Papers

Modern neural networks are often miscalibrated, with a tendency to overconfidence. Existing train-time calibration methods largely modify task losses or calibration penalties, leaving neighborhood structure in learned representations underexploited. We introduce graph smoothing as a general principle for train-time calibration, which encourages similar predictive distributions across neighboring samples in representation space. We analyze the effects of graph smoothing, deriving bounds that connect predictive divergence between neighboring samples to local confidence variation and to the propagation of pointwise calibration error, and characterize the conditions under which smoothing can or cannot improve calibration. In light of this analysis, we propose \modelNoSpace, a graph-based train-time regularizer that penalizes the Jensen–Shannon divergence between predictive distributions of neighboring samples. We present a thorough empirical analysis, showing that across standard calibration benchmarks, \model improves predictive quality, and the improvement is complementary to post-hoc calibration: after temperature scaling, \model attains the lowest NLL of all evaluated train-time methods in seven of the eight image and tabular settings. These findings demonstrate the value of graph smoothing over learned representations for neural network calibration.

Vision-language-action (VLA) models map visual observations and language instructions to continuous robot actions. This task requires a transition from representations that describe the scene and instruction to representations that support action generation. Many continuous-action VLAs leave this transition implicit and supervise it mainly through the final action-prediction loss. We introduce PAIR, a framework that learns a shared perception-action representation between these two spaces. During training, a Masked Action Autoencoder encodes expert action chunks into horizon-aligned Action Latent Tokens. A Bridge Module extracts task-relevant features from the current visual-language representations. PAIR aligns these features with the Action Latent Tokens to form Bridge Tokens that preserve task information and capture the structure of expert actions. The Bridge Tokens are then projected into the action-token space and injected into the initial Action Tokens, providing an action-ready starting point for Action Expert refinement. At inference, the autoencoder is removed, and the Bridge Tokens are generated only from the current observation and instruction. Experiments on LIBERO, LIBERO-Plus, and CALVIN ABC-D show gains for the evaluated OpenVLA-OFT and VLA-Adapter models. On LIBERO-Plus, PAIR raises VLA-Adapter's success rate from 59.1% to 64.2%. On CALVIN, it increases VLA-Adapter's average completed sequence length from 4.42 to 4.53. Across seven real-world tasks, PAIR raises OpenVLA-OFT's success rate from 51.4% to 65.0%. Representation analyses show that Bridge Tokens retain task information while making continuous-action information accessible before Action Expert refinement. These results support a shared intermediate representation as a useful interface between perception and action in continuous-action VLAs.

Diffusion models can generate high-quality images, yet aligning their outputs with individual user preferences remains challenging. A key bottleneck is accurately modeling diverse user preferences from limited feedback. Existing approaches often rely on labor-intensive manual preference annotations or vision-language models (VLM) to extract preference information from user interaction histories, introducing substantial annotation or computational costs that limit scalability. We propose an approach that learns personalized reward models directly from users' historical image preference pairs. First, we use an autoencoder to compress hundreds of visual attributes into 50 attribute-anchored preference dimensions and train an evaluator to score images along these dimensions. We then represent each user's preferences as a linear combination of the shared dimension scores, estimating the user-specific weights by maximizing the likelihood of their observed pairwise preferences under the Bradley-Terry model. This formulation reduces per-user adaptation to optimizing a low-dimensional weight vector, simplifying optimization and enabling data-efficient personalization from sparse feedback. The learned personalized rewards guide image generation at inference time while keeping the diffusion model frozen. Experiments on real-user preference data show that our approach achieves approximately 77% held-out pairwise preference prediction accuracy and improves the alignment of generated images with individual user preferences.

Looped LMs are parameter efficient and promise dynamic computation (saving memory and FLOPs on easy tokens). However, state-of-the-art open Looped LMs trained with this dynamic computation capability (Ouro models) do not realize it in practice as each loop iteration (depth) requires its own level of KV-cache, necessitating all loop computations. Moreover, Ouro's early-exit prior is enforced on each token equally, which results in static lower-depth like processing of all tokens regardless of difficulty. In this work, we propose a simple "best-available" KV caching strategy that works out-of-the-box, creating a new frontier in the performance vs depth space. Our approach enables up to 30% reduction in FLOPs and KV memory while retaining full-depth performance, showing the true flexibility of Looped LMs. Furthermore, training looped LMs with awareness about this KV caching strategy improves performance and efficiency. Finally, we apply a small but effective fix to the early-exit prior enforcement objective that makes tokens exit at truly heterogeneous depths based on effort. Our findings are validated on Ouro models as well as smaller looped LMs pre-trained from scratch.

Future generative patient digital twins may combine longitudinal health records with language-model agents and keep information across sessions. The wording of a proposed update does not reveal whether it comes from an allowed source, conflicts with the patient's record, or belongs to someone else. We present TwinGuard-Lite, a rule-based gateway that admits an update to a twin's persistent state only if it passes checkable approximations of two integrity properties. Grounded state consistency (GSC) is approximated by a provenance check and a contradiction check; cross-patient noninterference (CPN) is approximated by a namespace check against trusted transport metadata. We evaluate three attack families over 20 seeded person-level splits of a semi-synthetic stream built from the openly licensed eICU database demo, with 29,131 $\pm$ 2706 candidate updates per seed. A keyword filter and an anomaly detector detect 16% and 24% of attacks, respectively; a provenance-only ablation detects 59.9% but misses every cross-patient attack. Combining GSC and CPN yields 99.1% precision, 90.5% recall, a 94.6% F1 score, and a 0.033% false-positive rate. Every attack the full gateway admits falsely claims a trusted source; when the retrieval channel does so, 92.9% of retrieval attacks are admitted. The results hold under stated trust assumptions, and no language model, agent, or retriever is executed: TwinGuard-Lite is a mechanism-level proof of concept that motivates authenticated, patient-bound ingestion, not a clinical safeguard.

Function-correcting codes (FCCs) protect the value of a function $f$ of the message against $t$ errors. In the original formulation of Lenz et al. (2023), the encoding is systematic, and the lower bound of $2t$ on the redundancy relies on this form. Recently, D. Ho (arXiv, 2026) showed, for linear functions and linear encodings, that systematicity can cost redundancy. We begin with the OR function to show that the cost is not confined to the linear setting: a non-systematic encoding attains redundancy $1$ while every systematic encoding needs $2t$. For a linear function $f$ and a fixed linear code $C$, let $d_f$ denote the minimum distance between codewords of messages with different function values. Different generator matrices of $C$ assign different codewords to the messages and can give different values of $d_f$. We study which generator matrix of $C$ gives the largest $d_f$. We give an algorithm that constructs an optimal generator matrix and determines the optimal value as the weight of a codeword in a greedy basis of $C$. We then characterize, in terms of information sets, when a generator matrix in systematic form attains this optimum, and give a necessary condition that is checked on the low-weight codewords of $C$ alone. For two-valued functions, we drop both linearity and systematicity. Using the minimality of initial segments of the simplicial order with respect to Hamming neighbourhoods, we show that a non-systematic $(f,t)$-FCC of length $n$ exists if and only if a condition depending on $f$ only through the size of its smaller preimage holds. For $t=1$, redundancy $1$ is sufficient for every nonconstant two-valued function on $\mathbb{F}_2^k$ with $k\ge 10$. For general $t$, redundancy $1$ suffices for all two-valued functions once $k$ is large enough, and for each $s<2t$ we give an upper bound on the threshold in $k$ beyond which redundancy $s$ suffices.

Persistent memory allows an LLM agent to carry experience across conversations, but it also turns a local reasoning mistake into a durable one. During deliberation, an agent may consider a plan, simulate a tool result, report another speaker's belief, and then reject all of them. If memory retains only the resulting sentences, those once-useful possibilities can later return as facts. The record is neither fabricated nor irrelevant; it has simply been detached from the context in which it was valid. We identify this missing context as discourse ownership: the world, branch, or speaker that licenses a proposition. Our first finding is counterintuitive. Language models already carry a causally active signal for ownership, yet conventional memory interfaces discard it when they convert reasoning into records. We introduce CASK (Causally Anchored Scoping Keys), a commit rule that preserves this signal so that shared-world facts enter durable memory while provisional content remains available only within its original scope. Our second finding is that the most obvious way to preserve the signal—storing the discovered internal coordinates—is unreliable because equivalent representations need not keep the same coordinates. CASK instead preserves the stable relations that express ownership. Controlled long-conversation conflicts and tool-agent traces show that this design improves memory admission and prevents provisional content from contaminating later answers while complementing runtime provenance. The resulting commit boundary lets agents explore more possibilities without granting every intermediate sentence authority over future behavior.

Detection engineers must translate threat reports, forensic observations, and hunt hypotheses into precise, testable rules. General-purpose large language models (LLMs) can draft such rules, but often produce invalid YAML, incorrect log sources, unsupported fields, or overly broad detection logic. This paper presents Sigma-Hunter, a domain-adapted LLM for analyst-assistive Sigma rule generation and threat hunting. We build an instruction-tuning dataset from 3,635 validated open-source Sigma rules, expanded into 7,663 question-answer and analyst-reasoning examples. Each source rule is assigned to a single train, validation, or test partition before this expansion, so no rule leaks across splits. We fine-tune a 7B Mistral model and a Phi-4 model with LoRA and score held-out rule generations on syntax, approximate field consistency, and a semantic judgment of detection logic, completeness, selectivity, and log-source alignment. Sigma-Hunter-Mistral scores 8.17 overall, against 7.88 for the strongest general-purpose baseline and 4.61 for untuned Mistral. Two findings stand out: domain adaptation enables a compact 7B model to perform competitively with larger general-purpose models on this structured task, and syntactic validity is a weak proxy for semantic rule quality, as several baselines emit well-formed YAML carrying weak detection logic. The adapted models run locally, which suits detection engineering in disconnected environments where analysts cannot reach hosted model services.

This diploma thesis documents the conversion of a petrol-powered go-kart into a battery-electric kart with a 10 kW BLDC drive, a LiFePO$_4$ traction battery with battery management system, a slip-based traction control and regenerative braking. The traction control estimates the slip of the driven rear axle from three Hall-effect wheel-speed sensors as $\lambda = (v_R - v_F)/v_R$ and reduces the torque command of the throttle pedal when the axle slips. It runs on a 32-bit ARM Cortex-M3 microcontroller (SAM3X8E) in the signal path between pedal and motor controller, with galvanic isolation and an emergency stop. Regenerative braking uses the generator mode of the motor controller in three stages: motor brake on throttle release, light braking via a steering-wheel button, and blended braking with the hydraulic brake. Drivetrain calculations show that the kart is traction-limited. At rated torque, the drive force at standstill exceeds the transmissible traction force by a factor of 1.7 to 2.0, up to approx. 27 to 43 km/h. Traction control is therefore a functional requirement of the drivetrain. The calculated top speed is approx. 65 km/h. Regenerative braking reaches approx. 0.45 g and could cover up to about 30 % of the energy demand on a winding track. With 80 % of the nominal battery energy, approx. 44 min of driving at 50 % motor load result, so the target of one hour is missed. The initial charging measurement quantifies the flat LiFePO$_4$ voltage plateau at 0.7 to 1.8 mV per percent state of charge, which makes voltage-based state-of-charge estimation unreliable. Cold cells showed a voltage sag under load that triggered the low-voltage alarm. Validation of the control functions by instrumented driving tests is the main open point.

Number libraries, which implement number formats and their arithmetic in software, are used to simulate hardware, making hardware behavior reproducible and thus verifiable and easier to design. However, modern machine learning accelerators are difficult to simulate, as they increasingly use specialized number formats that existing number libraries do not support. It is costly to extend these libraries using traditional methods: each combination of operation, format, and rounding mode typically requires a bespoke implementation. An easier way is to double round - compute at higher precision, then re-round - so that one high-precision kernel serves many formats, but double rounding is only known to be correct in select cases. We give a precise, efficiently checkable characterization of when double rounding is correct across many formats and rounding modes. Our result rests on a novel abstract number format that unifies fixed- and floating-point representations, reducing the correctness of double rounding to format containment: whether every value of one format is representable in another. We mechanized these results in Lean 4. In addition, we introduce a format inference algorithm that, given a sequence of operations, bounds each expression by a number format guaranteed to contain its result. We apply these insights in two ways. First, we present MPFX, a correctly-rounded, multi-precision number library that exploits correct double rounding to efficiently simulate many number formats. MPFX's correctly-rounded operations are up to 11x (mean: 6.05x) faster than MPFR's, and competitive with SoftFloat's - between 0.46x and 1.63x as fast (mean: 0.94x) - at the same precision. Second, in a case study, we implement a software simulation of a hardware specification using both SoftFloat and MPFX's primitives; the MPFX version is up to 13.5x faster.

Does removing harmful information make open-weight models resistant to fine-tuning attacks? We show that mutual information at release alone cannot universally certify slow recovery. Function-preserving reparameterizations leave information unchanged while altering gradient-descent geometry, so an invariant certificate is bounded by the fastest reachable parameterization. We apply this principle to weight–data mutual information under training-data filtering and label–representation mutual information under capability removal. Training order can change recovery time at fixed weight–data information, while exact representation-level independence can preserve the entire parameter Jacobian. An explicit construction has both information quantities equal to zero and recovers in one gradient step. Controlled experiments illustrate order-dependent recovery and parameterization-dependent attack speed. These results identify the missing requirement for certification: constraints on attack dynamics beyond mutual information at release.

Autoregressive Large Language Models (LLMs) frequently struggle with deterministic multi-step algorithmic tasks such as multi-digit multiplication and long division. In this paper, we investigate the mechanics of multi-step arithmetic in compact "Tiny" Transformers (~10.6M non-embedding parameters, 49.3M total) trained on synthetic data across four basic operations (+, -, *, /) unrolled as step-by-step scratchpads. First, we establish the necessary training foundations: (1) dataloader sequence padding creates an 83% gradient starvation artifact that collapses accuracy from 40% to 1%, remediated via continuous sequence packing; (2) linguistic pretraining is an essential prerequisite (<= 2.0% without it); and (3) modern architectural primitives (RoPE, RMSNorm, SwiGLU) and Sparse Mixture of Experts (MoE) substantially improve additive reasoning over baseline GPT-2. Second, we demonstrate that algorithmic scratchpad formulation directly dictates success. Introducing a deterministic Digit-by-Digit Long Division scratchpad within a 4-stage Hierarchical Developmental Curriculum dramatically elevates single-digit division from 4.0% to 86.7% accuracy on a 4,000-problem held-out benchmark. In contrast, multi-digit multiplication remained challenging: detailed error analysis revealed that while the model correctly computed single-digit sub-products and place-value zeros, our FOIL scratchpad failed because it forced a simultaneous summation of up to nine multi-digit terms in a single step without pairwise intermediate accumulation. Finally, we identify two key boundaries: performance collapses to 0.00% on unseen 4-digit operands, and unbuffered training induces catastrophic forgetting, collapsing division accuracy from 86.7% down to 0.00%.

When a team of agents shares a reward for completed tasks, reporting and stopping unsafe work reduces the team's reward. Random audits that penalize silence can make universal reporting optimal without ensuring that a silent team learns to report. We study this problem in a game where any witness can stop a task by reporting. When a task's k witnesses share a policy and draw actions independently, the derivative of expected reward with respect to the shared silence probability at universal silence counts its benefit k times, while the comparison between universal reporting and silence counts it once. A fully shared policy can therefore be locally attracted to silence even when reporting is optimal. For any grouping into shared policies, we give an audit condition sufficient for exact policy-gradient updates to reach universal reporting and, outside boundary cases, necessary from near universal silence. In a balanced family, meeting the condition with prescribed margins costs k times as much for a fully shared policy as for one policy per role. We test these predictions with PPO on 24 witness graphs, starting from learned silence. Witness groups, which place co-witnesses in separate networks, reduce unsafe task completion by 33.59 percentage points relative to shuffled groups of the same sizes under the same audits (95% graph-bootstrap interval: 21.03-45.13). Only 9 of 48 witness-group runs achieve below 1% unsafe completion while retaining at least 90% legitimate completion. At the same audit budget, a fully shared network meets both thresholds in 0/48 runs with independent action draws and 48/48 with a common draw. On 24 further graphs with witness groups fixed, audits allocated by the condition reduce unsafe completion by 42.22 points relative to audits maximizing a static coalition deterrence ratio at the same budget.

As small language models (SLMs) are increasingly deployed on resource-constrained and on-device platforms, including as components of agentic systems, the integrity of locally stored model parameters becomes an important safety concern. We investigate whether safety-sensitive behavior in LLaMA-2-7B-Chat is concentrated within a sparse subset of parameters, creating a reduced fault surface for targeted analysis. We study two complementary localization methods: low-rank safety-associated subspace analysis and parameter-level safety–utility importance filtering. Both approaches reveal highly non-uniform safety sensitivity across the network, with the MLP down_proj consistently emerging as a prominent safety-sensitive component and o_proj providing a smaller contribution. Using parameter-level localization, modifying only 0.19% of model weights in down_proj yields 53% Basic ASR and 56% GCG ASR, while tinyBenchmarks accuracy remains at 51.6% compared with a 52.2% unmodified baseline. These results motivate targeted fault analysis and selective integrity protection for language models deployed in resource-constrained, on-device, and agentic settings.

Astra can act, yet reliable manipulation depends on the system through which it observes and controls the world. We introduce PhysEvo, a framework for physical recursive self-improvement (RSI) around a single frozen model. A task agent executes robot tasks; a meta-agent uses the resulting trajectories to diagnose failures, revise tools and skills, and test corrections. The meta-agent can also improve its own diagnostic tools, so retained revisions support both later action and later self-improvement. This process develops joint-level control, evidence-seeking observation, and reusable manipulation skills without model-weight updates or a separately trained action policy. Across 42 RoboDojo tasks, held-out-layout evaluation of retained task-specific deployment versions yields a five-dimension average score of 68.14/100 and 62.00% success, compared with 47.17% for RoboDawn's one-shot Astra agent, the strongest published reference in our comparison. On eight manipulation tasks challenging direct Astra, PhysEvo achieves 55.00% success, compared with 1.25% for the direct-Astra reference. Deploying the simulation-evolved harness on AgileX PiPER and continuing skill revision yields 90.60/100 average score and 84.00% success across 25 trials on five real-world tasks. PhysEvo turns the consequences of action into persistent, testable changes to how a frozen model acts and improves.

Speech large language models (speech LLMs) perform well on automatic speech recognition (ASR) when sufficient paired speech-text data is available, but their performance degrades in low-resource settings. A cascaded pipeline that performs speech-to-phoneme (S2P) conversion followed by phoneme-to-grapheme (P2G) conversion has been shown to outperform end-to-end speech LLMs in this regime, suggesting that phoneme-mediated processing is beneficial when paired data is scarce. We propose phoneme-guided initialization, a simple method that uses this insight within an end-to-end framework: we pre-train the audio encoder on S2P and the LLM on P2G tasks, then connect them and fine-tune the full model end-to-end on the target ASR task. Experiments on Japanese (CSJ), Chinese (AISHELL-1), and two low-resource languages from Common Voice 25.0 (Tatar and Urdu) show that our method matches or outperforms both the cascaded S2P-P2G baseline and the end-to-end model without P2G initialization.

As large language models become more powerful, self-evolving agents are able to tackle challenging tasks including AI for machine learning (AI4ML). In AI4ML, while empirical verification is available, it often requires computationally costly model training and evaluation, limiting the speed and scale of agent evolution. Yet verification efficiency remains under-explored, and frontier models provide only limited gains when used directly as idea selectors. We address this gap with specialized idea-level critic models that predict whether a proposed ML modification will improve upon the current solution, allowing agents to screen ideas and concentrate verification resources on the most promising candidates. We train the critic models through supervised fine-tuning on high-quality critiques synthesized by Gemini-3.1-Pro, followed by GRPO to further improve their predictive accuracy. Empirically, our critic models outperform Gemini-3.1-Pro in static idea evaluation, and these gains extend to agent inference, continual learning, and policy training. During inference-time evolution, they improve final solution quality under the same verification budget by selecting more promising ideas, with further gains from continual learning. During policy training, they serve as learned reward models, reserving empirical verification for uncertain cases and enabling substantially more policy updates with the same verification resources. Together, these results show that idea-level critic models help ML agents discover better solutions and learn stronger proposal policies under limited verification budgets.

We present REFIT, an input calibration for frozen activity-recognition models whose inertial sensors are worn differently at deployment than in training. When users move a watch to the other wrist or put a strap sensor back on turned, the model sees the same motion on changed axes. REFIT undoes such shifts without labels or retraining. It describes them by families of axis transforms, such as reflections and rotations, and fits each family to the user's data so that simple statistics match those of the training data. The family that removes most of the mismatch names the shift. REFIT fixes the shift by applying the best member of that family before the frozen model and re-estimating its normalization statistics. It tests the fixed model with a label-free accuracy estimate and asks the user to re-wear the sensor when it is low. Experiments on real left/right sensor pairs and on real and simulated re-attachment show that REFIT outperforms label-free test-time adaptation methods on every dataset and restores most of the accuracy lost to re-attachment. It names injected shifts far more reliably than a confidence-based selector. After a correction over all signed permutations of the axes, the estimate separates successful from failed corrections.

Graph indexes for billion-scale vector collections can exceed a single server's DRAM capacity. Passive RDMA-based disaggregated memory provides scalable capacity without memory-node computation, but conventional best-first search performs poorly in this setting. Fine-grained and unnecessary remote reads increase communication cost, while dependencies between candidate evaluation and subsequent expansion serialize traversal and leave CPUs idle. We present RiftANN, a graph-based approximate nearest neighbor search (ANNS) system for passive RDMA-based disaggregated memory. RiftANN navigates using compact vectors at compute nodes and selectively verifies exact vectors using a threshold calibrated from observed approximation errors. A bounded one-sided RDMA pipeline batches and overlaps the remaining remote accesses with local processing. RiftANN evaluates returned neighbors in parallel and incrementally incorporates completed results. An impact gate estimates whether unfinished evaluations may change the candidate set, allowing traversal to continue when their expected influence is small while preventing unsafe advancement from incomplete search state. A lightweight feedback controller coordinates RDMA concurrency with background evaluation capacity as search configurations and query loads change. We evaluate RiftANN on SIFT, DEEP, and SPACEV at 100M scale and SIFT1B. At matched recall, RiftANN achieves 1.6x to 4.3x latency speedups and 1.1x to 2.2x higher throughput than DistVS, and 1.6x to 5.6x latency speedups over SSD-based DiskANN and PipeANN. These results show that passive disaggregated memory can support low-latency graph-based vector retrieval without query-time computation at memory nodes.

While offline reinforcement learning (RL) enables policy optimization from static datasets without costly online interaction, it remains bottlenecked by the risk of executing out-of-distribution (OOD) actions. Recent approaches mitigate this by learning a behavior-cloning policy through flow matching and then performing RL within its constrained latent space. However, naively optimizing the latent policy can easily cause the policy to collapse into a brittle mode or exploit sharp artifacts of the learned critic. In this work, we find that entropy regularization is essential in latent-space RL for addressing these challenges. We introduce LASER, a novel offline RL algorithm that applies latent-space adjoint matching to achieve entropy-regularized latent-space RL with expressive flow policies while avoiding backpropagation through time. Through comprehensive experiments on 40 challenging OGBench tasks with varying dataset qualities, we show that LASER achieves state-of-the-art performance. Notably, LASER uses fixed method-specific hyperparameters across all tasks and outperforms the evaluated baselines, including those with task- and dataset-specific tuning, which highlights the robust applicability of LASER. Project website: https://mit-realm.github.io/laser/.

SAT solvers are empirically known to perform poorly when reasoning about multiplication. Yet for over a decade we have lacked a theoretical explanation for this phenomenon. CDCL SAT solvers implicitly search for resolution proofs, and no lower bound on proof size has ruled out the existence of short proofs that solvers simply fail to find. We give the first lower bound of this kind by showing that general resolution proofs of the associativity of $n$-bit multiplication require size $2^{\Omega((n/\log n)^{1/4})}$. This lower bound holds for a broad class of multiplier encodings based on partial product summation, including the standard array and Wallace-tree multipliers used to bit-blast multiplication in SMT solvers. This result resolves an open problem of Beame and Liew. The proof constructs a reduction from a perfect-matching principle on bounded-degree bipartite expander graphs to multiplier associativity. Itsykson, Slabodkin, and Sokolov proved that this principle is hard for resolution. The lower bound for multiplier associativity follows. The same reduction, when combined with Håstad's recent lower bound for the perfect-matching principle of the odd grid, yields an exponential lower bound for multiplier associativity in the stronger bounded-depth Frege proof systems.

The paper studies learning in reservoir computing systems through the lens of the internal model principle. The key idea is to model training signals as outputs of an exogenous signal generator, thus connecting reservoir computing to output regulation, observer theory, and frequency-domain interpolation. For linear signal generators, we characterize the steady-state response of a linear reservoir through invariant subspaces, establishing connections with Luenberger observers and classical frequency-domain interpolation. For nonlinear signal generators, we obtain analogous results using invariant manifolds, connecting synchronization to Kazantzis-Kravaris/Luenberger observers and readout training to nonlinear moment matching. Case studies illustrate how our perspective explains possible instability of trained predictors and informs reservoir design.

The aim of processing and analyzing experimental data from physical experiments is to obtain physically significant information about the phenomenon under study. This goal is achieved by multi-stage processing of experimental data, during which noise associated with measurements is suppressed and the dimensionality of the input data is reduced. In this paper, we propose a new method based on the use of neural networks such as autoencoders to extract essential features. The special value of the proposed approach lies in the possibility of its application to the analysis of multimodal data received simultaneously from several installations. We will apply this approach to a multimodal data (MMD) of the experiment TAIGA. Currently, the analysis of the MMD is carried out independently for each installation separately. Therefore, the development of methods for the joint analysis of MMD from TAIGA-type installations is an urgent task in cosmic ray physics and gamma-ray astronomy. Based on Monte Carlo simulation, it is shown that the proposed method allows for effective MMD analysis. It can also be used for MMD analysis at other experimental complexes.

Generative inpainting of brain MRI volumes is essential for synthesizing healthy tissue in pathological regions, improving the accuracy and reliability of automated downstream brain analysis applications such as image registration, brain extraction, and segmentation. However, standard 3D approaches are computationally prohibitive, while efficient 2D slice-wise methods suffer from severe inter-slice discontinuities. Furthermore, traditional models rely on conditional training, requiring task-specific learning of masked inputs. We propose a zero-shot brain MRI inpainting framework utilizing 2.5D unconditional flow priors to capture spatial context along the superior-inferior axis without the overhead of full 3D convolutions. During training, our flow matching model learns the joint distribution of adjacent axial slice triplets, modeling the manifold of healthy brain anatomy while explicitly excluding pathological regions from the loss function. At inference, the model processes the input triplets autoregressively along the depth axis. We employ the Restora-Flow solver to constrain the unconditional prior using the input mask, achieving accurate zero-shot inpainting. Evaluations show our 2.5D strategy resolves the structural discontinuities of 2D baselines, synthesizing plausible healthy tissue while maintaining volumetric consistency across the axial, sagittal, and coronal planes. As a final step, we generate and average an ensemble of multiple stochastic reconstructions to form the final prediction. Quantitative results benchmarked on the official BraTS 2026 Inpainting Challenge validation set demonstrate the effectiveness of our proposed approach, yielding an SSIM of 0.816 $\pm$ 0.112, MSE of 0.007 $\pm$ 0.005, and PSNR of 22.923 $\pm$ 4.343. Code is available at https://github.com/imigraz/brats2026-inpainting.

Magnetic field-based positioning is a resilient positioning technology that requires no external infrastructure and is hard to jam at scale. To facilitate research on magnetic field-based positioning for aerial platforms operating close to the Earth's surface, an open dataset is presented with measurements collected using an unmanned aerial vehicle carrying two optically pumped magnetometers, a type of quantum magnetometer, and a global navigation satellite system-aided inertial navigation system. The dataset includes measurements for both magnetic-field map learning and validation. Along with the dataset, a probabilistic framework for magnetic-field map learning and validation is presented and used to illustrate how the dataset may be used. Finally, we outline research directions that may be explored using the dataset.

Toeplitz matrices are among the simplest structured models of translation invariance, arising naturally in convolution, stationary covariance models, and discretizations of translation-invariant operators. For a pair of real matrices, the Böttcher–Wenzel form (BW form) is a nonnegative quartic measuring the gap in the corresponding commutator inequality. László conjectured that, when both matrices are Toeplitz, this quartic is a sum of squares for every matrix order. We show that the conjecture is false. More precisely, we identify an explicit family of corner-supported Toeplitz pairs, retaining only the outermost diagonals on the two sides, for which the associated BW form is not a sum of squares at all sufficiently large orders. The proof reduces the complete family of Gram representations to a finite complex test: its Gram-invariant part develops a strictly negative limiting direction, while the remaining Gram-dependent contribution vanishes. We also give an explicit sufficient threshold for the matrix order. The negative result is complemented by two positive regimes. If either Toeplitz factor is symmetric or skew-symmetric, then the corresponding BW form is SoS for every order, with the other factor allowed to be an arbitrary real Toeplitz matrix. For unrestricted Toeplitz pairs, we further prove SoS representability for every $2\le N\le50$, with formal Lean~4 verification through order 20. The large-order non-SoS theorem, including the explicit sufficient threshold, has also been formally verified in Lean 4.

Experience with invariant finite-difference schemes for one-dimensional hydro\-dynamic-type equations for a function $u(t,x)$ suggests that nonlinear polynomial schemes on orthogonal uniform meshes with the 9-point stencil cannot simultaneously preserve difference analogues of the energy and momentum conservation laws, with the multipliers given by the standard difference approximations of $u_t$ and $u_x$. For the 9-point stencil this hypothesis is proved for polynomials of arbitrary degree. On larger stencils it is investigated by means of the difference analogue of the direct method: for polynomials of bounded degree, such schemes are found to exist only on sufficiently large stencils, and the second-order equations they approximate are of Monge–Ampère type. As a by-product, a scheme for the homogeneous Monge–Ampère equation is obtained that has five conservation laws, admits most of the symmetries of the differential equation, and is invariant under the discrete dihedral group $D_4$. Numerical tests on exact solutions confirm its second order of approximation and show that the conservation laws are satisfied on these solutions with the same order of accuracy.

Streaming 3D reconstruction requires more than a sequence of geometric predictions: it requires a persistent scene state that can incorporate new evidence and remain renderable as observations arrive. Latent spatial tokens offer a promising representation for this purpose, but constructing them from an image collection leaves open how to maintain them online, where each observation may both revisit known regions and reveal new content. We introduce S2Tok, a feed-forward framework that maintains a size-adaptive, persistent scene state from uncalibrated image streams. Its central idea is to distinguish updates to the existing representation from selective expansion. A spatially informed transformer integrates each incoming observation with the persistent scene tokens, while a learned admission module selectively expands the representation to limit redundant storage. A hierarchical decoder and Gaussian head convert the evolving state into non-pixel-aligned 3D Gaussians, enabling novel-view rendering without caching previous frames. Experiments across four benchmarks demonstrate competitive streaming rendering quality with compact Gaussian representations. These results support latent spatial tokens as a persistent computational state for online 3D reconstruction, combining learned scene updates with explicit Gaussian rendering.

Accurate and low latency channel estimation is critical for modern MIMO systems, particularly under mobility, where channels exhibit structured sparsity and strong temporal correlation. This paper proposes a time-series conditioned diffusion framework for channel estimation that performs denoising in the angular domain. Starting from least squares (LS) observations, we train a diffusion denoiser whose conditioning information is encoded by a long short-term memory (LSTM) network over a short observation sequence, enabling the model to exploit temporal dynamics beyond per-snapshot estimation. To robustly balance observation fidelity and learned generative priors across a wide signal-to-noise ratio (SNR) range, we introduce a learnable SNR-gated late-fusion shortcut that injects the network input into the final decoding stage through a sigmoid gate with trainable center and scale. To reduce inference latency, we adopt deterministic denoising diffusion implicit model (DDIM) style reverse updates with SNR-adaptive truncation and step allocation, which significantly reduces the number of reverse diffusion steps at high SNR while maintaining strong performance in low SNR regimes. Simulations on time-evolving standardized channel models demonstrate that the proposed method achieves consistent performance gains over existing diffusion-based channel estimation baselines, while retaining low latency through SNR-adaptive inference.

A plethora of new adaptive optimizers are designed to efficiently estimate and use minibatch gradient statistics to shape parameter updates, but they are typically benchmarked at a single batch size. Hyperparameter scaling rules promise to preserve performance as batch size and gradient noise change, suggesting that the best optimizer at one batch size should remain the best at another. We challenge this approach to developing and evaluating optimizers by showing: (1) no principled scaling rule for Muon works consistently across training settings, and (2) the best optimizer for language model pretraining changes with batch size even after extensive hyperparameter tuning. To understand these failures, we analyze a noisy quadratic model and show that the batch-size scaling rule that preserves performance is direction-dependent, shifting from square-root to linear as a direction's curvature-to-noise ratio rises. We further prove that gradient noise drives a bias-variance tradeoff in preconditioning that can reverse optimizer rankings across batch sizes, even under optimal learning rate and momentum tuning. Consistent with this, when we increase the batch size $16\times$ partway through language model pretraining, keeping small-batch updates in only the sharpest $0.001\%$ of directions removes up to $59.5\%$ of the resulting loss gap over the next $8\%$ of training, while a random subspace of the same size barely helps. Taken together, our results show that principled optimizer design must account for batch size and empirical benchmarking should be performed across batch sizes.