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Feng Qi

Publications and source records attributed to Feng Qi.

At least 37 records · Page 2Linked to original sources
arXiv2025

QF: Quick Feedforward AI Model Training without Gradient Back Propagation

We propose Quick Feedforward (QF) Learning, a novel knowledge consolidation framework for transformer-based models that enables efficient transfer of instruction derived knowledge into model weights through feedforward activations without any gradient back propagation. Unlike traditional finetuning, QF updates are computed in closed form, require minimal parameter modification, and preserve prior knowledge. Importantly, QF allows models to train and infer within the same runtime environment, making the process more resource efficient and closely aligned with how the human brain operates. Code and models are open sourced on GitHub. I hope QF Learning inspires a more efficient and brain-like paradigm for AI systems.

cs.LG↗
arXiv2025

Uniform treatments of Bernoulli numbers, Stirling numbers, and their generating functions

In this paper, by virtue of a determinantal formula for derivatives of the ratio between two differentiable functions, in view of the Faà di Bruno formula, and with the help of several identities and closed-form formulas for the partial Bell polynomials $\operatorname{B}_{n,k}$, the author establishes thirteen Maclaurin series expansions of the functions \begin{align*} &\ln\frac{\operatorname{e}^x+1}{2}, && \ln\frac{\operatorname{e}^x-1}{x}, && \ln\cosh x, \\ &\ln\frac{\sinh x}{x}, && \biggl[\frac{\ln(1+x)}{x}\biggr]^r, && \biggl(\frac{\operatorname{e}^x-1}{x}\biggr)^r \end{align*} for $r=\pm\frac{1}{2}$ and $r\in\mathbb{R}$ in terms of the Dirichlet eta function $η(1-2k)$, the Riemann zeta function $ζ(1-2k)$, and the Stirling numbers of the first and second kinds $s(n,k)$ and $S(n,k)$. presents four determinantal expressions and three recursive relations for the Bernoulli numbers $B_{2n}$. finds out three closed-form formulas for the Bernoulli numbers $B_{2n}$ and the generalized Bernoulli numbers $B_n^{(r)}$ in terms of the Stirling numbers of the second kind $S(n,k)$, and deduce two combinatorial identities for the Stirling numbers of the second kind $S(n,k)$. acquires two combinatorial identities, which can be regarded as diagonal recursive relations, involving the Stirling numbers of the first and second kinds $s(n,k)$ and $S(n,k)$. recovers an integral representation and a closed-form formula, and establish an alternative explicit and closed-form formula, for the Bernoulli numbers of the second kind $b_n$ in terms of the Stirling numbers of the first kind $s(n,k)$. obtains three identities connecting the Stirling numbers of the first and second kinds $s(n,k)$ and $S(n,k)$.

math.CO↗
arXiv2025

Expressing the difference of two Hurwitz zeta functions by a linear combination of the Gauss hypergeometric functions

In the paper, the author expresses the difference $2^m\bigl[ζ\bigl(-m,\frac{1+x}{2}\bigr)-ζ\bigl(-m,\frac{2+x}{2}\bigr)\bigr]$ in terms of a linear combination of the function $Γ(m+1){\,}_2F_1(-m,-x;1;2)$ for $m\in\mathbb{N}_0$ and $x\in(-1,\infty)$ in the form of matrix equations, where $Γ(z)$, $ζ(z,α)$, and ${}_2F_1(a,b;c;z)$ stand for the classical Euler gamma function, the Hurwitz zeta function, and the Gauss hypergeometric function, respectively. This problem originates from the Landau level quantization in solid state materials.

math.CA↗
arXiv2024

Decreasing and complete monotonicity of two functions defined by three derivatives of a completely monotonic function involving the trigamma function

In the paper, by convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein's theorem for completely monotonic functions, and other analytic techniques, the authors verify decreasing property of a ratio between three derivatives of a function involving trigamma function and find necessary and sufficient conditions for a function defined by three derivatives of a function involving trigamma function to be completely monotonic. These results confirm previous guesses posed by Qi and generalize corresponding known conclusions.

math.GM↗
arXiv2024

GeoDecoder: Empowering Multimodal Map Understanding

This paper presents GeoDecoder, a dedicated multimodal model designed for processing geospatial information in maps. Built on the BeitGPT architecture, GeoDecoder incorporates specialized expert modules for image and text processing. On the image side, GeoDecoder utilizes GaoDe Amap as the underlying base map, which inherently encompasses essential details about road and building shapes, relative positions, and other attributes. Through the utilization of rendering techniques, the model seamlessly integrates external data and features such as symbol markers, drive trajectories, heatmaps, and user-defined markers, eliminating the need for extra feature engineering. The text module of GeoDecoder accepts various context texts and question prompts, generating text outputs in the style of GPT. Furthermore, the GPT-based model allows for the training and execution of multiple tasks within the same model in an end-to-end manner. To enhance map cognition and enable GeoDecoder to acquire knowledge about the distribution of geographic entities in Beijing, we devised eight fundamental geospatial tasks and conducted pretraining of the model using large-scale text-image samples. Subsequently, rapid fine-tuning was performed on three downstream tasks, resulting in significant performance improvements. The GeoDecoder model demonstrates a comprehensive understanding of map elements and their associated operations, enabling efficient and high-quality application of diverse geospatial tasks in different business scenarios.

cs.CV↗
arXiv2024

Low power consumption grating magneto-optical trap based on planar elements

The grating-based magneto-optical trap (GMOT) is a promising approach for miniaturizing cold-atom systems. However, the power consumption of a GMOT system dominates its feasibility in practical applications. In this study, we demonstrated a GMOT system based on planar elements that can operate with low power consumption. A high-diffraction-efficiency grating chip was used to cool atoms with a single incident beam. A planar coil chip was designed and fabricated with a low power consumption nested architecture. The grating and coil chips were adapted to a passive pump vacuum chamber, and up to 106 87Rb atoms were trapped. These elements effectively reduce the power consumption of the GMOT and have great potential for applications in practical cold-atom-based devices.

physics.atom-ph↗
arXiv2023

Closed-form formulas, determinantal expressions, recursive relations, power series, and special values of several functions used in Clark--Ismail's two conjectures

In the paper, by virtue of the famous formula of Faà di Bruno, with the aid of several identities of partial Bell polynomials, by means of a formula for derivatives of the ratio of two differentiable functions, and with availability of other techniques, the authors establish closed-form formulas in terms of the Bernoulli numbers and the second kind Stirling numbers, present determinantal expressions, derive recursive relations, obtain power series, and compute special values of the function $\frac{v^j}{1-\operatorname{e}^{-v}}$, its derivatives, and related ones used in Clark--Ismail's two conjectures. By these results, the authors also discover a formula for the determinant of a Hessenberg matrix and derive logarithmic convexity of a sequence related to the function and its derivatives.

math.CA↗
arXiv2023

Parametric kinds of generalized Apostol-Bernoulli polynomials and their properties

The purpose of this paper is to define generalized Apostol--Bernoulli polynomials with including a new cosine and sine parametric type of generating function using the quasi-monomiality properties and trigonometric functions. In this study, the Apostol-Bernoulli polynomials with three variable are defined with two new generating functions cosine and sine parameters. Then, we investigate multiplicative and derivative operators, diffrential equations, some summation formulas and partial differential equations for these polynomials. Moreover, we introduce Gould--Hopper--Apostol--Bernoulli type polynomials, Hermite--Appell--Apostol--Bernoulli type polynomials and truncated exponential Apostol--Bernoulli type polynomials. Finally, the special cases of these new polynomials are investigated, and the corresponding results are expressed.

math.CA↗
arXiv2023

Learning to Rank Normalized Entropy Curves with Differentiable Window Transformation

Recent automated machine learning systems often use learning curves ranking models to inform decisions about when to stop unpromising trials and identify better model configurations. In this paper, we present a novel learning curve ranking model specifically tailored for ranking normalized entropy (NE) learning curves, which are commonly used in online advertising and recommendation systems. Our proposed model, self-Adaptive Curve Transformation augmented Relative curve Ranking (ACTR2), features an adaptive curve transformation layer that transforms raw lifetime NE curves into composite window NE curves with the window sizes adaptively optimized based on both the position on the learning curve and the curve's dynamics. We also introduce a novel differentiable indexing method for the proposed adaptive curve transformation, which allows gradients with respect to the discrete indices to flow freely through the curve transformation layer, enabling the learned window sizes to be updated flexibly during training. Additionally, we propose a pairwise curve ranking architecture that directly models the difference between the two learning curves and is better at capturing subtle changes in relative performance that may not be evident when modeling each curve individually as the existing approaches did. Our extensive experiments on a real-world NE curve dataset demonstrate the effectiveness of each key component of ACTR2 and its improved performance over the state-of-the-art.

cs.LG↗
arXiv2022

A Practical Distributed ADMM Solver for Billion-Scale Generalized Assignment Problems

Assigning items to owners is a common problem found in various real-world applications, for example, audience-channel matching in marketing campaigns, borrower-lender matching in loan management, and shopper-merchant matching in e-commerce. Given an objective and multiple constraints, an assignment problem can be formulated as a constrained optimization problem. Such assignment problems are usually NP-hard, so when the number of items or the number of owners is large, solving for exact solutions becomes challenging. In this paper, we are interested in solving constrained assignment problems with hundreds of millions of items. Thus, with just tens of owners, the number of decision variables is at billion-scale. This scale is usually seen in the internet industry, which makes decisions for large groups of users. We relax the possible integer constraint, and formulate a general optimization problem that covers commonly seen assignment problems. Its objective function is convex. Its constraints are either linear, or convex and separable by items. We study to solve our generalized assignment problems in the Bregman Alternating Direction Method of Multipliers (BADMM) framework where we exploit Bregman divergence to transform the Augmented Lagrangian into a separable form, and solve many subproblems in parallel. The entire solution can thus be implemented using a MapReduce-style distributed computation framework. We present experiment results on both synthetic and real-world datasets to verify its accuracy and scalability.

cs.DS↗
arXiv2022

Several series expansions for real powers and several formulas for partial Bell polynomials of sinc and sinhc functions in terms of central factorial and Stirling numbers of second kind

In the paper, with the aid of the Faà di Bruno formula, in terms of central factorial numbers of the second kind, and with the terminology of the Stirling numbers of the second kind, the authors derive several series expansions for any positive integer powers of the sinc and sinhc functions, discover several closed-form formulas for partial Bell polynomials of all derivatives of the sinc function, establish several series expansions for any real powers of the sinc and sinhc functions, and present several identities for central factorial numbers of the second kind and for the Stirling numbers of the second kind.

math.CA↗
arXiv2021

An analytic generalization of the Catalan numbers and its integral representation

In the paper, the authors analytically generalize the Catalan numbers in combinatorial number theory, establish an integral representation of the analytic generalization of the Catalan numbers by virtue of Cauchy's integral formula in the theory of complex functions, and point out potential directions to further study.

math.CO↗
arXiv2021

Maclaurin's series expansions for positive integer powers of inverse (hyperbolic) sine and related functions, specific values of partial Bell polynomials, and two applications

In the paper, the authors establish Maclaurin's series expansions and series identities for positive integer powers of the inverse sine function, for positive integer powers of the inverse hyperbolic sine function, for the composite of incomplete gamma functions with the inverse hyperbolic sine function, for positive integer powers of the inverse tangent function, and for positive integer powers of the inverse hyperbolic tangent function, in terms of the first kind Stirling numbers and binomial coefficients, apply the newly established Maclaurin's series expansion for positive integer powers of the inverse sine function to derive a closed-form formula for specific values of partial Bell polynomials and to derive a series representation of the generalized logsine function, and deduce several combinatorial identities involving the first kind Stirling numbers. Some of these results simplify and unify some known ones. All of these newly established Maclaurin's series expansions of positive integer powers of the inverse (hyperbolic) sine and tangent functions can be used to derive infinite series representations of the circular constant Pi and of positive integer powers of Pi.

math.CO↗
arXiv2021

A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs

Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the solution quality. Currently, machine learning for combinatorial optimization (MLCO) has become a trending research topic, but most existing MLCO methods treat CO as a single-level optimization by directly learning the end-to-end solutions, which are hard to scale up and mostly limited by the capacity of ML models given the high complexity of CO. In this paper, we propose a hybrid approach to combine the best of the two worlds, in which a bi-level framework is developed with an upper-level learning method to optimize the graph (e.g. add, delete or modify edges in a graph), fused with a lower-level heuristic algorithm solving on the optimized graph. Such a bi-level approach simplifies the learning on the original hard CO and can effectively mitigate the demand for model capacity. The experiments and results on several popular CO problems like Directed Acyclic Graph scheduling, Graph Edit Distance and Hamiltonian Cycle Problem show its effectiveness over manually designed heuristics and single-level learning methods.

cs.LG↗
arXiv2021

Taylor's series expansions for real powers of functions containing squares of inverse (hyperbolic) cosine functions, explicit formulas for special partial Bell polynomials, and series representations for powers of circular constant

In the paper, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the light of properties of partial Bell polynomials, the author establishes Taylor's series expansions of real powers of two functions containing squares of inverse (hyperbolic) cosine functions in terms of the Stirling numbers of the first kind, presents an explicit formula of specific partial Bell polynomials at a sequence of derivatives of a function containing the square of inverse cosine function, derives several combinatorial identities involving the Stirling numbers of the first kind, demonstrates several series representations of the circular constant Pi and its real powers, recovers series expansions of positive integer powers of inverse (hyperbolic) sine functions in terms of the Stirling numbers of the first kind, and also deduces other useful, meaningful, and significant conclusions.

math.CO↗
arXiv2021

A framework for massive scale personalized promotion

Technology companies building consumer-facing platforms may have access to massive-scale user population. In recent years, promotion with quantifiable incentive has become a popular approach for increasing active users on such platforms. On one hand, increased user activities can introduce network effect, bring in advertisement audience, and produce other benefits. On the other hand, massive-scale promotion causes massive cost. Therefore making promotion campaigns efficient in terms of return-on-investment (ROI) is of great interest to many companies. This paper proposes a practical two-stage framework that can optimize the ROI of various massive-scale promotion campaigns. In the first stage, users' personal promotion-response curves are modeled by machine learning techniques. In the second stage, business objectives and resource constraints are formulated into an optimization problem, the decision variables of which are how much incentive to give to each user. In order to do effective optimization in the second stage, counterfactual prediction and noise-reduction are essential for the first stage. We leverage existing counterfactual prediction techniques to correct treatment bias in data. We also introduce a novel deep neural network (DNN) architecture, the deep-isotonic-promotion-network (DIPN), to reduce noise in the promotion response curves. The DIPN architecture incorporates our prior knowledge of response curve shape, by enforcing isotonicity and smoothness. It out-performed regular DNN and other state-of-the-art shape-constrained models in our experiments.

cs.LG↗