神经形态计算

Parameter initialization shapes training dynamics, convergence, and performance in neural networks. In spiking neural networks (SNNs), analytical initialization is complicated by three additional mechanisms—binary spike outputs, temporal recurrence (leak), and reset-induced drops in membrane potential—which together suppress activity propagation: (1) over time, where recurrence and reset reduce individual neurons' firing rate, and (2) across depth, where deficits in upstream activity compromise downstream layers, known as spike-rate collapse. Prior initialization methods address only subsets of these challenges. We derive closed-form weight and bias distributions for initialization that jointly account for temporal recurrence, refractory reset, and signal propagation across depth. The method is data-agnostic: it requires only the architecture and neuron hyperparameters. Our derivation centers around a bias correction that yields stationary firing rates and membrane variance, with a principled default spike probability of $p = 0.5$ that maximizes per-neuron Bernoulli entropy—counteracting dead neurons ($p \approx 0$) and saturated neurons ($p \approx 1$) at initialization. In controlled simulations across 30 layers, it maintains target firing rates and membrane variance at the individual-neuron level, unlike alternatives tested. Across UEA multivariate time-series classification, neuromorphic classification, and continuous-control reinforcement learning, our SNNs rank first in every paradigm without per-paradigm tuning.

Spiking Neural Networks (SNNs) offer a promising energy-efficient alternative to Artificial Neural Networks (ANNs) through event-driven, multiplication-free computation. However, when applied to downstream tasks such as Neural Radiance Fields (NeRF), SNNs suffer from significant information loss, resulting in a noticeable performance gap. In this paper, we present \textit{Spik-NeRF v2} to advance SNN-based neural rendering. We propose the $\pm$I-LIF spiking neuron, which extends I-LIF to support signed integer values during training, thereby mitigating information loss. During inference, it is converted to ternary spikes $\{-1, 0, 1\}$, preserving event-driven properties with addition-only operations. Furthermore, we introduce a re-parameterization technique that transforms a trained I-LIF-based Spik-NeRF with $t$ timesteps into an equivalent $\pm$I-LIF-based model with $t/2$ timesteps. This enables faster inference while preserving rendering quality, overcoming the suboptimal performance of directly trained $\pm$I-LIF models with reduced timesteps. Extensive experiments on synthetic and realistic datasets demonstrate that Spik-NeRF v2 surpasses existing SNN-based NeRF methods and achieves rendering quality comparable to ANN-based approaches.

Matrix multiplications dominate the inference cost of modern transformer-based vision models, yet existing efficiency techniques such as post-training quantization and mixed-precision inference are largely limited to the small set of fixed-width formats—INT4, INT8, BF16, and FP16—supported by conventional accelerators. We revisit stochastic computing (SC) as a way to lift this constraint: viewed as a dense adaptive quantizer, SC controls precision by bit-stream length L rather than a fixed datapath, while each multiplication reduces to a single AND/XNOR gate. We build a GPU library that emulates SC matrix multiplication at scale, exposes stream lengths as first-class kernel arguments, and evaluates SC end-to-end on image classification, object detection and instance segmentation, class-conditional image generation, and visual world-model planning. On top of this substrate, we develop a dynamic per-row mixed-precision policy that assigns stream length per token or group at matched average budget, requires no retraining, and uses the same SC hardware across schedules. Across tasks, SC remains competitive with fixed-format INT quantization at matched bit budgets, while per-row mixed precision helps maintain accuracy at lower average stream lengths. These results provide software-level feasibility evidence that SC can serve as a dense-precision substrate for fine-grained mixed-precision inference on modern vision transformers.

Spiking reservoir computing, and reservoir computing more generally, is a powerful and efficient framework for neuromorphic and biological applications, in which a fixed random reservoir drives a trained readout. Yet its performance depends critically on the reservoir initialization. Enriching the reservoir with adaptive, unsupervised plasticity rules offers a natural solution to this limitation. However, it is unclear which rules work, or why, and how to find the best-suited rules for specific tasks without exhaustive and expensive search. Here, we learn how to play the Atari game Pong in a plastic spiking reservoir network. We systematically characterize a large family of local plasticity rules that were meta-learned in prior work. We then show that their performance is predictable and structured: high-scoring rules are characterized by strong differentiation between neurons encoding the ball trajectory and the background, with stable weight dynamics, and consistent readout alignment across time. Rule performance can be estimated from rule parameters alone. Finally, conditioning simulation-based inference (SBI) on high scores allows us to sample directly from promising regions of the rule space, to discover rules that exceed the performance of those found in the prior distribution and reveal stable, high-performing configurations. Together, these results offer competitive performance against classical reservoir computing while providing a transparent, interpretable account of what makes a plasticity rule useful for neuromorphic hardware and biological computing.

Large Language Models (LLMs) have shown strong capabilities in code generation and reasoning, motivating extensive benchmarks for evaluating functional correctness. However, performance optimization in High-Performance Computing (HPC) poses fundamentally different challenges that are not captured by existing evaluations: HPC performance depends on low-level code, intricate memory access patterns, and computational kernels embedded within sophisticated execution contexts. We introduce HPC-Bench, a performance-grounded benchmark for evaluating LLMs as optimizers of computational kernels in realistic HPC workloads, including $114$ workloads across $16$ HPC computational motifs. HPC-Bench provides a fully automated, end-to-end evaluation pipeline that combines program-level correctness verification with two correctness-gated metrics, $\mathrm{Fast}@k$ and $\mathrm{Speedup}@k$, to characterize reliability and speedup under a fixed sampling budget. Our evaluation of three representative LLMs across serial CPU, OpenMP, and CUDA settings shows that stricter speedup requirements substantially reduce the probability of finding a correct and fast optimization. HPC-Bench is available at https://github.com/neuripspaper2026/NeurIPS_26.

Spiking neural networks (SNNs) are a promising paradigm for efficient neuromorphic computing, yet their training remains challenging due to the non-differentiability nature of spike firing. Backpropagation through time (BPTT) with surrogate gradients (SG) has become a mainstream approach due to its superior performance. However, this method incurs high computational and memory demands during training, while its update rule depends on specific neuronal dynamics. Furthermore, when targeting neuromorphic hardware implementation, the temporal error-propagation process and the full membrane-potential access required by SG are difficult to realize; these can introduce additional readout overhead, measurement noise, or perturbations to the system dynamics. To address these issues, we propose the input-driven derivative-free training (IDDFT) method. Rather than relying on membrane-potential-based surrogate derivatives, IDDFT constructs derivative-free error signals by applying a relaxed nonlinearity to the inputs, thereby avoiding the temporal error-propagation process and reducing the dependence of the update rule on specific neuronal dynamics. By eliminating access to internal membrane-potential states, our method reduces computational and memory costs, enhances compatibility with neuromorphic hardware, and enables training of black-box SNN models. We validate the IDDFT method through theoretical analysis and systematic experiments, demonstrating its effectiveness as an input-driven, derivative-free mechanism for constructing update signals. When integrated with a biologically inspired training strategy, IDDFT maintains comparable performance while substantially enhancing robustness to the choice of relaxed nonlinearities. Based on the resulting bio-inspired combined framework, we conduct evaluations on CIFAR-10, CIFAR-100, CIFAR10-DVS, and Tiny-ImageNet. Experimental results demonstrate that our method achieves performance comparable to BPTT and state-of-the-art methods, while exhibiting remarkable robustness under adversarial attacks.

Echo State Networks (ESNs) are designed to be \emph{stable}—the echo state property makes the reservoir state a well-defined function of the input history—but it remains unclear how \emph{geometrically rich} the reachable reservoir states are and what controls that richness. We give a partition-free, fractal-geometric theory of contractive reservoirs by viewing a quantized-input ESN as a contractive random dynamical system and, equivalently, an iterated function system (IFS). This identifies the reachable set as the IFS attractor and the stationary reservoir-state law under i.i.d.\ inputs as the unique invariant IFS measure. We prove entropy–contraction (entropy–Lyapunov) bounds on the intrinsic dimension of this measure, and in a conformal/similarity regime with standard separation conditions we obtain sharp closed-form dimension laws of the form “input entropy divided by contraction.” These results yield a quantitative \emph{criticality principle}: weakening contraction drives a transition from low-dimensional to full-dimensional state representations at an explicit threshold set by input entropy and contraction rates, providing practical design guidance for tuning leak/spectral radius and input scaling.

For $p \ge 1$, the $p$-Wasserstein distance measures the minimum cost of transporting probability mass, where moving mass between two points costs the $p$th power of their distance. For discrete distributions in one dimension, full transport is especially simple: after sorting, mass is matched in order along the line. By contrast, partial and unbalanced transport on the line remains much less understood. Recently, Chapel and Tavenard [ICLR'25] showed that, for $p=1$, all optimal partial transport plans between distributions supported on $n$ points, with uniform mass at each point, can be computed in $O(n\log n)$ time by exploiting the metric structure of the cost. For $p>1$, this structure no longer applies, and existing approaches require $\Omega(n^2)$ time. Our main contribution is an FFT-based data structure for balanced-interval transport queries, which bypasses this quadratic bottleneck and yields an $O(p\ n\log^2 n)$-time algorithm for computing all optimal partial transports on the line for every finite $p\ge 1$. We also provide an open-source C++ implementation that outperforms the state-of-the-art baseline on a range of synthetic instances. Finally, we establish a conditional lower bound for $p=\infty$: any subquadratic-time algorithm for computing all optimal partial transport plan costs on the line would violate the $(\min,+)$-Convolution Hypothesis. This separates the problem from full optimal transport, which is solvable in $O(n\log n)$ time.

Spiking reservoir computing combines the training efficiency of fixed random recurrent networks with the energy efficiency of event-driven inference, where computation is triggered by sparse spikes rather than executed densely at every timestep. However, existing spiking reservoirs almost exclusively rely on Leaky Integrate-and-Fire (LIF) neurons, whose low-pass dynamics limit their ability to distinguish information encoded at different temporal frequencies. We introduce HRF-Res, a liquid state machine in which LIF neurons are replaced by a heterogeneous population of Harmonic Resonate-and-Fire (HRF) neurons. These neurons exhibit intrinsic oscillatory dynamics and selectively respond to input frequencies, enabling the reservoir to capture frequency-specific temporal patterns. The result is more discriminative representations and higher classification accuracy than LIF-based reservoirs, achieved without sacrificing the energy efficiency of spiking computation, with 9–14× lower energy consumption than an equivalent non-spiking oscillatory reservoir. Evaluated on eight benchmarks spanning time series, sequential images, audio spike trains, and neuromorphic vision, HRF-Res achieves competitive or state-of-the-art performance among spiking reservoir methods. These results demonstrate that introducing frequency-selective dynamics into spiking reservoirs improves representational quality and classification performance while preserving their inherent energy efficiency.

We propose a machine-learning framework based on the principle that learning can be achieved through algebraic decomposition rather than numerical optimization. A learning task is encoded as axioms of an algebra, and learning proceeds by computing a subdirect decomposition of the algebra into subdirectly irreducible components. We show that suitable subsets of these components form models that generalize to unseen data because they approximate the underlying rule in the training data. The method has no dataset-specific hyperparameters to tune and shows no evidence of classical overfitting in our experiments, so we run it without a validation dataset. We compare against multilayer perceptrons as generic parametric baselines without task-specific inductive biases. Across 24 classification datasets, the algebraic method is applied only once to each training set without hyperparameter tuning, whereas the multi-layer perceptrons are selected from many configurations using validation data or cross-validation. Nevertheless, the resulting test accuracies are statistically indistinguishable. Moreover, adding a statistical readout on top of the algebraic representation, using untuned logistic regression, improves over the best multilayer perceptrons selected by validation or cross-validation. More broadly, because task axioms may encode examples, formal knowledge, or both, this approach provides a common algebraic framework and the same algorithm for data-driven problems such as classification, formally specified problems such as computing Hamiltonian cycles from specifications, and mixed settings combining data with formal constraints.