# A large deviation view of stationarized fully lifted blirp interpolation

arXiv: https://arxiv.org/abs/2506.19273 · HTML: https://mlsanity.com/paper/2506.19273/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 114 references that are in the map.
- First posted on arXiv 24 Jun 2025.

## Builds on (most cited first, 29 of 29)

- [Statistical Query Lower Bounds for Robust Estimation of High-dimensional Gaussians and Gaussian Mixtures](https://mlsanity.com/paper/1611.03473/) (2016)
- [The power of sum-of-squares for detecting hidden structures](https://mlsanity.com/paper/1710.05017/) (2017)
- [Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localization](https://mlsanity.com/paper/2203.05093/) (2022)
- [Subdominant Dense Clusters Allow for Simple Learning and High Computational Performance in Neural Networks with Discrete Synapses](https://mlsanity.com/paper/1509.05753/) (2015)
- [Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors](https://mlsanity.com/paper/1512.02337/) (2015)
- [Tensor principal component analysis via sum-of-squares proofs](https://mlsanity.com/paper/1507.03269/) (2015)
- [The Franz-Parisi Criterion and Computational Trade-offs in High Dimensional Statistics](https://mlsanity.com/paper/2205.09727/) (2022)
- [Unveiling the structure of wide flat minima in neural networks](https://mlsanity.com/paper/2107.01163/) (2021)
- [Another look at the Gardner problem](https://mlsanity.com/paper/1306.3979/) (2013)
- [Limits of local algorithms over sparse random graphs](https://mlsanity.com/paper/1304.1831/) (2013)
- [Local entropy as a measure for sampling solutions in Constraint Satisfaction Problems](https://mlsanity.com/paper/1511.05634/) (2015)
- [Proof of the Contiguity Conjecture and Lognormal Limit for the Symmetric Perceptron](https://mlsanity.com/paper/2102.13069/) (2021)
- [Upper-bounding ℓ1-optimization weak thresholds](https://mlsanity.com/paper/1303.7289/) (2013)
- [Discrete perceptrons](https://mlsanity.com/paper/1306.4375/) (2013)
- [On the Complexity of Random Satisfiability Problems with Planted Solutions](https://mlsanity.com/paper/1311.4821/) (2013)
- [Lifting ℓ1-optimization strong and sectional thresholds](https://mlsanity.com/paper/1306.3770/) (2013)
- [Lifting/lowering Hopfield models ground state energies](https://mlsanity.com/paper/1306.3975/) (2013)
- [Algorithmic pure states for the negative spherical perceptron](https://mlsanity.com/paper/2010.15811/) (2020)
- [Binary perceptron: efficient algorithms can find solutions in a rare well-connected cluster](https://mlsanity.com/paper/2111.03084/) (2021)
- [Typical and atypical solutions in non-convex neural networks with discrete and continuous weights](https://mlsanity.com/paper/2304.13871/) (2023)
- [Binary perceptrons capacity via fully lifted random duality theory](https://mlsanity.com/paper/2312.00073/) (2023)
- [Clustering of solutions in the symmetric binary perceptron](https://mlsanity.com/paper/1911.06756/) (2019)
- [Algorithms and Barriers in the Symmetric Binary Perceptron Model](https://mlsanity.com/paper/2203.15667/) (2022)
- [Spherical perceptron as a storage memory with limited errors](https://mlsanity.com/paper/1306.3809/) (2013)
- [Hardness of sampling solutions from the Symmetric Binary Perceptron](https://mlsanity.com/paper/2407.16627/) (2024)
- [Average-Case Complexity of Tensor Decomposition for Low-Degree Polynomials](https://mlsanity.com/paper/2211.05274/) (2022)
- [Discrepancy Algorithms for the Binary Perceptron](https://mlsanity.com/paper/2408.00796/) (2024)
- [Bounds on restricted isometry constants of random matrices](https://mlsanity.com/paper/1306.3779/) (2013)
- [Asymmetric Little model and its ground state energies](https://mlsanity.com/paper/1306.3978/) (2013)

## Abstract (arXiv)

We consider bilinearly indexed random processes (blirp) and study their interpolating comparative mechanisms. Generic introduction of the fully lifted (fl) blirp interpolation in [105] was followed by a corresponding stationarization counterpart in [103]. A large deviation upgrade of [105] introduced in companion paper [106] is complemented here with the corresponding one of [103]. Similarly to [106], the mechanism that we introduce extends the range of [103]'s applicability so that it encompasses random structures atypical features. Among others these include the local entropies (LE) which explain atypical solutions clusterings in hard random optimization problems believed to be directly responsible for the presumable existence of the so-called computational gaps. Moreover (and similar to [105]), despite on occasion somewhat involved technical considerations, the final forms of the uncovered fundamental interpolating parameters relations are rather elegant and as such provide a valuable tool readily available for further use.