These findings suggest testing both whether a verifier accepts a correct solution and whether it accepts other solutions permitted by the task. The project page and dataset are publicly available.

General-purpose manipulation requires reliable behavior across embodiments, objects, and task demands. We introduce HandsOn, a composable simulation platform and benchmark for cross-embodiment dexterous manipulation. It supports five robotic arms, six dexterous hands, and approximately 200 rigid, articulated, and deformable assets in randomized scenes. The benchmark pairs 18,000 curated human demonstrations with 66 human-verified tasks: Core-50 supports demonstration-based learning and execution tests, while Transfer-16 evaluates asset and relation transfer, skill composition, and deformable manipulation without target-task training demonstrations. Qualitative real-robot rollouts illustrate sim-to-real transfer. Across diffusion, vision-language-action, world-action, and prompted VLM-based methods, the best trained multi-task policy achieves 29.1% Core-50 success. Without benchmark finetuning, GPT-6 using move_eef for palm-and-finger control achieves 5.2% on Core-50 and 1.9% on Transfer-16 over 660 trials. Trained-policy stage diagnostics expose failures in contact establishment, action coordination, and maintaining achieved goals, with additional sequencing errors in composed tasks. HandsOn provides a shared basis for investigating manipulation generalization and the limits of reliable physical interaction.

We develop a model-reduction technique based on Lie group theory for general engineering models described by a system of algebraic, ordinary, and/or partial differential equations with an arbitrary number of inputs, outputs, and constant parameters. The proposed method reduces the parameter space of these models without changing their external behavior, that is, their input-output maps. We apply this method to phase-field models used for high-fidelity simulations in electrochemistry to accelerate the analysis and design of metal-ion batteries.