#01Nov 12, 2026
math.ST
Linear Regression with Self-Selection Bias in Polynomial Time
Felix Zhou
We revisit the problem of estimating $k$ linear regressors with self-selection bias in $n$ dimensions up to error $\varepsilon$ with the maximum self-selection criterion, as introduced by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [CDIZ23, STOC]. Our main result is a $\mathrm{poly}(n,k,1/\varepsilon)$ time algorithm for the unknown-index variant of this problem, thereby improving upon the running times of the best known algorithms due to Gaitonde and Mossel [GM24] and Kalavasis, Mehrotra, and Zhou [KMZ26, COLT] with exponential dependence on $k$. Our algorithm succeeds in the presence of correlated noise between regressors, which captures the related setting of max-affine regression. Consequently, we also give the first polynomial-time algorithm for this problem, improving on the prior works of Ghosh, Pananjady, Guntuboyina, and Ramchandran [GPGR22, IEEE Transactions on Information Theory] and Gaitonde and Mossel [GM24] with exponential dependence on $k$. Prior works exhaustively search over a $k$-dimensional subspace spanned by the regressors, using conditional moments of the response to test candidates. In contrast, our algorithm is driven by an improved understanding of the moments of the covariates. We show that, restricting to observations with large response values, the degree-$(\log n)$ Hermite moment of the covariates approximately decomposes as a sum of tensor powers of the regressors. The first step of our algorithm can be viewed as a tensor decomposition algorithm for these implicitly represented high-order tensors, which outputs unit vectors parallel to the regressors. A secondary step based on a simple variant of ordinary least squares extracts estimates for the regressors given these unit vectors. We believe our analytic insight and algorithmic components may have applications to designing efficient algorithms for other latent-variable problems.
#02Nov 12, 2026
cs.CV
FLEX-LBP: Learning Local Binary Patterns with Exact Binary Inference for Texture Classification
Mohamed Alimoussa, Amal El Kaid
Local Binary Patterns (LBP) remain among the most widely used texture descriptors, from industrial inspection to medical imaging. Yet their radius, sampling angles, color transform and thresholds are fixed by hand for each dataset. We present FLEX-LBP, which learns these parameters by backpropagation while every forward pass computes exact binary codes and hard histogram counts. A straight-through estimator acts only in the backward pass, so the deployed descriptor is an interpretable hard-binary LBP with 90 learnable parameters and unchanged inference cost. In a controlled ablation on six color texture benchmarks, the component worth learning is dataset-dependent. One configuration, applied unchanged everywhere, learns the geometry and thresholds with the color transform frozen. It improves the nearest-neighbor accuracy of the identical fixed descriptor by 3.55 points on average over five seeds, significantly on five of six benchmarks and never significantly worse. With a linear discriminant readout, it gains 0.9 points; the fully learned descriptor gains 2.7 and has the highest mean. FLEX-LBP is more accurate than five classical LBP-family descriptors, PCANet and a neural LBP on five of six benchmarks. Its mean nearest-neighbor accuracy exceeds that of frozen ImageNet ResNet-50 features (23.5 million parameters). On the Kather colorectal cancer histology benchmark, the fully learned descriptor reaches 93.8%, significantly above the best classical descriptor (Completed LBP, 92.8%). The learned radii adapt in directions that recur across seeds. Noise drowns single-pixel comparisons and illuminant change flips inter-channel ones; median sampling or gray-world normalization restores 96-97%. The code is available as a drop-in PyTorch layer at https://github.com/medalimoussa/FLEX-LBP.
#03Nov 12, 2026
cs.LG
Introducing Feedback Delays to Non-Delayed Adversarial MDPs: Optimal $\sqrt S$ and $\sqrt K$ Dependencies in Tabular and Linear AMDPs
Aarush Kulkarni, Khang Nguyen, William Chang and 1 more
We study regret minimization in episodic Adversarial Markov Decision Processes (AMDPs) with unknown transitions and bandit feedback. In tabular AMDPs with $S$ states, $A$ actions, and horizon $H$, the best known $K$-episode regret is $\tilde O(HS\sqrt{AK})$, whose $\sqrt S$ gap to the $Ω(H\sqrt{SAK})$ lower bound has long remained open. In linear AMDPs with $d$-dimensional features, after a five-year line of improvements starting from $K^{14/15}$, computationally efficient algorithms without a simulator or exploratory assumptions still only attain $\tilde O(K^{3/4})$ regret. A common challenge in both settings is to estimate the Q-function of a changing policy: past data comes from earlier policies that differ from (and are correlated with) the current one, while freezing the policy for future episodes worsens the dependency on $K$. We instead propose a general technique called introduced feedback delays: we estimate the Q-function of the policy using future episodes while still updating the policy, as if the feedback were delayed. While feedback delays are usually an obstacle imposed by the environment, here they are introduced voluntarily and, perhaps surprisingly, come at no extra cost. We develop Geometric Resampling with Rejection (GRR) to account for policy changes during the delay, and threshold the visitation probabilities to avoid long delays on rarely visited state-action pairs. With this unified technique, our policy optimization algorithms achieve, with high probability, $\tilde O(\text{poly}(H)\sqrt{SAK})$ regret in tabular AMDPs, resolving the open problem; and $\tilde O(\text{poly}(d,H)\sqrt K)$ regret in linear AMDPs, giving the first efficient algorithm optimal in $K$. They also naturally extend to delayed AMDPs with a total feedback delay $\mathfrak D$, yielding the first bounds optimal in $S$ and $\mathfrak D$ (tabular) and in $K$ and $\mathfrak D$ (linear).
#04Nov 12, 2026
cs.DS
Sketching Language Models for Context Attribution
Christopher Liaw, Aranyak Mehta, Grigoris Velegkas and 1 more
Context attribution asks how removing parts of a prompt changes a language model's output. We study leave-one-out (LOO) attribution for a prompt of $n$ tokens and a fixed measurement function. Computing all LOO values directly requires $n$ model evaluations. Under a stability assumption, our algorithm estimates all LOO values to error proportional to $\varepsilon$ with constant probability using $O(\sqrt{\log(1/\varepsilon)}/\varepsilon)$ evaluation calls. To complement our upper bound, we prove a matching $Ω(\sqrt{\log(1/\varepsilon)}/\varepsilon)$ lower bound on the number of evaluation calls in an oracle model. Empirically, we verify coefficient decay consistent with stability and evaluate the performance of our sketching algorithm on a small language-model retrieval task. Technically, our result is based on a sketching algorithm for arithmetic circuits whose Taylor coefficients satisfy the stability condition recently introduced by Gunn [Gun26]. A direct adaptation of their forward differentiation sketches would require $\widetilde{O}(\log(n)/\varepsilon^2)$ evaluation calls. Our key observation is that we can apply forward differentiation to the backpropagation circuit, with only constant overhead over a forward sketch of the same Taylor degree. This reduces the variance of the sketches and is key to our improved evaluation bound. Our lower bound builds on the techniques of Amsel, Chen, Duman Keles, Halikias, Musco, and Musco [ACDH+26, SIAM Journal on Matrix Analysis and Applications] for lower bounding the number of matrix-vector queries to estimate the diagonal elements of random matrices.
#05Nov 12, 2026
cs.CV
Unbundling Multimodal Vision Encoding
Ellis Brown, Chris Hoang, Shengyi Qian and 9 more
How multimodal language models should encode visual input remains up for debate. Most models use a pretrained vision encoder, while some recent recipes train the encoder from scratch with the language model or remove it entirely. Vision encoders bundle together three design choices: a visual prior from upstream pretraining, dedicated vision capacity, and pre-fusion placement of that capacity (i.e., before the multimodal backbone). Because published models also differ in data, architecture, and compute, comparing them cannot isolate the effect of each choice. We disentangle these choices via a controlled framework where we pretrain all models from scratch on common data and compare them on visual question answering and language benchmarks at matched lifetime compute. We find that the visual prior is not necessary; an encoder trained jointly from scratch is on par with a pretrained one, without a separate training stage. What matters instead is dedicated vision capacity: an encoder-free model trails on visual understanding even when its backbone is enlarged by the encoder's parameter count. Yet that capacity need not precede multimodal fusion, as vision-only modules added in-fusion to early backbone layers perform comparably to a pre-fusion encoder and can lower time to first token. These results also hold across backbone sizes, when encoder pretraining is treated as free, and when starting from a pretrained language model. Overall, our findings favor dedicated vision capacity trained jointly with the backbone and placed early within it.