Quantum coherent transceivers toward Holevo-limited communications

The Holevo limit bounds the channel capacity of a communication channel in which information is encoded in quantum states in a Hilbert space at the transmitter and decoded using quantum measurements at the receiver. Saturating the Holevo limit requires quantum-limited transceivers that either generate quantum states of light or employ quantum-limited measurements. Here, we demonstrate an integrated photonic-electronic quantum-limited coherent receiver (QRX) achieving 14.0 dB shot noise clearance (SNC), 520 $μ$W knee power, 2.57 GHz 3-dB bandwidth, 3.50 GHz shot-noise-limited bandwidth, and 90.2 dB common-mode rejection ratio ($\mathrm{CMRR}$). We scale this design to a 32-channel QRX array with median 26.6 dB $\mathrm{SNC}$, and automatic $\mathrm{CMRR}$ correction yielding a median 76.8 dB $\mathrm{CMRR}$ at minimum. Using the integrated QRX and fiber-optic transmitter, we measure $0.15\pm0.01$ dB of squeezing below the shot noise limit, limited by off-chip losses. We propose a squeezed light communication scheme that can surpass the Shannon limit, with a path toward the Holevo limit.

Conservation Law Breaking at the Edge of Stability: A Spectral Theory of Non-Convex Neural Network Optimization

Why does gradient descent reliably find good solutions in non-convex neural network optimization, despite the landscape being NP-hard in the worst case? We show that gradient flow on L-layer ReLU networks without bias preserves L-1 conservation laws C_l = ||W_{l+1}||_F^2 - ||W_l||_F^2, confining trajectories to lower-dimensional manifolds. Under discrete gradient descent, these laws break with total drift scaling as eta^alpha where alpha is approximately 1.1-1.6 depending on architecture, loss function, and width. We decompose this drift exactly as eta^2 * S(eta), where the gradient imbalance sum S(eta) admits a closed-form spectral crossover formula with mode coefficients c_k proportional to e_k(0)^2 * lambda_{x,k}^2, derived from first principles and validated for both linear (R=0.85) and ReLU (R>0.80) networks. For cross-entropy loss, softmax probability concentration drives exponential Hessian spectral compression with timescale tau = Theta(1/eta) independent of training set size, explaining why cross-entropy self-regularizes the drift exponent near alpha=1.0. We identify two dynamical regimes separated by a width-dependent transition: a perturbative sub-Edge-of-Stability regime where the spectral formula applies, and a non-perturbative regime with extensive mode coupling. All predictions are validated across 23 experiments.

Weighted Bayesian Conformal Prediction

Conformal prediction provides distribution-free prediction intervals with finite-sample coverage guarantees, and recent work by Snell \& Griffiths reframes it as Bayesian Quadrature (BQ-CP), yielding powerful data-conditional guarantees via Dirichlet posteriors over thresholds. However, BQ-CP fundamentally requires the i.i.d. assumption -- a limitation the authors themselves identify. Meanwhile, weighted conformal prediction handles distribution shift via importance weights but remains frequentist, producing only point-estimate thresholds. We propose \textbf{Weighted Bayesian Conformal Prediction (WBCP)}, which generalizes BQ-CP to arbitrary importance-weighted settings by replacing the uniform Dirichlet $\Dir(1,\ldots,1)$ with a weighted Dirichlet $\Dir(\neff \cdot \tilde{w}_1, \ldots, \neff \cdot \tilde{w}_n)$, where $\neff$ is Kish's effective sample size. We prove four theoretical results: (1)~$\neff$ is the unique concentration parameter matching frequentist and Bayesian variances; (2)~posterior standard deviation decays as $O(1/\sqrt{\neff})$; (3)~BQ-CP's stochastic dominance guarantee extends to per-weight-profile data-conditional guarantees; (4)~the HPD threshold provides $O(1/\sqrt{\neff})$ improvement in conditional coverage. We instantiate WBCP for spatial prediction as \emph{Geographical BQ-CP}, where kernel-based spatial weights yield per-location posteriors with interpretable diagnostics. Experiments on synthetic and real-world spatial datasets demonstrate that WBCP maintains coverage guarantees while providing substantially richer uncertainty information.

Gated-SwinRMT: Unifying Swin Windowed Attention with Retentive Manhattan Decay via Input-Dependent Gating

We introduce Gated-SwinRMT, a family of hybrid vision transformers that combine the shifted-window attention of the Swin Transformer with the Manhattan-distance spatial decay of Retentive Networks (RMT), augmented by input-dependent gating. Self-attention is decomposed into consecutive width-wise and height-wise retention passes within each shifted window, where per-head exponential decay masks provide a two-dimensional locality prior without learned positional biases. Two variants are proposed. \textbf{Gated-SwinRMT-SWAT} substitutes softmax with sigmoid activation, implements balanced ALiBi slopes with multiplicative post-activation spatial decay, and gates the value projection via SwiGLU; the Normalized output implicitly suppresses uninformative attention scores. \textbf{Gated-SwinRMT-Retention} retains softmax-normalized retention with an additive log-space decay bias and incorporates an explicit G1 sigmoid gate -- projected from the block input and applied after local context enhancement (LCE) but prior to the output projection~$W_O$ -- to alleviate the low-rank $W_V \!\cdot\! W_O$ bottleneck and enable input-dependent suppression of attended outputs. We assess both variants on Mini-ImageNet ($224{\times}224$, 100 classes) and CIFAR-10 ($32{\times}32$, 10 classes) under identical training protocols, utilizing a single GPU due to resource limitations. At ${\approx}77$--$79$\,M parameters, Gated-SwinRMT-SWAT achieves $80.22\%$ and Gated-SwinRMT-Retention $78.20\%$ top-1 test accuracy on Mini-ImageNet, compared with $73.74\%$ for the RMT baseline. On CIFAR-10 -- where small feature maps cause the adaptive windowing mechanism to collapse attention to global scope -- the accuracy advantage compresses from $+6.48$\,pp to $+0.56$\,pp.

Bridging Theory and Practice in Crafting Robust Spiking Reservoirs

Spiking reservoir computing provides an energy-efficient approach to temporal processing, but reliably tuning reservoirs to operate at the edge-of-chaos is challenging due to experimental uncertainty. This work bridges abstract notions of criticality and practical stability by introducing and exploiting the robustness interval, an operational measure of the hyperparameter range over which a reservoir maintains performance above task-dependent thresholds. Through systematic evaluations of Leaky Integrate-and-Fire (LIF) architectures on both static (MNIST) and temporal (synthetic Ball Trajectories) tasks, we identify consistent monotonic trends in the robustness interval across a broad spectrum of network configurations: the robustness-interval width decreases with presynaptic connection density $β$ (i.e., directly with sparsity) and directly with the firing threshold $θ$. We further identify specific $(β, θ)$ pairs that preserve the analytical mean-field critical point $w_{\text{crit}}$, revealing iso-performance manifolds in the hyperparameter space. Control experiments on Erdős-Rényi graphs show the phenomena persist beyond small-world topologies. Finally, our results show that $w_{\text{crit}}$ consistently falls within empirical high-performance regions, validating $w_{\text{crit}}$ as a robust starting coordinate for parameter search and fine-tuning. To ensure reproducibility, the full Python code is publicly available.

GAIN: Multiplicative Modulation for Domain Adaptation

Adapting LLMs to new domains causes forgetting because standard methods (full fine-tuning, LoRA) inject new directions into the weight space. We propose GAIN, which re-emphasizes existing features through multiplicative modulation W_new = S * W. The learned diagonal matrix S is applied to the attention output projection and optionally the FFN. The principle mirrors gain modulation in neuroscience, where neurons adapt to context by scaling response strength while preserving selectivity. We evaluate GAIN on five models from four families (774M to 70B), adapting sequentially across eight domains. GAIN-FFN matches LoRA's in-domain adaptation, but their effects on previously trained domains are opposite: GAIN-FFN improves them by 7-13% (validation PPL), while LoRA degrades them by 18-36%. Downstream accuracy confirms the pattern: for example, after seven sequential adaptations on Qwen2.5, GAIN-FFN degrades BoolQ by only 0.8% while LoRA damages it by 14.9%. GAIN adds 46K-230K parameters per model and can be absorbed into the pretrained weights for zero inference cost.

Compressible Softmax-Attended Language under Incompressible Attention

Across every attention head in five transformer language models (124M--7B parameters, four architecture families), the logit energy field $\tilde{E}$ reaches 90\% of its variance in 2--11 singular components. The \emph{learned} interaction matrix $W_Q^\mathrm{T} W_K$ needs 38--75 components for the same threshold out of $d_h \in \{64, 128\}$. The spectral gap is $5$--$25\times$ in effective rank. The attention mechanism allocates capacity uniformly across all $d_h$ dimensions, but language concentrates the actual interaction into a few. The compressibility of softmax-attended language is a property of the data, not the frame that analyzes it.

Deep Kuratowski Embedding Neural Networks for Wasserstein Metric Learning

Computing pairwise Wasserstein distances is a fundamental bottleneck in data analysis pipelines. Motivated by the classical Kuratowski embedding theorem, we propose two neural architectures for learning to approximate the Wasserstein-2 distance ($W_2$) from data. The first, DeepKENN, aggregates distances across all intermediate feature maps of a CNN using learnable positive weights. The second, ODE-KENN, replaces the discrete layer stack with a Neural ODE, embedding each input into the infinite-dimensional Banach space $C^1([0,1], \mathbb{R}^d)$ and providing implicit regularization via trajectory smoothness. Experiments on MNIST with exact precomputed $W_2$ distances show that ODE-KENN achieves a 28% lower test MSE than the single-layer baseline and 18% lower than DeepKENN under matched parameter counts, while exhibiting a smaller generalization gap. The resulting fast surrogate can replace the expensive $W_2$ oracle in downstream pairwise distance computations.

L-SPINE: A Low-Precision SIMD Spiking Neural Compute Engine for Resource-efficient Edge Inference

Spiking Neural Networks (SNNs) offer a promising solution for energy-efficient edge intelligence; however, their hardware deployment is constrained by memory overhead, inefficient scaling operations, and limited parallelism. This work proposes L-SPINE, a low-precision SIMD-enabled spiking neural compute engine for efficient edge inference. The architecture features a unified multi-precision datapath supporting 2-bit, 4-bit, and 8-bit operations, leveraging a multiplier-less shift-add model for neuron dynamics and synaptic accumulation. Implemented on an AMD VC707 FPGA, the proposed neuron requires only 459 LUTs and 408 FFs, achieving a critical delay of 0.39 ns and 4.2 mW power. At the system level, L-SPINE achieves 46.37K LUTs, 30.4K FFs, 2.38 ms latency, and 0.54 W power. Compared to CPU and GPU platforms, it reduces inference latency from seconds to milliseconds, achieving an up to three orders-of-magnitude improvement in energy efficiency. Quantisation analysis shows that INT2/INT4 configurations significantly reduce memory footprint with minimal accuracy loss. These results establish L-SPINE as a scalable and efficient solution for real-time edge SNN deployment.

Generalization Bounds and Statistical Guarantees for Multi-Task and Multiple Operator Learning with MNO Networks

Multiple operator learning concerns learning operator families $\{G[α]:U\to V\}_{α\in W}$ indexed by an operator descriptor $α$. Training data are collected hierarchically by sampling operator instances $α$, then input functions $u$ per instance, and finally evaluation points $x$ per input, yielding noisy observations of $G[α][u](x)$. While recent work has developed expressive multi-task and multiple operator learning architectures and approximation-theoretic scaling laws, quantitative statistical generalization guarantees remain limited. We provide a covering-number-based generalization analysis for separable models, focusing on the Multiple Neural Operator (MNO) architecture: we first derive explicit metric-entropy bounds for hypothesis classes given by linear combinations of products of deep ReLU subnetworks, and then combine these complexity bounds with approximation guarantees for MNO to obtain an explicit approximation-estimation tradeoff for the expected test error on new (unseen) triples $(α,u,x)$. The resulting bound makes the dependence on the hierarchical sampling budgets $(n_α,n_u,n_x)$ transparent and yields an explicit learning-rate statement in the operator-sampling budget $n_α$, providing a sample-complexity characterization for generalization across operator instances. The structure and architecture can also be viewed as a general purpose solver or an example of a "small'' PDE foundation model, where the triples are one form of multi-modality.