Learning Discrete Diffusion of Graphs via Free-Energy Gradient Flows

Diffusion-based models on continuous spaces have seen substantial recent progress through the mathematical framework of gradient flows, leveraging the Wasserstein-2 (${W}_2$) metric via the Jordan-Kinderlehrer-Otto (JKO) scheme. Despite the increasing popularity of diffusion models on discrete spaces using continuous-time Markov chains, a parallel theoretical framework based on gradient flows has remained elusive due to intrinsic challenges in translating the ${W}_2$ distance directly into these settings. In this work, we propose the first computational approach addressing these challenges, leveraging an appropriate metric $W_K$ on the simplex of probability distributions, which enables us to interpret widely used discrete diffusion paths, such as the discrete heat equation, as gradient flows of specific free-energy functionals. Through this theoretical insight, we introduce a novel methodology for learning diffusion dynamics over discrete spaces, which recovers the underlying functional directly by leveraging first-order optimality conditions for the JKO scheme. The resulting method optimizes a simple quadratic loss, trains extremely fast, does not require individual sample trajectories, and only needs a numerical preprocessing computing $W_K$-geodesics. We validate our method through extensive numerical experiments on synthetic data, showing that we can recover the underlying functional for a variety of graph classes.

Breaking the KV Cache Bottleneck: Fan Duality Model Achieves O(1) Decode Memory with Superior Associative Recall

We present FDM (Fan Duality Model), a linear sequence architecture that resolves the fundamental tension between memory efficiency and associative recall in sequence modeling. FDM separates sequence processing into two components: a wave component (recurrent scan via phase-preserving Givens rotations) that compresses long-range patterns into a fixed-size complex hidden state, and a particle component (local-global cache) that retrieves specific tokens via learned associative addressing with W+K=272 slots independent of sequence length N. This yields strictly O(1) decode memory: 867 MB fixed across all prompt lengths 128-8,192 tokens, versus Transformer's 853-4,247 MB (4.9x reduction at N=8,192). Beyond the architecture, we discover that jointly training the wave and particle components leads to suboptimal convergence. We propose Freeze-Scan, a two-phase training strategy that freezes the recurrent scan and optimizes the cache jointly with embeddings, achieving PPL=64.9 on WikiText-103 in 44K steps -- a 7.5x improvement over full fine-tuning (PPL=487). On Multi-Query Associative Recall (MQAR), FDM achieves 0.966 accuracy, surpassing Transformer (0.606) by 59.5%, while pure scan without cache scores only 0.011, confirming the necessity of the particle component. Finally, we introduce Holographic Reference Beam Decoding, interpreting the complex hidden state h_t as a holographic plate encoding the entire temporal history. Using the current input x_t as a reference beam to modulate h_t reduces PPL by up to 2.13 points (PPL=62.79) with a 4-head orthogonal reference beam using only 1.3M additional parameters, providing empirical support for the holographic interpretation. Code and pretrained weights: https://github.com/YasongFan/FDM

A 129FPS Full HD Real-Time Accelerator for 3D Gaussian Splatting

Rendering large-scale, unbounded scenes on AR/VR-class devices is constrained by the computation, bandwidth, and storage cost of 3D Gaussian Splatting (3DGS). We propose a low-power, low-cost 3DGS hardware accelerator that renders full-HD images in real time, together with a hardware-friendly compression pipeline that combines iterative Gaussian pruning and fine-tuning, progressive spherical harmonics (SH) degree reduction, and vector quantization of all SH coefficients and colors. The scheme achieves a $51.6\times$ model-size reduction with a 0.743 dB PSNR loss. The accelerator uses a frame-level pipeline that integrates point-based culling and projection with tile-based sorting and rasterization, skips zero-Jacobian matrix multiplications (reducing processing elements by 63\% and computation by 53\%), and adopts comparison-free tile-based sorting with deterministic latency. Implemented in a TSMC 28-nm process at 800 MHz, the design occupies $0.66~\text{mm}^2$ with 1.1438 M gates and 120 kB SRAM, consumes 0.219 W, and delivers 1219 Mpixels/J at 267.5 Mpixels/s, enabling 1080p at 129 FPS. Overall, it is $5.98\times$ smaller in area, $5.94\times$ higher throughput, and delivers $7.5\times$ higher energy efficiency than prior 3DGS accelerators.

Biologically-Grounded Multi-Encoder Architectures as Developability Oracles for Antibody Design

Generative models can now propose thousands of \emph{de novo} antibody sequences, yet translating these designs into viable therapeutics remains constrained by the cost of biophysical characterization. Here we present CrossAbSense, a framework of property-specific neural oracles that combine frozen protein language model encoders with configurable attention decoders, identified through a systematic hyperparameter campaign totaling over 200 runs per property. On the GDPa1 benchmark of 242 therapeutic IgGs, our oracles achieve notable improvements of 12--20\% over established baselines on three of five developability assays and competitive performance on the remaining two. The central finding is that optimal decoder architectures \emph{invert} our initial biological hypotheses: self-attention alone suffices for aggregation-related properties (hydrophobic interaction chromatography, polyreactivity), where the relevant sequence signatures -- such as CDR-H3 hydrophobic patches -- are already fully resolved within single-chain embeddings by the high-capacity 6B encoder. Bidirectional cross-attention, by contrast, is required for expression yield and thermal stability -- properties that inherently depend on the compatibility between heavy and light chains. Learned chain fusion weights independently confirm heavy-chain dominance in aggregation ($w_H = 0.62$) versus balanced contributions for stability ($w_H = 0.51$). We demonstrate practical utility by deploying CrossAbSense on 100 IgLM-generated antibody designs, illustrating a path toward substantial reduction in experimental screening costs.

Sharp description of local minima in the loss landscape of high-dimensional two-layer ReLU neural networks

We study the population loss landscape of two-layer ReLU networks of the form $\sum_{k=1}^K \mathrm{ReLU}(w_k^\top x)$ in a realisable teacher-student setting with Gaussian covariates. We show that local minima admit an exact low-dimensional representation in terms of summary statistics, yielding a sharp and interpretable characterisation of the landscape. We further establish a direct link with one-pass SGD: local minima correspond to attractive fixed points of the dynamics in summary statistics space. This perspective reveals a hierarchical structure of minima: they are typically isolated in the well-specified regime, but become connected by flat directions as network width increases. In this overparameterised regime, global minima become increasingly accessible, attracting the dynamics and reducing convergence to spurious solutions. Overall, our results reveal intrinsic limitations of common simplifying assumptions, which may miss essential features of the loss landscape even in minimal neural network models.

IatroBench: Pre-Registered Evidence of Iatrogenic Harm from AI Safety Measures

Ask a frontier model how to taper six milligrams of alprazolam (psychiatrist retired, ten days of pills left, abrupt cessation causes seizures) and it tells her to call the psychiatrist she just explained does not exist. Change one word ("I'm a psychiatrist; a patient presents with...") and the same model, same weights, same inference pass produces a textbook Ashton Manual taper with diazepam equivalence, anticonvulsant coverage, and monitoring thresholds. The knowledge was there; the model withheld it. IatroBench measures this gap. Sixty pre-registered clinical scenarios, six frontier models, 3,600 responses, scored on two axes (commission harm, CH 0-3; omission harm, OH 0-4) through a structured-evaluation pipeline validated against physician scoring (kappa_w = 0.571, within-1 agreement 96%). The central finding is identity-contingent withholding: match the same clinical question in physician vs. layperson framing and all five testable models provide better guidance to the physician (decoupling gap +0.38, p = 0.003; binary hit rates on safety-colliding actions drop 13.1 percentage points in layperson framing, p < 0.0001, while non-colliding actions show no change). The gap is widest for the model with the heaviest safety investment (Opus, +0.65). Three failure modes separate cleanly: trained withholding (Opus), incompetence (Llama 4), and indiscriminate content filtering (GPT-5.2, whose post-generation filter strips physician responses at 9x the layperson rate because they contain denser pharmacological tokens). The standard LLM judge assigns OH = 0 to 73% of responses a physician scores OH >= 1 (kappa = 0.045); the evaluation apparatus has the same blind spot as the training apparatus. Every scenario targets someone who has already exhausted the standard referrals.

IKKA: Inversion Classification via Critical Anomalies for Robust Visual Servoing

We introduce IKKA (Inversion Classification via Critical Anomalies), a topologically motivated weighting framework for robust visual servoing under distribution shift. Unlike conventional outlier handling, IKKA treats maverick points as structurally informative observations: points where small perturbations can induce qualitatively different control responses or class assignments. The method combines local extremality, boundary transversality, and multi-scale persistence into a single anomaly weight, W(x) = E(x) x T(x) x M(x), which modulates control updates near ambiguous decision regions. We instantiate IKKA in a CPU-only embedded visual-servoing pipeline on Raspberry Pi 4 and evaluate it across 230 reproducible runs under nominal and stress conditions. In stress scenarios involving dim illumination and transient occlusion, IKKA reduces the 95th-percentile lateral error by 24% relative to a hybrid baseline (0.124 to 0.094) while increasing throughput from 20.0 to 24.8 Hz. Non-parametric analysis confirms a large effect size (Cliff's delta = 0.79).

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.

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.

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.