machine learning developers

Abstract: Embodied agents are expected to accomplish real-world goals by deciding for themselves how and when to interact with their surroundings. For many such goals, changing the physical state of the world is the means rather than the end: the agent changes the state of a system through interaction, observes the feedback, and explores until it either achieves the goal itself (e.g., discovering physical laws) or learns what the goal requires; it acts to know. Manipulation benchmarks stop at acting to change, with the target state given; scientific discovery benchmarks evaluate knowing but replace physical experimentation with symbolic actions or numerical queries. We introduce EmbodiedLab, a benchmark in which a robot must act to know. Quantitative science experiments make this setting controllable: the parameters of the system are resampled for every instance, so the result cannot be known in advance, yet it can be scored exactly. Across 30 experiments in five disciplines on 14 apparatus platforms, the agent receives an objective and the apparatus, chooses its own procedure, and operates a physics-based simulated laboratory, reading the instruments through its cameras. Evaluation checks what the agent came to know, grounded in readings recorded during the episode, as well as the physical state the task requires; every experiment is verified to be solvable. We evaluate six frontier models in their developers' coding agents with native observation and control, with added perception and motion planning, and with manipulation skills distilled from the strongest agents. With native control, even the strongest agent succeeds less than half the time; for every agent, most failures arise in interacting with the apparatus, and manipulation skills help weaker agents more than perception and planning. The benchmark and its evaluation code are available at https://github.com/HexaFuture/EmbodiedLab.

Abstract: Image tokenizers convert pixels into compact latent sequences for efficient generative modeling. Most approaches arrange latents on a downsampled two-dimensional grid, tying sequence length to image resolution. We compare two variable-length strategies: computationally efficient patch-derived tokens, which inherit explicit spatial organization, and more demanding register tokens, which have no predefined spatial layout. Our reconstruction results reveal that patch-derived tokens perform substantially better under extreme compression, whereas register tokens achieve slightly better reconstruction quality at intermediate budgets. At high token budgets, both approaches achieve similar reconstruction quality. For downstream generative tasks, register tokens outperform patch-derived tokens. Adding representation alignment with external pretrained visual encoders substantially improves the generative performance of patch-derived tokens, allowing them to match or outperform register tokens depending on the token budget. We further find that both approaches learn spatially localized representations. Patch-derived tokens largely retain their explicitly imposed spatial organization, while register tokens develop an implicit two-dimensional spatial structure despite having no predefined layout. Representation alignment reduces this spatial organizational constraint, enabling individual tokens to exert a stronger non-local influence.

Abstract: The three-dimensional Navier-Stokes equations govern fluid turbulence, a chaotic and non-linear physical phenomenon characterized by complex eddies interacting across vast spatial and temporal scales. A numerically accurate modeling of this multi-scale energy cascade requires fully resolving both the fine spatial structures and the continuous temporal evolution of the flow field. In this paper, we leverage massive, time-resolved direct numerical simulations, which exceed 28 TB per run, to assess how numerical choices govern the resolved (3+1)-dimensional physics of turbulent flows. Building on this analysis, we study how neural networks represent the recorded turbulent motion. Our results highlight that spatial and temporal assessments can disagree for both numerical records and learned representations. We therefore call on the machine learning community to treat (3+1)-dimensional turbulence as a four-dimensional phenomenon.

Abstract: Photonic crystal fibers (PCFs) underpin critical applications in telecommunications, sensing, and high-power laser delivery, yet their design remains a manual, expert-intensive process that couples geometric intuition with deep waveguide physics. Vision-language models (VLMs) offer a promising path toward automating PCF design, but can they truly reason about photonic physics from microscopy images, or do they merely recognize visual patterns? We introduce PCFBench, the first comprehensive benchmark for evaluating VLMs on the perception, reasoning, and decision steps of the photonic inverse-design loop. PCFBench spans 26 tasks organized into six categories of increasing cognitive demand (Geometry Perception, Physics Understanding, Text Generation, Multi-modal Reasoning, Inverse-Design Decision, and Code Generation), built from over 220K FDTD simulation samples across 18 structurally diverse fiber families. We evaluate both individual VLMs on isolated tasks and multi-agent systems (MAS) on the full sequential pipeline from perception to design. Our results reveal a striking perception-design gap: current models can identify fiber geometry with moderate success, yet consistently fail to translate that visual understanding into physics-aware design actions. Moreover, cascading agents through the pipeline exposes significant error propagation, where upstream perception mistakes compound into downstream design failures. These findings suggest that neither model scaling nor naive agent chaining suffices, and that closing the loop demands explicit physical grounding. PCFBench provides the community with a rigorous, multi-dimensional testbed to measure progress toward AI-assisted photonic engineering. The project is available at https://pcfbench.github.io/.

Abstract: Probabilistic computing has proved useful for combinatorial optimization, but conventional implementations rely on binary stochastic units and sigmoid-based updates. Extending these systems to continuous variables requires binary encoding. Here we introduce a continuous probabilistic computer (CPC) whose continuous probabilistic bits sample bounded states from conditional distributions defined by local energies. Separating random-source generation from conditional sampling provides a route to using physical random sources with different native distributions. A field-programmable gate array (FPGA) prototype updates finite-precision states using digital randomness. The same framework supports product constraints, memory recovery and solution-space exploration. For the tested 7-bit factorization case, fixed-temperature FPGA CPC reduces mean core solving time approximately 33,000-fold relative to the evaluated quadratic unconstrained binary optimization software implementation. The FPGA recovers stored MNIST patterns without pretrained networks, achieving final success rates of 100%. Software CPC reaches 90% reference coverage of the feasible area in approximately 18% of the time required by restarted Adam.

Abstract: Collisions are a basic probe of unknown distributions, used for testing and for counting substructures in graphs, and they underlie Rényi entropy, a fundamental measure of uncertainty with applications in cryptography, machine learning, physics, and biology. Motivated by this, we study the natural birthday estimator. We prove Bernstein-type concentration for it and show that it is minimax optimal, uniformly and jointly in alphabet size, order, accuracy, and confidence, with no sample splitting, clipping, or median aggregation. This, in particular, settles the sample complexity of integer-order Rényi entropy estimation up to absolute constants in all regimes, closing the gap between the best known upper and lower bounds. Our concentration bound rests on a sensitivity analysis of collision count, and the matching lower bound on a sharp analysis of detecting a hidden spike in a plateau distribution.

Abstract: Vision-language trackers (VLTs) accept descriptions intended to assist tracking, but accepting text does not establish that its content changes tracking decisions, particularly as visual evidence deteriorates. We introduce DISTRACT, a matched-intervention benchmark that holds video, target, and distractor fixed while crossing four text priors with four image degradations along a controlled severity axis. We evaluate five VLTs on four datasets using behavioral contrasts, layerwise representation probes, and activation patching. Molmo2 and JointNLT exhibit directed text use. Some effects contract under degradation, whereas others show no significant endpoint change after multiplicity correction. UVLTrack, MMTrack, and DUTrack respond only weakly to changes in text semantics, with no directed behavioral effect surviving FDR correction in the tested settings. Model-internal analyses reveal that at decision-near states, correct-versus-conflicting text is decodable in Molmo2 and JointNLT but not in the other three systems. In the responsive models, decodability peaks at late states where replacement produces little behavioral change, whereas replacing selected earlier states redirects conflict-associated trajectories toward the target. Because matched-correct donors do not significantly outperform unrelated donors, these interventions identify earlier intervention-sensitive states without establishing target-specific semantic rescue. DISTRACT thus exposes when and where text affects tracking under degraded visual evidence.

Abstract: We give faster algorithms for sampling from the uniform distribution over a polytope. Our main result is an algorithm that, when applied to a polytope with $m$ constraints in $n$ dimensions, uses $m \cdot \mathrm{poly}\log(\frac m δ)$ iterations, each running in time $O(mn^{ω- 1})$, to return a sample within total variation distance $δ$ to the uniform distribution. When $m =O(n)$ and $δ= \mathrm{poly}(\frac 1 n)$, our runtime improves upon all prior works by an $Ω(n^{2/3})$ factor. Our sampler is based on the recent \emph{functional stochastic localization} framework of [GST26], and achieves an iteration count nearly matching the Poincaré constant of the uniform distribution with respect to the logarithmic barrier.

Abstract: Multi-objective optimization involves diverse preferences over conflicting objectives. Rather than returning a finite set of trade-off solutions, preference-conditioned Pareto set learning seeks to map a specified preference directly to a corresponding Pareto optimal solution. Yet in many real-world scenarios, optimization must proceed offline without further objective evaluations, leaving only a limited static dataset that sparsely covers the decision and objective spaces. Existing methods either optimize separately for each preference or train a problem-specific Pareto solution model, requiring repeated search across preferences or repeated training across problems. We introduce in-context preference-conditioned Pareto set learning (ICPSL), a framework that amortizes both preference-wise solution search and problem-specific model construction. ICPSL pretrains a foundation-style hypernetwork on a large and diverse set of synthetic prior data. Given the offline observations of an unseen problem, the pretrained hypernetwork learns to generate a problem-specific, preference-conditioned Pareto solution model in a single forward pass. The generated model can then be reused to predict solutions for arbitrary preferences without problem-specific training or preference-wise search. Experiments on synthetic and real-world problems show that ICPSL produces high-quality Pareto solutions while providing substantial speedups in problem-specific solution-model construction.

Abstract: Physics-guided networks for underwater image restoration predict transmission and backscatter and invert the image-formation model, yet rarely test whether this physics does any work. We audit one representative design, PhysGuide-Net, with four controlled experiments: five-seed ablations on UIEB with zero-shot evaluation on the complete LSUI (4279 pairs) and AUIED3K (3000 pairs) sets; a data-efficiency study with a capacity-matched control that removes the formation model; and a validation of the predicted maps against measured range on Sea-thru. With all 800 training images the physics module gives no zero-shot gain (mean PSNR differences of at most 0.16 dB; all 95% intervals include zero) at 3.4x the FLOPs. With 80 images it helps more (+0.65 dB on UIEB, +1.48 dB on AUIED3K; seed-to-seed s.d. on AUIED3K from 1.3 to 0.5 dB), although not individually significant after correction, and the control does not reproduce this (0.8-1.0 dB lower). Yet the predicted transmission does not behave like a physical quantity: its correlation with range is no stronger than for the range map of a different image (pooled difference +0.02, versus -0.06 for the dark-channel prior), and a Beer-Lambert fit explains 0.4% of its variance. The effect of the module also changes sign with degradation severity between datasets. The benefit thus comes from a physics-shaped inductive bias, not from physics. We further show that single-run ablations can reverse sign and document implementation defects that invalidate loss ablations.

Abstract: Gauge-equivariant graph neural networks generate ordered products of gauge links through local message passing, but the geometry of these internal structures is not captured by the receptive field alone. We investigate the statistical ensemble of closed lattice walks generated by recursive node- and edge-feature operations, independently of network training. Analytical and numerical results reveal a separation between rapid growth of contour length and much slower spatial expansion: deeper compositions generate increasingly long paths through repeated traversal of relatively compact regions. Loop expansions of fermionic observables provide a physical interpretation of this hierarchy, showing how spatial locality remains compatible with high-order dependence on nearby gauge fields. These findings identify complementary roles of network depth in extending spatial reach and enriching the representations constructed within that reach, providing a geometrical perspective on learning lattice gauge observables.

Abstract: This chapter provides a mathematical introduction to operator surrogates, which are finite-parametric maps approximating complex (typically nonlinear) operators between infinite-dimensional (function) spaces. A typical approach to constructing operator surrogates is the encoder-approximator-decoder paradigm, whereby infinite-dimensional inputs are mapped to a finite-dimensional latent space, processed, and then mapped back to the infinite-dimensional output space. We discuss various methods for creating efficient representation systems, including stable linear frameworks like Banach frames and data-driven techniques such as Principal Component Analysis (PCA), Active Subspaces, and nonlinear autoencoders. Subsequently, we survey key surrogate architectures, contrasting spectral methods, based on polynomial chaos expansions and related technologies, with more recent neural network approaches. We further discuss architectures that do not rely on representation systems, such as Fourier Neural Operators and transformers. We elaborate on their relationship and how they relate to other neural network operator surrogates, particularly those obtained by so-called "algorithm-unrolling". Additionally, we provide an introduction to the theoretical analysis of approximation and generalization errors. We explain how underlying low-dimensional structures, provided for example by holomorphy, are essential to overcome the so-called "curse of dimensionality": this refers to the fact that the complexity of numerical algorithms tends to increase exponentially in the problem dimensionality. We present convergence rate bounds for holomorphic operators that depend on the number of trainable parameters and the regularity of the input and output data. Throughout, we prioritize intuition over detailed technical proofs and provide precise pointers to the literature for detailed arguments.

Abstract: We present a method for enforcing exactly Dirichlet, Neumann, and Robin conditions on general triangular domains with arbitrarily curved boundaries. The algorithmic constructions developed here complements those in a previous work for general quadrilateral domains. Our method combines (i) the exact mapping between a general curved triangular domain and the standard triangle, (ii) TFC constrained expressions, and (iii) Barnhill transfinite interpolations, to provide explicit closed-form trial ansatze that mathematically satisfy the imposed boundary conditions exactly. Corner compatibility induced by the boundary conditions is pivotal, and enforcing exactly the imposed boundary conditions hinges on the exact enforcement of the induced compatibility constraints. The corner compatibility associated with the acute vertices of the standard triangle and the coupling between gradient components when the hypotenuse corresponds to a Neumann/Robin boundary pose particular challenges. Two strategies are critical to resolving these issues, by reformulating conditional corner constraints into equivalent unconditional forms and by introducing a separate TFC-style auxiliary edge construction together with an associated linear solve on the hypotenuse. We analyze the corner compatibility constraints and present formulations for the general form of functions that exactly satisfy the imposed Dirichlet, Neumann, or Robin conditions on curved triangular domains. The proposed method has been implemented using extreme learning machine type randomized neural networks for solving PDE problems. We present ample numerical experiments with linear/nonlinear PDE problems on a variety of domains with complex boundary geometries. Numerical results show that the current method has enforced the Dirichlet, Neumann, and Robin conditions on curved domain boundaries to the machine precision.

Abstract: Variational inference is a flexible tool for modeling experimental data and has proven useful in crystallography. Pathwise gradient estimators provide low-variance gradients for reparameterized variational inference, but are not readily available for some distributions central to crystallography. This work derives and implements implicit and explicit reparameterized gradient estimators for the folded Normal and Rice distributions in \prog{PyTorch}, and compares their variance analytically and empirically. In each case the implicit estimator achieves lower variance for the location derivative, particularly at small location-to-scale ratios, while the scale-derivative variances are nearly equal. For both distributions, implicit estimator is proved to be the conditional expectation of the explicit estimator given the sampled magnitude, so its variance is never larger. As a practical application, French-Wilson scaling is formulated as a variational inference problem, using the folded Normal and Rice distributions as variational families for centric and acentric reflections, respectively. Both estimators recover the exact posterior to better than $1\%$ on the amplitude, and converge at the same rate. The implementations are available in the open-source package \prog{rs-distributions}.

Abstract: Functional brain connectome represents neural connectivity as a matrix of pairwise interactions between brain regions. Generation of functional connectomes is not only a question of validity; rather, having satisfied the constraints on the correlation matrix, the next step is to recover the class-conditional geometry buried under coarse labels. We propose MAGNET, a Manifold-Aware Graph Diffusion Network which uses a normalized-Cholesky representation of the manifold of correlation matrices that guarantees validity. MAGNET lifts noisy latent states into ROI-level region tokens and performs denoising with a relational inductive bias over brain atlas regions. To deal with structural problems induced by coarse labels, MAGNET employs class-anchored conditioning, amortized structural bridge, and relevance-preserving corruption. Across ABIDE, ADNI, and OASIS-3, MAGNET consistently achieves favorable results compared to previous manifold-aware approaches, demonstrating improvements of 7-21% in class-conditional fidelity ($α,β$-F1) across three cohorts and better sampling efficiency. Moreover, while training only with strict binary labels, MAGNET is capable of maintaining clinical heterogeneity through fine substructure of the connectomes in a zero-shot setting, improving subclass covariance alignment ($λ$-MSE) by over 30%. These results suggest that geometric validity is a necessary but insufficient condition for clinical utility in connectome synthesis. Moreover, efforts in making the diffusion denoising class-conditional manifold aware finds utility beyond the highly curved brain connectome generation as this is a critical problem in various general settings. The code repository can be found at https://github.com/protyayofficial/MAGNET.

Abstract: Tool-augmented vision-language agents compose perception and measurement to reason about spatial relationships, but effective execution also requires tracking geometric assumptions and checking intermediate evidence. Preserving this experience across tasks requires retaining procedural knowledge together with the computations it governs. We introduce EvoSpatial, an experience-driven framework that evolves a library of linked skills and tools. Our key insight is that successful and failed spatial trajectories reveal both how to compute and when to trust the result. EvoSpatial retrieves skills, reuses tools, and synthesizes reusable computational functions (generated helpers) during reasoning. After answer submission, supervised outcome feedback guides skill refinement and tool consolidation for subsequent tasks. Across 20 benchmarks, EvoSpatial attains the highest average score among the compared spatial agents, exceeding SpatialClaw by 4.0 percentage points. Further experiments show cross-benchmark transfer and improved reasoning through skill-guided distillation without external skills at evaluation. These results support accumulating spatial experience for both inference-time reuse and trajectory-based training.

Abstract: Reinforcement learning (RL) can substantially improve the reasoning capabilities of large language models, but an effective training run requires considerable resources. Reusing the computation acquired through RL across models would extend the value of that training. We propose GrowRL, an RL method that organizes learned updates into compact computational pathways through structural growth. GrowRL freezes the pretrained backbone and adds an independent causal attention branch and a feed-forward network branch at each Transformer layer. Zero-initialized output projections preserve the pretrained policy at initialization, and RL updates only the added pathways. The learned pathways remain explicit after training, allowing transfer to structurally compatible target models and subsequent adaptation with the target backbone frozen. The architecture also supports sequential transfer of additional pathways. By keeping the learned attention and feed-forward computation separate from the pretrained weights, GrowRL provides an explicit structure for preserving and reusing the outcome of an RL run. Experiments across five backbones show competitive mathematical reasoning and out-of-distribution performance with a small number of trainable parameters. Learned pathways provide immediate gains across all three transfer directions, with performance after only 10 target-side updates already close to that after 100 updates in every case. These results support computational pathways as parameter-efficient and reusable units of reinforcement learning adaptation.

Abstract: World Action Models (WAMs) enable generalist robot manipulation by conditioning an action expert on representations from a pretrained video Diffusion Transformer (DiT). In closed-loop control, the video DiT runs at every chunk to encode the current observation into layerwise key-value (KV) pairs that the action expert queries. This prefill dominates the per-chunk computational cost, yet existing training-free accelerations leave it fully dense. We present WAM-Cache, a training-free framework that retains layerwise key-value representations across chunks and recomputes only a sparse refresh set of tokens. Crucially, we find that the intuitive heuristic of refreshing visually drifted tokens plateaus far below the dense baseline, even with an oracle predicting ground-truth KV drift. Downstream action accuracy is instead governed by where the action expert attends, not by what moved. WAM-Cache therefore selects the refresh set by uniting the action expert's cross-attention with visual latent surprise, complemented by a strict age bound that suppresses compounding error. On Fast-WAM, WAM-Cache cuts video DiT prefill FLOPs by 32-42% across RoboTwin 2.0, LIBERO, and real-world experiments, while staying within 0.7-1.8 percentage points of the dense policy in simulation and 2.5 points on a real robot.

Abstract: Kernels encode the inductive bias of a wide range of machine learning models, yet automated kernel design faces a fundamental dilemma. A fixed grammar of base kernels and operators guarantees validity but limits the search to structures expressible by those building blocks. Conversely, unrestricted programs remove this limitation but no longer guarantee validity. In our stress tests, 22-58% of LLM-generated kernels that pass numerical checks on random inputs fail when evaluated at different scales or dimensions. We propose Kernel Autoresearch (Kernaut), which treats kernel design as open-ended model discovery. Coding agents write kernels as programs, while construction contracts ensure that every accepted kernel is valid. A quality-diversity archive retains high-performing kernels with distinct behaviors, and novelty screening steers agents toward functionally new candidates. Our experiments demonstrate that the discovered kernels encode reusable inductive biases that generalize to unseen tasks. On held-out black-box optimization families, a discovered kernel outperforms a meta-learned deep kernel trained on the same episodes. Furthermore, kernels discovered from ten enzyme-kinetic rate laws achieve lower error than tuned ARD and deep kernel baselines on five unseen mechanisms. The discovered kernels are also interpretable programs that human researchers can refine: a human-refined version of one further reduces the held-out predictive error by 5.7% and optimization regret by 7.8%.

Abstract: Functional backdoor recovery finds any trigger whose attack success rate is at least a given threshold rather than to recover the planted trigger. We study the minimum number of queries required for this task under label feedback which returns the predicted class label. We construct two finite families of victim models that have exactly the same attack success rate for every victim and trigger candidate. The distribution of returned labels for every query is also identical under a uniformly chosen victim. These families form an explicit counterexample that despite the matched quantities, their optimal adaptive query complexities are \(Θ(\log H)\) and \(Θ(H)\) where \(H\) is the number of possible victims. The difference arises because the same non-target labels are associated with different sets of victims, so successive queries eliminate possible victims at different rates. This separation disappears when the response is reduced to binary feedback, which reports only whether the target label is returned. The separation also persists for every fixed failure probability below one. Finally, we realize the same recovery problems with trained CIFAR-10 ResNet-18 classifiers and verify the predicted optimal query budgets. These results show that attack success rate and the distribution of returned labels for each query are insufficient to determine the query complexity of functional backdoor recovery.

Abstract: Some diffusion posterior samplers construct Gaussian-tilted intermediate distributions along the reverse process. We observe that these targets can be pulled back to clean-space posteriors with weaker conditioning, with samples transported analytically to the corresponding noisy-space target through a Gaussian bridge. For the sequential Monte Carlo (SMC) sampler MCGDiff, the effective observation variance of this pulled-back problem is up to twice the diffusion-noise variance. We exploit this structure to initialize MCGDiff directly at an intermediate time: an approximate solver samples the softened clean-space posterior, the Gaussian bridge maps these samples to the tilted target, and only the remaining SMC suffix is run. This trades asymptotic consistency for finite-particle performance. With moment-matching posterior sampling (MMPS) as the solver, the hybrid improves sliced Wasserstein distance by roughly $2\times$ at matched particle count on a structured Gaussian-mixture inverse problem, and by more than an order of magnitude when the posterior-relevant mode is rare under the prior. A prior-initialization control, which retains the bridge but drops the clean-space conditioning, shows that on MCGDiff's standard Gaussian-mixture benchmark most of the improvement is insensitive to the conditioning. Conditioning the initialization gives a further consistent gain on the structured problem, and becomes decisive on a rare-mode problem, where resampling cannot repopulate a mode absent from the initial population.

Abstract: We present an oracle-optimal method for finite-sum monotone inclusions under mean-square Lipschitz continuity. Our switching regularization method finds a point $y$ and a certificate $g\in G(y)$ with $(\mathbb{E}\|F(y)+g\|^2)^{1/2}\le\varepsilon$ using $\mathcal{O}(n+\sqrt{n}LR/\varepsilon)$ expected component evaluations and resolvent evaluations. It removes the additive $n\log n$ cost of restarting a variance-reduced solver at every regularization stage by switching to a centered stochastic proximal iteration at regularization strength $L/\sqrt{n}$. Carrying an operator estimate between the remaining stages limits their total cost to $\mathcal{O}(n)$. A matching $Ω(n+\sqrt{n}LR/\varepsilon)$ lower bound holds for randomized linear-span component-oracle algorithms with adaptive stopping and expected query budgets. Thus, for $0<\varepsilon\le LR/2$, our method attains the optimal worst-case expected component complexity in this oracle model, up to universal constants.

Abstract: An agent with long-term memory can answer from a record it should no longer use, such as a plan the user later cancelled. We ask what a memory store must expose for an agent to know this before retrieving anything, and we score that judgment on its own, as metamemory monitoring. Readers see only a value-free summary: record counts by lifecycle state and a list of attribute names. Each of 148 questions is asked against three versions of one store that differ in one attribute, so wording cannot give the answer away. What a model adds depends on the length of that list. On the short lists the benchmark's ground truth produces (2.6 names on average), none of five language models reliably beats a cosine-similarity lookup over the names, and the three stronger ones are equivalent to it within 0.05. Under a control that fixes counts and list length, none is reliably above it and none is shown equivalent. On lists longer than the stores we tested write, padded to 60 names, the lookup loses 0.18; GPT-5.6 Luna and Sol lose 0.06 to 0.07 and lead it by 0.13 to 0.14, while the other three fall with it. The lead holds for Sol against a sibling padded to the same length and counts. Reworded to share no word with the names, the lookup loses 0.02 and one stronger reader edges 0.04 ahead. On the short lists the three stronger readers lead only where the summary counts a state without naming it, and one count feature closes that lead within a question, though not when items are pooled. The backends we tested omit or misstate this information: under FR-Bank's own metadata, GPT-4.1 mini, Haiku 4.5 and the lookup fall from 0.73, 0.82 and 0.75 to 0.60, 0.71 and 0.59. In these tests, what the store wrote down limited every reader we gave it to. All stores are synthetic; control, whether a better judgment yields a better answer, is left to a later study.

Abstract: Can response safety be scored by cosine similarity to the mean embedding of known-safe responses? A recent sleeper-agent detector proposes exactly this score, yet the raw positive-centroid rule is not identified: positive observations locate the safe class relative to an encoder origin, but do not determine which direction separates safe from unsafe responses. We audit the rule on two prompt-controlled, human-labeled corpora and one auxiliary jury-labeled source control, using four frozen encoders and prompt-grouped splits. On the human-labeled corpora the safe prototype reaches ROC-AUC 0.457-0.545, with two cells significantly below chance and one above, while an explicit safe-minus-unsafe reference reaches 0.588-0.738 on the same embeddings; on the jury control the prototype is inverted (0.358-0.405) and the reference reaches 0.754-0.793. At validation-calibrated 5% false-safe thresholds, the reference accepts more safe responses on PKU-SafeRLHF (0.153-0.263 versus 0.039-0.061 across encoders) and Aegis (0.189-0.291 versus 0.004-0.045), but not reliably on BeaverTails. A fully unlabeled held-out reference recovers part to most of the referenced ranking, much less when only 5% of the pool is unsafe, whereas 80-634 labeled unsafe responses recover most of it. Prompt-only ablations show that prompt-label composition can inflate uncontrolled evaluations. This is a bounded result about a raw positive centroid, not all one-class methods or safety-specialized guards. A class mean is a location, not necessarily a safety direction; a declared reference with enough unsafe mass identifies orientation.

Abstract: Dynamic architectures leave a per-example routing trace beside each prediction, and diffuse routing is easy to read as a sign that the prediction is unreliable. We audit that reading for routing entropy in Attention-Residual (AR) variants of Swin-Tiny and DeiT-Small, trained from scratch on CIFAR-10/100 with a soft-binned calibration auxiliary loss, asking whether the trace carries information about correctness beyond what the model's own confidence already reveals. Three checks probe this increment: does a routing signal appear at fixed confidence, does it replicate across training seeds, and can a held-out predictor exploit it against output-only and shuffled-trace controls? A sensitivity audit then injects effects of known size and measures the fraction of each that the probes recover. No test in the fixed 30-test binned family survives multiplicity correction, and neither the nominal hit nor a borderline result recurs in its sibling seeds. Across 24 paired runs a scalar routing probe yields no pooled improvement in routing-stratified calibration, and an entropy-profile probe predicts correctness better than the same probe given shuffled profiles yet worse than a confidence-only predictor in both binary log-loss and Brier score: a gain over shuffled traces does not become a gain over the output. Conditioning on the complete logit vector leaves the corresponding comparison unresolved. The audit bounds how far these non-detections can be read: at an injected effect of 0.010 nats the profile probe recovers 24-59% of the oracle gain, and a reference-preserving correction probe recovers 8% and 23% in the two CIFAR-100 settings, below the threshold we fixed for applying it to real labels. The results establish control-dependent gains and incomplete estimator recovery, not the absence of conditional routing information.

Abstract: Mixed-integer linear programs (MILP) model many real-world decision problems, motivating machine-learning methods that exploit recurring structure to accelerate MILP solving. MILPs can admit many equivalent formulations: integrality-preserving changes of variables and the addition of redundant constraints can alter their formulations while preserving the optimization problem. We leverage these reformulations as a source of self-supervision for learning general-purpose representations of MILP variables and constraints. We characterize the affine reformulations that are valid for every input instance, and distinguish re-descriptions, which leave variables unchanged, from substitutions, which transform them predictably. Building on equivariant self-supervised learning, we introduce ReMILP (reformulation-contrastive MILP representation learning), which jointly trains a graph neural network and a hypernetwork to predict how variable embeddings transform under changes of variables. Without solver-derived labels, ReMILP learns representations that exhibit the intended invariance and equivariance on unseen problem classes. Across binary solution, constraint activity and integrality gap prediction, these representations carry task-relevant information when frozen and provide a useful initialization for fine-tuning.

Abstract: Partial Optimal Transport (POT) extends the classical optimal transport problem by relaxing the strict mass conservation constraint, enabling its use in a wide range of real-world applications. In many of these settings, sparse transport plans are preferred for their interpretability and computational benefits. While smooth and strongly convex regularizers - such as quadratic or elastic net - have been vastly used in various machine learning applications to induce sparsity and accelerate computation, they have received less algorithmic attention compared to entropic approaches for computational POT. In this paper, we propose a new optimization framework that leverages these regularizers through a penalty-based reformulation, enabling efficient gradient-based updates while preserving the structure of the original problem. Our method accommodates a broad class of regularizers that promote structured and sparse transport plans. Building on this formulation, we design an accelerated first-order algorithm that alternates between smooth updates and simple projection steps. Through empirical benchmarks on color transfer, domain adaptation, and point cloud registration, our approach consistently outperforms established baselines - achieving lower transport cost, higher sparsity, and faster convergence - making it a practical and scalable solution for modern transport problems.

Abstract: Training data variation, whether through designing a domain randomization (DR) scheme in simulation or curating demonstrations for imitation learning, is a primary lever for improving the robustness of robotic manipulation policies. Yet its underlying mechanisms remain poorly understood, and practitioners typically select randomization parameters through expensive trial and error. We investigate these mechanisms through a series of case studies, randomizing object size, color, and type as well as scene lighting and linguistic prompts across settings including pick-and-place RL in ManiSkill and fine-tuning of vision-language-action (VLA) models on LIBERO and RoboTwin. We examine both model behavior and internal representations, using the empirical neural tangent kernel (NTK) as our primary diagnostic tool. We show that the NTK distinguishes a shift in the internal learning mechanism from \textit{memorizing} different situations with insufficient variation (e.g.\ learning what to do for a large cube, and what to do for a small cube) to \textit{adapting} to the situation at hand with sufficient variation. An NTK-based signal-to-noise ratio also helps distinguish when policies have learned to \emph{ignore} task-irrelevant factors (e.g.\ treating blue and red cubes identically, instead of learning a blue sub-policy and a red sub-policy). We use these diagnostics to develop practical guidance for designing DR schemes, selecting models, and detecting shortcut learning. We further compare different kinds of representations and validate our findings with real-world hardware experiments using ACT-based imitation learning.

Abstract: Evaluations of graph reconstruction by language models typically report a single aggregate distance between the original and the reconstructed graph. We prove that for the Wasserstein distance between Laplacian spectra such a summary is bracketed by two edge counts, the net change in edge number from below and the symmetric difference from above, each scaled by $2/n$ where $n$ is the number of vertices. The bracket is sharp: its two ends coincide exactly when the reconstruction only adds edges or only deletes them, and on that class the distance is a rescaled edge count that says nothing about which edges changed. When the ends differ, the residual between the distance and the lower end is positive only if the reconstruction both invented and lost edges, which turns it into a certificate of mixed editing computable from the reported summaries alone. We characterize these regimes in 135 reconstructions produced by three open-weight models over 45 synthetic graphs. Seventy-seven outputs are one-sided and 29 mixed outputs have $X > 0$, including cases where edge count is exactly preserved while nineteen edges were simultaneously invented and lost. The three models differ in editing policy, ranging from copying the input to attempting completion at the cost of large hallucination volume, a distinction that aggregate distortion does not reveal.

Abstract: Existing product matching benchmarks primarily contain English-language product data and are often dominated by a single product category, such as electronics. This paper introduces Billiger.de Products, a bilingual German and English entity matching benchmark covering thirteen consumer product categories, including difficult-to-handle categories such as clothing and furniture. The benchmark data originates from the German price comparison platform billiger.de. Following the design of WDC Products, the benchmark offers multiple variants that differ in the fraction of corner cases, the size of the development set, and the fraction of entities unseen during training. An aligned English translation of every offer keeps all pairs, splits, and labels fixed, while cross-language test sets combine German and English records within individual pairs. We validate the benchmark using six supervised matchers and zero-shot GPT-5.2 on both language versions and the cross-language test sets. The validation shows the difficulty of the benchmark. The comparison of the results on the English version of the benchmark to the results on the German version shows that most matchers score on average higher on the English version. The difference is largest for RoBERTa and HierGAT, while the zero-shot LLM runs are largely insensitive to the language. Comparing the F1 scores achieved by PLM-based matchers on the English version of Billiger.de Products with their performance on existing English-language benchmarks, such as WDC Products and Abt-Buy, shows that Billiger.de Products is more difficult than these benchmarks.

Abstract: Before invoking external tools, an agentic LLM must select among a K-way action space: executing a call, seeking clarification, answering directly, or declining. While internal activation steering can alter these pre-execution decisions, conventional aggregate metrics obscure where altered states land and what collateral damage they inflict. We present SAKIKO, an auditing framework that formalizes representation repair via directional error discovery, router-conditioned intervention, destination-resolved verification, and prospectively frozen statistical licensing. Across seven LLMs on When2Call and MetaTool, channel-keyed interventions induce direction-specific net gains in five models; across three sealed evaluations, none of 59 budget-matched random directions matches calibrated target gain. Crucially, destination auditing shows that behavioral movement does not equal repair: an intervention achieving +55 net gain corrupts over half of the baseline-correct decisions it touches, and promising point estimates on Qwen3-4B and Gemma-2-9B are formally declined due to finite-sample uncertainty. SAKIKO establishes the necessity of outcome-resolved adjudication before claiming internal repair. Code: https://github.com/ruizheliUOA/mechanistic-tool-use-llm.

Abstract: World models learn environment dynamics from interaction experience. These dynamics depend on the current state and actions, as well as on properties that persist across interactions. Yet standard predictive training can reduce error using local evidence alone, without organizing persistent information into reusable context. We introduce SPRII, a training principle that uses relations between interactions as weak supervision for persistent context while retaining the learner's native objective. For example, different trajectories of the same system share persistent properties even when their states and actions differ. SPRII uses such relations to guide context learning without numerical property labels. Two composable components encourage contexts from related interactions to agree (Align) and use one interaction's context to predict another's future (Cross). Our analysis distinguishes three linked questions: what persistent information is accessible in the learned context (Formation), how that context influences a fixed predictor (Use), and whether it reduces task error (Value). Success at one stage does not guarantee success at the next. Controlled experiments show that more reliable relations improve representation organization, but adding a shared-property constraint can reduce access to a property that remains shared. Context substitutions change predictions at fixed model weights, while the benefit from history depends on prediction horizon and readout. Evaluations span thirteen settings, including controlled physical systems, public dynamics tasks, robotic and tactile data, and partner interaction, across multiple learner families. Relative to the corresponding baselines, SPRII yields average gains of over 10% in downstream task performance and over 15% in persistent-property readout. The project page is available at https://persistent-learning-review.netlify.app/interactive.html.

Abstract: Adversarial attacks against object detectors are traditionally studied from an optimization perspective, where attack difficulty is regarded as an outcome observed only after adversarial optimization. This raises a fundamental question: \emph{can the relative attack difficulty of different inputs be characterized before optimization begins?} In this paper, we investigate this question for person-vanishing attacks by introducing the concept of pre-optimization attack difficulty, which captures intrinsic differences in optimization effort across input images. To estimate this latent difficulty before optimization, we propose Quad-CLEVER, an efficient geometry-based estimator derived from a quadratic approximation of the local person-vanishing margin along the most attack-relevant direction. Extensive experiments across multiple attack algorithms demonstrate that Quad-CLEVER consistently correlates with the observed optimization cost, providing empirical evidence that attack difficulty exhibits a predictable pre-optimization structure. Building upon this finding, we further propose a difficulty-aware attack framework that leverages the estimated difficulty to adaptively allocate optimization budgets for a base attack under a fixed computational budget. On BDD100K, the proposed framework improves the image-level attack success rate by up to 5.78$\%$ while reducing the average optimization cost by up to 11.42 iterations. On the more challenging EventPed dataset, it saves 2.25 optimization iterations while maintaining comparable attack performance. These results demonstrate that attack difficulty can be meaningfully estimated before optimization and that exploiting such estimates enables more computationally efficient adversarial attacks.

Abstract: We present a new class of near-linear algorithms for efficiently integrating general tensor fields defined on trees with distance dependent kernels, the Structure-Adaptive Tree Field Integrators (STAD-TFIs). STAD-TFIs exploit the tree's underlying structure through decompositions built around path backbones and single vertex separators, and use two-dimensional fast Fourier transforms to compute interactions jointly. By exploiting this structural information, STAD-TFIs achieve more computationally efficient integration than their regular efficient tree field integrators (TFI) counterparts. We provide a detailed theoretical analysis of our proposed approach and complement it with an exhaustive empirical evaluation, ranging from speed tests on synthetic trees, through accelerated Sinkhorn-based relaxations of the Optimal Transport algorithms on real meshes, to Topological Attention Transformers for vision tasks. To the best of our knowledge, we provide some of the first results showing that efficient to compute and accurate relaxations of the geodesic Sinkhorn-based solutions of the Optimal Transport problem can be derived by applying fast TFI methods.

Abstract: Understanding quantum phases of matter has long relied on physicists' intuition and mathematical tools such as symmetry and topology. Remarkably successful as these approaches have been, they provide no universal way to explore a Hamiltonian space whose organizing principle is not known in advance. In this work, we introduce a fully autonomous system combining differentiable programming and unsupervised learning for quantum phase discovery. The search evaluates ground-state data along an adaptive trajectory rather than on a predetermined parameter grid. We demonstrate the system with three different solvers and benchmark it against random sampling at equal ground-state-evaluation budgets. On a generalized cluster chain hosting up to $200$ distinct phases, the search finds up to $25$ more phases at the same budget, and matches random sampling given thirty times its budget. On a $50$-parameter Chern insulator, it reaches sectors not obtained by the simple harmonic constructions considered here, in a family whose inverse problem remains open, while recovering all sectors found by sampling. Our results establish autonomous, gradient-driven exploration of Hamiltonian space as a practical route to discovering quantum phases without phase labels or a prescribed target phase.

Abstract: Predictive coding (PC) is a local, energy-based alternative to backpropagation (BP) whose iterative inference dynamics make it attractive for implementation on analog hardware. However, standard nonlinear PC requires evaluating the derivative of the activation function during both inference and learning, which can be difficult to realise physically. Here, we introduce \textit{activation-matched Bregman PC}, replacing standard squared-error energies with Bregman divergences matched to the activation function. This formulation eliminates activation derivatives and, when combined with inference via mirror descent, yields local inference and learning rules requiring only weighted sums, local prediction errors, state integration, and the activation function. In digital experiments, Bregman PC performs comparably to standard PC and BP on classification and generative tasks, while preserving characteristic learning dynamics of PC and its convergence to BP under stable large-model parameterisations. These results provide a more analog-friendly formulation of nonlinear PC while retaining its key computational properties.

Abstract: Hyperbolic geometry has emerged as a principled space for representing hierarchical graphs. However, existing hyperbolic graph neural networks typically rely on shared curvature configurations and feature-driven attention, failing to explicitly exploit local hierarchical topological patterns. To bridge this gap, we introduce the Hyperbolic Sombor Index (HSO) as a lightweight structural prior for capturing hierarchy-indicative degree stratification. Building on this, we propose \textbf{HSO-GAT}, a topology-adaptive hyperbolic graph attention network that unifies geometric adaptation and message propagation. Specifically, it comprises two complementary modules: HSO-Guided Local Curvature Adaptation, which performs adaptive node-wise geometric scaling from aggregated node-level HSO signals, and HSO-Gated Hyperbolic Graph Attention, which enables structure-aware message passing through feature-conditioned gating. Theoretically, we establish the monotonic sensitivity of edge-level HSO to degree imbalance and analyze the validity and radial scaling properties of node-adaptive hyperbolic mappings. Extensive experiments on eight benchmark datasets demonstrate that HSO-GAT consistently achieves state-of-the-art performance in both node classification and link prediction tasks.

Abstract: Standard autoencoder (AE) inference uses a single encoder-decoder pass, though the latent may not be optimal for each sample under a fixed decoder. We ask whether a trained AE can reveal information for improving its own reconstruction. Repeated application of a frozen AE to its reconstruction produces transient image- and latent-space trajectories, termed Self-Reconstruction Dynamics (SRD). Although this degrades fidelity in the AEs studied here, SRD contains sample-specific information for correcting the reconstruction. We propose SRD-guided Reconstruction Refinement (SRD-RR), which predicts a latent correction from a short SRD with the AE frozen and no per-sample test-time optimization. We also introduce MSE-recov, an MSE recovery ratio relative to an empirical decoder-optimized reference. Across six datasets, SRD-RR recovers 38.6% of the empirically recoverable MSE gap with one transition and 45.3% with two. A two-transition variant trained without direct access to original images, using an SRD-derived pseudo-target, achieves 40.7% recovery and a 1.74 dB average PSNR gain. Removing trajectory information reduces the gain, while cross-sample trajectory assignment causes severe degradation, confirming strong sample specificity. Nonlinear SRD-conditioned refinement consistently outperforms fixed and trained linear latent correction. On a pretrained DINOv2-based representation autoencoder (RAE) with substantially different latent dynamics, SRD conditioning again improves a matched trajectory-free predictor. However, pixel-MSE latent refinement reveals a strong mismatch between pixel fidelity and perceptual quality, while the SRD-derived pseudo-target mitigates this degradation. Overall, SRD is a useful sample-specific refinement signal, while the objective determines how it translates into pixel and perceptual quality.

Abstract: We study whether benchmarks reliably guide model selection as developers adapt to evaluation feedback across multiple criteria. We find that the worst-case test-set size needed to estimate the best score among $k$ adaptively chosen models, under any convex combination of the criteria, grows exponentially with the number of criteria, reaching the $Θ(\sqrt{k})$ cost of answering $k$ adaptive statistical queries with only $O(\log k)$ criteria, at fixed accuracy and confidence. In attacks on multi-task large language model benchmarks with five to ten criteria, feedback restricted to nondominated task profiles produces large reused-to-held-out score gaps and frequent false winners. These results challenge a prominent explanation for prior observed reliable benchmark reuse---that developers mainly respond to convincing improvements over the current best---in rich-feedback settings, while leaving open how often ordinary model development encounters this vulnerability.

Abstract: Inference in LLMs is conventionally a fixed-depth, fixed-order forward pass through every layer, regardless of how difficult the input is. The human brain does not work this way: using the thalamus as a central hub, it routes information flexibly to all regions of the cortex according to demand. Li et al. (2026) recently showed, with a system they call program-of-layers (PoLar), that transformers can be given an analogous flexibility if their layers are treated as a library of functions rather than a fixed sequence. Performance improves over the standard forward pass when each input is dynamically routed through an adaptive sequence of skipped or repeated contiguous layer blocks. We reconstructed PoLar's diagnostic MCTS in more detail than the original paper and applied it across 5 models. We reproduced several of PoLar's findings: skipping outperformed the standard pass, repeating outperformed skipping, and combining both outperformed either alone. Shorter programs sufficed for easier questions, while harder questions required more layer repeats. However, we failed to replicate the main claim regarding their learned router for single-shot inference: its top-ranked prediction consistently collapsed back to the standard pass, even though its top-k predicted programs, taken together, did show a real accuracy gain. Beyond reproduction, we find that a small number of generic programs are enough to solve most of the questions. We also provide a much deeper analysis of these programs' structure and robustness: for example, we found that programs that correct errors are highly brittle: undoing even a single edit inside a program typically breaks the correction. Connecting this to the brain's routing mechanisms, PoLar mirrors principles of thalamo-cortical coordination between cortical-area-like transformer layers. We publicly release the code at https://datexis.github.io/RE-PoLar/

Abstract: For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant. This removes the dependence on the Poincaré constant in the theorem of Kothari and Steinhardt (arXiv:1711.07465), recovering the optimal moment bounds for log-concave distributions. As an immediate corollary, we obtain computationally efficient algorithms with dimension-free error guarantees for a wide range of high-dimensional statistical estimation problems. Our proof uses stochastic localization to decompose $P$ as an average of random strongly log-concave measures, whose centered moments admit the subgaussian certificates of Diakonikolas, Hopkins, Pensia, and Tiegel (STOC 2025; arXiv:2410.21194). With a covariance-adapted choice of localization, we show that a fourth-moment certificate derived from Letwin's variance inequality for quadratic forms (arXiv:2607.24164) suffices to control this averaging at every even degree.

Abstract: Explanations are central to causal reasoning, and cognitive science has long established that the human drive to explain is itself a mechanism for learning about causality. Despite this, learning from those abductive signals is largely ignored in artificial intelligence. While explainable AI (XAI) increasingly draws on causal models to generate explanations, the converse direction about what explanations can do for causality remains largely unexplored. To fill this gap, we propose xWhyL, a formal framework connecting causality and XAI by learning causal models from explanations. We develop a mathematical theory that translates explanations into a learning signal complementary to observational data, and demonstrate how it enables overcoming the limits of observational causal discovery. As explanations can be derived from incorrect beliefs and clash with data, a tension we call the Causal Tug-of-War, we prove conditions under which our framework rejects misspecified explanations rather than absorbing them. Our practical instantiation, Causal Interactive Learning (CIL), shows how expert explanations can efficiently support causal discovery and distinguish correct from incorrect explanations.

Abstract: Multi-task optimization (MTO) addresses a set of optimization tasks simultaneously, often suffering from inaccurate inter-task relationship estimation under limited evaluation budgets, leading to negative transfer. This paper introduces In-Context Guidance Multitask Optimization (ICG-MTO), a novel framework that leverages numerical foundational models to improve inter-task coupling estimation in few-shot scenarios. Unlike conventional methods that rely solely on scarce observed data, ICG-MTO employs a frozen foundational model to infer auxiliary guidance through in-context learning. The framework operates through three stages: constructing an algorithm-specific in-context query from evaluated solutions, using the foundational model to infer a guidance signal characterizing predictive relationships among tasks, and translating this signal into algorithm-specific guidance for maximum-a-posteriori coupling estimation. This approach provides regularization during the early, data-scarce stages of optimization and gradually relinquishes control as task-specific observations accumulate. We instantiate the framework in multitask Bayesian optimization as ICG-MTBO, using directional fitness-class queries to guide inter-task coupling estimation, and further instantiate it in MFEA-II using decision-space-overlap queries to guide random mating probability estimation. Experiments across synthetic benchmarks and a real-world robot arm control problem, together with evaluations under different acquisition functions and evolutionary multitasking, demonstrate the effectiveness and generality of ICG-MTO for few-shot multitask optimization.

Abstract: Discrete action tokenization is central to autoregressive vision-language-action (VLA) models, yet action representations are often evaluated primarily through reconstruction fidelity. We ask which representation properties actually matter for closed-loop control by comparing fixed analytical, data-driven linear, and nonlinear neural representations under a unified tokenization interface. Across rate-distortion analysis, sequence-modeling diagnostics, and 3,500 LIBERO rollouts, representation rankings change with the evaluation criterion. PCA achieves lower nominal reconstruction error than Temporal-DCT, but produces less predictable token sequences and 3.0 percentage points lower mean seen-task success across three policy-training seeds, with the policy ordering reversing in one seed. In a matched seed-42 ablation, an autoencoder further reduces reconstruction error yet does not yield the strongest policy and exhibits greater sensitivity to discrete token perturbations. These findings show that reconstruction fidelity alone cannot reliably select action representations for autoregressive control, motivating joint evaluation of geometric fidelity, sequence predictability, decoder stability, and closed-loop performance.

Abstract: Modern embodied agents achieve impressive success rates, yet their actual instruction-following ability is far weaker than these numbers suggest. We trace this illusion to a structural property we term low scene entropy: when a visual scene admits only one valid task, language becomes redundant and a policy can score highly while barely using it. We introduce RoboFollow, a diagnostic benchmark with three principles: (1) High Scene Entropy: each training scene supports multiple kinematically distinct task branches, making vision alone insufficient and forcing reliance on language. (2) Hierarchical Diagnostic Protocol: a four-level protocol (L0--L3) progressively perturbs visual layout and semantics, probing whether equivalent instructions yield consistent behavior and distinct ones yield discriminable behavior across spatial relations, attributes, trajectory constraints, and logic. (3) Confound-Controlled Diagnosis: we simplify interaction objects, restrict actions to the trained repertoire and report stage-wise Intent and Execution scores, isolating comprehension from motor execution. Evaluation of nine VLA and WAM policies shows that strong L0 performance, where attained, does not reliably transfer to L1--L3 under our fine-tuning setup. Representative mitigations, including stronger VLM backbones, QA co-training, LangForce, and Classifier-Free Guidance, all fail to close this gap. RoboFollow exposes genuine instruction following as a critical, overlooked bottleneck. Code and dataset are available at https://github.com/AutoLab-SAI-SJTU/RoboFollow and https://huggingface.co/datasets/AutoLab-SJTU/robofollow-data.

Abstract: We study the complexity of finding $(δ,ε)$-Goldstein stationary points of nonsmooth nonconvex Lipschitz functions. By now, it is known that randomized first-order algorithms can solve this task with a dimension-free oracle complexity [Zhang et al., 2020], whereas deterministic algorithms cannot, as their complexity must scale at least linearly with the dimension $d$ [Jordan et al., 2023, Tian and So, 2024]. This leaves open whether deterministic algorithms can nevertheless solve the problem with oracle complexity polynomial in $d$. We answer this question negatively by proving a lower bound of order $(1/ε)^{Ω(d)}$ for deterministic algorithm, closing the exponential gap between the previously known lower and upper bounds and resolving an open problem posed by Jordan et al. [2023]. We further discuss several extensions and implications of this result to weaker stationarity notions, finding a descent direction and deterministic smoothing. Overall, our results establish an exponential computational advantage in nonsmooth nonconvex optimization offered by randomization.

Abstract: Communication can bring agents into agreement while making their decisions worse. We identify two limits of aggregate descriptions of communication gain in distributed inference. First, stable linear systems with fixed evidence, network and readout can have interaction and finite-time state operators with identical eigenvalue and singular-value spectra, yet produce gains of opposite sign. Changing only message orientation raises accuracy from 72.6% to 91.2% or lowers it to 65.9%. A standard task-projected local-response approximation retains the directional information missing from spectral summaries. Using labeled calibration data separate from the test set, it predicts multi-round gains in small trained nonlinear agents with a root-mean-square error of 0.45 percentage points on two synthetic tasks; tests with natural edge changes and handwritten digits extend the evaluation. Second, under community-shared bias, higher mean individual accuracy can coexist with harm to unaffected communities or lower global-vote accuracy. At fixed communication rounds, calibration constraints reduce observed community harm while retaining much of the mean benefit, but do not guarantee protection. Full direct calibration performs similarly. The results connect spectral insufficiency, task-aware prediction and the distribution of communication benefits, while leaving broad transfer and practical superiority open.

Abstract: We study differentially private covariance estimation in operator norm for mean-zero sub-Gaussian distributions with unknown covariance support and at most $k$ nonzero entries per row. We develop a multiscale random-threshold algorithm with sample complexity $\ot(k^2/α^2+k\sqrt d/(α\varepsilon))$ for $(\varepsilon,δ)$-differential privacy and error at most $ασ^2$, where $d$ is the dimension and $σ$ is a known sub-Gaussian scale. The bound improves the privacy-dependent term of the existing $\ot(k^2/α^2+k^{3/2}\sqrt d/(α\varepsilon))$ \citep{kumar2026curse} upper bound by a factor of $\sqrt k$, and matches the lower bound of $\widetildeΩ(k^2/α^2 + k\sqrt{d}/(α\varepsilon))$ in its applicable parameter regime. Our key technical ingredient is a direct operator-norm bound on the centered fluctuations of an ideal reconstruction, exploiting conditional independence rather than accumulating entrywise errors across each row. A multiscale allocation of threshold tests balances reconstruction variance against query sensitivity. Together, these ingredients sharpen the trade-off between approximation error and privacy protection, removing the additional $\sqrt{k}$ factor from the privacy-dependent sample complexity.

Abstract: Recent advances in video generation allow robots to learn manipulation trajectories from generated videos. However, these approaches produce purely kinematic trajectories that lack force information, causing failures in contact-rich tasks where appropriate contact forces are essential for success. In this work, we explore augmenting generated video with audio to shape a bounded, time-varying desired-force profile using the loudness of generated contact sounds. We present a pipeline that jointly leverages generated video and audio to derive motion trajectories and corresponding desired-force profiles from a structured natural-language task prompt. We execute these force-aware trajectories on a Franka Panda robot using a closed-loop force regulator that tracks the audio-shaped force profile during contact. We evaluate our pipeline on multiple tasks that require making contact and demonstrate successful manipulation where a kinematic-only baseline fails. We also use the pipeline as a data generation engine to train policies that achieve the tasks in a closed-loop manner. Project website, videos, and dataset: https://dreamingcontactsound.github.io/

Abstract: Recent work shows that models that learn to reward hack on RL environments can become broadly misaligned, and that reframing reward hacking as acceptable behavior during training (inoculation prompting, or IP) blocks this generalization. We ask whether synthetic document finetuning (SDF) can inoculate a model against future training we don't intervene on. We add synthetic documents framing reward hacking as acceptable behavior to a model's midtraining corpus, and then train these models with RL on exploitable environments, teaching them to reward hack. Behaviorally, midtraining succeeds: models describe reward hacking favorably and are more approving of reward-hacking outputs they produce. However, they show strong EM after learning to reward hack, while IP in the same setting prevents EM. We show that SDF can predictably steer downstream generalization when inserting new associations, but struggles and has unpredictable effects when overriding existing associations, such as that between reward hacking and misalignment that produces EM. Our results suggest that, at the scales we test, SDF can make a model appear aligned with desired beliefs while steering its generalization from later training in unintended ways.

Abstract: Alignment applied after pretraining is shallow in a measurable way: a single direction in a model's residual stream can be edited out, and the model stops refusing harmful requests. That fact says how easily refusal can be removed, not what the refusal decision was reading in the first place. We ask what it reads, and we separate that from what the model comprehends. Across four open-weight models spanning three families, moral comprehension is native to pretraining: a low-rank moral subspace crystallizes during pretraining, and alignment rotates it once without rebuilding it. The refusal gate, in contrast, is a fresh post-training construction with only a weak pretraining precursor, written into a narrow control-token channel where the refusal decision is orthogonal to the moral-judgment decision. The central result is causal and comes from one model, OLMo-3. A nested interchange rank sweep patches successively larger slices of the moral subspace between matched requests and reads how much of refusal's response transfers: as the basis widens, moral judgment keeps reading more of it, while refusal levels off at the level of a single harm direction, and about three-quarters of refusal's causal input lies outside the moral subspace altogether. Refusal reads the harm percept, not the moral content that judgment reads on the same patches. The picture is not uniform across families. Llama reads broad moral content; Qwen reads beyond the single harm cue but is unresolved at our sample size; GPT-OSS reads harm, and its refusals can be argued in either direction by its own reasoning trace. Where refusal reads only a low-rank slice and routes around the bulk of what the model knows, a rank-one edit removes it. Whether widening what refusal reads would also deepen the behavior is the open question this raises.

Abstract: Cryptanalytic extraction attacks recover the parameters of a neural network given only black-box access to its raw output. However, all existing attacks rely on a fundamental assumption: the attacker knows the network architecture. For example, regarding ReLU activation-based fully connected networks, the network depth and the dimension of each hidden layer are known. In this paper, we study whether this assumption can be removed. We focus on ReLU fully connected networks and propose a guess-and-determine framework that recovers the architecture and the parameters jointly. The core of our approach is a simple but powerful observation: dimension guessing leaves architecture-sensitive traces in the parameter recovery process. We identify two such traces: (i) a \emph{zero suffix} in the merged weight vectors produced by signature recovery, whose length reveals the number of excess guesses; and (ii) an \emph{equality pattern} in the preimage-based sign recovery, which occurs only when the dimension guess is correct. These two signals give rise to two complementary recovery routes. We further propose two criteria for identifying the second-to-last layer, which is necessary for terminating the guessing process. We implement end-to-end attacks on a wide range of ReLU networks, including both expansive and non-expansive architectures. To the best of our knowledge, this is the first cryptanalytic extraction attack that removes the assumption of known network architecture.

Abstract: Identifiability of tensor decompositions is often established through linear-algebraic conditions on the factor families. For nonnegative decompositions, however, positivity provides additional information that is not captured by dimension and independence alone: nonnegative terms cannot cancel, and their supports constrain competing decompositions. We introduce a positive scattering term that quantifies this additional source of identifiability and combine it with the dimension budget underlying the Lovitz--Petrov generalization of Kruskal's theorem. For every subset of components, we obtain two sufficient conditions: a threshold of $2|S|-2$ guarantees minimality and nonnegative rank, while the stronger threshold $2|S|-1$ guarantees uniqueness among nonnegative decompositions of the same length. The key result is a positive splitting inequality for irreducible exchanges of nonnegative rank-one tensors, which combines the dimension constraint with support-induced geometric rigidity. Although the scattering term is defined through an optimization over intermediate factor spaces, we show that its mode costs are exactly $0$, $1$, or $+\infty$, yielding an exact activation characterization in terms of graph connectivity. The resulting criterion can strictly certify sparse nonnegative tensor decompositions beyond the reach of Kruskal and Lovitz--Petrov conditions, including examples for which those conditions fail even after reshaping. In the matrix case, the two criteria reduce respectively to full-rank factorization and two-sided separability.

Abstract: Hard symmetry constraints reduce model complexity, but can also erase label information. Statistical symmetry release determines when finite data and quantum measurements justify relaxing such a constraint, which directions to open, and how far to move. We connect global signal detection to local, loss-dependent improvement. A two-copy twirl--swap gate estimates task information in the symmetry-breaking complement with a dimension-independent copy count under paired-state and group-unitary access; reweighting the same records resolves representation sectors. An exact duality distinguishes this Hilbert--Schmidt signal from the larger signal accessible to bounded-outcome readouts. Local improvement is governed by the release gradient and a loss-corrected double-commutator matrix. Simultaneous confidence bounds convert empirical direction selection into certified descent, using either shared Pauli measurements or scalar probes with state-independent truncation bounds. Gaussian testing lower bounds quantify the cost of searching over unknown directions in the calibrated local experiment. Independent validation controls adaptively generated models, and a fast squared-loss bound preserves the approximation--estimation rate of a nested release path. On an eight-qubit Ising model, shared measurements certify release with 6300 times fewer shots than the specified scalar estimator on the tested budget grids. Quotient quantum natural gradient then controls parameter redundancy during training. Together, these results turn symmetry relaxation into a statistically justified model-selection decision.

Abstract: A wrong answer does not show whether the model lacked the needed information or held it and failed to use it. On an entity-obligation binding task, a language model can emit an incorrect prompt-supplied binding while a linear probe can recover the correct one from its frozen hidden state. We measure how often this occurs across 16 public checkpoints, each evaluated with three seeds. We fit a probe on a training fold, select its layer on a validation fold, and report results on a disjoint test fold. On the trials each model gets wrong, probe accuracy exceeds the strict present-obligation baseline, 1/K = 0.125, by +0.196 (95% CI [+0.101, +0.296], bootstrapped over models). A query-entity counterfactual rules out token presence and recency. A score built from the sign of probe-output disagreement improves failure detection over the model's own confidence by +0.079 AUROC (95% CI [+0.036, +0.126]). Raw probe confidence gives no measurable improvement over model confidence. Steering the residual stream toward the probe-decoded binding, with no gold label, raises accuracy on all eight models tested by a mean of +0.168 (95% CI [+0.066, +0.280]). Where recent studies report that probe-detected errors are resistant to interventions, we find that in-context binding is a setting in which probes are actionable.

Abstract: Motivated by data produced by generative systems, \cite{LZ26b} formulates similarity-aware statistics via a weighted similarity graph, replacing equality with similarity in classical frequency-based statistics. Although this framework captures semantic relationships between nonidentical items, under general similarity functions even coarse one-pass approximation can require linear space. We therefore ask whether the geometric structure present in natural vector similarities can overcome this barrier. We answer this question affirmatively for the Gaussian kernel. For fixed-dimensional Euclidean vector streams, we study similarity-aware analogues of classical frequency statistics, including the number of distinct elements and frequency moments, through the diversity index and Gaussian density moments. We give one-pass sublinear-space approximation algorithms that exploit the geometric and analytic properties of the Gaussian kernel, and complement them with lower bounds. Our results show that geometric structure can fundamentally change the streaming complexity of similarity-aware statistical analysis.

Abstract: Simulatability is an evaluation protocol for explanations that quantifies their usefulness by how well they help a user predict a task model's outputs. Since human evaluation is costly, automated simulatability replaces human explainees with LLM simulators, as proposed in ConSim (Poché et al., 2025) for large-scale experiments. We qualitatively replicate and extend ConSim's ranking of explanation methods across the tested datasets, explanation families, and simulator LLMs, and identify two limitations. First, when class names are meaningful, simulators can obtain high simulatability by solving the classification task directly, without relying on the explanations. Second, class anonymization can reward explanations for leaking the hidden label mapping, a limitation we expose with a new classes-as-concepts baseline. These results are consistent with a shortcut hypothesis: in the tested settings, simulator predictions mainly rely on task priors, while explanations produce small changes. We derive recommendations for more robust automated simulatability evaluations.

Abstract: Robotic manipulation often requires acting on information that is no longer visible, yet Vision-Language-Action policies are usually evaluated when the current observation largely determines the next action. Existing robotic memory benchmarks expose this gap, but they still rely mainly on final task success and therefore conflate forgetting with manipulation failure. We present \textbf{MEMOBench}, a benchmark for process level memory evaluation in robotic manipulation. MEMOBench includes 30 history dependent tasks, 1{,}500 expert demonstrations, and 4{,}200 executable checkpoint instances from 84 templates. Each checkpoint pairs coarse to fine language with a simulator predicate and labels one memory operation: Storage, Update, or Compression. These annotations define Memory Storage Rate, Memory Update Rate, and Memory Compression Rate, which measure memory fidelity alongside task success. Across standard and memory augmented VLA policies, the strongest memory module baseline reaches only 31.9\% average success rate, and high storage often coexists with weak update and compression. Checkpoint language also supervises semantic, contrastive, and framewise memory alignment objectives, yielding modest gains across different memory operations. MEMOBench provides a diagnostic evaluation suite and training supervision for memory grounded robotic policies. The project page is available at https://github.com/Collab-Gen/MEMOBench.