Résultats de recherche pour « Leaky RBM »

Restricted Boltzmann Machine (RBM) is a bipartite graphical model that is used as the building block in energy-based deep generative models. Due to numerical stability and quantifiability of the likelihood, RBM is commonly used with Bernoulli units. Here, we consider an alternative member of exponential family RBM with leaky rectified linear units -- called leaky RBM. We first study the joint and marginal distributions of leaky RBM under different leakiness, which provides us important insights by connecting the leaky RBM model and truncated Gaussian distributions. The connection leads us to a simple yet efficient method for sampling from this model, where the basic idea is to anneal the leakiness rather than the energy; -- i.e., start from a fully Gaussian/Linear unit and gradually decrease the leakiness over iterations. This serves as an alternative to the annealing of the temperature parameter and enables numerical estimation of the likelihood that are more efficient and more accurate than the commonly used annealed importance sampling (AIS). We further demonstrate that the proposed sampling algorithm enjoys faster mixing property than contrastive divergence algorithm, which benefits the training without any additional computational cost.

In the absence of external excitation, light trapped within a dielectric medium generally decays by leaking out, and also by getting absorbed within the medium. We analyze the leaky modes of solid dielectric spheres by examining solutions of Maxwell's equations for simple homogeneous, isotropic, linearly dispersive media that admit complex-valued oscillation frequencies. We show that, under appropriate circumstances, these leaky modes constitute a complete set into which an initial electromagnetic field distribution inside a dielectric sphere can be expanded. We provide the outline of a completeness proof, and also present results of numerical calculations that illustrate the close relationship between the leaky modes and the resonances of solid dielectric spherical cavities.

We study zero forcing and $\ell$-leaky zero forcing on induced subgraphs of $d$-dimensional grid graphs. Using $\ell$-leaky forts, we prove structural results showing that for $\ell \le 2d-1$, every nonempty $\ell$-leaky fort in an induced subgraph of $P_{n_1}\square\cdots\square P_{n_d}$ intersects the boundary of the graph. These results give general bounds and, in certain settings, exact values for the $\ell$-leaky forcing number of induced subgraphs. Motivated by this framework, we introduce an integer lattice based definition of the Hopi rectangle graphs $HD(a,b)$ as induced subgraphs of $P_{a+b}\square P_{a+b}$. For this particular family of graphs, we show that the zero forcing number equals the maximum nullity, and we completely characterize the $\ell$-leaky forcing number for all $\ell\ge 1$.

The test suites used as RLVR rewards for code have natural false positives: per-task, persistent, asymmetric errors that accept the same wrong programs every time they appear, unlike the symmetric or resampled noise assumed by existing noise-robustness analyses. We run a preregistered two-arm causal contrast on a deployed suite: GRPO on identical MBPP tasks, seeds, and compute, rewarded by the original MBPP tests (leaky) versus the MBPP+ extra tests (hardened). Two further families replicate the design under a preregistration frozen before their data existed. [C] The average held-out effect is bounded: non-inferior under a preregistered 1.5-pt margin (gap 0.20 pt, one-sided 95% upper bound 0.75 pt). [C] Rewarded false-positive mass tracks a cheap static leakiness audit computed before training (Spearman 0.80), and the registered train-side test puts the leak-stratum FP share +43.8 pt above clean tasks. [E] Auditing every rewarded FP under signed, human-adjudicated rules finds a large residual of verified genuinely wrong code: 47.57% record-weighted; both replication families reproduce a large share. The reward paid for real bugs, not merely suite artifacts. [E] Mechanism evidence is consistent with selection of pre-existing error modes rather than learned exploitation: FP incidence does not grow within our horizon, and untrained base models already produce the same wrong outputs under the leaky filter. We then turn the same instrument on the frontier judges themselves: on their own false positives they self-assess only weakly, a same-author test is unresolved, and even the highest-scoring reader we probe stays far below its score on a weaker policy's errors -- two subjects on MBPP, licensing nothing about frontier models in general. A cheap static audit locates exposure before training; hardening the reward removes the measurement inflation, though here it buys little capability.

The statistics of the output activity of a neuron during its stimulation by the stream of input impulses that forms the stochastic Poisson process is studied. The leaky integrate-and-fire neuron is considered as a neuron model. A new representation of the probability distribution function of the output interspike interval durations is found. Based on it, the moment-generating function of the probability distribution is calculated explicitly. The latter, according to Curtiss theorem, completely determines the distribution itself. In particular, explicit expressions are derived from the moment-generating function for the moments of all orders. The first moment coincides with the one found earlier. Formulas for the second and third moments have been checked numerically by direct modeling of the stochastic dynamics of a neuron with specific physical parameters.