With direct access to human-written reference as memory, retrieval-augmented generation has achieved much progress in a wide range of text generation tasks.

With direct access to human-written reference as memory, retrieval-augmented generation has achieved much progress in a wide range of text generation tasks. Since better memory would typically prompt better generation (we define this as primal problem). The traditional approach for memory retrieval involves selecting memory that exhibits the highest similarity to the input. However, this method is constrained by the quality of the fixed corpus from which memory is retrieved. In this paper, by exploring the duality of the primal problem: better generation also prompts better memory, we propose a novel framework, selfmem, which addresses this limitation by iteratively employing a retrieval-augmented generator to create an unbounded memory pool and using a memory selector to choose one output as memory for the subsequent generation round. This enables the model to leverage its own output, referred to as self-memory, for improved generation. We evaluate the effectiveness of selfmem on three distinct text generation tasks: neural machine translation, abstractive text summarization, and dialogue generation, under two generation paradigms: fine-tuned small model and few-shot LLM. Our approach achieves state-of-the-art results in four directions in JRC-Acquis translation dataset, 50.3 ROUGE-1 in XSum, and 62.9 ROUGE-1 in BigPatent, demonstrating the potential of self-memory in enhancing retrieval-augmented generation models. Furthermore, we conduct thorough analyses of each component in the selfmem framework to identify current system bottlenecks and provide insights for future research.

In the appendix, we start from the proofs of theorem 2.1 and theorem 2.2 in section A. Then, we prove the correctness of proposition 2.2 and proposition 2.3 in section B. After that, the detailed derivation of our proposed loss is provided in section C. At last, the sensitivity of some important Before providing the proofs of the theorems, we restate some important notations first. Here, we also restate some important notations first. Here, we illustrate the detailed derivation of our approximated loss for learning the discriminator. Figure 1(a) demonstrates the effects of the embeddings size (i.e., Figure 1(b) shows the effects of the number of item sample set for learning the discriminator. Figure 1(c) reports the effects of the number of item and context sample set for learning the generator.

With direct access to human-written reference as memory, retrieval-augmented generation has achieved much progress in a wide range of text generation tasks.

On the COMP AS dataset, we use a three-layer feed-forward neural network activated by ReLU as the classification model. For optimization we use momentum SGD with learning rate 0.01 and The batch size is 128. On the CelebA dataset, we use a ResNet18 as the classification model. The remaining 45000 training samples consist the training set. The batch size is 128.

With direct access to human-written reference as memory, retrieval-augmented generation has achieved much progress in a wide range of text generation tasks. Since better memory would typically prompt better generation (we define this as primal problem). The traditional approach for memory retrieval involves selecting memory that exhibits the highest similarity to the input. However, this method is constrained by the quality of the fixed corpus from which memory is retrieved. In this paper, by exploring the duality of the primal problem: better generation also prompts better memory, we propose a novel framework, selfmem, which addresses this limitation by iteratively employing a retrieval-augmented generator to create an unbounded memory pool and using a memory selector to choose one output as memory for the subsequent generation round.

We establish the theoretical framework for implementing the maximumn entropy on the mean (MEM) method for linear inverse problems in the setting of approximate (data-driven) priors. We prove a.s. convergence for empirical means and further develop general estimates for the difference between the MEM solutions with different priors $\mu$ and $\nu$ based upon the epigraphical distance between their respective log-moment generating functions. These estimates allow us to establish a rate of convergence in expectation for empirical means. We illustrate our results with denoising on MNIST and Fashion-MNIST data sets.

Many partial differential equations (PDEs) such as Navier--Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do not have an exact, primal variational structure. Recently, a variational principle based on the dual (Lagrange multiplier) field was proposed. The essential idea in this approach is to treat the given PDE as constraints, and to invoke an arbitrarily chosen auxiliary potential with strong convexity properties to be optimized. This leads to requiring a convex dual functional to be minimized subject to Dirichlet boundary conditions on dual variables, with the guarantee that even PDEs that do not possess a variational structure in primal form can be solved via a variational principle. The vanishing of the first variation of the dual functional is, up to Dirichlet boundary conditions on dual fields, the weak form of the primal PDE problem with the dual-to-primal change of variables incorporated. We derive the dual weak form for the linear, one-dimensional, transient convection-diffusion equation. A Galerkin discretization is used to obtain the discrete equations, with the trial and test functions chosen as linear combination of either RePU activation functions (shallow neural network) or B-spline basis functions; the corresponding stiffness matrix is symmetric. For transient problems, a space-time Galerkin implementation is used with tensor-product B-splines as approximating functions. Numerical results are presented for the steady-state and transient convection-diffusion equation, and transient heat conduction. The proposed method delivers sound accuracy for ODEs and PDEs and rates of convergence are established in the $L^2$ norm and $H^1$ seminorm for the steady-state convection-diffusion problem.

In this work, we address three non-convex optimization problems associated with the training of shallow neural networks (NNs) for exact and approximate representation, as well as for regression tasks. Through a mean-field approach, we convexify these problems and, applying a representer theorem, prove the absence of relaxation gaps. We establish generalization bounds for the resulting NN solutions, assessing their predictive performance on test datasets and, analyzing the impact of key hyperparameters on these bounds, propose optimal choices. On the computational side, we examine the discretization of the convexified problems and derive convergence rates. For low-dimensional datasets, these discretized problems are efficiently solvable using the simplex method. For high-dimensional datasets, we propose a sparsification algorithm that, combined with gradient descent for over-parameterized shallow NNs, yields effective solutions to the primal problems.