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Saturday 26 September

Neurons and Cognition

From Signals to Trajectories: A Primer on Low-Dimensional Dynamics in Human EEG and MEG

Vanessa Hadid, Hamza Abdelhedi, Annalisa Pascarella et al. (+3 more)

Neural activity unfolds not as a set of independent signals, but as a coordinated dynamical process that can be described as a point moving through a high-dimensional state space. This perspective has contributed substantially to recent developments in systems neuroscience, especially through studies of directly recorded neuronal population activity, but remains comparatively underused in non-invasive human recordings such as EEG and MEG. In this primer, we present a neural trajectory analysis based on Principal Component Analysis (PCA) as an accessible route into extending the concepts of neural trajectories in state space to human electrophysiology. We explain how EEG/MEG activity can be organized into neural state representations, projected onto axes organized by decreasing covariance, truncated into low-dimensional representations, and visualized as trajectories that capture how distributed activity evolves over time. We show how trajectory geometry can be used to compare conditions and relate neural dynamics to behavior or clinical outcomes. An example of EEG motor execution and imagery, accompanied by a tutorial notebook, illustrates the workflow from conventional EEG summaries to trajectory-based analysis. We also clarify the limits of PCA, including its linear, variance-driven nature, and discuss EEG/MEG-specific challenges such as spatial mixing, preprocessing sensitivity, validation, and overinterpretation. Finally, we situate PCA within a broader family of state-space methods. By making neural trajectories practical and interpretable, this primer offers a guide for bringing the conceptual framework of population-level dynamics into mainstream human cognitive neuroscience.
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All authors Vanessa Hadid, Hamza Abdelhedi, Annalisa Pascarella, Sara A. Solla, Paul Cisek, Karim Jerbi

Statistical Mechanics

Continuously varying exponents in the distribution of waiting times in the symmetric exclusion process on a percolation cluster

Arpan Chatterjee, Kabir Ramola and Deepak Dhar

We study the waiting-time distribution of hard-core interacting particles in the symmetric exclusion process on one- and two-dimensional lattices with side branches attached to each lattice site in the steady state. We use numerical simulations together with an approximate analytical treatment of particles trapped in side branches in the steady state. Such a two-dimensional carpet serves as a simplified model for trapping of a supercritical percolation cluster. At high particle densities, the system exhibits strong dynamical heterogeneity, with the distribution of logarithms of waiting times developing well-separated peaks corresponding to particles trapped at different depths from the backbone. We show that the probability that a tagged particle occupies the same position at time $t_0+t$ as at time $t_0$ decays algebraically as $t^{-\omega}$, where the exponent $\omega$ varies continuously with particle density for densities above a threshold value $\rho^*<1$. We also investigate the correlations between successive waiting times along the trajectory of a tagged particle.
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Robotics

MemTransfer: Benchmarking Memory Beyond Matched Experience in Embodied Decision-Making

Haiming Tang, Xianjie Dai, Gujie Shao et al. (+5 more)

Memory lets an embodied agent reuse past experience, yet retaining useful information does not ensure that the agent can apply it when conditions change. We present MemTransfer, a benchmark comparing six memory representations, a working-memory baseline and five representations of past experience, under a shared frozen vision-language-model policy. It comprises 100 navigation cases across ten task types in a simulated warehouse, with expert demonstrations supplying the history. Three comparisons vary the starting pose, route availability, and amount and task relevance of history. With one demonstration per task, Full-context and Episodic memory reach 95.3% and 100.0% success at the original demonstration start, but lose 48-49 percentage points at a new test start. Summary changes little between these two test starts, yet with four demonstrations per task it retains a smaller fraction of its unchanged-route success after blocking (39.3%) than Working memory (44.8%) or the two trajectory memories (56-58%). At the new test start, increasing from one to four relevant demonstrations raises Episodic success by 14.3 percentage points, while the other evaluated representations gain no more than 1.3 percentage points. Replacing half of the relevant histories with other-task experience lowers success for both trajectory memories. These results show that robustness to one kind of mismatch does not imply robustness to another, motivating evaluation of both stored information and its use at decision time.
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All authors Haiming Tang, Xianjie Dai, Gujie Shao, Zuyi Guo, Jingguang Li, Kailang Ma, Yihong Tang, Heye Huang

Artificial Intelligence

Delayed Supervision for Test-Time Language Models

Jinha Kim and Taksh Kothari

Test-time language models adapt a compact memory while processing the input sequence. This perspective encompasses nonlinear fast-weight learning in LaCT, associative delta-rule updates in DeltaNet, and generalized delta-rule state updates in RWKV-7. Training these models to predict the next token does not explicitly require a fact to remain accessible after many subsequent memory updates. We study delayed supervision for this test-time memory: during post-training, ask a simulator-grounded question only after a long interval of unrelated events, and supervise its answer alongside ordinary next-token prediction. Questions are evaluated on disposable branches, so their answers never enter the continuing event stream. The construction distinguishes retention from revision: a retained fact must remain valid throughout the delay, whereas a revised fact must be answered with its latest value. We evaluate this approach on LaCT-760M and plain DeltaNet-1.3B using TextWorld training trajectories and shared BABILong and RULER evaluation panels, and include a separately reported RWKV-7 comparison. Relative to event-only training, delayed QA improves BABILong by 5.48 percentage points for LaCT and 1.32 points for DeltaNet, and single-needle RULER by 1.45 and 3.27 points, respectively. The RWKV-7 comparison reports gains of 4.60 and 7.00 points on its own panels. These results support delayed semantic supervision as a practical outer training objective for usable test-time memory, while leaving open how much of the benefit derives specifically from delay rather than general question-answering and answer-termination supervision.
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Statistical Methodology

Doubly Robust Estimation under Covariate Dependent Censoring in Semi-Competing Risks Data

Jiyue Qin, Yuyao Wang and Ronghui Xu

Semi-competing risks occur when individuals may experience a non-terminal event and a terminal event, where the terminal event censors the non-terminal event but not vice versa. In the presence of covariate-dependent censoring, augmented inverse probability of censoring weighting (AIPCW) framework has not been developed for the special setting of semi-competing risks which, unlike competing risks, have asymmetric event time structure and complex estimands. Using semiparametric theory on coarsened data, we carefully develop an AIPCW framework for semi-competing risks. When treatment effects are of interest, we further integrate this approach with augmented inverse probability of treatment weighting (AIPTW), yielding a framework for estimating causal estimands under covariate-dependent censoring. The resulting estimators are shown to be doubly robust. Using the proposed framework, we estimate treatment specific risks of: i) non-terminal event, ii) terminal event without the non-terminal event, and iii) terminal event following the non-terminal event. We evaluate the finite sample performance through simulations, and apply the method to data from the Honolulu Asia Aging Study to assess the causal effects of midlife heavy drinking on late life cognitive impairment and mortality.
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Quantum Physics

Conserved and relaxing modes enable polynomial-success coherent Carleman lattice Boltzmann evolution

Hua-Dong Yao and Sauro Succi

Carleman linearization represents nonlinear lattice Boltzmann collision dynamics in a form amenable to quantum block encoding, but low postselection probabilities in existing population-space encodings make coherent multi-step evolution exponentially unlikely to succeed. We present a quantum Carleman lattice Boltzmann scheme based on the multi-relaxation-time collision operator in a weighted Hermite moment basis. In this basis, the lifted collision operator separates into small coupled blocks whose norm exceeds unity because of the coupling between conserved and relaxing modes. This block structure enables a norm-attaining block encoding with a single-step success probability close to unity. Crucially, scaling the pair sector for a prescribed evolution horizon makes the combined encoding and sector-selection overhead grow polynomially rather than exponentially with the number of steps. For a hundred-step evolution, the resulting complete-run success probability exceeds that of population-space encodings by orders of magnitude. Over horizons of several tens of steps, the truncated dynamics reproduces the nonlinearly generated modes of a benchmark flow to within a few percent. We verify the combined preparation, evolution and readout protocol as a single unitary circuit and give a complete gate-level resource estimate for extracting a nonlinear observable of the benchmark flow from a coherent Carleman evolution. The block structure of conserved and relaxing modes holds equally on three-dimensional lattices and provides a constructive route to norm-attaining encodings for lattice Boltzmann models with quadratic equilibria.
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Artificial Intelligence

PhiFold: Towards Dynamic Protein Design with Physics-Structured Covariance Modeling

Yutian Liu, Mujie Lin, LanqianZhang et al. (+4 more)

Protein design is moving beyond structural correctness toward function-aware design, yet existing generative models typically treat dynamics as a downstream property estimated through simulation or prediction after structure generation. Using MD trajectories as a generative target is also undesirable because stochastic, path-dependent trajectories over-specify the underlying equilibrium ensemble. We introduce PhiFold, a framework for jointly generating protein backbones and their second-order dynamics, represented by residue-displacement covariance. Rather than predicting the quadratically sized full covariance, PhiFold decomposes dynamics into three interpretable components: local flexibility, a low-rank collective-motion representation, and residue-wise collective participation. These components are assembled into a positive-definite covariance matrix with exact marginal consistency, yielding a compact and physically constrained representation of equilibrium dynamics. Across generated proteins, PhiFold improves recovery of local fluctuations and long-range residue coupling while remaining competitive on dominant collective-motion subspaces. It further enables bidirectional control of residue flexibility while preserving backbone designability. By unifying structure generation with an explicit representation of equilibrium dynamics, PhiFold lays a foundation for designing proteins not only by how they look, but also by how they move.
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All authors Yutian Liu, Mujie Lin, LanqianZhang, Meng Fan, Chang Liu, ZhiweiNie, Siwei Ma

Data Structures and Algorithms

SparseDesign: Scaling Exact Coding-Sequence Design

Hao Lin and Jingjin Yu

Exact optimization of synonymous coding sequences under a joint folding-energy and codon-usage objective is limited by expensive dynamic-programming splits and large working sets. SparseDesign applies candidate sparsification to the multiloop recurrence of a Turner~2004 dangle-0 solver over a weighted codon automaton. A direct branch is retained only when it strictly improves on every partitionable or endpoint-unpaired realization of the same endpoint states. We prove equivalence to the dense recurrence in real arithmetic, under an explicit scalar branch-interface assumption. With $N$ automaton states, edge set $E$ and $Z$ retained candidates, multiloop work is $O(N^2+N|E|+NZ)$; worst-case time remains cubic for bounded-width automata and total memory remains quadratic. Endpoint ownership permits parallel candidate construction without locks. While synthetic stress families can benefit little from sparsification and exhibit near-quadratic candidate growth, natural proteins show substantial candidate-count reductions. In our 7,600-task campaign, the 2,000-protein human-table panel has median retention of only 3.53% at $\lambda=0$ and 2.15% at $\lambda=4$, corresponding to approximately 28.3-fold and 46.4-fold reductions relative to all feasible direct intervals. The primary performance experiments use an AMD EPYC 7313 server. For human Dp427c (11,031 nt, $\lambda=0$), 16-thread packed SparseDesign achieves five-run medians of 236.54 seconds wall-clock time and 14.43 GiB peak RSS. Compared with the single-thread local dense LinearDesign fork on the same server (4,912 seconds, 402.10 GiB RSS), this gives a 20.8-fold wall-clock speedup and a 27.9-fold peak-memory reduction. On a Core i9-14900KF commodity PC with 64 GiB RAM, the same input, layout and thread count achieve 126.42 seconds and 14.43 GiB RSS.
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Physics and Society

Hydrogen mon amour

Christophe Grojean and Patrick Janot

The FCC's projected average electricity consumption is 1.3 TWh per year. If supplied entirely by nuclear power, this would represent about 10% of the annual output of a large third-generation nuclear reactor, together with a corresponding share of its radioactive waste. By 2050, however, renewable sources could provide up to 80% of this electricity on a substantially decarbonised European grid, supported by long-term power-purchase agreements and flexible operation. This could reduce the residual nuclear requirement, and its associated waste, by up to a factor of five. This essay asks whether hydrogen could help bridge the remaining periods of low wind and solar generation. It examines production from renewable electricity, transport as hydrogen or ammonia, storage and conversion back into electricity, together with their efficiency losses and carbon footprints. It then considers the still uncertain prospect of naturally occurring hydrogen. None of these routes offers a ready-made solution. But the decades before the FCC begins operation leave time to develop one–and CERN could help accelerate that development by becoming a credible long-term customer.
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High Energy Astrophysical Phenomena

Constraints on Supermassive Black Hole Binaries from the Lack of Resolvable Sources in the NANOGrav 15-yr Dataset

Emiko C. Gardiner, Kayhan Gültekin, Philippe Turgeon et al. (+116 more)

Pulsar timing arrays (PTAs) have found evidence of a gravitational wave background (GWB) consistent with a population of supermassive black hole binaries (SMBHBs), but have not yet resolved a continuous wave (CW) from an individual binary. We present the first SMBHB population constraints incorporating PTA upper limits on CWs, based on the NANOGrav 15-year (NG15) data. Using semi-analytic models to generate simulated populations, we calculate each sample's GWB likelihood by free spectral comparison and CW nondetection (nCW) likelihoods by (1) mapping each realization's highest CW signal-to-noise ratio (S/N) to a detection probability and (2) counting the fraction of realizations without a binary close enough that NG15 would have detected it. CW nondetection favors populations in which many lower-mass sources, rather than a few ultramassive ones, dominate the GWB. This information is complementary to that provided by the GWB amplitude, breaking the degeneracy between the masses and number of binaries required to reproduce the observed spectrum. Relative to GWB-only constraints, the joint posteriors favor higher galaxy merger rates, lower $M_\mathrm{BH}$-$M_\mathrm{bulge}$ scatter, shorter binary lifetimes, and steeper small-separation hardening. The most detectable sources in the S/N-weighted joint posterior have chirp masses $\sim 10^{9.6} M_\odot$, luminosity distances $\sim$1300 Mpc, and frequencies $\sim$6 nHz, while the nCW-only constraints favor lower frequencies, coinciding with the NG15 4 nHz candidate. These constraints will tighten if CW nondetection continues.
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All authors Emiko C. Gardiner, Kayhan Gültekin, Philippe Turgeon, Bence Bécsy, Laura Blecha, Nikita Agarwal, Gabriella Agazie, Akash Anumarlapudi, Anne M. Archibald, Zaven Arzoumanian, Anjana Ashok, Jeremy G. Baier, Paul T. Baker, Adam Brazier, Paul R. Brook, Sarah Burke-Spolaor, Rand Burnette, Robin Case, J. Andrew Casey-Clyde, Maria Charisi, Shami Chatterjee, Tyler Cohen, James M. Cordes, Neil J. Cornish, Fronefield Crawford, H. Thankful Cromartie, Kathryn Crowter, Megan E. DeCesar, Paul B. Demorest, Heling Deng, Lankeswar Dey, Timothy Dolch, Graham M. Doskoch, Elizabeth C. Ferrara, William Fiore, Emmanuel Fonseca, Gabriel E. Freedman, Nate Garver-Daniels, Peter A. Gentile, Kyle A. Gersbach, Joseph Glaser, Deborah C. Good, Aiden Gundersen, C. J. Harris, Jeffrey S. Hazboun, Ross J. Jennings, Aaron D. Johnson, Megan L. Jones, David L. Kaplan, Anala Kavumkandathil Sreekumar, Luke Zoltan Kelley, Matthew Kerr, Joey S. Key, Nima Laal, Michael T. Lam, William G. Lamb, Bjorn Larsen, T. Joseph W. Lazio, Natalia Lewandowska, Tingting Liu, Duncan R. Lorimer, Jing Luo, Ryan S. Lynch, Chung-Pei Ma, Dustin R. Madison, Ashley Martsen, Cayenne Matt, Alexander McEwen, James W. McKee, Maura A. McLaughlin, Natasha McMann, Bradley W. Meyers, Patrick M. Meyers, Matthew T. Miles, Chiara M. F. Mingarelli, Andrea Mitridate, Cherry Ng, David J. Nice, Shania A. Nichols, Stella Koch Ocker, Daniel J. Oliver, Ken D. Olum, Timothy T. Pennucci, Benetge B. P. Perera, Polina Petrov, Nihan S. Pol, Henri A. Radovan, Scott M. Ransom, Paul S. Ray, Joseph D. Romano, Jessie C. Runnoe, Alexander Saffer, Shashwat C. Sardesai, Ann Schmiedekamp, Carl Schmiedekamp, Kai Schmitz, Levi Schult, Brent J. Shapiro-Albert, Xavier Siemens, Joseph Simon, Sophia V. Sosa Fiscella, Ingrid H. Stairs, Daniel R. Stinebring, Kevin Stovall, Abhimanyu Susobhanan, Joseph K. Swiggum, Jacob Taylor, Stephen R. Taylor, Mercedes S. Thompson, Jacob E. Turner, Michele Vallisneri, Rutger van Haasteren, Joris P. W. Verbiest, Sarah J. Vigeland, Haley M. Wahl, Kevin P. Wilson, Caitlin A. Witt, David Wright, Olivia Young

Fluid Dynamics

Benchmark of no-slip boundary conditions for meshless Lattice Boltzmann Method in Stokes flow

Dawid Strzelczyk, Pavel Eichler and Maciej Matyka

The introduction of the approximated streaming to the standard Lattice Boltzmann Method (LBM) decouples the space and velocity discretizations. Although many no-slip implementations knwon from LBM can be directly adopted to the models with approximated streaming, their exact behavior in the off-lattice setting remains unexplored. In this work, we investigate the meshfree off-lattice D2Q9 model equipped with several no-slip implementations – non-equilibrium extrapolation, simple and interpolated bounceback, and moment-based boundaries – applied to a Stokes flow around a cylinder. We compare the pressure, velocity and velocity gradient fields obtained with various no-slips, on polar and hybrid polar-scattered discretizations. We find that non-equilibrium extrapolation performs the best of all the studied no-slip realizations, giving smooth stresses and zero velocity on the solid walls. Other no-slips suffer from oscillations and/or discontinuities in the hydrodynamic fields. Hybrid discretizations are found to give higher errors than the polar grid, but improve the stability of the solution. Finally, we simulate the deformation of an elastic ring under the stresses obtained with the studied no-slips to highlight the importance of the sensible choice of the no-slip realization in more complex problems.
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Statistics Applications

Assessing the impact of climate change and rising temperatures on life insurance portfolios

Jiacheng Min, Han Li, Jean-François Bégin et al. (+1 more)

Climate change may materially affect long-term life insurance liabilities by altering both the level and seasonal pattern of mortality. This article develops a multi-population mortality framework that combines a Hermite spline model with a distributed lag non-linear model to capture age-, region-, and temperature-specific mortality effects. We apply the framework to mortality and temperature data from 15 Spanish NUTS-2 regions and project future mortality under three shared socioeconomic pathway (SSP) scenarios. We then assess the implications for a hypothetical whole life insurance portfolio through expected death-benefit payments and portfolio profit and loss. The results reveal an important seasonal offset: warmer conditions reduce expected payoffs during winter periods but increase them during summer periods, with these effects becoming more pronounced under more severe climate scenarios and for policies issued in later years. Over longer horizons, adverse summer mortality effects become increasingly important. The portfolio analysis further shows that climate-related mortality risk can materially increase the dispersion and downside risk of portfolio outcomes, particularly under SSP5-8.5. These findings highlight the importance of incorporating temperature-related mortality effects into long-term life insurance liability projections and risk assessment.
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All authors Jiacheng Min, Han Li, Jean-François Bégin, Shuanming Li

Artificial Intelligence

Train4Merge: RL or SFT—Which Yields Better Teachers for OPD-Based Model Merging?

Jingyuan Huang, Zuming Huang, Yucheng Shi et al. (+4 more)

Domain experts trained from a shared checkpoint can transfer their specialized capabilities to a single student through on-policy distillation (OPD). Existing research primarily focuses on improving this merging process, while the algorithms used to train the experts have received limited systematic comparison. We investigate which training algorithm produces teachers better suited to OPD through controlled single-teacher comparisons of supervised fine-tuning (SFT) and reinforcement learning (RL) across Agentic, Reasoning, and Perception. We further examine whether this advantage extends to multi-teacher OPD (MOPD). Teachers and students share the same Qwen3.5-9B initialization, and the two teacher types are compared at similar task performance. Our single-teacher experiments show that RL teachers yield stronger students and higher recovery of teacher performance gains across all three domains. In MOPD, the RL teacher group also yields a student with a higher three-domain mean score and higher overall teacher gain recovery than the SFT teacher group. Our further analysis shows that RL teachers undergo smaller parameter displacements from the shared initialization than SFT teachers. Teacher–student Top-K overlap also increases faster early in OPD or remains consistently higher with RL teachers than with SFT teachers. These findings support the hypothesis that RL teachers' smaller departures from the student's starting point facilitate learning through OPD, resulting in stronger students.
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All authors Jingyuan Huang, Zuming Huang, Yucheng Shi, Zhongzhi Li, Xiaoming Zhai, Wei Chu, Ninghao Liu

Machine Learning

On the Capability and Limitation of Hard Prompt

Lijia Yu, Shuaitong Liu, Gaojie Jin et al. (+2 more)

Prompt engineering has become an indispensable tool for using large language models (LLMs), turning LLMs into task-specific experts without changing their weights. Despite notable theoretical advances in prompt engineering, the theory for the more practical hard or discrete prompts is largely open. In this paper, we try to fill this gap either by providing a complete solution or by making substantial progress on the three core theoretical questions regarding hard prompts. First, we show that determining the existence of a hard prompt for a transformer to solve a downstream task is NP-complete and that finding an optimal hard prompt is NP-hard, which is the first computational complexity result for hard prompting, as far as we know. Second, we show that, unlike soft or continuous prompts, hard prompts have essential limitations: hard prompts are not complete; short hard prompts do not significantly enhance the ability of transformers; and long hard prompts exhibit the "prompt dominating answer phenomenon," meaning that, with high probability, the same answer is given for all queries of the same length. On the other hand, linear hard prompts do not have the limitations of short or long prompts. Third, we provide a tight bound on the size of the task in terms of the prompt length for the performance of prompts on the finite task to generalize to the entire data distribution, leading to a necessary and sufficient condition for generalizability. This is the first result on generalization for prompting, as far as we know. Our findings not only offer the first theoretical insights into hard prompts but also provide provably reliable practical guidance for real-world LLM usage.
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All authors Lijia Yu, Shuaitong Liu, Gaojie Jin, Xinyu Li, Xiao-Shan Gao

Machine Learning

When Does Synergy Help Active Feature Acquisition? A PID-Based Study

Jie Li, Maruf A. Dhali and Hjalmar R. Bouma

Active feature acquisition (AFA) sequentially selects informative features under budget constraints. However, existing policies rarely distinguish whether information contributed by interacting features is redundant, unique, or synergistic. We introduce SynAFA, a state-dependent AFA policy that combines pairwise joint information and conditional information, with Partial Information Decomposition (PID) characterizing its information structure. Across five tabular datasets and MNIST-loop, performance is heterogeneous. SynAFA shows its strongest gains at low budgets on PhysioNet, where synergistic and redundant feature pairs are supported by permutation tests, but its advantage diminishes as budgets increase and does not depend on pair proposals. SynAFA performs significantly worse than nearly all baselines on MiniBooNE, and than CAE on MNIST-loop. Controlled synthetic experiments further show that, within budget, SynAFA's advantage rises as joint information becomes more synergy-dominated, including when total joint information is held approximately constant. Further analyses show that the budget-dependent erosion is not resolved by non-greedy local search, which improves a diagnostic set-level objective but leaves predictive performance no better, often significantly worse, and that improvements in this objective are weakly aligned with the fixed classifier's predictive utility. These findings characterize when pairwise synergy can benefit AFA while exposing a persistent challenge in translating local information into effective acquisition objectives.
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Differential Geometry

Equivariant isometric immersions of surfaces in hyperbolic space

Jean-Marc Schlenker

Let $S$ be a closed, oriented surface of genus at least $2$, let $h$ be a smooth Riemannian metric on $S$ with curvature $K\in (-1,0]$, and let $c\in \cT_S$ be a conformal structure on $S$. There exists a unique equivariant isometric immersion of $(S,h)$ in $\HH^3$ such that the pull-back by the hyperbolic Gauss map of the conformal structure at infinity is $c$. Dually, if $h^*$ is a smooth metric on $S$ with curvature $K^*\in (-\infty, 0)$ and if $c\in \cT_S$, there exists a unique equivariant immersion of $S$ into $\HH^3$ with third fundamental form $h^*$ and such that the pull-back of the conformal class at infinity by the Gauss map is $c$. Equivalently, given $h$ and $c\in \cT_S$, there is a unique pair $(E,u)$ where $E$ is a hyperbolic end with conformal structure at infinity $c$ and $u$ is an isometric embedding of $(S,h)$ in $E$. Given $h^*$ and $c$, there exists a unique pair $(E,u^*)$, where $E$ is a hyperbolic end with conformal structure at infinity $c$, and $u^*:S\to E$ is an embedding inducing the third fundamental form $h^*$. Those statements can be considered as a smooth counterpart of known or conjectural statements on the grafting map and on circle patterns.
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Information Theory

A DSP Framework for ISAC with random signals: From Physical Transceiver to Periodic Models

Junjie Chen

Communication-centric integrated sensing and communication~(ISAC) directly employs random data-bearing communication signals for both information transmission and environmental sensing. Existing studies generally describe pulse-shaped transmission in continuous time or directly adopt periodic discrete-time sensing models, leaving the digital signal processing~(DSP) operations connecting the physical transceiver and the periodic models unclear. This paper develops a DSP-oriented transceiver framework for single-antenna communication-centric ISAC. A common transmitter is constructed through modulation, cyclic-prefix~(CP) insertion, upsampling, and pulse shaping. For communication reception, the physical transceiver chain is reduced to a symbol-rate equivalent linear channel, which becomes circulant after CP removal and thereby supports frequency-domain equalization. For sensing reception, a high-rate reference waveform is extracted from the transmitted waveform and equivalently represented by circular pulse shaping. CP removal at the receiver then converts physical target delays into circular shifts of this reference waveform, leading to a periodic matched-filtering model and the corresponding range profile. Numerical results validate the developed framework through target range estimation and the symbol error rate performance of pulse-shaped CP-OFDM over frequency-selective Rayleigh fading channels.
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Machine Learning

Refresh or Realize? Compute Allocation in Drifting Models

Sipeng Chen, Xu Zheng and Shibo Li

Drifting Models train a one-step generator by recomputing a finite-sample drift field at every iteration and taking an optimizer step toward the drifted target. The field says how generated samples should move, but the step is taken in parameters shared by all samples, so the motion the network actually makes need not match the motion it was given. This leaves a basic training question open: should extra compute go into fitting the current target more closely, or into recomputing the field? We study it on ImageNet 256x256. Holding the target fixed for k optimizer steps and measuring the realized displacement, we find that deeper fitting does bring the network closer to the frozen target, and that the number of steps needed before it makes any net progress drops from about sixteen early in training to one later on. When the extra steps come for free, k=2 also lowers FID. Once they are paid for, the result flips: at approximately matched measured wall-clock, spending the budget on fresh fields gives lower FID than deeper fitting, on both training seeds. The target itself shows why a fresh field is worth so much. Redrawing the finite support rotates its direction far more than a parameter update does (cosine ~0.3-0.6 against ~0.95), and a correction that is optimal in field space is not reliably better in FID than a parameter-free one. For Drifting, fitting each target well and spending compute well are different goals.
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Artificial Intelligence

Agentsensus: Consensus-Compressed Shared Memory for Multi-Agent Story Worlds

Yu Pan

A agentic story world is a dynamic system simulating who learned what, when, and from whom – yet the standard design gives each character a private memory stream. A shared event is therefore stored once per witness, large duplication will be incurred in terms of storage. We present Agentsensus, a story-world simulation framework in which there is an unified long-term memory. Records of the same event merge into one owned by all its witnesses, and semantically relevant memory records are linked. We evaluate on four worlds – two classical Chinese novels, Hamlet, and a real-world conflict timeline – run for 40 to 80 rounds against three per-character memory designs under an equal-granularity protocol. Agentsensus writes 22-44% fewer entries than the closest baseline and is the only design whose memory becomes shared (14-28% of records held by more than one character, some by 10) and linked (94-99%), at judged simulation quality indistinguishable or even better than the baselines. An ablation attributes this to the merge itself: disabling it multiplies the store by 3.1x and takes sharing to exactly zero. Sharing also compounds with the horizon rather than saturating early, rising 6% to 9% to 14% as one world is re-run at 10, 20 and 40 rounds.
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Machine Learning

FUND: Density Flow for Sampling Unnormalised Distributions

Vikas Kanaujia and Vipul Arora

Efficient sampling from Boltzmann distributions is central to modelling complex physical systems. Markov Chain Monte Carlo (MCMC) methods suffer from critical slowing down, high autocorrelation, and poor mode-mixing, limiting their scalability. Recent advances, like Boltzmann Generators, offer a promising alternative but remain constrained by costly MCMC-based training, inefficient sampling, and poor ergodicity. We introduce an algorithm for learning Boltzmann distributions that does not require any true samples for training. Our approach draws inspiration from flow matching but departs fundamentally from sample-trajectory matching to distribution-trajectory matching. The algorithm iteratively reshapes the target distribution, using model generated samples to guide learning and ensure comprehensive mode coverage. We validate our method on standard benchmarks, including a 2D Gaussian mixture, Many-Well distributions, and high-dimensional scalar $\phi^4$ theory. The proposed approach not only improves sampling performance and accuracy over traditional MCMC and flow-based baselines but also establishes a new method for sample-free learning of complex physical distributions.
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Artificial Intelligence

GLIDE: Generalized Layer-wise Intrinsic Distributional Evaluation for Heterogeneous LLM Agents

Wei Zhu, Yiming Wang, Rui Wang et al. (+3 more)

LLM agents require reliable step-level evaluation to compare candidate branches and allocate computation effectively. However, lightweight evaluation remains challenging. External verifiers introduce additional inference cost, while agent-produced confidence or self-evaluation scores can be miscalibrated, especially when candidates are generated by heterogeneous agents. We propose Generalized Layer-wise Intrinsic Distributional Evaluation (GLIDE) for LLM agents. GLIDE derives intrinsic step evidence from layer-wise residual coherence, which measures whether local residual updates consistently support the global residual change induced by a candidate step. It calibrates this evidence against the recent score distribution of the generating agent and converts it into a pessimistic reward that jointly accounts for absolute residual evidence and agent-relative standing. The reward provides a cross-agent value signal for MCTS branch selection, while normalized predictive uncertainty guides adaptive branching. Experiments on multi-hop reasoning, sequential decision making, and symbolic logic show that GLIDE improves task performance, step-level ranking quality, and computational efficiency without external verifiers or task-specific supervision.
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All authors Wei Zhu, Yiming Wang, Rui Wang, Lixing Yu, Kun Yue, Zhiwen Tang

Rings and Algebras

Global and local triviality for extensions of ample groupoids: an algebraic approach

Nathan Brownlowe, Lisa Orloff Clark, Enrique Pardo et al. (+1 more)

Using the duality between the categories of inverse semigroups and ample groupoids, we prove the triviality (global and local) of the central term of the extension in terms of twisted crossed products.
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All authors Nathan Brownlowe, Lisa Orloff Clark, Enrique Pardo, Aidan Sims

Computation and Language

TRAP: Understanding and Mitigating Privacy Memorization in Language Models

Muhammed Ustaomeroglu, Ziyue Xu, Hanshen Xiao et al. (+3 more)

Fine-tuning a language model on sensitive records can leave it able to reproduce them. We ask when this memorization arises and how to prevent it without knowing in advance which spans are sensitive. Our starting point is that most memorization scores and attacks share one statistical core: whether the model assigns a token more probability than some reference would. Taking as the reference a model trained on the complementary half of the same corpus gives the Target Reference Advantage (TRA), a per-token signal that separates what a model fit to a particular record from what it learned across records, and is cheap and differentiable. We then study what drives memorization during fine-tuning: it keeps growing well past the validation minimum, is larger on small datasets and at higher learning rates, and higher when the underlying task is harder. Early stopping removes much of it, but because it is chosen by aggregate validation loss it helps least for rare, hard-to-predict spans embedded in otherwise learnable text, which is exactly what sensitive information tends to be. We therefore introduce TRAP, a one-sided penalty on tokenwise TRA that acts only where the target model pulls ahead of its reference. On student essays with annotated personal information and clinical cases with patient identifiers, TRAP brings memorization near the level of an untrained model at little utility cost, where generic regularizers barely move and differential privacy gives up most of what fine-tuning bought.
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All authors Muhammed Ustaomeroglu, Ziyue Xu, Hanshen Xiao, Peter Cnudde, Guannan Qu, Holger R. Roth

Robotics

Affordance-Conditioned Decision Making: Bridging the Semantic-Spatial Gap in Zero-Shot Cross-Floor Vision-and-Language Navigation

Xuekang Yang, Lu Chen, Shuang Luo et al. (+4 more)

Vision-and-language navigation increasingly relies on general-purpose semantic planners, yet translating correct high-level intent into reliable physical execution remains difficult in spatially constrained transitions. Reaching a staircase, doorway, or narrow passage does not ensure traversal; the agent must identify an executable affordance pose and recover from accumulated action errors. We propose PACE (Preference-refined Affordance-Conditioned Execution), a supervised local execution module that augments frozen zero-shot semantic planners for reliable cross-floor navigation. PACE grounds transition-related semantics into a long-horizon, agent-centric traversable affordance pose and conditions short-horizon action generation on this spatial target, thereby aligning semantic goals with physical execution. We further post-train PACE through failure-aware preference refinement using rollout-derived pairs that contrast normal or recovery behaviors with deviation-amplifying behaviors, thereby improving closed-loop correction. We integrate PACE into six open-source zero-shot VLN navigators and demonstrate consistent improvements on the cross-floor subsets of R2R-CE and RxR-CE, increasing the average success rate from 16.35% to 27.65% and from 4.76% to 12.06%, respectively. Real-world experiments further demonstrate PACE's applicability in unseen environments, highlighting the potential of traversable affordances to bridge semantic intent and reliable embodied behavior.
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All authors Xuekang Yang, Lu Chen, Shuang Luo, Jialing Zhu, Qi Zhang, Yue Gao, Xiang Zhang

Computational Engineering

ScentGen: Hierarchical Multimodal Olfactory Semantic Modeling for Molecular Odor Description Generation

Zhiliang Wu, Zhaolin Hu, Hehe Fan et al. (+1 more)

In this paper, we introduce a molecular odor description generation task, which aims to generate natural language odor descriptions from molecular structures. Unlike conventional methods that describe molecular odor using discrete labels, this task generates expressive and human-interpretable sensory descriptions. To address this task, we propose a hierarchical multimodal olfactory semantic modeling framework, named ScentGen. ScentGen consists of three key components: an odor semantic planner, a semantic adapter, and a description generator. The odor semantic planner integrates complementary molecular information from 1D SMILES sequences, 2D molecular graphs, and 3D molecular conformations to learn discriminative and structured olfactory semantics. The semantic adapter further maps the learned olfactory representation into the hidden space of a large language model, transforming molecular odor semantics into language-compatible continuous prompts. Conditioned on these prompts, the description generator produces coherent odor descriptions that reflect plausible sensory characteristics of the input molecule. Considering the lack of molecular datasets with natural language odor descriptions, we further construct a molecular odor description dataset containing paired multimodal molecular representations and human-interpretable odor descriptions. Extensive experiments demonstrate that ScentGen generates coherent and expressive odor descriptions, providing a more flexible solution for molecular odor understanding beyond discrete odor label prediction.
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All authors Zhiliang Wu, Zhaolin Hu, Hehe Fan, Weisi Lin

Machine Learning

A Journey to the Edge of Stability

Jaerin Lee and Kyoung Mu Lee

It has recently been found that deep learning often occurs at the "edge of stability (EoS)," where the maximum Hessian eigenvalue of the model is stabilized at a value reciprocal to the learning rate. However, what happens before we reach that regime? We fix a deep learning problem and vary first order optimization methods with dense learning rate sweeps. We then track the characterizing quantities of a learning trajectory: the loss, the sharpness, and the alignment between consecutive gradients. To our surprise, if we scale the learning rate by the dc gain of the optimizer, these traces from the sweeps from different optimizers almost perfectly overlap across a large range of learning rates. The dc-normalized optimizers have another role that only becomes apparent in high learning rates: they select when the sharpness value detaches from this universal curve and enters the edge of stability. Upon this discovery, we specify three distinct regimes with respect to the dc-adjusted learning rate: the low-LR regime where the trajectory is nearly insensitive to the optimizer, the high-LR regime, where the optimizer governs the sharpness according to the EoS reciprocal rule, and the in-between mid-LR regime where so-called progressive sharpening originates independently of the optimizer. This distinguishes the role of the optimizer, the learning rate, and the model in shaping the learning progress.
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Systems and Control

Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees

Omkar Sudhir Patil

Neural ODEs learn dynamics from trajectory losses, but their adjoint gradients lack the regressor-times-parameter-error structure on which Lyapunov analyses of online adaptation rest, so training on streaming data comes without stability guarantees. We show that this structure is in fact present: the adjoint gradient decomposes exactly into a positive semi-definite trajectory operator acting on the parameter error plus a nonlinear perturbation with explicit, horizon-dependent bounds. A quadratic Lyapunov function then certifies online Neural ODE training over sliding windows under computable gain and horizon conditions, and the same certificate extends to stored data: its drift branch recovers concurrent learning, and its trajectory branch yields NODE-CL, a stored-segment Gauss-Newton method built on batched forward sensitivities that needs no state-derivative estimates. On four DeepMind Control Suite domains, NODE-CL attains the lowest median prediction error on three under velocity measurement noise, where observer-based concurrent learning degrades by up to 8x; with clean measurements it is best on the pendulum and within a factor of 1.6 of the best stored-data baseline on the cartpole and reacher.
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Machine Learning

A Solvable Theory of Pre-training Data Poisoning: Regime-Dependent Scaling Exponents

Indranil Halder, Rastri Dey and Cengiz Pehlevan

Pre-training data poisoning of large language models is usually studied using targeted backdoors and their survival through safety post-training, which leaves open a more basic question: how does a model's clean data performance degrade as the poison rate $\varepsilon$ grows? Motivated by our controlled pre-training runs of OLMo-style models, in which the relative clean data validation perplexity increase $\Delta$ between poisoned and clean models matched in architecture, token budget, and optimization schedule is well fit by a power law $\Delta\approx C\varepsilon^{a}$ with a non-integer exponent, we ask what such a law requires theoretically. We first prove an analyticity barrier: whenever the contaminated objective depends analytically on $\varepsilon$ around a nondegenerate clean data optimum, $\Delta$ is generically quadratic in $\varepsilon$, so a generic non-integer exponent is a signature of genuinely singular structure. We then supply that structure in solvable truncated ridge regression with heavy-tailed covariates, controlled by $q_\star$, and a label-shift poisoning. Our central result is that the excess risk scaling exponent depending on the order of limits: in the higher dimensional proportional regime it is $\epsilon^{q_\star/(q_\star+2)}$, whereas taking the ample-data limit first gives $\epsilon^{2-2/q_\star}$, and the limits do not commute. We confirm this prediction through several numerical simulations. Finally, we argue that finite training time plays the role of truncation on the curvature spectrum in local LLM pre-training, deriving the observed scaling law under heavy tailed inverse curvature spectrum as a modeling hypothesis.
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Commutative Algebra

Bernstein–Sato ideals might not be linear

Lei Wu

Let $F=(f_1,\dots,f_r)$ be a family of nonzero polynomials on $\mathbb C^n$. More than ten years ago, Budur conjectured that $B_F$, the Bernstein–Sato ideal of $F$, is generated by products of linear polynomials with rational coefficients. With the aid of AI, we construct two counterexamples to Budur's conjecture. The examples indicate that main results in [Wu26] provide the optimal linearity properties that the zero locus of Bernstein-Sato ideals satisfies in general.
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Game Theory

Single-or-Sample: Online Fair Allocation for Combinatorial Agents

Shuchi Chawla, Zhiyi Huang, Pooja Kulkarni et al. (+2 more)

We study the fair allocation of $m$ indivisible goods among $n$ heterogeneous agents arriving online, under maximin share (MMS) fairness. The key challenge lies in making allocation decisions in an adversarial setting without knowing future agents' valuations. No guarantees were known prior to our work in adversarial settings. Our main positive result is an online allocation algorithm for submodular agents that with probability at least $0.4$ guarantees a $1/24$-approximation to MMS to all agents simultaneously. Our algorithm intersperses a greedy-style adaptive sampling-without-replacement protocol with single-good reduction rounds. For XOS valuations, we adapt this single-or-sample approach to guarantee a $c$-MMS for all agents simultaneously with probability $1-O(c)$ for any parameter $c\in O(1/\log n)$. A key technical contribution of our work is in establishing Chernoff-style tail bounds on item allocation events for this adaptive sampling process despite strong positive correlations among the items, a result that may be of independent interest. The approximation versus success probability tradeoffs achieved by our algorithms are asymptotically tight. We show that even for binary additive valuations, no randomized algorithm can ensure $c$-MMS to all agents with probability exceeding $(1-c^2/5)$, for any $c\in (0,1]$. For XOS valuations, stronger lower bounds hold: no randomized algorithm can ensure $c$-MMS to all agents with probability exceeding $(1-c/3)$, for any $c\in (0,1]$. Furthermore, no algorithm can achieve $\omega(1/\log \log n)$-MMS with any constant probability. All our lower bounds hold even for simple binary instances whose MMS values and MMS partitions can be computed in linear time.
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All authors Shuchi Chawla, Zhiyi Huang, Pooja Kulkarni, Ruta Mehta, Parnian Shahkar