One reason is that the notion of interpretability is notoriously challenging to pin down, andtherefore existing CBMs rely ondifferent heuristics--such asencouraging theconcepts tobe sparse [1], orthonormal to each other [5], or match the contents of concrete examples [3]--with unclear properties and incompatible goals.

InIRsystems, theretrievermodule directly influences theperformance ofdownstream tasks, such as retrieval-augmented generation [20, 29, 30] and knowledge-intensive question answering [34, 52]. However, these methods do not explicitly consider targeted optimization for tool usage or the impact on complex multi-stage tasks.

Markov chain Monte Carlo (MCMC) is an inference mechanism that approximates a target probability distribution by a sequence of states (a.k.a.

The first two permit using subgradients andstochastic gradients, andareshowntoensureaO(1/ t) convergencerate.

The first two permit using subgradients andstochastic gradients, andareshowntoensureaO(1/ t) convergencerate.

Language models have been shown to be very effective in predicting brain recordings of subjects experiencing complex language stimuli.

In this section, we review some key results on the Wasserstein distance. Wpp Rπ(t,θi),Rρ(t,θi), (4) where the approximation comes from using Monte-Carlo integration by samplingθi uniformly in SD 1 [2]. M,M is the number of points used to approximate the integral. Calculating the Wasserstein distance with the empirical distribution function is computationally attractive. To do that, we first sortxms in an ascending order, such thatxi[m] xi[m+1], where i[m]istheindexofthesortedxms. Hamiltonian Monte Carlo (HMC)[24]isahighly-efficient MarkovChain Monte Carlo (MCMC) method used to generate samples from the posteriorw p(w|y).

The bottleneck introduced by the low-dimensional latent space is what characterizes the compression and representation learning capabilities ofautoencoders.