Paper proves hardness of learning various complex models under local pseudorandom generators.
problem Hardness of learning various complex models.
method Existence of local pseudorandom generators.
result Proves hardness of learning shallow ReLU neural networks and other models.
This work connects hardness of approximation and learning.
problem Hardness of approximation and learnability in machine learning.
method Shows a single hardness property implying both approximation and learning hardness.
result Obtains new results on hardness of approximation and learnability of specific functions.
Hardness proven for learning neural networks with polynomial size and Gaussian inputs.
problem Learning one hidden layer ReLU neural networks with polynomial size and Gaussian inputs.
method Based on the hardness of the Continuous Learning with Errors (CLWE) problem.
result Hardness of learning neural networks is proven under standard cryptographic assumptions.
New unsupervised method selects hard negative samples for contrastive learning.
problem How to select good negative examples for contrastive learning without using true similarity information.
method Developed a new family of unsupervised sampling methods for hard negative selection.
result Improves downstream performance across multiple modalities.
Hard instances, which require a long time for a specific algorithm to solve, help (1) analyze the algorithm for accelerating it and (2) build a good benchmark for evaluating the performance of algorithms. There exist several efforts for automatic generation of hard instances. For example, evolutionary algorithms have b…
Study shows exponential sample complexity for stabilizing certain linear systems.
problem Statistical hardness of learning to stabilize linear time-invariant systems.
method Analysis of sample complexity and co-stabilizability using robust control ideas.
result Sample complexity increases exponentially with system dimension.
DC3 uses deep learning to solve hard-constrained optimization problems efficiently.
problem Hard constraints in optimization problems make classical solvers slow and infeasible.
method DC3 employs a differentiable procedure to enforce feasibility and unrolls corrections for inequality constraints.
result DC3 achieves near-optimal solutions while maintaining feasibility in both synthetic and real-world tasks.
Paper investigates hardness of learning neural networks under manifold hypothesis.
problem Hardness of learning neural networks under the manifold hypothesis.
method Extending proofs of hardness in the SQ and cryptographic settings to the geometric setting.
result Learning is hard under input manifolds of bounded curvature but learnable with additional assumptions on manifold volume.
Hardness proven for neural networks with natural weights.
problem Difficulty in learning neural networks with weights from natural distributions.
method Proved hardness for depth-2 networks with natural weights distributions.
result Most networks are hard to learn with natural weights.
Study shows challenges in reinforcement learning math problems, proposing enhancements and a hardness measure.
problem Challenges in reinforcement learning finding rare high-reward instances.
method Combining combinatorial group theory, algorithmic enhancements, and topological hardness measure.
result Resolved mathematical questions and proposed enhancements for reinforcement learning.
New findings show learning deeper neural networks is hard even with Gaussian inputs and non-degenerate weights.
problem The computational complexity of learning neural networks, especially deeper ones.
method Smoothed analysis framework and local pseudorandom generators.
result Learning depth-3 ReLU networks under Gaussian input distribution is hard even if weight matrices are non-degenerate.
Hardness proof for agnostically learning halfspaces from worst-case lattice problems.
problem Agnostically learning halfspaces in the presence of noise.
method Reduction to worst-case lattice problems (GapSVP, SIVP).
result No efficient algorithm can achieve misclassification error better than 1/2 - γ under given hardness assumptions.
Meta-learning strategy improves few-shot classification performance.
problem Few-shot classification with deep neural networks struggles when labeled samples are limited.
method Proposes an easy-to-hard expert meta-training strategy to arrange training tasks based on task hardness.
result Meta-learners achieve better results with the proposed expert training strategy.
Paper improves deep learning for solving evolutionary equations with trainable hard constraints.
problem Low computational accuracy of standard PINNs in large temporal domains.
method Sequential learning strategies and trainable influence functions for hard constraints.
result Significantly improved computational accuracy and universality of the method.
Model shows feature learning can improve neural scaling laws for hard tasks.
problem Understanding and improving neural network scaling laws for various task difficulties.
method Developed a solvable model of neural scaling laws, identified three scaling regimes, and demonstrated feature learning's impact on scaling exponents.
result Feature learning can improve scaling with training time and compute for hard tasks, nearly doubling the exponent.
Researchers prove NP-hardness of learning parameter-bounded Bayes nets.
problem Learning parameter-bounded Bayes nets is computationally hard.
method Proved NP-hardness of learning parameter-bounded Bayes nets and a promise search variant.
result Proved NP-hardness of a promise search variant of LEARN.
There has recently been significant interest in hard attention models for tasks such as object recognition, visual captioning and speech recognition. Hard attention can offer benefits over soft attention such as decreased computational cost, but training hard attention models can be difficult because of the discrete la…
Paper characterizes causal graphs from hard interventions and proposes a learning algorithm.
problem Discovering causal structure from hard interventions and observational data.
method Proposes graphical constraints and a learning algorithm based on do-calculus.
result Characterizes interventional equivalence classes of causal graphs with latent variables.
The paper explores when linear system identification is hard or easy, especially for under-actuated systems.
problem Statistical hardness of learning linear systems, especially under-actuated or under-excited systems.
method Using tools from minimax theory and recent statistical tools for finite sample analysis of system identification.
result The controllability index of linear systems affects the sample complexity of identification, making some systems hard to learn.
Reduces learning periodic neural networks to lattice problems, proving hardness under cryptographic assumptions.
problem Learning single periodic neurons in noisy environments.
method Reduction to worst-case lattice problems, using LLL algorithm.
result Polynomial-time algorithms for learning these functions are hard under cryptographic assumptions.
Study on learning halfspaces under adversarial perturbations, finding computational hardness.
problem Learning halfspaces in the presence of adversarial noise.
method Introduced an efficient learning algorithm and proved a nearly matching computational hardness result.
result The L ∞ L_{\infty} L ∞ perturbations case is provably computationally harder than 2 ≤ p < ∞ 2 \leq p < \infty 2 ≤ p < ∞ . In this article supervised learning problems are solved using soft rule ensembles. We first review the importance sampling learning ensembles (ISLE) approach that is useful for generating hard rules. The soft rules are then obtained with logistic regression from the corresponding hard rules. In order to deal with the p…
New research shows deep learning struggles with hard problems due to biased data generation.
problem Deep learning's limitations in solving computationally hard problems.
method Proved that polynomial-time sample generators for NP-hard problems sample from easier sub-problems.
result Machine learning models trained on biased datasets overestimate their accuracy for hard problems.
IHT improves sparse distribution learning.
problem Learning sparse discrete distributions.
method Iterative hard thresholding as a solution, with a greedy approximate projection.
result IHT achieves state of the art results for sparse distribution learning.
The paper explores when to prioritize easy or hard samples in learning tasks.
problem Determining the optimal order of learning easy or hard samples.
method Theoretical analyses and experiments were conducted to propose and validate four priority modes.
result Four priority modes (easy-first, hard-first, medium-first, two-ends-first) can be flexibly applied.
Optimal CL requires perfect memory and is NP-hard.
problem Designing CL algorithms that perform reliably and avoid catastrophic forgetting.
method Theoretical approach to derive computational properties of optimal CL algorithms.
result Optimal CL algorithms generally solve an NP-hard problem and require perfect memory.
Paper introduces scalable neural architecture for solving NP-hard problems.
problem Solving NP-hard reasoning problems from natural inputs.
method Scalable neural architecture and loss function for discrete Graphical Models.
result Empirically shows efficient learning of NP-hard problems.
Introduces a continuous version of LWE problem.
problem Hardness of learning mixtures of Gaussians.
method Polynomial-time quantum reduction from CLWE to lattice problems.
result CLWE shares hardness with LWE.
Study shows optimal RL with transition look-ahead is NP-hard for ℓ ≥ 2 \ell \geq 2 ℓ ≥ 2 .
problem Optimal reinforcement learning with transition look-ahead is computationally hard.
method Proved NP-hardness for ℓ ≥ 2 \ell \geq 2 ℓ ≥ 2 using linear programming. result There is a precise boundary between tractable and intractable cases for RL with look-ahead.
MAML outperforms NAL in diverse task landscapes.
problem Understanding when and how MAML outperforms NAL in various task landscapes.
method Analytical and numerical studies in a linear regression setting with a mixture of easy and hard tasks.
result MAML gains over NAL when there is task hardness discrepancy and optimal solutions of hard tasks are closely packed.
This paper shows how optimizing with hard negative examples improves image retrieval.
problem Training with hard negative examples leads to poor training behavior.
method Characterize the space of triplets, derive why hard negatives fail, and offer a fix to the loss function.
result Optimizing with hard negative examples leads to more generalizable features and better image retrieval.
APT-Gen generates tasks to help RL learn in hard problems.
problem Learning in hard exploration problems.
method APT-Gen uses a task generator to create tasks from a parameterized space, balancing performance and similarity to target tasks.
result APT-Gen outperforms baselines in grid world and robotic manipulation tasks.
Theoretical comparison of three invariance approaches in deep linear networks.
problem Understanding invariance in deep linear networks.
method Data augmentation, regularization, and hard-wiring approaches.
result Regularization introduces additional critical points, but they remain saddles except for the global optimum.
We continue the study of statistical/computational tradeoffs in learning robust classifiers, following the recent work of Bubeck, Lee, Price and Razenshteyn who showed examples of classification tasks where (a) an efficient robust classifier exists, in the small-perturbation regime; (b) a non-robust classifier can be l…
Gradient descent struggles to learn equivariant neural networks, even with symmetries.
problem Learning equivariant neural networks via gradient descent is hard.
method Lower bounds for various equivariant neural network classes.
result Gradient descent struggles to learn equivariant neural networks, even with symmetries.
Binary classification is a common statistical learning problem in which a model is estimated on a set of covariates for some outcome indicating the membership of one of two classes. In the literature, there exists a distinction between hard and soft classification. In soft classification, the conditional class probabil…
RL pipeline simplifies knot diagrams, including very hard unknots.
problem Simplifying complex knot diagrams, especially very hard unknots.
method Reinforcement learning for move proposals and heuristic navigation of Reidemeister moves.
result Trained agent simplifies diagrams, including a 4 1 # 9 10 4_1\#9_{10} 4 1 # 9 10 link to a three-step unknotting process. HardNet adds hard constraints to neural networks without sacrificing performance.
problem Ensuring adherence to input-dependent constraints in neural networks.
method Appends a differentiable enforcement layer to neural networks for end-to-end training with hard constraint guarantees.
result HardNet retains neural networks' universal approximation capabilities and enables efficient optimization.
Transformers struggle to learn Markovian dynamics, showing NP-hard optimization challenges.
problem Understanding transformers' limitations in learning Markovian dynamical functions.
method Investigated through a structured ICL setup, analyzing loss landscapes and parameter optimization.
result Recovering optimal transformer parameters for Markovian functions is NP-hard.
New lower bounds show learning intersections of halfspaces is hard even for a few halfspaces.
problem Learning intersections of halfspaces in polynomial time under standard assumptions.
method Unified connection to parallel pancakes distribution for proving hardness.
result Learning ω ( log log N ) ω(\log \log N) ω ( log log N ) halfspaces in dimension N N N requires super-polynomial time under standard assumptions. It is becoming increasingly important to understand the vulnerability of machine learning models to adversarial attacks. In this paper we study the feasibility of robust learning from the perspective of computational learning theory, considering both sample and computational complexity. In particular, our definition of…
This work tackles learning Markov games with adversarial opponents and achieves both average reward and exploitation.
problem Achieving both average reward and exploiting adaptive opponents in Markov games.
method Develops efficient algorithms and proves hardness results for learning Markov games with adversarial opponents.
result Achieves K \sqrt{K} K -regret bounds for certain conditions on opponent policies, complemented by an exponential lower bound. Hard visual attention is a promising approach to reduce the computational burden of modern computer vision methodologies. Hard attention mechanisms are typically non-differentiable. They can be trained with reinforcement learning but the high-variance training this entails hinders more widespread application. We show h…
Detecting adversarial examples is as hard as classifying them.
problem The difficulty of detecting adversarial examples in machine learning models.
method Proved a general hardness reduction between detection and classification of adversarial examples.
result The hardness reduction implies that detecting adversarial examples is computationally infeasible.
Catastrophic forgetting occurs when a neural network loses the information learned in a previous task after training on subsequent tasks. This problem remains a hurdle for artificial intelligence systems with sequential learning capabilities. In this paper, we propose a task-based hard attention mechanism that preserve…
Over recent years, devising classification algorithms that are robust to adversarial perturbations has emerged as a challenging problem. In particular, deep neural nets (DNNs) seem to be susceptible to small imperceptible changes over test instances. However, the line of work in provable robustness, so far, has been fo…
Single T-gate makes distribution learning hard for deep circuits.
problem Learning probability distributions from quantum circuits.
method Characterization of learnability and simulatability of quantum circuit outputs.
result Injection of a single T-gate into depth n^Ω(1) circuits makes distribution learning hard.
Hard to learn ReLU with Gaussian data, but can approximate efficiently.
problem Learning a ReLU with Gaussian marginals under arbitrary labels.
method Proved hardness and developed an efficient approximation algorithm.
result Efficient approximation algorithm for best-fitting ReLU with error O ( o p t 2 / 3 ) O(\mathsf{opt}^{2/3}) O ( opt 2/3 ) .