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Alejandro Jimenez Rodriguez

Publications and source records attributed to Alejandro Jimenez Rodriguez.

3 recordsLinked to original sources

AVCG: A Generalized Variational Framework for Counterfactual Generation under Hypothesis Distributions

Counterfactual explanations formalize "what-if" scenarios by identifying modifications to an input instance that obtain a desired alternative prediction. Traditionally, whether generated via instance-specific optimization or amortized single pass models, these approaches rely on a single, deterministic point-estimate predictor. However, this ignores predictive uncertainty and hypothesis variability, leading to brittle explanations that frequently become invalid if the underlying model is retrained or updated. To address this fragility, we propose the Amortized Variational Counterfactual Generator (AVCG), a generalized optimization framework that formulates counterfactual generation as optimization over an arbitrary distribution of plausible predictive hypotheses rather than a single deterministic predictor. This formulation naturally accommodates Bayesian posteriors, Rashomon-restricted hypothesis spaces, and other uncertainty representations within a unified optimization framework. Evaluation across multiple benchmark datasets demonstrates that the AVCG framework produces counterfactual explanations that remain highly valid under predictive uncertainty and model changes, while maintaining competitive plausibility and single-pass runtime performance.

cs.LG

Heterogeneous gain distributions in neural networks I:The stationary case

We study heterogeneous distribution of gains in neural fields using techniques of quantum mechanics by exploiting a relationship of our model and the time-independent Schrödinger equation. We show that specific relationships between the connectivity kernel and the gain of the population can explain the behavior of the neural field in simulations. In particular, we show this relationships for the gating of activity between two regions (step potential), the propagation of activity throughout another region (barrier) and, most importantly, the existence of bumps in gain-contained regions (gain well). Our results constitute specific predictions that can be tested in vivo or in vitro.

q-bio.NC

Well posedness and stationary solutions of a neural field equation with synaptic plasticity

We consider the initial value problem associated to the neural field equation of Amari type with plasticity \[ u_t(x,t)=-u(x,t)+\int_Ωw(x,y)[1+γg( u(x,t) - u(y,t) )] f(u(y,t))\; dy, \;(x,t) \in Ω\times (0, \infty), \] where $Ω\subset\mathbb{R}^m$, $f$ and $g$ are bounded and continuously differentiable functions with bounded derivative, and $γ\ge0$ is the plasticity synaptic coefficient. We show that the problem is well posed in $C_b(\mathbb{R}^m)$ and $L^1(Ω)$ with $Ω$ compact. The proof follows from a classical fixed point argument when we consider the equation's flow. Strong convergence of solutions in the no plasticity limit ($γ\to0$) to solutions of Amari's equation is analysed. Finally, we prove existence of stationary solutions in a general way. As a particular case, we show that the Amari's model, after learning, leads to the stationary Schrödinger equation for a type of gain modulation.

math.AP