Papers

We study the behavior of the characteristic and chromatic polynomials of certain families of graphs and their relation to homomorphism counts, focusing on polynomial dependence of the coefficients at each fixed codegree on the graph family parameter. We prove that the characteristic polynomials of strongly regular graphs with polynomial parameters form a two-level polynomial of infinite depth in the sense of Bogart and Woods. In contrast, the chromatic polynomials of Paley graphs have maximal constant depth two: their coefficient of codegree three is not eventually polynomial in the number of vertices. We also prove that both the chromatic and characteristic polynomials of every strongly polynomial graph sequence, in the sense of de La Harpe and Jaeger, have infinite depth. Finally, we investigate homomorphism counts between two strongly polynomial graph sequences. We show that infinite depth need not hold in general, but we construct target sequences for which it holds for every strongly polynomial source sequence.

We develop a framework for identification, computation, and inference in econometric models with a linear-in-measures representation. These models express maintained restrictions as moment conditions linear in the joint probability measure of observed and latent inputs, and map that measure linearly to the distribution of outputs, even with nonlinear outcome equations. We construct an adversarial discrepancy function whose zeros characterize the identified set for structural and counterfactual parameters. With finite output support, finite linear programs compute the discrepancy function or provide certified bounds even when latent inputs have infinite support, and a penalized bootstrap yields confidence sets with uniform per-point coverage. We apply the framework to two open cases in binary choice panels with fixed effects and discrete covariates: sequential exogeneity with unspecified conditional marginal error distributions, and known conditional marginal error distributions with unrestricted serial dependence. In an entry game with multiple equilibria, the framework recovers the known sharp identification region.

This paper presents a constrained iterative Linear Quadratic Regulator (Box-iLQR) method for nonlinear aerospace optimal-control problems with bounded states and controls. Logarithmic barrier functions are used with a two-fold objective: the barrier parameter is reduced toward zero to recover the constrained optimal trajectory, while a finite barrier is retained to construct a smooth, constraint-aware feedback policy for closed-loop operation. The method is demonstrated on spacecraft attitude control, a minimum-fuel planar orbit transfer, and an L2 to L2 halo-orbit transfer. Box-iLQR respects the imposed constraints and produces nominal trajectories together with time-varying feedback policies. Closed-loop simulations under disturbance, measurement noise, and control uncertainty show substantial reductions in terminal error. These results demonstrate that Box-iLQR provides both high-accuracy constrained trajectory optimization and practical constraint-aware feedback within a single framework.

Experiments have shown that modifications in communication hardware can enable unauthorized exfiltration of data from transmitters. We study the resulting Transmitter Trojan channel, in which a malicious encoder embedded within a legitimate transmitter perturbs the transmitted codeword on a symbol-by-symbol basis. The model reflects the limited footprint, delay, and computational complexity available to such hardware modifications. We derive achievable rogue message rate and achievable rates for the legitimate message under the mismatch induced by the Trojan. We also analyze decoding error exponents for the legitimate and rogue receivers, including operational exponent lower bounds obtained through channel-resolvability transfer arguments. Finally, we study Trojan detection at the legitimate receiver under different levels of statistical knowledge, including likelihood-ratio detection when the ensemble-averaged induced channel is known and goodness-of-fit detection when only the nominal channel is known. The resulting detection error exponents, together with the achievable rate and decoding error exponents, quantify tradeoffs among rogue message rate, legitimate message rate, decoding reliability, and Trojan detectability. We specialize the analysis to the binary symmetric channel and the additive white Gaussian noise channel, and illustrate the resulting tradeoffs numerically.

Transition-state searches remain a major bottleneck in reaction discovery, as identifying valid saddle-point structures requires numerous expensive quantum-chemical calculations. Generative models can reduce this burden by proposing candidates from reactant and product geometries, but supervised training on geometries alone does not enforce the physical conditions required of a transition state, while enforcing them during sampling is costly. We introduce Trèfle, a one-step flow model that amortizes physics-guided generation into training: a mean-flow objective replaces multi-step sampling, a low-cost surrogate replaces density functional theory (DFT) reward evaluations, and reinforcement-learning post-training with rewards that enforce those conditions replaces inference-time guidance. Trèfle generates accurate transition states at $30\times$ the throughput of multi-step baselines. It transfers few-shot to ten unseen transition metals and generalizes zero-shot to molecules far larger than any in training. With DFT refinement and reaction-path validation, Trèfle-seeded searches recover all 13 unseen $\gamma$-ketohydroperoxide channels, while post-training raises per-attempt recovery from 28% to 50% across 85 unseen bimolecular channels. Trèfle thus provides fast, reliable seeds for automated reaction discovery.

We survey Bernstein–Nikolskii inequalities for polynomials and entire functions of exponential type, with particular emphasis on sharp constants and extremal functions. We discuss both classical results and recent developments, including limit relations between Nikolskii constants for polynomials and entire functions of exponential type, weighted and multidimensional versions, and inequalities on constrained classes of functions. Special attention is given to the difficult case $p=1$ and to methods based on reproducing kernels, duality, and extremal approximation. We also describe connections of sharp Bernstein–Nikolskii inequalities with approximation theory, the Riemann zeta function, spherical designs, Turán–Delsarte type problems, and sphere packing. Several open problems concerning sharp constants, extremal functions, and multidimensional extensions are formulated.

In holography, analytically continued finite temperature correlation functions $G(t)$ exhibit signatures of the black hole singularity. These take the form of singularities at certain values of $t$ whose bulk origin is a null geodesic worldline "bouncing off" the black hole singularity. We study certain quantum corrections to this effect in 2D dilaton gravity that are captured by gravitational backreaction of the worldline onto the black hole geometry. These corrections smooth out the bouncing geodesic singularities. By following the backreacted geodesic saddle in a steepest descent analysis we find instead that the black hole singularity physics gets encoded in a subtle way involving a Stokes phenomenon near the coincident point singularity of $G(t)$ at $t=0$ (and its thermal image). We point out a parallel between the structure of Stokes lines uncovered in this analysis and the structure present in the analysis of forbidden singularities in large $c$ 2D conformal blocks. Finally we make some preliminary remarks about the significance of quantum corrections in these models beyond backreaction.

Nonlinear inverse Compton scattering (NICS) in high-density targets offers a promising route for generating high flux, broadband sources of MeV $\gamma$-photons which are important for applications like radiography, photonuclear physics, and pair production. Microstructured targets enable control over the NICS process to help shape the photon energy, angular distribution, and total yield. This work presents particle-in-cell (PIC) simulations exploring target microstructures compatible with two-photon polymerization (TPP) additive manufacturing, which is a promising technique that allows high-volume and reproducible printing of sub-wavelength features as small as 200 nm. We investigate how microstructures influence NICS radiation and merge simulation analysis with simple analytical models that guide target design. These results establish pathways to optimize targets for low-divergence, high-energy photon beams with 2.0$\cdot$10$^{8}$ photons/J exceeding 100 MeV and targets for high yields delivering upwards of 2.0$\cdot$10$^{11}$ photons/J above 1 MeV in the multi-PW regime.

Vision–language–action (VLA) models provide strong priors for robotic manipulation but are typically deployed as frozen policies, unable to improve from their own failures. Real-world reinforcement learning (RL) offers a path to continued improvement, yet manual environment resets and task-success supervision hinder autonomous learning. We introduce FIND, an agentic real-world RL framework that closes the loop between scene understanding, weakness-aware practice, self-evaluation, and policy improvement in a persistent workspace. FIND reframes autonomous practice as a scene-conditioned, performance-aware task-selection problem: instead of restoring a predefined scene after each rollout, it uses the resulting scene to determine what to practice next. A vision–language agent identifies feasible tasks from a predefined library, prioritizes those with lower recent success rates, and evaluates outcomes using paired pre- and post-execution observations. We instantiate FIND with a frozen $\pi_{0.5}$ VLA and residual off-policy RL. Across eight real-world manipulation tasks, the independent human-assessed success rate improves from $55\%$ to $71.9\%$. A representative run completes 456 autonomous episodes within 6 hours of interaction, requiring 30 scene-recovery interventions and no human-provided reward labels during online learning. Ablations and systematic evaluations further examine key design choices, agent evaluation accuracy, and human intervention requirements. Our website is made publicly available at: FIND.github.io.

Motion retargeting transfers motion across characters with different skeletal structures while preserving semantic intent and physical plausibility. Despite recent progress, two fundamental questions remain: (i) how can reliable source-motion semantics be learned without high-quality paired retargeting data, and (ii) how should retargeting be formulated when no reliable paired motion can serve as a definitive regression objective? Existing methods commonly preserve semantics by constraining predictions toward copied motions. However, such initializations entangle useful articulation cues with artifacts caused by mismatched skeletal proportions and body geometry. Moreover, directly regressing a final motion in one forward pass is restrictive because retargeting is inherently underdetermined, and the desired solution must balance semantic fidelity with target-specific physical and temporal constraints rather than match a unique paired target. Motivated by these limitations, we propose ReFM, a source-mesh-agnostic, energy-guided model that reformulates motion retargeting as progressive refinement. First, an SO(3) canonicalizer removes redundant global-orientation variations. Second, a cross-character semantic encoder, pretrained through contrastive learning, provides a character-invariant representation for both optimization guidance and semantic evaluation. ReFM then progressively refines an initialized target motion through a learned flow guided by semantic consistency, physical plausibility, temporal coherence, and minimal motion modification. The framework is compatible with different initialization strategies, including both direct motion copying and Autodesk HumanIK, an industry-standard full-body inverse-kinematics retargeting system.

The quantum baker map is a standard model of quantum chaos, but rigorous analysis of how it spreads random perturbations remains difficult. Following the repeated “baker plus refreshed diagonal perturbation” architecture of Schack and Caves, we study a tractable strong-noise model based on the Balazs–Voros quantization: at each time step, its unitary propagator is followed by a diagonal unitary whose entries are independent and uniform on the unit circle. The resulting random propagator is a structured random walk on $\U(N)$, $N=2^k$. We quantify how quickly the baker dynamics spreads this basis-local randomness at three levels: ensemble means, two-copy statistics, and the full law of the accumulated propagator. The walk becomes an exact unitary $1$-design at time $k+1$, while its fixed-accuracy $2$-design mixing time is $\Theta(\log N)$. Thus the induced state ensembles reproduce Haar means and two-copy statistics on the Ehrenfest scale. The full law mixes much more slowly. A phase-adapted path coupling gives normalized Wasserstein mixing in $O_\varepsilon(N)$ steps, whereas metric-entropy and Haar small-ball estimates give an $\Omega_\varepsilon(N/\log N)$ lower bound and asymptotically maximal distance at every $t=o(N/\log N)$. The law remains singular with respect to Haar measure for every $t<N$. The moment results and the Wasserstein upper bound are driven by the unistochastic Markov kernel associated with $B_N$, an affine dyadic chain whose nonconstant Fourier modes vanish exactly after $k$ steps. The resulting hierarchy separates Ehrenfest-scale randomization of state ensembles from near-Heisenberg-scale exploration of the full unitary group.

In this paper, an arbitrary Lagrangian-Eulerian (ALE)-based finite element method (FEM) is developed and studied in a monolithic framework for a class of two-phase Stokes flow problems with moving interfaces and jump coefficients, where the mixed finite element approximation to Stokes moving interface problems is established and analyzed in both semi- and fully discrete schemes based on the ALE formulation. The key analytical technique involves a specific H^1-projection associated with the ALE-induced mesh motion due to the evolving interface. Optimal convergence properties of the proposed H^1-projection and its ALE temporal derivative are proved in both H^1 and L^2 norms, with which optimal error estimates are obtained for both semi- and fully discrete mixed finite element approximations to the studied Stokes moving interface problem in both H1 and L2 norms as well. Numerical experiments are carried out to validate all derived theoretical results. The developed analytical approach can be extended to Taylor-Hood and MINI mixed elements, as well as to more general two-phase flow problems.

We propose a conjecture on how to recover an algebraic curve from the isogeny classes of its Prym varieties. Motivated by this conjecture, we analyze constructions of pairs of curves with isogenous Jacobians and several isogenous Pryms.

This paper presents Grasp2Twist, a bimanual dexterous manipulation system that learns to grasp and twist open jar lids using reinforcement learning. Learning this task raises three challenges: learning a unified policy for a multi-stage task, sustaining lid twisting, and sim-to-real transfer. To address the first challenge, we introduce a continuous enclosure measure to guide grasp formation and a binary enclosure indicator to guide the grasp-to-twist transition for unified policy learning. We derive both from the geometric relationship between the object center and the convex hull formed by the hand's palm and fingertips. Kinematic constraints limit how far the hand can rotate the lid with fixed contacts, so sustained twisting requires finger contact reconfiguration. We use a three-stage curriculum to facilitate exploration of these contact changes and also improve robustness for sim-to-real transfer. With our approach, the learned policy demonstrates finger gaiting, reconfiguring hand-object contacts to sustain lid rotation. It transfers zero-shot to the physical system and achieves an 88% task success rate across six household containers, including peanut-butter, vitamin, and instant-coffee jars. Ablations further validate the roles of the geometric enclosure in grasp formation and the curriculum in contact-reconfiguration exploration.

We derive the axion Weak Gravity Conjecture (aWGC) from the nonperturbative fragmentation of Euclidean wormholes into charged defects. Requiring fragmentation to lower the Euclidean action fixes the axion action-to-charge bound and its order-one coefficient. Without additional scalars, this coefficient coincides with that of the Imaginary Distance Bound (IDB), while additional scalars strengthen the bound. The aWGC in the presence of multiple axio-dilaton pairs is discussed, leading to geometric representations. Axions satisfying the aWGC render the corresponding wormholes unstable, potentially suppressing their proliferation and resolving associated factorization problems.

Although $\mathbb{E}[\mathrm{dropout}(x)] = x$, here we show that $\mathbb{E}[\mathrm{LayerNorm}(\mathrm{dropout}(x))]$ is not equal to $\mathrm{LayerNorm}(x)$. Accordingly, the pattern of a Dropout layer followed by a LayerNorm, which is common to many AlphaFold2-based protein structure predictors, produces a systematic bias at evaluation time that can hamper performance. To address this, we derive a closed-form, first-order correction for this gap, which we call a Dropout-LayerNorm Correction (DLC). DLC empirically matches the performance boost of large Monte Carlo dropout ensembles. We evaluate its effect across nine protein structure models (ESMFold, OpenFold, ABB3, FlashABB, Ibex, NbForge, Genie1, Genie2, Genie3) on both paired and single-chain antibody structures as well as one protein-ligand docking model (QuickBind). The correction is computationally negligible and improves accuracy in all ten models tested ($\sim0.3\%-13\%$), with a modest but consistent improvement in ESMFold and OpenFold and a substantial improvement in antibody-specific models. This work identifies the mathematical consequence of chaining together Dropout and LayerNorm and provides a free, principled adjustment to improve the evaluation performance of many pretrained models. Code to reproduce the experiments is available at https://github.com/oxpig/DLC.

We propose an AI safety framework that binds worker agents to contracts specifying their permitted actions. We show how these contracts can be enforced and specified by assigning distinct responsibilities to monitor agents and judges, and asymmetric computational resources to monitors and workers. Our framework allows us to empirically measure statistical safety guarantees. The framework applies to a wide range of settings, including code security and escape-the-box scenarios.

How many bits does a network need before its accuracy collapses, and how does this grow with depth? We study the precision floor, the perturbation level or bit-width at which accuracy falls halfway to chance, in MLPs, CNNs, Vision Transformers and nine pretrained language models, under post-training quantization (PTQ) and quantization- or noise-aware training (QAT). (i) A first-order theory sets the floor through one full-precision quantity, the predictive amplification $G$: $\eta_c=\Lambda/G$, and $G^2$ grows linearly in depth at a rate proportional to the squared residual branch scale. (ii) The predicted equality $\alpha_{PTQ}=\rho$ of depth exponents holds within 95% intervals in twelve of thirteen trained architectures and in GPT-2 from 12 to 48 layers, with $\Lambda=1.45\pm14\%$ across trained architectures. (iii) Residual branches scaled by $1/\sqrt{D}$ and pre-normalisation remove the depth penalty, and each quantizer turns noise into bits at a rate fixed by its step rule, giving $b_c=(\alpha/\gamma)\log_2 D+C$. (iv) A QAT paradox: noise-aware training roughly doubles the tolerable noise of shallow networks, but the gain decays with depth, so the depth law steepens ($\alpha_{QAT}/\alpha_{PTQ}=1.45$-$1.47$ on two datasets, ten seeds each). Decision margins, cross-layer error cancellation and heavy tails do not set the floor.

We study charged soliton branches in quasi-one-dimensional chiral magnetic systems with Dzyaloshinskii–Moriya (DM) interaction, easy-axis anisotropy, and Zeeman coupling. The same static magnetic functional is equipped with two different dynamical completions: an antiferromagnetic model with second-order time derivatives and a ferromagnetic model with Berry-phase dynamics. On the helical branch selected by the static DM interaction, the problem reduces to an analytically tractable one-dimensional system for the polar angle of the order parameter. We derive the existence conditions for polar Q-balls from the curvature of the reduced effective potential and the presence of a nonzero turning point. In the antiferromagnetic case, the allowed frequency window is symmetric and can be completely closed by the combined effect of the DM coupling and the Zeeman field. At zero Zeeman field, the same reduction also supports antiferromagnetic Q-kinks, for which we obtain explicit profiles, charges, energies, and reduced-sector fission criteria. In the ferromagnetic case, the Berry phase makes the rotation frequency act as a shifted Zeeman field. As a result, north- and south-pole charged droplets are selected by opposite signs of the shifted rotation. We also show that a formal pole-to-pole solution of the ferromagnetic mechanical problem does not generally correspond to a finite-energy magnetic soliton, because the Berry term does not renormalize the physical Hamiltonian. These results clarify how charged-soliton mechanisms depend on the underlying magnetic dynamics, even when the static chiral energy is the same.

It is shown that the reduced group C*-algebra $\mathrm{C}_r^*(\mathbb{F}_2)$ is singly generated, where $\mathbb F_2$ is the free group on two generators. With respect to the generator constructed in the paper, the topological free entropy dimension of $\mathrm{C}_r^*(\mathbb{F}_2)$ is shown to be $2$.

Tools for code review present code changes file-by-file. We argue that, oftentimes, changes can be better organized around a call graph of the changed code. From an empirical study of GitHub pull requests (PRs) in-the-wild, we find that (1) in around 40% of the PRs, more than half of the changed functions (and methods) are connected by call graphs, and (2) necessary callees are often located in different files from their callers. Based on these findings, we develop the notion of CG-Diffs, subgraphs derived by decomposing a call graph of the changed code into smaller and more navigable directed graphs. We then implement a web-based interface for viewing PRs that restructures the PR around these CG-Diffs. Through a within-subject study comparing our interface against GitHub's PR view, we find that CG-Diffs help orient participants and provide them with more meaningful structures to navigate the PR. We also found several limitations: function nodes repeated across multiple CG-Diffs can be disorienting, and changes not contained in a function (e.g. globals, imports) are not as immediately apparent. Our study shows promise in using call graphs to help contextualize and navigate unfamiliar codebases, which may benefit new contributors to open source, and reviewers of unfamiliar LLM-generated PRs.

Achieving precise control over multiple properties without sacrificing chemical validity remains a central challenge in molecular inverse design. Existing reinforcement learning (RL) methods fine-tune graph diffusion models by treating **reverse** sampling as a sequential policy, using a single terminal reward to optimize hundreds of coupled decisions. They often suffer from instability, validity collapse, and limited property gains. We introduce GraphFDM (Graph Forward Distribution Matching), a new online RL paradigm for graph diffusion that performs optimization through the **forward** process. GraphFDM uses valid generations to define a reward-tilted target distribution jointly optimized over graph size and molecular structure for each property condition, incorporating reinforcement signals into supervised learning without storing reverse trajectories. We derive the unique optimal target, prove a condition-wise improvement guarantee, and show that the fixed graph-size prior of standard graph diffusion leaves an irreducible matching gap. In multi-conditional polymer and small-molecule generation, GraphFDM achieves the lowest MAE on every target property, with reductions of up to 53.0% relative to the strongest baselines and chemical validity above 0.99. It further generalizes to out-of-distribution property combinations.

Cloud vendors push ambitious in-network processing (e.g., crypto, telemetry) onto the NIC to offload servers even as link rates climb to terabit speeds. Vendors have responded with heterogeneous SmartNICs. For example, NVIDIA BlueField-3 interposes—between the wire and the host CPUs—a line-rate eSwitch, a multithreaded Data-Path Accelerator, general-purpose ARM cores, and a sea of fixed-function accelerators. These devices are notoriously hard to program, and harder still to predict. Applications can be implemented in many ways, with each choice potentially hitting a different bottleneck. A designer ideally needs to know—cheaply, and before a line of code is written—feasible choices and their bottlenecks, and design patterns to improve performance. Our paper offers a starting point to answer these questions using what we call the ZRAM model. It pairs a platform graph of processing zones and their channels with a program graph of tasks and their traffic fractions. The application designer or a compiler chooses a placement that maps the program graph onto the platform graph. Three metrics computed directly from this mapping—capability, roofline, and capacity—score the placement, deciding its feasibility and naming the bottleneck resource. We use a DDoS detector as a primary case study, and briefly explore two other applications, decision-tree inference and RDMA traversal. We distill seven design patterns for programming SmartNICs including a key one we call sifting. ZRAM generalizes to other SmartNICs such as Intel IPU E2200 and AMD Pensando Salina 400, and opens a new research agenda that includes compilers and hardware design.

The LHC dijet program has searched extensively for resonances decaying to inclusive jets and, more recently, to bottom-quark jets, where the sensitivity enhancement from suppression of the background outweighs the loss of signal efficiency in bottom-quark tagging. However, no dedicated search for dijet resonances containing charm-tagged jets has been performed. We study the charm-tagging performance required to make such searches competitive with the inclusive dijet search. Using the ATLAS 13 TeV dijet mass spectrum with 139 fb$^{-1}$, we predict the expected charm-tagged spectra from simulated jet-flavor fractions and parameterized charm-, bottom-, and light-jet tagging efficiencies, and estimate the sensitivity of a profile-likelihood search in exclusive one- and two-tag categories. At the loosest working point of the current tagger, charm-tagged searches improve the expected sensitivity to a resonance decaying to two charm quarks across the full resonance mass range considered, although the quantitative sensitivity depends on the poorly constrained high-$\pt$ behavior of charm-tagging efficiencies and on the simulated heavy-flavor composition of the dijet background. These results provide performance targets for charm taggers and motivate the development of dedicated charm-tagged dijet resonance searches at the LHC.

Recent developments in theories of partitions, quasimodular forms, multiple zeta values and $q$-multiple zeta values have led to connections between partitions and primes. Central to this progress are prime-detecting quasimodular forms, which are $q$-series whose non-negative coefficients vanish if and only if the input is prime. In this paper, we use properties of these quasimodular forms to motivate a proof of the infinitude of primes, to construct a novel partition theoretic factorization algorithm, and to show that the distribution of these coefficients relate to existence of primes in intervals. We also prove analogs of these results for primes in arithmetic progressions and discuss potential extensions of our results, including to Linnik's problem.

We study the VC-dimension of distance graphs of large subsets of vector spaces over finite fields. For $3\leq k\leq d$, we prove the distance graph of $E\subset \F_q^d$ has VC-dimension at least $k$ provided that $|E|>Cq^{d-\lfloor \frac{d-k}{3}\rfloor-1}$. We also show that this exponent is sharp in the $k=d$ case.

This work studies the expansion of the level sets of the solutions of a Fisher-KPP type reaction- diffusion equation, the diffusion being given by a nonnegative, compactly supported, even kernel. Because the latter is not assumed to be spherically symmetric, the level sets advance at an asymptotic speed given by a Freidlin-Gärtner type formula. The main contribution of this paper is to push the expansion up to terms that vanish as time goes to infinity, consisting in an asymptotically logarithmic delay corrected by an function that is constant in time, but depends on the direction of propagation.

Recent advances in speech synthesis and voice cloning have increased the need for reliable synthetic-speech detection, yet high-accuracy detectors increasingly rely on large pretrained models that are costly to invoke on every recording. Rather than replacing such detectors, we investigate a compact front-end screen that processes all inputs cheaply and forwards only suspicious recordings for more expensive analysis. To enable lightweight screening without a large learned encoder, we exploit spectral traces introduced by speech-generation operations. We analyze how learned upsampling and inverse short-time Fourier transform synthesis can produce predictable spectral artifacts and measure their presence directly in generated waveforms. Because the strength of these artifacts varies across generators, we combine decoder-guided spectral measurements with complementary descriptors of short-time spectral shape and temporal variation in a compact gradient-boosted tree. Across seven speech generators and two human-speech sources, the proposed screen achieves an equal error rate of 0.021% with an estimated model storage of 151 KiB. When used as the first stage of a simulated cascade with a 1.15-billion-parameter detector, it reduces estimated detection energy by 84.4% while operating at a 0.050% synthetic-speech miss rate, demonstrating the potential of decoder-guided acoustic evidence for low-cost front-end screening.

As autonomous LLM agents are deployed across multi-session environments, conventional memory architectures suffer from Associative Blindness (inability to traverse multi-hop relational dependencies), Scaffolding Amnesia (temporal decay evicting core persona invariants), and Static Topology Stagnation (immutable graphs ignoring usage dynamics). Grounded in Complementary Learning Systems (CLS) principles, we propose EngramRAG, an adaptive memory architecture coupling a low-latency Waking State reflex with an asynchronous background Dreaming State consolidation cycle. EngramRAG introduces: (1) Usage-Modulated Personalized PageRank (U-PPR), where transition probabilities adapt via Hebbian plasticity to promote persistent entities into high-centrality Epistemic Macro-Hubs; (2) Consolidation-Activated Topology Decay (CATD), which scales retention half-life by topological load-bearing weight rather than wall-clock recency, protected by a cold-start grace period (N_grace >= 4); (3) Directed SUPERSEDES DAG filtering to suppress obsolete state during fact mutations; and (4) Triple-source hybrid retrieval fusing dense vectors, BM25, and U-PPR via dynamic Reciprocal Rank Fusion (RRF). Evaluating on all 1,982 QA pairs across 10 long-term conversations in the LoCoMo benchmark, EngramRAG achieves +38.9% relative improvement in Recall@5 (53.21% vs. 38.29%, p < 0.001) and +43.1% in MRR (0.4203 vs. 0.2937) over dense vector RAG, significantly outperforming Okapi BM25 (48.66%) and isolated static graph retrieval (8.50%). On temporal reasoning, EngramRAG reaches 62.33% Recall@5 (+16.67 points over dense vectors). In controlled mutation tests, SUPERSEDES suppresses split-brain hallucinations from 70.0% to 0.0%, while 90-day simulations show 100.0% scaffolding retention under a 26.21ms interactive retrieval reflex.

Model misspecification poses a fundamental challenge in multi-agent reinforcement learning, where transition uncertainty can be amplified by strategic interactions among agents. Distributionally robust Markov games (DRMGs) provide a principled framework for addressing such uncertainty, yet existing methods often rely on restrictive assumptions or scale poorly to large state and joint action spaces. We study online learning in general-sum DRMGs with general function approximation and $\phi$-divergence uncertainty sets. We propose RoMEX-$\phi$, a model-free framework that integrates equilibrium-based exploration with dual fitted learning. Through a functional dual representation of the robust multi-agent Bellman operator, RoMEX-$\phi$ enables tractable worst-case value estimation from nominal interaction data using a centered empirical robust discrepancy. We introduce the robust Multi-Agent Decoupling Coefficient (robust MADC) to characterize the intrinsic exploration complexity arising from strategic interactions and adversarial transition uncertainty. We establish sublinear robust regret guarantees governed by the robust MADC rather than explicitly by the state and joint action space sizes, replacing tabular dependence with intrinsic function-class complexity. Numerical experiments on a scalable general-sum DRMG under total variation uncertainty show that RoMEX-$\phi$ is substantially more resilient to transition shifts than its non-robust counterpart while remaining competitive with an exact tabular robust baseline. Our results provide a scalable framework for distributionally robust multi-agent reinforcement learning with general function approximation.