The Investment Acceleration Principle Revisited by means of a Neural Network
Authors: Guido Fioretti
Organizations: Universität Stuttgart Institute for Theoretical Physics and Synergetics Stuttgart, Germany · International Centre for Economic Research Turin, Italy
The investment acceleration principle is a heuristic for modelling investment time series out of consumption time series. The model presented herein develops a disaggregated accelerator equation whose coefficients are the weights of a Kohonen neural net that represents firms' decision-making. According to this model, investments take place when managers recognise emerging technological patterns. Furthermore, a technique borrowed from the theory of self-organising systems is used in order to disentangle innovation-driven investments from plant-replication investments.
Figures & tables
Figure 1: Decision-making by a firm in the final goods sector. The Kohonen neuron consists of a summator of inputs Δci and Δe with weights ai and bi , respectively. Both sets of weights are influenced by a feed-back ϕ and a feed-forward γ , respectively. Left of the neuron, a first differences operator Δ performs the discrete-time derivative of the demand for final goods c and state-of-affairs in technology e , respectively. Right of the neuron, a summator performs the discrete-time integration of investments Δk , yielding capital stock k .
Figure 2: Decision-making by a firm in the capital goods sector. The Kohonen neuron consists of a summator of inputs Δki with weights di . These weights are influenced by a feed-back ϕ and a feed-forward γ , respectively. Left of the neuron, a first differences operator Δ performs the discrete-time derivative of the demand for capital goods k . Right of the neuron, a summator performs the discrete-time integration of demand for labour Δl′′ , yielding employment l′′ .
Figure 3: The structure of information flows within a productive system. Each neuron represents decision-making by one firm. The left layer represents firms in the final goods sector, the right layer represents firms in the capital goods sector, respectively. A double feed-back arises through the labour market.
Figure 4: A sequence of a hundred vectors e from t=1 to t=100 , horizontal sections at e=0 . Black areas denote regions where e>0 , white areas denote regions where e≤0 . The sinusoid spans 100 goods with 5 periods of 20 goods each, its amplitude increasing from Amin=0 at t=1 to Amax=2 at t=100 . Upon it, a normal distribution centred around zero adds noise with variance decreasing from σmax2=1 at t=1 to σmin2=0 at t=100 . In order to simplify the image only one out of four goods and one out of four time periods have been shown, resulting in a 25×25 grid.
Figure 5: Investments by each single firm. Each curve represents a different Δki for i=1,2,…100 during one single simulation. In order to depict zero values of investments on the logarithmic scale, a one has been added to all values.
Figure 6: Aggregate investments produced by ten different simulations (dashed lines) and their average (thick line). In order to depict zero values of investments on the logarithmic scale, a one has been added to all curves.
Figure 7: Variation of matrices A , B , D illustrated by indicators α , β , δ , respectively. Indicators α , β , δ are defined as the sum of the absolute variations of all elements of A , B , D , respectively. The graph illustrates the average of ten simulations.
Figure 8: Aggregate investments calculated by assuming that information vectors Δc and Δk vary with infinite speed. The figure illustrates ten single runs (dashed lines) as well as their average (thick solid line).
Figure 9: Variation of matrices A , B , D illustrated by indicators α , β , δ , respectively. Indicators α , β , δ are defined as the sum of the absolute variations of all elements of A , B , D , respectively. The graph illustrate the averages of ten simulations.
Figure 10: Aggregate investments according to the original model (thin line) and aggregate investments according to the two-regimes model (thick line). Both curves depict the average of ten simulation runs.
Venture capital (VC) investment decisions face distinct challenges, such as multi-source heterogeneous data, non-stationary time series, and the demand for explainable predictions in high-stakes, low-data settings. To overcome these issues, we introduce FinInvest-GTCN, a Graph-Temporal-Causal Network that redefines the task from content recommendation to quantitative risk-return assessment. This architecture combines a relational graph encoder to capture the investment ecosystem's topology, a multi-scale temporal fusion module to handle long-term dependencies and non-stationarity, and a causal decision head that generates risk-adjusted predictions with interpretable causal attributions. A core innovation is the Meta-Causal Adaptation (MCA) strategy, which facilitates robust fine-tuning for new, data-scarce sectors by aligning updates with causally-plausible structures derived from meta-pretraining. Comprehensive experiments on proprietary VC datasets show that FinInvest-GTCN delivers state-of-the-art results, markedly lowering the primary Risk-Adjusted Mean Squared Error (RA-MSE) to 2.51 from a baseline of 3.05 and boosting the cumulative return of a simulated portfolio by 18.7%. Ablation studies underscore the essential role of each component, while additional analyses confirm the model's stability, interpretability, and enhanced adaptability. This work pioneers a data-driven, explainable framework for investment decision support.
Junyan Tan, Yifan Li, Minghao Wang +2
Department of Computer Science Zhejiang University
We show that a deep neural network (DNN) trained to construct a stochastic discount factor (SDF) admits an additive decomposition separating nonlinear characteristic discovery from the pricing rule that aggregates them. This decomposition yields a linear factor representation governed by the Portfolio Tangent Kernel (PTK), which summarizes the network's learned features. In population, the implied SDF converges to a ridge-regularized version of the true SDF, with the degree of regularization determined by spectral complexity. Empirically, using U.S. equity data, the PTK representation delivers economically and statistically significant performance gains, while rising spectral complexity imposes tighter limits on finite-sample pricing.
Bryan Kelly, Boris Kuznetsov, Semyon Malamud +1
Yale School of Management, AQR Capital Management, and NBER · AQR Capital Management · NBER +5
Neural networks applied to financial time series operate in a regime of underspecification, where model predictors achieve indistinguishable out-of-sample error. Using large-scale volatility forecasting for S&P 500 stocks, we show that different model-training-pipeline pairs with identical test loss learn qualitatively different functions. Across architectures, predictive accuracy remains unchanged, yet optimizer choice reshapes non-linear response profiles and temporal dependence differently. These divergences have material consequences for decisions: volatility-ranked portfolios trace a near-vertical Sharpe-turnover frontier, with nearly 3× turnover dispersion at comparable Sharpe ratios. We conclude that in underspecified settings, optimization acts as a consequential source of inductive bias, thus model evaluation should extend beyond scalar loss to encompass functional and decision-level implications.
Federico Vittorio Cortesi, Giuseppe Iannone, Giulia Crippa +2
Massachusetts Institute of Technology, Cambridge, MA, USA · Princeton University, Princeton, NJ, USA.