Papers

Many generative systems return multiple candidate responses and are evaluated according to the best one. Recent work shows that, when demonstrations are optimal, pass@$k$ can reduce the sample complexity of learning from demonstrations by a logarithmic factor in $k$. We ask what happens when the demonstrator is not assumed to be optimal. We find that multiple responses provide a qualitatively stronger benefit in this setting. In a finite reward-class model with no reward feedback, moving from pass@$1$ to any pass@$k$ with $k\ge2$ changes the worst-case dependence on target accuracy from $1/\varepsilon^2$ to $1/\varepsilon$, uniformly over demonstrator quality. Under standard evaluation, where an unknown reward is fixed before training, increasing $k$ provides an additional and distinct benefit: the optimal dependence on a reward class of size $N$ improves from $\log N$ to $\log N/\log k$. We further show that these two effects can be separated. Under robust evaluation, where one learned policy must compete with the demonstrator simultaneously for every reward in the class, the fast $1/\varepsilon$ dependence persists, while the $1/\log k$ improvement can disappear. We establish matching upper and lower bounds in the corresponding regimes and give a greedy multiplicative-weights learner achieving the upper bounds without any assumption on demonstrator quality.

We study robust reconstruction for the \(q\)-state Potts broadcast process on a Galton-Watson tree in the growing-alphabet regime \(q\to\infty\), with boundary depth growing sufficiently quickly in relation to \(q\). We show that, in the regime \(d\lambda >1\), where \(d\) is the expected number of offspring and \(\lambda\) is the nontrivial eigenvalue of the Potts transition matrix, the root posterior is asymptotically unchanged by a broad class of noise channels applied independently to the boundary labels. This remains true even when the probability of retaining the true label at an individual boundary vertex tends to zero as \(q\to\infty\). More precisely, under suitable moment and noise assumptions, the noiseless and noisy root posteriors converge to one another in expected total variation, and hence have the same asymptotic Bayes-optimal reconstruction accuracy.

Hyun, Kim, Wu and Yue constructed optimal and minimal binary linear codes from order ideals of hierarchical posets with two levels. Two different generalizations of the underlying antichain (simplicial complex) setting to odd characteristic are known: down-sets of $\mathbb{F}_p^n$ under the componentwise order, and support-closed subsets of $\mathbb{F}_q^m$. No generalization of the poset setting itself has appeared. We introduce generalized order ideals of a poset of order $p-1$, obtained by attaching multiplicities in ${0,\dots,p-1}$ to the elements of a poset, and study the two natural notions of order ideal that arise for hierarchical posets with two levels. Whenever the ideal meets the upper level, the resulting defining sets are neither down-sets nor support-closed. We determine the weight distributions of the associated complement codes, exhibit a family of Griesmer codes in which the upper element carries an arbitrary multiplicity, and, via the characteristic function of a generalized order ideal, obtain an infinite family of minimal $p$-ary codes of length $p^n-1$ and dimension $n+1$ violating the Ashikhmin–Barg condition.

We study stochastic fixed-point iterations $x_{n+1}=\theta_nx_0+(1-\theta_n)\widehat T(x_n)$ for nonexpansive and contractive operators on Hilbert spaces, with a single-point unbiased oracle of bounded variance. Deterministically, every anchor schedule $\theta_n=c_n/(n+2)$ whose density $c_n\in(0,1]$ does not oscillate between scales is either polynomially suboptimal on contractions or super-polynomially slow on rotations; for constant densities $\theta_n=c/(n+2)$ the tradeoff is exact, with $\norm{x_n}\asymp\Gamma(c+1)(n\varphi)^{-c}$ on rotations by angle $\varphi$ ($\varphi\to0$, $n\varphi\to\infty$) and, for the classical schedule, $\norm{x_n}=\frac{2|\sin(n\varphi/2)|}{n\varphi}+O(\frac1n)$. The dichotomy fails exactly under lacunary anchor concentration: an explicit $\gamma$-oblivious schedule, one per target accuracy, is simultaneously contraction-optimal and rotation-polynomial with exponent $1/\alpha_0$, $\alpha_0=\log_2(3/2)$, and, for each fixed target accuracy, the matching lower bound holds for Lebesgue-a.e.\ angle. For stochastic contractions, the minimax rate is $\Theta(\sigma^2\eps^{-2}(1-\gamma)^{-2})$ on affine maps, and within the anchored class $\Theta(\sigma^2\eps^{-2}(1-\gamma)^{-2}+(1-\gamma)^{-1}\ln(D/\eps))$ for known modulus via geometric batching; without a certified modulus bound no sound distance certificate exists, and a certified ceiling is the exact boundary. For nonexpansive maps we prove $O(K\sigma^2D^2\eps^{-4})$ in every $2$-uniformly smooth Banach space and the Hilbert rate $\tilde\Theta(\sigma^2\eps^{-2}+D\eps^{-1})$ by reduction to monotone inclusions. Numerical experiments are consistent with every scaling prediction.

A subspace design is a collection of subspaces $H_1,\ldots,H_n$ of $\mathbb{F}_q^k$ with the property that no low-dimensional subspace $W$ intersects the collection "too much". Subspace designs and related objects in linear-algebraic pseudorandomness have found a broad range of applications, ranging from list decoding, to derandomizing algorithms. We construct explicit strong subspace designs over every finite field. In the extremal case where the co-dimension $t$ of each $H_i$ is equal to the dimension of $W$, for every constant field size our construction attains $n=\Omega(k)$ and matches the probabilistic intersection bound up to a constant factor. All previous constructions required the field size to grow with $t$ (or $k$). Our subspace designs also imply new construction of rank condensers over arbitrary finite fields. This result is the first to achieve an optimal dependence on $k$ while maintaining both a constant output entropy rate and a constant field size. As an application, we construct lossless rank extractors for linear sources of rank $r$, for all $r < q$, with parameters matching those of Guo, Raj, Shangguan and Zhang (FOCS '26), thereby generalizing their result to prime fields and smaller field sizes. Our construction is based on an algebraic-geometric version of the Parvaresh-Vardy codes (Parvaresh-Vardy FOCS '05, Guruswami ECCC '05), extending the framework underlying the condensers of Guruswami, Umans and Vadhan (JACM '09). We view our construction as a linear-algebraic analysis - tailored to affine sources - of the GUV construction, generalized to functions over algebraic curves. More specifically, inspired by Ta-Shma and Umans (CCC 12') we develop a two-level evaluation scheme, where we first evaluate a function on a curve at extension-field points, and then evaluate a corresponding affine-linear polynomial to obtain outputs over the base field.

Domain Adaptation (DA) often lacks worst-case guarantees, while Distributionally Robust Optimization (DRO) based only on source data centers its ambiguity set at the source law and ignores available target structure. To bridge this gap, we introduce a doubly-anchored DRO framework whose ambiguity set is the intersection of $\phi$-divergence balls centered at the source law and a source-completed target reference law, the latter pairing the target covariate law with the source conditional law. We derive dual-induced adversarial bridge geometries for symmetric and asymmetric divergence pairings, notably introducing a Kullback–Leibler/squared-Hellinger (KL/HD) bridge. This asymmetric formulation yields a Lambert-$W$ geometry in which source-side exponential risk tilting and target-side Hellinger stabilization enter through distinct terms, attenuating, but not bounding, the effect of large likelihood ratios. Furthermore, without imposing covariate shift, we establish finite-sample generalization bounds for the minimizer of a structural, loss-agnostic density-bridge risk under bounded-overlap conditions; these bounds do not apply directly to the loss-aware DRO min–max estimator. We translate our framework into a bridge-weighted Nadaraya–Watson estimator, proving uniform consistency for the source regression function and pointwise asymptotic normality, with target recovery when the source and target regression functions coincide, as under covariate shift. Finally, an empirical evaluation on a domain-shifted Fashion-MNIST dataset illustrates the finite-sample stability of the asymmetric KL/HD bridge under severe synthetic target-covariate corruption.

Drifting models enable one-step generation by amortizing distribution transport into training, but this efficiency places greater demands on the transport field estimated at each update. In large-scale training, the field is computed from finite mini-batches of generated and real samples, which provide only imperfect approximations to the underlying distributions. Balanced optimal transport enforces exact mass matching within every mini-batch, making the estimated field sensitive to the particular composition of the real-data batch. We find that generated and real samples should be treated asymmetrically: letting the mass assigned to real samples adapt while keeping every generated sample fully transported improves generation across six feature-space metrics in controlled ablations, and is more robust to the relaxation strength than relaxing both marginals simultaneously, which falls below balanced transport under stronger relaxation. Motivated by this observation, we propose Unbalanced Optimal Transport Gradient Flow (UOT-GF), which keeps the generated-sample marginal fixed and relaxes only the real-data marginal. Under identical settings at DiT-B/2 on ImageNet-256, UOT-GF improves Fréchet Inception Distance (FID) from 1.53 to 1.46 over the balanced W-Flow baseline; scaling the same recipe yields 1.34 and 1.22 FID at L/2 and XL/2, the best FID among the one-step models we compare. We further derive the induced UOT transport force, establish a kinetic Vlasov–Fokker–Planck formulation whose overdamped zero-temperature limit recovers the drifting dynamics, and characterize non-target stationary states together with sufficient conditions for convergence.

Networks of interacting Hebbian networks have recently been shown to perform a task beyond associative memory, namely pattern disentanglement: when fed with a spurious mixture of stored patterns, the different modules spontaneously specialize on, and retrieve, the different constituents of the mixture. So far, this capability has only been established for pairwise interactions, which limits the number of patterns that can be handled. Here we introduce a dense extension of these modular networks, in which both the auto-associative couplings within each module and the hetero-associative couplings among modules are promoted to higher-order Hebbian interactions. We show that, with a suitable choice of the interaction orders, the network disentangles mixtures while storing a number of patterns that scales linearly with the module size, a regime where its pairwise counterpart fails. Through a statistical-mechanical analysis based on Guerra's interpolation, we derive the self-consistency equations for the order parameters and draw the phase diagrams identifying the region where disentanglement is achieved; these predictions are confirmed by Monte Carlo simulations. Finally, we show that disentanglement provides a natural decoding primitive, and we illustrate it with two applications: the explicit reconstruction of all the hidden patterns from the Hebbian tensors and a stream of unlabeled mixtures, and a proof-of-concept communication protocol in which each message token is transmitted as a masked mixture of hidden patterns and decoded by the network dynamics. Owing to its attractor-based decoding, the protocol degrades gracefully under strong channel corruption, where conventional secure-transmission pipelines fail abruptly.

We prove an exponential strong converse for the unassisted private capacity of every finite-dimensional degradable quantum channel. We use a single error criterion: the infidelity between the actual message-estimate-environment state and an ideal state consisting of uniformly distributed, perfectly correlated messages that are independent of the environment. At every rate strictly above the channel's maximum coherent information, the optimized fidelity to this ideal state decays exponentially in the number of channel uses. The same bound holds when the ideal environment state is fixed to the actual environment marginal. The proof applies to arbitrary mixed-state encoders and arbitrary collective decoders. Its main operator ingredient is an overlap bound for privacy tests: two receiver placements with a common subsystem of dimension $d_C$ have overlap at most $d_C/M$, where $M$ is the key size, independently of both shield dimensions. We combine this bound with the signed averaging construction presented in arXiv:2608.01308 and a single-filter reduction to symmetric states. A Gaussian filter replaces the common receiver subsystem by a system of controlled dimension from which the original correlations can be approximately recovered using quantum side information. The filter preserves exact exchange symmetry, and a uniform smooth-entropy estimate bounds its output dimension for arbitrary correlated channel inputs. We also obtain an exponential strong converse at zero for antidegradable channels under the same joint criterion and, consequently, for the private capacity of the quantum erasure channel throughout its parameter range.

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.

Optimal experimental design is often formulated as the maximization of the Expected Information Gain (EIG), which measures the expected reduction in uncertainty about a parameter of interest after observing the data. For nonlinear forward models and nonGaussian priors, computing the EIG typically requires costly nested Monte Carlo estimators or sophisticated density-approximation techniques. In this work, we derive new upper and lower bounds on the EIG using dimensional logarithmic Sobolev inequalities. The proposed bounds are expressed in terms of signal-to-noise ratios (SNR), preserving the simple matrix-based structure of the EIG in the linear-Gaussian setting and depending solely on covariance matrices and Fisher information matrices. We introduce two families of bounds: conservative bounds, designed to retain the entire information content, and incremental bounds, that prioritize early information acquisition for sequential experimental design. When model gradients are available, we further derive computable approximations of the Fisher-information terms that require only a small number of gradient evaluations, yielding substantial computational savings. The tightness of these bounds is controlled by the nonlinearity of the forward model, and in the linear-Gaussian setting, these bounds recover the exact value of the EIG. By eliminating the nested-sampling bottleneck, the proposed framework offers a tractable and theoretically grounded alternative to direct EIG estimation for large-scale Bayesian experimental design, while retaining the interpretability of the SNR-based bounds.

Pinching-antenna systems (PASS) reconfigure wireless channels by activating radiating elements at selected locations along dielectric waveguides. Port selection is a core issue in improving the performance of multiuser PASS systems. In this paper, we study joint port selection and precoder design for multiuser sum rate maximization, which leads to a large-scale nonconvex mixed-integer problem coupling discrete port selection with continuous precoder design. We propose a discrete diffusion method that does not require optimal or near-optimal port selection solutions as training labels and recasts the resulting optimization problem as sampling from a target distribution. Instead, we learn a potential function from local objective differences between neighboring feasible realizations. The learned potential is incorporated into a Metropolis–Hastings sampling rule to guide a parallel diffusion process while preserving the port selection constraints. Simulation results show that the proposed method approaches exhaustive search within a $0.30\%$ sum rate gap while achieving over $150\times$ speedup, and outperforms state-of-the-art methods including greedy and beam search. In particular, it also achieves an $18.8\times$ speedup over greedy search.

The support recovery problem in mixture of linear classifiers aims to identify the features relevant to the underlying decision rules when data is generated by a mixture of several linear decision rules. In particular, the goal is to recover the support (nonzero coordinates) of $l$ unknown $k$-sparse vectors from sign measurements. Each measurement is generated by selecting one of the $l$ vectors uniformly at random, and returning the sign of its inner product with a chosen measurement vector. In this paper, we propose adaptive and non-adaptive schemes that significantly improve upon prior results by simultaneously reducing the number of measurements and achieving sublinear decoding time. In particular, our adaptive constructions substantially reduce measurements compared to existing approaches, while also lowering decoding complexity from super-quadratic to sublinear in the ambient dimension. We further provide a non-adaptive scheme that improves previous measurement bounds while maintaining efficient decoding. Overall, our approach yields a more efficient trade-off between sample complexity and decoding time for support recovery in mixture models compared to previously known methods.

The design of optimal causal linear feedback schemes for additive white Gaussian noise (AWGN) channels with noisy output feedback has remained an open problem for over 60 years. Prior work has focused on restricted policy classes, especially passive (uncoded) noisy output feedback, where only the transmitter performs feedback coding. However, passive noisy output feedback fundamentally lacks the degrees of freedom required to attain the information-theoretic performance limit in general. In this paper, we consider the active (coded) noisy output feedback setting, where both the transmitter and the receiver perform feedback coding. We then develop a constructive KKT-optimal active linear feedback design that asymptotically attains the Elias-Butman SNR converse bound, thereby establishing MSE/SNR optimality over the entire class of causal linear schemes. Furthermore, we prove that the optimal passive feedback solution is recovered as a special case of the active design. This passive solution admits a Geometric Toeplitz (GT) structure with a Chance-Love (CL)-style one-shot polynomial characterization, and can be computed with O(log T) complexity. Thus, our results provide an affirmative answer to the long-standing optimality question for noisy output feedback under causal linear feedback coding, and our numerical results support the theoretical findings.

Complementary waveform libraries yield impulse-like aggregate delay responses at zero Doppler, but pulse-dependent Doppler phases degrade their sidelobe cancellation. This paper develops a linear-algebraic formulation for coordinating a (D)-ary transmission schedule and slow-time receive weights for paraunitary MIMO waveform libraries. Using a modal decomposition of the CPI ambiguity matrix, prescribed-order Doppler-nulling conditions for the (D-1) nonzero modes are expressed as homogeneous linear constraints on the receive weights for a fixed schedule. This representation gives the SNR-optimal fixed-schedule weights by subspace projection and reduces the remaining design to a discrete schedule search. Degrees-of-freedom and modal-growth analyses relate the design to the CPI length, null order, and waveform dimension. Numerical examples compare the resulting designs with established binary constructions and demonstrate Doppler suppression across the full ambiguity matrix of a four-waveform configuration.

How much entropy must a physical classifier produce to achieve a prescribed accuracy? Rate–distortion theory specifies the minimum information required, but does that information threshold suffice to determine the physical cost? We show that it does not, even for a binary task and a two-state memory. For a uniform binary target observed through a finite symmetric experiment, replacing the classification-error constraint with its necessary mutual-information threshold strictly lowers the infimum of entropy production under a common operation time, integrated mobility budget, and sufficiently large finite transition-rate cap. The separation holds whenever the target error lies strictly between the Bayes error of the observations and chance. Two results establish this physical gap. First, ordering observations by posterior confidence gives exact transport–risk and transport–information frontiers. Observations with the same Bayes error can have different cost frontiers. Second, we construct bounded-rate protocols that realize prescribed encoders with write probabilities below one, starting from exact reset, with an explicit excess cost above the transport bound. An achievable information-constrained cost then falls below a lower bound valid for every task-feasible protocol. Examples with repeated noisy observations illustrate the separation. The results identify a limitation of information-only benchmarks for physical classification: task accuracy and kinetic constraints must be retained explicitly. The cost analyzed is total entropy production during memory writing, excluding data acquisition, controller operation, and subsequent reset.

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.

What should a compressed representation preserve when the information of interest lies in relationships among elements rather than in the elements themselves? We formulate relational compression in the classical source-description-reconstruction sense, but with relational structure itself as the fidelity-bearing content. Each instance specifies the source relation, retained description, reconstructed or evaluated relation, fidelity criterion, and constrained resource. We use this interface to situate selected methods from graph summarization, spectral sparsification, similarity-preserving representation, and relational distillation within a common formulation while keeping their different reconstruction and resource assumptions explicit. We develop finite-codeword collision as one concrete realization. Same-codeword probability yields a relational geometry linking pair-specific alignment and separation to aggregate Rényi-2 occupancy and the spherical geometry of categorical assignments, with exact objective correspondences to squared-Euclidean centroid reconstruction and normalized graph association and cut. Graph and image studies illustrate complementary routes within the finite-codeword family: graph- and teacher-defined relational requirements act directly on equality or collision, while reconstruction acts through a joint decoder. Together, these results illustrate how distinct relational requirements can be formulated and tested within a common constrained-representation framework.

We prove dimension-independent stability for the Courtade-Kumar inequality: a Boolean function $f:\{-1,1\}^n\to\{-1,1\}$ whose information is close to the dictator value is close in probability to a signed dictator. The correlation dependence is sharp in order near zero and, for increasing functions, also at the noiseless endpoint.

Neural representational dissimilarity quantifies differences between neural response distributions, and is essential for comparing neural codes across stimuli, brain areas, tasks, and models. Commonly used distance metrics involve different assumptions and are estimated with separate methods. Here, we show that a variety of distance metrics can be unified under a flow matching framework developed in deep generative models. That is, these distances arise as Jeffreys divergences under different velocity constraints. We find that flow matching has advantages for estimating distances involving complicated distributions and continuous variables. Furthermore, this framework enables the design of new distance metrics in a principled way. Together, flow matching provides a unified approach for understanding, estimating, and designing neural representational dissimilarity metrics.

Sipser-Spielman codes and Dijkgraaf-Witten twisted gauge theories are among the most profound ideas in the last few decades in the areas of computer science and mathematical physics respectively. This work unifies them in the same framework using the language of sheaf cohomology, and produces a new framework of twisted sheaf gauge theories describing a class of quantum low-density parity-check (qLDPC) codes with non-Abelian $D_4$ topological order. The corresponding twisted Clifford-stabilizer qLDPC code can be obtained from gauging a new type of 0-form sub-complex symmetry from a qLDPC code defined on a general sheaf complex, and can be interpreted as a topological defect network of non-Abelian $D_4$ patches glued together with proper gapped interfaces. As an application, one can use this to realize a magic state fountain via the gauging measurement of the addressable logical CZ gates as 0-form subcomplex symmetries in a 2D hypergraph-product (HGP) sheaf code. This includes a scheme of subdividing an arbitrary constant-rate 2D HGP code with parameters $[[n,\Theta(n), \Omega(n^{1/2})]]$ into a quantum sheaf code which allows preparation of $\Theta(n^{1/2})$ logical CZ magic states in parallel, equivalent to the recent geometric construction using the code-to-manifold mapping in (arXiv:2601.06736). Moreover, using the recent sheaf complex and algebraic code constructions by Golowich-Tamo-Zhu (arXiv:2609.27801) with parameters $[[n,\Theta(n^{1-\epsilon}), \Omega(n^{(1-\epsilon)/2})]]$ for arbitrary small $\epsilon$, one can prepare $\Theta(n^{1-\epsilon})$ CZ magic states in parallel and hence achieve an almost-constant magic rate.

The goal of personalized immunogenomics is to recover an individual's germline immunoglobulin gene segments from 'repertoire sequences' altered by trimming, extension, and mutation. In this work, we study the fundamental trace complexity (or the number of samples/traces required for accurate reconstruction) of D-gene reconstruction under three biologically motivated trace-generation models introduced by Bhardwaj et al. (2021) and develop practical algorithms for reconstruction problems left open in the original work. First, for the TrimSuffixAndExtend model, we establish the optimal trace complexity to be {\Theta(n)}, and develop a low-complexity Prefix-Filtered Mode (PFM) decoder that achieves this scaling. Second, for the closely related two-sided TrimAndExtend model, we show that the optimal trace complexity is instead {\Theta(n^2)}, and is achieved by the simple Bit-Wise Mode (BWM) decoder. Third, for the SuffixExtend-t(TrimSuffix) model, we establish polynomially separated lower and upper bounds on trace complexity. Our results follow from information-theoretic lower bounds coupled with tight analyses of the proposed reconstruction algorithms.

In 2025, Jordan et al. introduced Decoded Quantum Interferometry (DQI), a quantum algorithm for combinatorial optimization based on decoding. They considered Reed-Solomon decoding and its associated optimization problem, called Optimal Polynomial Intersection (OPI), which may be viewed as a polynomial regression problem over a finite field. DQI exhibits provable speedups on certain problem instances and establishes a connection between decoding problems and optimization tasks. Leveraging the well-understood dual structure and decoding theory of algebraic geometry codes from other curve families, we introduce COFI: Curve-based Optimal Function Intersection. By considering two-point Hermitian codes, Suzuki codes, and extended norm-trace codes, we broaden the range of algebraic geometry codes used in DQI and identify families that offer further improvements over one-point Hermitian codes in the Hermitian Optimal Polynomial Intersection framework considered by Jordan and Gu. Depending on the family and parameter regime, these curves can reduce quantum resource requirements or increase the number of constraints that can be considered.

We introduce lower bounds on the minimum distance of one-generator quasi-cyclic codes of arbitrary index, obtained by puncturing and shortening the code at the level of its blocks. For balanced codes, these bounds form a nondecreasing chain whose first term is the Jensen bound. We apply these bounds to conduct a computer search and obtain many Hermitian LCD codes with good parameters. Among them there are six codes of length at most 30 which improve the corresponding lower bounds of Araya and Harada. These codes further give maximal-entanglement entanglement-assisted quantum codes, which we compare with the parameters currently recorded in the literature.

Finite-aperture near-field sensing leads to a super-resolution geometry fundamentally different from the translation-invariant Fourier setting. In the Fresnel regime, wavefront curvature introduces a range-dependent quadratic aperture phase, so distinguishability is governed by incomplete quadratic exponential sums of the form \( \sum_{n=0}^{N_r-1} a_n e^{i(\omega_1 n+\omega_2 n^2)} \), rather than by angular separation alone. We develop a deterministic recovery theory for sparse measures with ranges on a finite grid and continuous angles, and introduce a support-uniform quadratic-phase aperture criterion replacing classical minimum separation. Under this criterion, total-variation minimization exactly recovers every sparse measure in the admissible support class, uniformly over all nonzero complex amplitudes. The proof develops nonasymptotic support-uniform bounds for finite quadratic sums and combines them with a gauged Hermite dual certificate controlling interpolation, local curvature, and off-support leakage. We further construct a finite-harmonic Bessel-Vandermonde lift with explicit truncation error. In the far-field limit, the quadratic phase disappears and the theory reduces to Fourier-type angular super-resolution.

Shift-invariant permutations of $\mathbb F_2^n$ are particularly attractive in symmetric cryptography because of their regularity and implementation efficiency. Constructing such permutations with an explicit algebraic structure remains a challenging problem. In this paper, we study a family of shift-invariant transformations of $\mathbb F_2^n$ constructed from a recursively defined sequence of mappings $\{\gamma_j\}_{j\ge 0}$ associated with landscapes. First, we prove that, under an explicit dimension condition relating $n$ to the support of the landscape, the sequence $\{\gamma_j\}_{j\ge 0}$ has the polynomial composition property if and only if the corresponding landscape is quasi-conserved on $\mathbb F_2^n$ with a nonzero special index. Then, we determine the eventual zero or periodic behavior of $\{\gamma_j\}_{j\ge0}$, including the exact index at which the sequence either first vanishes or becomes periodic, together with the least eventual period, and establish linear independence until the first linear relation occurs. When the polynomial composition property holds, we establish an explicit isomorphism between the group of permutation elements in the monoid generated by these mappings and the unit group of a quotient ring $\mathbb F_2[z]/\langle p(z)\rangle$, where $p(z)$ is a monomial or a binomial determined by the landscape. This framework reduces the tasks of testing bijectivity, computing iterates, and determining compositional inverses and orders of permutation elements to polynomial computations. Finally, we apply the results to mappings represented by binomials and trinomials in the quotient ring, obtaining explicit criteria and formulas, and tabulate more than one hundred representative constructions of shift-invariant permutations, recovering and unifying several previously studied families.

We study Bayesian optimization (BO) through the lens of information geometry. Pulling back the Fisher information metric through the surrogate posterior map yields a local sensitivity tensor on the input space, which leads to an upper bound on the gradient of reparameterizable acquisition functions. This view explains vanishing-gradient behavior in high-dimensional BO and provides a common interpretation of heuristics such as RAASP and dimension-scaled lengthscales. Building on this analysis, we propose FITR, a trust-region-based BO method that replaces lengthscale-based scaling by local pullback-Fisher weights. FITR is not restricted to GP kernels with explicit lengthscales. On GP benchmarks with an SE kernel, experiments show competitive performance using FITR. The proposed method also easily generalizes to non-isotropic surrogates, although the gains are more task-dependent in that setting.

We study fundamental information-theoretic limits of robust stochastic optimization when the distribution is known only through its exact moment sequence. We develop a unified framework that produces families of distinct distributions sharing all moments yet inducing radically different optimal decisions, thereby establishing strong impossibility results for a range of decision problems under moment ambiguity. Our approach gives two explicit constructions: a binary and an $N$-way construction showing that distributions with identical moment sequences can nevertheless exhibit arbitrarily different quantiles, order-statistics and threshold regions, forcing incompatible optimal actions. These families of distributions yield, in fact, strong impossibility results across several stochastic optimization problems. First, for the newsvendor problem, moment equivalence causes quantile ambiguity, inducing any fixed or randomized order quantity to fail arbitrarily badly. Second, for revenue maximization, no deterministic or randomized posted pricing scheme can secure a nontrivial approximation relative to the full-information benchmark. Third, for the secretary with cardinal observations setting, the worst-case robust value over all exact moment disclosures is exactly the classical $1/e$ finite-horizon value as opposed to the celebrated result of $0.58$ success probability with full-information by Gilbert and Mosteller (J. Am. Stat. Assoc., 1966). We also recover and expand upon the recent impossibility result of Correa et al. (STOC, 2026) for prophet inequalities with moment knowledge. Indeed, exact moment knowledge can yield at best a $\Theta(1/\log n)$ competitive ratio, even when competing against relaxed benchmarks based on expected $r$-th order statistics or when the algorithm is allowed to select $r$ items.

Pinching-antenna systems (PASS) create reconfigurable wireless channels by moving dielectric antennas along a waveguide. Mechanical position errors translate into phase errors that degrade performance, yet almost all prior PASS studies assume ideal placement. This paper models this position error, derives the resulting phase error, and analyzes its impact on time-division multiple access (TDMA) and non-orthogonal multiple access (NOMA), obtaining their ergodic-rate bounds and closed-form outage probabilities. Analyses and simulations reveal that single-antenna TDMA is immune to position error, whereas multi-antenna TDMA loses array gain and NOMA suffers an interference floor that cannot be overcome by increasing transmit power.

The study of preordered semirings is motivated by applications in computer science, graph theory, and information theory, and provides tools for understanding the asymptotic preorder, which compares large powers of a pair of elements. This paper studies sequences which behave approximately as sequences of powers, but are not necessarily equivalent to geometric sequences. Our main result is that preordered semirings admit completions where such sequences, that we call approximately geometric, become equivalent to geometric sequences, and that existing characterizations of the asymptotic preorder extend to the completion. We provide several classes of examples of approximately geometric sequences in the semiring of tensors, and in the semiring of graphs. As a concrete application, we determine the strong converse exponent for binary hypothesis testing with composite Markov hypotheses.